Method for fabricating liquid crystal optical elements with wide-field polarizing switches and pre-tilt.

Abstract

To provide a switchable optical assembly.SOLUTION: A switchable optical assembly comprises a switchable waveplate configured to be electrically activated and deactivated to selectively alter the polarization state of light incident thereon. The switchable waveplate comprises first and second surfaces and a first liquid crystal layer disposed between the first and second surfaces. The first liquid crystal layer comprises a plurality of liquid crystal molecules that are rotated about respective axes parallel to a central axis, where the rotation varies with an azimuthal angle about the central axis. The switchable waveplate additionally comprises a plurality of electrodes to apply an electrical signal across the first liquid crystal layer.SELECTED DRAWING: Figure 40

Description

[Technical Field]

[0001] (Cross-reference of related applications) This application claims priority to U.S. Provisional Patent Application No. 62 / 685,858, filed on June 15, 2018, titled "WIDE FIELD-OF-VIEW POLARIZATION SWITCHES AND METHODS OF FABRICATING LIQUID CRYSTAL OPTICAL ELEMENTS WITH PRETITLT," the contents of which are incorporated herein by reference in their entirety. (Integrated by reference)

[0002] This application, by reference, refers to the following patent applications: U.S. Patent Application No. 14 / 555,585, filed on November 27, 2014, and published on July 23, 2015, as U.S. Patent Publication No. 2015 / 0205126; U.S. Patent Application No. 14 / 690,401, filed on April 18, 2015, and published on October 22, 2015, as U.S. Patent Publication No. 2015 / 0302652; U.S. Patent Application No. 14 / 212,961, filed on March 14, 2014, and currently U.S. Patent No. 9,417,452, issued on August 16, 2016; and U.S. Patent Application No. 14 / 212,961, filed on July 14, 2014, and published on October 29, 2015. This incorporates the entirety of U.S. Patent Application No. 14 / 331,218, published as No. 2015 / 0309263; U.S. Patent Application No. 15 / 795,067, filed on 26 October 2017 and published on 24 May 2018 as U.S. Patent Publication No. 2018 / 0143470; U.S. Patent Application No. 15 / 815,449, filed on 16 November 2017 and published on 24 May 2018 as U.S. Patent Publication No. 2018 / 0143485; and International Application PCT / US2018 / 057604, filed on 25 October 2018 and published on 2 May 2019 as International Publication No. WO2019 / 084334.

[0003] The present disclosure relates to display systems, and more particularly, to augmented and virtual reality display systems. **Background Art**

[0004] Modern computing and display technologies have facilitated the development of systems for so-called "virtual reality" or "augmented reality" experiences, where digitally reproduced images or portions thereof are presented to a user in a manner that appears or can be perceived as being real. Virtual reality, i.e., a "VR" scenario, typically involves the presentation of digital or virtual image information without transparency to other actual real-world visual inputs, and augmented reality, i.e., an "AR" scenario, typically involves the presentation of digital or virtual image information as an augmentation to the visualization of the actual world around the user. A mixed reality or "MR" scenario is a type of AR scenario that typically involves virtual objects integrated into and responsive to the natural world. For example, in an MR scenario, AR image content is perceived as being blocked by or otherwise interacting with objects within the real world.

[0005] Referring to FIG. 1, an augmented reality scene 10 is depicted, and to a user of AR technology, a real-world park-like setting 20 characterized by people, trees, buildings in the background, and a concrete platform 30 is visible. In addition to these items, a user of AR technology also "sees" "virtual content" such as a robotic image 40 standing on the real-world platform 30 and an avatar character 50 in the form of a flying cartoon that appears anthropomorphic like a honeybee, even though these elements 40, 50 do not exist within the real world. The human visual perception system is complex, and the generation of AR technology that promotes a comfortable, natural, and rich presentation of virtual image elements among other virtual or real-world image elements is difficult.

[0006] The systems and methods disclosed herein address various issues associated with AR or VR technology. **Summary of the Invention**

Means for Solving the Problem

[0007] On one side, the switchable optical assembly comprises a switchable waveplate that is electrically activated and deactivated and configured to selectively modify the polarization state of light incident thereon. The switchable waveplate comprises a first and a second surface, and a first liquid crystal layer disposed between the first surface and the second surface. The first liquid crystal layer comprises a plurality of liquid crystal molecules that rotate about individual axes parallel to the central axis, and the rotation varies with the azimuth angle about the central axis. The switchable waveplate further comprises a plurality of electrodes for applying an electrical signal across the first liquid crystal layer.

[0008] On another side, the switchable optical assembly comprises a switchable waveplate that is electrically activated and deactivated and configured to selectively modify the polarization state of light incident thereon. The switchable waveplate comprises a first and a second surface, and a liquid crystal layer disposed between the first surface and the second surface. The liquid crystal layer comprises a plurality of liquid crystal molecules that are longer than the width along individual longitudinal directions, and the longitudinal directions of the liquid crystal molecules are oriented such that they extend radially from the axis in a plurality of radial directions to the first and second surfaces and the axis of the liquid crystal layer. The switchable waveplate further comprises a plurality of electrodes for applying an electrical signal across the liquid crystal layer.

[0009] On another side, a method of processing an optical element includes providing a substrate having a normal extending along a horizontal direction and oriented perpendicular thereto. The method further includes providing a first vertical alignment layer and providing a second horizontal alignment layer. The method further includes providing a liquid crystal layer comprising liquid crystal molecules that are oriented at an oblique angle with respect to the vertical and horizontal directions with respect to the first vertical alignment layer and the second horizontal alignment layer. The first vertical alignment layer orients the liquid crystal molecules more vertically than in the absence of the first vertical alignment layer, and the second horizontal alignment layer orients the liquid crystal molecules more horizontally than in the absence of the second horizontal alignment layer.

[0010] In another aspect, the optical element comprises a substrate having a normal extending along the horizontal direction and directed perpendicular thereto. The optical element further includes the steps of providing a first vertically aligned layer and a second horizontally aligned layer. The optical element further comprises a liquid crystal layer comprising liquid crystal molecules relative to the first vertically aligned layer and the second horizontally aligned layer such that the liquid crystal molecules are oriented at certain oblique angles with respect to the vertical and horizontal directions. The first vertically aligned layer orients the liquid crystal molecules more vertically than in the absence of the first vertically aligned layer, and the second horizontally aligned layer orients the liquid crystal molecules more horizontally than in the absence of the second horizontally aligned layer.

[0011] For the purpose of summarizing the advantages achieved by the present invention over the prior art, certain objectives and advantages are described herein. Naturally, it should be understood that not all such objectives or advantages necessarily need to be achieved according to any particular embodiment. Therefore, for example, those skilled in the art will recognize that the present invention may be embodied or performed in a manner that achieves or optimizes one advantage or group of advantages without necessarily achieving other objectives or advantages.

[0012] All of these embodiments are intended to fall within the scope of the invention disclosed herein. These and other embodiments will be readily apparent to those skilled in the art from the following detailed description with reference to the accompanying drawings, and the invention is not limited to any particular disclosed embodiment. The present invention provides, for example, the following: (Item 1) A switchable optical assembly, A switchable waveplate, the switchable waveplate is configured to be electrically activated and deactivated to selectively alter the polarization state of light incident thereon, and the switchable waveplate is The first and second surfaces, A first liquid crystal layer disposed between the first surface and the second surface, wherein the first liquid crystal layer comprises a plurality of liquid crystal molecules that rotate about individual axes parallel to the central axis, and the rotation varies with respect to the azimuthal angle about the central axis, and the first liquid crystal layer Multiple electrodes for applying an electrical signal across the first liquid crystal layer and A switchable waveplate A switchable optical assembly equipped with [specific features / features]. (Item 2) The switchable optical assembly according to item 1, wherein the first and second surfaces are planar surfaces. (Item 3) The first and second surfaces are planar surfaces provided on a planar substrate, as described in item 1 or 2, for the switchable optical assembly. (Item 4) The switchable optical assembly according to any one of items 1-3, wherein the central axis is normal to the first and second surfaces. (Item 5) A switchable optical assembly according to any one of items 1-4, wherein the liquid crystal molecules are longer than they are wide in their respective longitudinal directions, and the liquid crystal molecules rotate about a separate axis parallel to the central axis such that the liquid crystal molecules have separate elongated sides in their respective longitudinal directions facing the central axis. (Item 6) The switchable optical assembly according to any one of items 1-5, wherein the liquid crystal molecules are longer than they are wide in their respective longitudinal directions, and the liquid crystal molecules rotate about separate axes parallel to the central axis such that the liquid crystal molecules form one or more concentric rings about the central axis. (Item 7) The switchable optical assembly according to any one of items 1-6, wherein the liquid crystal molecules have a length greater than their width along their individual longitudinal directions, and the liquid crystal molecules rotate about individual axes parallel to the central axis such that the individual longitudinal directions are radially perpendicular from the central axis to the liquid crystal molecules. (Item 8) The switchable optical assembly according to any one of items 1-7, wherein the plurality of liquid crystal molecules have an orientation such that the plurality of liquid crystal molecules are arranged in a rotatably symmetrical arrangement about the central axis. (Item 9) The switchable optical assembly according to any one of items 1-8, wherein the first liquid crystal layer comprises a plurality of sublayers, and the liquid crystal molecules are contained within the first sublayer of the plurality of sublayers. (Item 10) The switchable optical assembly according to item 9, wherein the plurality of sublayers include additional sublayers having liquid crystal molecules, the liquid crystal molecules being positioned laterally or radially and oriented in the same way as the liquid crystal molecules contained in the first sublayer. (Item 11) The switchable optical assembly according to item 9, wherein the plurality of sublayers include additional sublayers having liquid crystal molecules, the liquid crystal molecules being positioned laterally or radially in the same way as the liquid crystal molecules contained in the first sublayer, and being gradually twisted about an axis parallel to the central axis, the amount of twisting increasing with increasing distance from the first sublayer. (Item 12) A switchable optical assembly as described in any one of items 1-11, further comprising a second liquid crystal layer. (Item 13) The switchable optical assembly according to item 12, wherein the second liquid crystal layer comprises a plurality of sublayers, each having liquid crystal molecules positioned laterally or radially, similar to the liquid crystal molecules contained in the first sublayer of the first liquid crystal layer, and the liquid crystal molecules in the plurality of sublayers in the second liquid crystal layer are gradually twisted about an axis parallel to the central axis, the amount of twisting increasing with distance from the first liquid crystal layer. (Item 14) The switchable optical assembly according to item 12 or 13, wherein the second liquid crystal layer has liquid crystal molecules that are twisted with respect to distance from the first liquid crystal layer so as to reflect the twisting of the liquid crystal molecules in the first liquid crystal layer. (Item 15) A switchable optical assembly according to any one of items 12-14, wherein the first liquid crystal layer comprises a plurality of sublayers, the second liquid crystal layer comprises a plurality of sublayers, and the sublayer of the second liquid crystal layer closest to the first liquid crystal layer comprises liquid crystal molecules having substantially the same orientation as the liquid crystal molecules in the sublayer of the first liquid crystal layer closest to the second liquid crystal layer. (Item 16) A switchable optical assembly according to any one of items 12-15, wherein the first liquid crystal layer comprises a plurality of sublayers, the second liquid crystal layer comprises a plurality of sublayers, and the sublayer of the second liquid crystal layer furthest from the first liquid crystal layer comprises liquid crystal molecules having substantially the same orientation as the liquid crystal molecules in the sublayer of the first liquid crystal layer furthest from the second liquid crystal layer. (Item 17) The switchable optical assembly according to any one of items 12-16, wherein the first and second liquid crystal layers provide increased uniformity when modifying the polarization state of light incident thereon across multiple wavelengths, compared to an optical assembly having only one of the first and second liquid crystal layers and not having the other. (Item 18) The switchable waveplate is configured to diffract light with a diffraction efficiency of more than 95% within a wavelength range including at least 450 nm to 630 nm, as described in any one of items 12-17 of the switchable optical assembly. (Item 19) The liquid crystal molecules in the first and second liquid crystal layers have opposing twist orientations, as described in any one of items 12-18, for a switchable optical assembly. (Item 20) The first and second liquid crystal layers are a switchable optical assembly as described in any one of items 12-19, having opposing torsion angles. (Item 21) The switchable optical assembly according to any one of items 12-20, wherein the liquid crystal molecules of the first and second liquid crystal layers are twisted symmetrically by a net angle of about 60 to 80 degrees with respect to the interface between the first and second layers. (Item 22) A switchable optical assembly according to any one of items 12-21, further comprising at least one electrode configured to apply a signal across the second liquid crystal layer. (Item 23) The switchable optical assembly further comprises a first waveplate lens having a liquid crystal layer, the first waveplate lens having different refractive powers for different polarizations of light incident thereon, The aforementioned switchable optical assembly A first lens state configured to have a first refractive power, A second lens state configured to have a second refractive power different from the first refractive power, A switchable optical assembly as described in any one of items 1-22, configured to be selectively switched between at least two lens states, including (Item 24) The aforementioned second refractive power is zero refractive power, as described in item 23 of the switchable optical assembly. (Item 25) The plurality of liquid crystal molecules having rotation that varies with respect to the azimuthal angle around the central axis extend across the first liquid crystal layer for at least 1 cm 2 A switchable optical assembly as described in any one of items 1-24, comprising at least 50% liquid crystal molecules extending over a range. (Item 26) The plurality of liquid crystal molecules having rotation that fluctuates with respect to the azimuthal angle around the central axis extend across the first liquid crystal layer for at least 2 cm 2 A switchable optical assembly as described in any one of items 1-24, comprising at least 50% liquid crystal molecules extending over a range. (Item 27) The plurality of liquid crystal molecules having rotation that varies with respect to the azimuthal angle around the central axis extend across the first liquid crystal layer for at least 1 cm 2 A switchable optical assembly as described in any one of items 1-24, comprising at least 80% liquid crystal molecules extending over a range. (Item 28) The plurality of liquid crystal molecules having rotation that fluctuates with respect to the azimuthal angle around the central axis extend across the first liquid crystal layer for at least 2 cm 2 A switchable optical assembly as described in any one of items 1-24, comprising at least 80% liquid crystal molecules extending over a range. (Item 29) The plurality of liquid crystal molecules are oriented such that they have at least four rotational symmetries about the central axis, as described in any one of items 1-28, for a switchable optical assembly. (Item 30) A switchable optical assembly, A switchable waveplate, the switchable waveplate is configured to be electrically activated and deactivated to selectively alter the polarization state of light incident thereon, and the switchable waveplate is The first and second surfaces, A liquid crystal layer disposed between the first surface and the second surface, wherein the liquid crystal layer comprises a plurality of liquid crystal molecules having a length greater than its width along individual longitudinal directions, and the liquid crystal molecules are oriented such that the longitudinal direction extends radially in a plurality of radial directions from the axis of the first and second surfaces and the liquid crystal layer, Multiple electrodes for applying an electrical signal across the liquid crystal layer A switchable waveplate A switchable optical assembly equipped with [specific features / features]. (Item 31) The first and second surfaces are planar surfaces, as described in item 30, for the switchable optical assembly. (Item 32) The first and second surfaces are planar surfaces provided on a planar substrate, as described in item 30 or 31, for the switchable optical assembly. (Item 33) The switchable optical assembly according to any one of items 30-32, wherein the axis is normal to the first and second surfaces. (Item 34) The plurality of liquid crystal molecules are rotated about an axis parallel to the axis, in a switchable optical assembly as described in any one of items 30-33. (Item 35) The switchable optical assembly according to any one of items 30-34, wherein the longitudinal direction of the liquid crystal molecules is parallel to the first and second surfaces. (Item 36) A switchable optical assembly according to any one of items 30-35, configured to transmit light to the eye of a viewer at a certain distance from the switchable optical assembly, wherein the longitudinal direction of the liquid crystal molecules extends along individual projections of light paths from individual locations in the field of view of the viewer's eye to the eye, projected onto the liquid crystal layer. (Item 37) A switchable optical assembly as described in any one of items 30-36, further comprising a waveplate lens with a diffractive lens. (Item 38) A switchable optical assembly according to any one of items 30-37, further comprising a waveplate lens having a liquid crystal layer, wherein the liquid crystal layer of the waveplate lens is arranged such that the waveplate lens has a birefringence (Δn) that varies radially outward from the central region of the first waveplate lens. (Item 39) A switchable optical assembly according to any one of items 30-38, wherein when the switchable waveplate is in a first state, the switchable waveplate acts as a half-waveplate configured to reverse the polarity of circularly polarized light passing through it, while when the switchable waveplate is in a second state, the switchable waveplate is configured to preserve the polarity of circularly polarized light passing through it. (Item 40) The switchable optical assembly according to any one of items 30-39, wherein the liquid crystal layer comprises a plurality of sublayers, and the liquid crystal molecules are contained within the first sublayer of the plurality of sublayers. (Item 41) The switchable optical assembly according to item 40, wherein the plurality of sublayers include additional sublayers having liquid crystal molecules, the liquid crystal molecules being oriented and positioned laterally or radially, similar to the liquid crystal molecules contained within the first sublayer. (Item 42) The switchable optical assembly further comprises a first waveplate lens having a liquid crystal layer, the first waveplate lens having different refractive powers for different polarizations of light incident thereon, The aforementioned switchable optical assembly A first lens state configured to have a first refractive power, A second lens state configured to have a second refractive power different from the first refractive power, A switchable optical assembly as described in any one of items 30-41, configured to be selectively switched between at least two lens states, including (Item 43) The aforementioned second refractive power is zero refractive power, as described in item 42 of the switchable optical assembly. (Item 44) The plurality of liquid crystal molecules, whose individual vertical directions are oriented so as to extend radially from the axis in multiple radial directions from the axis, are arranged to span the liquid crystal layer for at least 1 cm 2 A switchable optical assembly as described in any one of items 30-43, comprising at least 50% liquid crystal molecules extending over a range. (Item 45) The plurality of liquid crystal molecules, whose individual vertical directions are oriented so as to extend radially from the axis in multiple radial directions from the axis, are oriented so as to extend at least 2 cm across the liquid crystal layer. 2 A switchable optical assembly as described in any one of items 30-43, comprising at least 50% liquid crystal molecules extending over a range. (Item 46) The plurality of liquid crystal molecules, whose individual vertical directions are oriented so as to extend radially from the axis in multiple radial directions from the axis, are arranged to span the liquid crystal layer for at least 1 cm 2A switchable optical assembly as described in any one of items 30-43, comprising at least 80% liquid crystal molecules extending over a range. (Item 47) The plurality of liquid crystal molecules, whose individual vertical directions are oriented so as to extend radially from the axis in multiple radial directions from the axis, are oriented so as to extend at least 2 cm across the liquid crystal layer. 2 A switchable optical assembly as described in any one of items 30-43, comprising at least 80% liquid crystal molecules extending over a range. (Item 48) The axis comprises the central axis of the first and second surfaces and the liquid crystal layer, as described in any one of items 30-47, for the switchable optical assembly. (Item 49) A method for processing optical elements, To provide a substrate that extends along the horizontal direction and has a normal pointed perpendicular to it, To provide a first vertically aligned layer, To provide a second horizontally aligned layer, The present invention provides a liquid crystal layer comprising liquid crystal molecules in a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, wherein the first vertically aligned layer orients the liquid crystal molecules more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer orients the liquid crystal molecules more horizontally than in the case without the second horizontally aligned layer. Methods that include... (Item 50) The method according to item 49, wherein the first vertically aligned layer is configured to orient liquid crystal molecules proximal to it along the vertical direction rather than the horizontal direction. (Item 51) The method according to item 49 or 50, wherein the second horizontally aligned layer is configured to orient liquid crystal molecules proximal to it along the horizontal direction rather than the vertical direction. (Item 52) The method according to any one of items 49-51, wherein the second horizontally aligned layer comprises a patterned layer. (Item 53) The method according to item 52, wherein the second horizontally aligned layer comprises an imprint layer. (Item 54) The method according to item 52 or 53, wherein the second horizontally aligned layer comprises a nanoimprint layer. (Item 55) The nanoimprint layer is formed using a nanoimprint template, as described in item 54. (Item 56) The patterned layer is formed using a lithography technique or an etching technique, as described in item 55. (Item 57) The first vertically aligned layer and the second horizontally aligned layer are arranged across the substrate, as described in any one of items 49-56. (Item 58) The first vertically aligned layer is disposed between the second horizontally aligned layer and the substrate, as described in any one of items 49-57. (Item 59) The second horizontally aligned layer is disposed between the first vertically aligned layer and the substrate, as described in any one of items 49-58. (Item 60) The method according to any one of items 49-59, wherein the second horizontally aligned layer has first and second regions, the first region being configured to cause the liquid crystal molecules to be more horizontal than the second region. (Item 61) The method according to item 60, wherein the first and second regions of the second horizontally matched layer are characterized, and the features in the first region are larger in size than the features in the second region such that the liquid crystal molecules more proximal to the first region are more horizontal than the liquid crystal molecules more proximal to the second region. (Item 62) The method according to item 60 or 61, wherein the first and second regions of the second horizontally matched layer are characterized, and the features in the first region have a greater height than the features in the second region such that the liquid crystal molecules more proximal to the first region are more horizontal than the liquid crystal molecules more proximal to the second region. (Item 63) The method according to any one of items 60-62, wherein the first and second regions of the second horizontally matched layer are characterized, and the features in the first region are wider than the features in the second region such that the liquid crystal molecules more proximal to the first region are more horizontal than the liquid crystal molecules more proximal to the second region. (Item 64) The method according to any one of items 60-63, wherein the first and second regions of the second horizontally matched layer are characterized, and the features in the first region have a wider pitch than the features in the second region such that the liquid crystal molecules more proximal to the first region are more horizontal than the liquid crystal molecules more proximal to the second region. (Item 65) The method according to any one of items 60-64, wherein the first and second regions of the second horizontally matched layer are characterized, and the features in the first region have a higher duty cycle than the features in the second region such that the liquid crystal molecules more proximal to the first region are more horizontal than the liquid crystal molecules more proximal to the second region. (Item 66) The method according to any one of items 60-65, wherein the first and second regions of the second horizontally aligned layer are characterized, and the features in the first region have a different profile from the features in the second region in order to make the liquid crystal molecules more proximal to the first region more horizontal than the liquid crystal molecules more proximal to the second region. (Item 67) The method according to any one of items 60-66, wherein the first and second regions of the second horizontally aligned layer are characterized, and the features in the first region have a different aspect ratio from the features in the second region in order to make the liquid crystal molecules more proximal to the first region more horizontal than the liquid crystal molecules more proximal to the second region. (Item 68) The method according to any one of items 49-67, wherein the second horizontal matching layer comprises a region configured to prevent the oblique angle from becoming more horizontal. (Item 69) The method according to any one of items 49-69, wherein the second horizontal matching layer comprises at least one region configured to prevent the angle from becoming more horizontal, located between two regions of the second horizontal matching layer configured to make the angle more horizontal. (Item 70) The method according to any one of items 49-69, wherein the first vertically aligned layer has first and second regions, the first region being configured to align the liquid crystal molecules more perpendicularly than the second region. (Item 71) The method according to item 70, wherein the first region and the second region of the first horizontally matched layer have different thicknesses such that the liquid crystal molecules more proximal to the first region are more perpendicular to the liquid crystal molecules more proximal to the second region. (Item 72) The method according to any one of items 49-71, wherein the first vertically aligned layer comprises a region configured to prevent the oblique angle from becoming more vertical. (Item 73) The method according to any one of items 49-72, wherein the first vertical alignment layer comprises at least one region configured to prevent the angle from becoming more vertical, located between two regions of the first vertical alignment layer configured to make the angle more vertical. (Item 74) The method according to any one of items 49-73, wherein the angle depends on the relative strength of the first vertically matched layer and the second horizontally matched layer. (Item 75) To provide a third vertically aligned layer, To provide a fourth horizontally aligned layer It further includes, The method according to any one of items 49-74, wherein the first vertically aligned layer orients the liquid crystal layer more vertically than when the third vertically aligned layer is absent, and the fourth horizontally aligned layer orients the liquid crystal molecules more horizontally than when the fourth horizontally aligned layer is absent. (Item 76) The liquid crystal layer is disposed between the first vertically aligned layer and the third vertically aligned layer, as described in item 75. (Item 77) The liquid crystal layer is disposed between the second vertically aligned layer and the fourth vertically aligned layer, as described in item 75 or 76. (Item 78) The method according to any one of items 49-77, wherein the angle of inclination is 0° to 90° with respect to the horizontal direction. (Item 79) The method according to any one of items 49-77, wherein the angle for most of the liquid crystal molecules in the liquid crystal layer is 5° to 85° with respect to the horizontal direction. (Item 80) The method according to any one of items 49-79, wherein the angle for most of the liquid crystal molecules in the liquid crystal layer is 5° to 45° with respect to the horizontal direction. (Item 81) The optical element comprises a waveplate, as described in any one of items 49-80. (Item 82) The optical element comprises a switchable waveplate, as described in any one of items 49-80. (Item 83) The method according to any one of items 49-82, further comprising forming electrodes configured to apply an electrical signal to the liquid crystal layer. (Item 84) The optical element comprises a waveplate lens, as described in any one of items 48-83. [Brief explanation of the drawing]

[0013] [Figure 1] Figure 1 illustrates the user's view of augmented reality (AR) through an AR device.

[0014] [Figure 2] Figure 2 illustrates a conventional display system for simulating a three-dimensional image for the user.

[0015] [Figure 3] Figures 3A-3C illustrate the relationship between the radius of curvature and the radius of focus.

[0016] [Figure 4A] Figure 4A illustrates the representation of the accommodation-vergence response of the human visual system.

[0017] [Figure 4B] Figure 4B illustrates an example of different near and far accommodative states and convergence / divergence motion states of a pair of user eyes.

[0018] [Figure 4C] Figure 4C illustrates an example of how the upper and lower figures represent a user viewing content through a display system.

[0019] [Figure 4D] Figure 4D illustrates another embodiment of the representation of the upper and lower figures of a user viewing content through a display system.

[0020] [Figure 5] Figure 5 illustrates aspects of an approach to simulating a 3D image by correcting wavefront divergence.

[0021] [Figure 6] Figure 6 illustrates an example of a waveguide stack for outputting image information to the user.

[0022] [Figure 7] Figure 7 illustrates an example of an output beam produced by a waveguide.

[0023] [Figure 8] Figure 8 illustrates an embodiment of a stacked waveguide assembly, where each depth plane includes an image formed using multiple different primary colors.

[0024] [Figure 9A] Figure 9A shows a cross-sectional side view of an embodiment of a stacked waveguide set, each including an internally coupled optical element.

[0025] [Figure 9B] Figure 9B shows a perspective view of an embodiment of the multiple stacked waveguides shown in Figure 9A.

[0026] [Figure 9C] Figure 9C shows top and bottom plan views of the embodiment of the multiple stacked waveguides shown in Figures 9A and 9B.

[0027] [Figure 9D] Figure 9D illustrates an embodiment of a wearable display system.

[0028] [Figure 10] Figure 10 illustrates an embodiment of a display system comprising a pair of adaptive lens assemblies.

[0029] [Figure 11] Figure 11A illustrates an embodiment of the display system of Figure 10, which displays virtual content to the user in a virtual depth plane. Figure 11B illustrates an embodiment of the display system of Figure 10, which provides the user with a view of real-world content.

[0030] [Figure 12A] Figure 12A illustrates an embodiment of a waveplate lens assembly that includes liquid crystal.

[0031] [Figure 12B] Figure 12B illustrates an embodiment of a switchable waveplate lens equipped with liquid crystal.

[0032] [Figure 13A] Figure 13A shows a cross-sectional view of an embodiment of a switchable waveplate layer comprising a twisted nematic liquid crystal layer.

[0033] [Figure 13B] Figure 13B illustrates an embodiment of a switchable waveplate assembly comprising the switchable waveplate shown in Figure 13A, which is interposed between a pair of quarter-waveplates, with the switchable waveplate being activated or deactivated during operation.

[0034] [Figure 13C] Figure 13C illustrates an embodiment of a quarter-wave plate comprising multiple layers of twisted nematic liquid crystal layers.

[0035] [Figure 13D] Figure 13D illustrates an embodiment of a switchable waveplate assembly, comprising the switchable waveplates of Figure 13A interposed between a pair of quarter-waveplates, which are integrated as a single stack using an adhesive layer.

[0036] [Figure 13E] Figure 13E illustrates an embodiment of a switchable waveplate assembly comprising a layer of twisted nematic liquid crystal interposed between a pair of quarter-waveplates, which are integrated as a single stack.

[0037] [Figure 13F] Figure 13F illustrates an embodiment of a switchable waveplate assembly comprising a layer of twisted nematic liquid crystal interposed between a pair of quarter-waveplates in Figure 13C, which are integrated as a single stack.

[0038] [Figure 14A]Figure 14A shows a perspective view of one embodiment of a pair of transparent electrodes for switching the liquid crystal layers.

[0039] [Figure 14B] Figure 14B shows a perspective view of the other embodiment of a pair of transparent electrodes for switching the liquid crystal layers.

[0040] [Figure 14C] Figure 14C shows a perspective view of an embodiment of a pair of vertically separated transparent electrodes for switching layers of liquid crystal.

[0041] [Figure 15A] Figure 15A shows a plan view of an embodiment of a pair of horizontally intersecting transparent electrodes for switching between liquid crystal layers.

[0042] [Figure 15B] Figure 15B shows a cross-sectional view of an embodiment of a switchable waveplate assembly, including the pair of horizontally intersecting transparent electrodes shown in Figure 15A.

[0043] [Figure 16A] Figure 16A shows a plan view of an embodiment of a waveplate lens equipped with liquid crystal.

[0044] [Figure 16B] Figure 16B shows a plan view of an embodiment of a waveplate lens equipped with liquid crystal.

[0045] [Figure 16C] Figure 16C illustrates an embodiment of a waveplate lens that provides different refractive powers depending on the polarization of the light and the side from which the light is incident, causing the light passing through it to diverge or focus.

[0046] [Figure 16D] Figure 16D illustrates an embodiment of a waveplate lens that provides different refractive powers depending on the polarization of the light and the side from which the light is incident, causing the light passing through it to diverge or converge.

[0047] [Figure 17A] Figure 17A illustrates an embodiment of an adaptive lens assembly comprising a waveplate lens and a switchable waveplate.

[0048] [Figure 17B] Figure 17B illustrates an embodiment of the adaptive lens assembly shown in Figure 17A, in which the switchable waveplate is activated during operation.

[0049] [Figure 17C] Figure 17C illustrates an embodiment of the adaptive lens assembly shown in Figure 13A, in which the switchable waveplate is deactivated during operation.

[0050] [Figure 18A] Figure 18A illustrates an embodiment of a display device comprising a waveguide between a pair of adaptive lens assemblies, each having a waveplate lens and a switchable waveplate, with the switchable waveplate being activated during operation.

[0051] [Figure 18B] Figure 18B illustrates an embodiment of the display device shown in Figure 18A, in which the switchable waveplate is deactivated during operation.

[0052] [Figure 19A] Figure 19A shows a plan view of an exemplary arrangement of liquid crystal molecules closest to the substrate of a broadband waveplate lens containing liquid crystal.

[0053] [Figure 19B] Figure 19B illustrates a broadband waveplate lens, which focuses light having a first circular polarization, and is equipped with liquid crystals arranged as shown in Figure 19A.

[0054] [Figure 19C] Figure 19C illustrates a broadband waveplate lens comprising liquid crystals arranged as shown in Figure 19A, which emit light having a second circular polarization.

[0055] [Figure 20A] Figure 20A illustrates a plan view of an exemplary arrangement of liquid crystal molecules in a broadband waveplate lens comprising multiple layers of twisted nematic liquid crystals.

[0056] [Figure 20B] Figure 20B shows a cross-sectional view of an embodiment of a broadband waveplate lens comprising multiple layers of twisted nematic liquid crystal.

[0057] [Figure 21] Figure 21 shows a cross-sectional view of an embodiment of a broadband waveplate lens comprising a liquid crystal layer having birefringence that increases with increasing wavelength.

[0058] [Figure 22A] Figure 22A shows a cross-sectional view of an embodiment of a deactivated, switchable broadband waveplate lens that diverges and converts the polarization of light having a first circular polarization.

[0059] [Figure 22B] Figure 22B illustrates a cross-sectional view of an embodiment of a deactivated, switchable broadband waveplate lens that focuses and converts the polarization of light having a second circular polarization.

[0060] [Figure 22C] Figure 22C illustrates a cross-sectional view of an example of an activated, switchable broadband waveplate lens that allows circularly polarized light to pass through without substantially converging or diverging, while preserving its polarization.

[0061] [Figure 23A] Figure 23A illustrates an embodiment of a broadband adaptive waveplate lens assembly comprising a pair of broadband switchable waveplate lenses, both of which are deactivated during operation.

[0062] [Figure 23B]Figure 23B illustrates the broadband adaptive waveplate lens assembly of Figure 23A, in which one of the switchable waveplate lenses is activated during operation.

[0063] [Figure 23C] Figure 23C illustrates the broadband adaptive waveplate lens assembly of Figure 23A, in which one of the switchable waveplate lenses is activated during operation.

[0064] [Figure 23D] Figure 23D illustrates an embodiment of a broadband adaptive waveplate lens assembly comprising a pair of broadband switchable waveplate lenses, both of which are activated during operation.

[0065] [Figure 24A] Figure 24A illustrates an embodiment of an integrated broadband adaptive waveplate lens assembly, which includes a switchable broadband waveplate lens interposed between a pair of active broadband switchable waveplate lenses.

[0066] [Figure 24B] Figure 24B illustrates the broadband adaptive waveplate lens assembly shown in Figure 24A when operating as a combination of broadband half-waveplate lenses.

[0067] [Figure 24C] Figure 24C illustrates the broadband adaptive waveplate lens assembly of Figure 24B, with the switchable broadband waveplate activated during operation.

[0068] [Figure 24D] Figure 24D illustrates the broadband adaptive waveplate lens assembly of Figure 24B, with the switchable broadband waveplate deactivated during operation.

[0069] [Figure 25A]Figure 25A illustrates the simulated diffraction efficiency versus wavelength in the visible spectrum for the broadband adaptive waveplate lens assembly of Figure 24A with the switchable broadband waveplate activated.

[0070] [Figure 25B] Figure 25B illustrates the simulated diffraction efficiency versus wavelength in the visible spectrum for the broadband adaptive waveplate lens assembly shown in Figure 24A, with the switchable broadband waveplate deactivated.

[0071] [Figure 26A] Figure 26A illustrates the simulated actual net refractive power against the target for an exemplary broadband adaptive waveplate lens assembly, which includes three broadband switchable waveplate lenses, using single and multiple lens states for blue wavelengths.

[0072] [Figure 26B] Figure 26B illustrates the simulated actual net refractive power against the target for an exemplary broadband adaptive waveplate lens assembly, which includes three broadband switchable waveplate lenses, using single and multiple lens states for the green wavelength.

[0073] [Figure 26C] Figure 26C illustrates the simulated actual net refractive power against the target for an exemplary broadband adaptive waveplate lens assembly, which includes three broadband switchable waveplate lenses, using single and multiple lens states for red wavelengths.

[0074] [Figure 27] Figures 27A-27C illustrate exemplary manufacturing methods for broadband waveplates or broadband waveplate lenses.

[0075] [Figure 28] Figure 28 illustrates an exemplary method for constructing a matching layer for matching liquid crystal molecules within a broadband waveplate or broadband waveplate lens using two-beam exposure.

[0076] [Figure 29] Figures 29A-29B illustrate an exemplary method for constructing a matching layer for matching liquid crystal molecules within a broadband waveplate or broadband waveplate lens using a master lens.

[0077] [Figure 30A] Figures 30A-30B illustrate an exemplary method for constructing a nanoimprint matching layer to match liquid crystal molecules within a broadband waveplate or broadband waveplate lens using a master lens and a single-beam exposure. [Figure 30B] Figures 30A-30B illustrate an exemplary method for constructing a nanoimprint matching layer to match liquid crystal molecules within a broadband waveplate or broadband waveplate lens using a master lens and a single-beam exposure.

[0078] [Figure 30C] Figure 30C illustrates an exemplary nanoimprint matching layer for matching liquid crystal molecules in a broadband waveplate lens using the exemplary method of Figures 30A-30B.

[0079] [Figure 31] Figures 31A-31C illustrate an exemplary method for fabricating a switchable broadband waveplate or a switchable broadband waveplate lens with liquid crystal using a gap-filling process.

[0080] [Figure 32-1] Figures 32A–32E illustrate an exemplary method for fabricating a switchable broadband waveplate or a switchable broadband waveplate lens with liquid crystal using a layer transfer process. [Figure 32-2] Figures 32A–32E illustrate an exemplary method for fabricating a switchable broadband waveplate or a switchable broadband waveplate lens with liquid crystal using a layer transfer process.

[0081] [Figure 33]Figure 33 illustrates an embodiment of a switchable broadband waveplate or a switchable broadband waveplate lens, which is formed on a portion of a substrate and includes liquid crystal.

[0082] [Figure 34] Figure 34 illustrates an exemplary method for forming a switchable broadband waveplate or a switchable broadband waveplate lens with liquid crystal on a portion of a substrate by selective coating.

[0083] [Figure 35] Figures 35A-35C illustrate an exemplary method for forming a switchable broadband waveplate or a switchable broadband waveplate lens with liquid crystal on a portion of a substrate by blanket coating and subtractively removing a layer of liquid crystal.

[0084] [Figure 36] Figures 36A-36C illustrate an exemplary method for forming a switchable broadband waveplate or a switchable broadband waveplate lens with liquid crystal on a portion of a substrate by using selective optical patterning of a matching layer.

[0085] [Figure 37] Figures 37A-37B illustrate an exemplary method for forming a switchable broadband waveplate or a switchable broadband waveplate lens with liquid crystal on a portion of a substrate by using selective nanoimprinting of a matching layer.

[0086] [Figure 38] Figure 38 illustrates an embodiment of an adaptive lens assembly comprising a waveplate lens and a switchable waveplate that receives light from a wide field of view. Light from objects at the periphery of the field of view is incident on the switchable waveplate at an angle that reduces the efficiency of polarization rotation. This adaptive lens produces afterimages in a false depth plane when such elements are used as variable focus elements for augmented reality devices.

[0087] [Figure 39] Figure 39 is a plot illustrating the efficiency of a switchable waveplate in rotating the polarization of light incident on it at different angles. Bright areas (e.g., at the periphery) indicate reduced efficiency.

[0088] [Figure 40] Figure 40 illustrates yet another exemplary design for a switchable waveplate configured to increase the efficiency of polarization rotation for light from objects on the periphery of the field of view. The switchable waveplate includes a liquid crystal layer comprising molecules that are rotated about an axis parallel to a central axis passing through the switchable waveplate. The amount of rotation, and therefore the orientation of the molecules, varies with respect to the azimuthal angle about the central axis, such that the elongated molecules generally form concentric rings about the central axis. The longitudinal directions of the molecules 4332 can be aligned along concentric ring-shaped paths of at least 3, 4, 5, 6, 8, 9, 10, 12, 14, 20, 40, or greater (or any range between any of these values). This configuration increases the uniformity in the efficiency of polarization rotation of the switchable waveplate, even with respect to highly off-axis field of view angles.

[0089] [Figure 41] Figure 41 illustrates yet another exemplary design for a switchable waveplate configured to increase the efficiency of polarization rotation for light from objects at the periphery of the field of view. The switchable waveplate includes a liquid crystal layer having molecules that are longer than its width along its longitudinal direction. The molecules are oriented such that the longitudinal direction extends radially from the central axis through the switchable waveplate for multiple radial directions from the central axis. This configuration also increases the uniformity in the efficiency of polarization rotation of the switchable waveplate, even with respect to highly off-axis field angles.

[0090] [Figure 42A] Figures 42A and 42B illustrate an embodiment of a switchable waveplate comprising multiple layers of twisted liquid crystal layers with a wide-field structure similar to either Figure 40 or Figure 41, and providing broadband operation over wavelengths similar to Figure 20B. [Figure 42B] Figures 42A and 42B illustrate an embodiment of a switchable waveplate comprising multiple layers of twisted liquid crystal layers with a wide-field structure similar to either Figure 40 or Figure 41, and providing broadband operation over wavelengths similar to Figure 20B.

[0091] [Figure 43A] Figures 43A-43D illustrate a method for matching LC molecules using a first layer and matching layers having different orientations, for example, comprising vertical and horizontal matching layers. In this embodiment, the horizontal matching layer comprises a patterned nanostructure. [Figure 43B] Figures 43A-43D illustrate a method for matching LC molecules using a first layer and matching layers having different orientations, for example, comprising vertical and horizontal matching layers. In this embodiment, the horizontal matching layer comprises a patterned nanostructure. [Figure 43C] Figures 43A-43D illustrate a method for matching LC molecules using a first layer and matching layers having different orientations, for example, comprising vertical and horizontal matching layers. In this embodiment, the horizontal matching layer comprises a patterned nanostructure. [Figure 43D] Figures 43A-43D illustrate a method for matching LC molecules using a first layer and matching layers having different orientations, for example, comprising vertical and horizontal matching layers. In this embodiment, the horizontal matching layer comprises a patterned nanostructure.

[0092] Throughout the drawings, reference numbers may be reused to indicate correspondences between the referenced elements. The drawings are provided to illustrate exemplary embodiments described herein and are not intended to limit the scope of this disclosure. [Modes for carrying out the invention]

[0093] AR systems can still display virtual content to a user or viewer while allowing the user to see the world around them. Preferably, this content is displayed on a head-mounted display, for example, as part of eyewear, which projects image information onto the user's eyes. In addition, the display may also transmit light from the surrounding environment to the user's eyes, allowing them to view that environment. As used herein, “head-mounted” or “head-mountable” display is understood to be a display that can be mounted on the head of a viewer or user.

[0094] In some AR systems, multiple waveguides may be configured to form virtual images in multiple virtual depth planes (also simply referred to herein as “depth planes”). Different waveguides of the multiple waveguides may have different refractive powers and may be formed at different distances from the user’s eye. The display system may also include multiple lenses that provide, or in addition to, refractive power. The refractive powers of the waveguides and / or lenses may provide images in different virtual depth planes. Undesirably, waveguides and lenses may each increase the overall thickness, weight, and cost of the display.

[0095] Advantageously, in the various embodiments described herein, the adaptive lens assembly may be used to provide a variable refractive power, for example, to correct wavefront divergence of light propagating through the lens assembly and to provide a virtual depth plane at different perceptual distances from the user. The adaptive lens assembly may include a pair of waveplate lenses having a switchable waveplate positioned between them. Each of the first and second waveplate lenses may be configured to modify the polarization state of light passing through it, and the switchable waveplate may be switchable between a plurality of states, for example, a first state that allows light to pass through without changing the polarization of the light, and a second state that modifies the polarization of the light (for example, by changing the polarity of the polarization). In some embodiments, one or both of the waveplate lenses may be switchable between these first and second states, and the intervening switchable waveplate described above may be omitted.

[0096] It should be understood that an adaptive lens assembly may comprise a stack of multiple waveplate lenses and multiple switchable waveplates. For example, an adaptive lens assembly may comprise multiple subassemblies, each comprising a pair of waveplate lenses with an intervening switchable waveplate. In some embodiments, the adaptive lens assembly may include alternating waveplate lenses and switchable waveplates. Advantageously, such alternating arrangements allow for reductions in thickness and weight by sharing a common waveplate lens with neighboring switchable waveplates. In some embodiments, discrete levels of refractive power beyond two may be provided by switching the states of various combinations of switchable plates in the stack.

[0097] In some embodiments, the adaptive lens assembly, together with the waveguide assembly, forms a display device that forms images in different virtual depth planes. In various embodiments, the display device comprises a pair of adaptive lens assemblies interposed by a waveguide assembly. The waveguide assembly includes a waveguide configured to propagate light (e.g., visible light) through it (e.g., via total internal reflection) and to externally couple the light. For example, the light may be externally coupled along the optical axis normal to the main surface of the waveguide. One of the pair of adaptive lens assemblies may be formed on the first side of the waveguide assembly and may be configured to provide a variable refractive force and modify the wavefront of the light passing through the adaptive lens assembly to form images in each of a plurality of virtual depth planes. For example, the adaptive lens assembly may focus or diverge the externally coupled light received from the waveguide assembly. To compensate for the correction of the real-world view caused by the convergence or divergence of ambient light propagating through the adaptive lens assembly and / or waveguide assembly, the other of a pair of adaptive lens assemblies is provided, in addition, on the second side of the waveguide assembly opposite to the first side. When the switchable waveplate of each adaptive lens assembly is in the corresponding state, the adaptive lens assembly may have a refractive force with opposite signs such that the other of the adaptive lens assemblies compensates for the distortion caused by the adaptive lens assembly on the first side of the waveguide assembly.

[0098] Advantageously, for a continuously variable adaptive lens with continuously variable optical elements, utilizing a switchable waveplate that can be switched between two states simplifies the driving of the adaptive lens assembly and reduces the computational power required to determine how to properly activate the adaptive lens assembly for the desired refractive power. In addition, by allowing the adaptive lens assembly to correct the wavefront divergence of the light output by the waveguides, the number of waveguides required to provide multiple depth planes is reduced compared to an array where each waveguide provides a certain amount of wavefront divergence.

[0099] Here, we refer to the diagrams, where similar reference numbers refer to the same parts throughout. Unless otherwise indicated, the diagrams are schematic and not necessarily drawn to exact scale. (Example display system)

[0100] Figure 2 illustrates a conventional display system for simulating a three-dimensional image for a user. It should be understood that when a user's eyes are spaced apart and viewing a real object in space, each eye may have a slightly different view of the object and may form an image of the object in different locations on the retina of each eye. This may be called binocular parallax and can be used by the human visual system to provide a sense of depth. Conventional display systems simulate binocular parallax by presenting two distinctly different images 190, 200, one for each eye 210, 220, with slightly different views of the same virtual object, corresponding to the view of the virtual object that each eye would see as a real object at a desired depth. These images provide binocular cues that the user's visual system can interpret to derive a sense of depth.

[0101] Continuing with Figure 2, images 190 and 200 are spaced 230 units away from eyes 210 and 220 on the z-axis. The z-axis is parallel to the viewer's optical axis when the eye is fixated on an object at optical infinity directly in front of the viewer. Images 190 and 200 are flat and at a fixed distance from eyes 210 and 220. Based on slightly different views of the virtual object in the images presented to eyes 210 and 220, respectively, the eyes may rotate so that the image of the object comes to the corresponding point on the respective retina of the eye, maintaining monobiocular vision. This rotation can converge the lines of sight of eyes 210 and 220 to a point in space where the virtual object is perceived to exist. As a result, the provision of three-dimensional images conventionally involves manipulating the convergence and divergence movements of the user's eyes 210 and 220 and providing binocular cues that the human visual system interprets to provide depth perception.

[0102] However, generating a realistic and comfortable perception of depth is difficult. It should be understood that light from an object at different distances from the eye has wavefronts with different amounts of divergence. Figures 3A-3C illustrate the relationship between distance and ray divergence. The distance between the object and the eye 210 is expressed in the order of decreasing distances R1, R2, and R3. As shown in Figures 3A-3C, the ray diverges more as the distance to the object decreases. Conversely, as the distance increases, the ray becomes more collimated. In other words, the light field generated by a point (object or part of an object) can be said to have a spherical wavefront curvature, which is a function of the distance the point is from the user's eye. As the curvature increases, the distance between the object and the eye 210 decreases. Only a monocular eye 210 is illustrated in Figures 3A-3C and various other figures herein for the sake of clarity in the illustration, but the discussion with respect to the eye 210 can be applied to the binocular eyes 210 and 220 of a viewer.

[0103] Continuing to refer to Figures 3A-3C, light from an object that a viewer's eye is fixated on may have different wavefront divergences. Due to the different wavefront divergences, the light may be focused differently by the eye's lens, which may require the lens to take on different shapes and form focused images on the retina. If a focused image is not formed on the retina, the resulting retinal blur acts as a cue for accommodation, causing a change in the shape of the eye's lens until a focused image is formed on the retina. For example, a cue for accommodation induces relaxation or contraction of the ciliary muscle surrounding the eye's lens, thereby modulating the force applied to the suspensory ligament that holds the lens, and thus changing the shape of the eye's lens until the retinal blur of the fixed object is eliminated or minimized, thereby forming a focused image of the fixed object on the retina (e.g., the fovea). The process by which the lens of the eye changes shape can be called accommodation, and the shape of the lens required to form a focused image of the object being fixed on onto the retina of the eye (e.g., the fovea) can be called the accommodative state.

[0104] Referring here to Figure 4A, the representation of the accommodation-convergence-divergence response of the human visual system is illustrated. Eye movement to fixate on an object causes the eye to receive light from the object, and the light forms an image on each retina of the eye. The presence of retinal blur in the image formed on the retina can provide cues for accommodation, and the relative location of the image on the retina can provide cues for convergence-divergence movement. The cues for accommodation produce accommodation, resulting in the lens of the eye taking on a specific accommodative state in which a focused image of the object is formed on the retina of the eye (e.g., the fovea). On the other hand, the cues for convergence-divergence movement produce convergence-divergence movement (rotation of the eye) so that the image formed on each retina of each eye is at the corresponding retinal point that maintains monobiocular vision. At these positions, the eye can be said to be in a specific convergence-divergence state. Continuing to refer to Figure 4A, accommodation can be understood as the process by which the eye achieves a specific state of accommodation, and convergence / divergence can be understood as the process by which the eye achieves a specific state of convergence / divergence. As shown in Figure 4A, the state of accommodation and convergence / divergence of the eye can change when the user fixates on a different object. For example, the accommodated state can change when the user fixates on a new object at a different depth on the z-axis.

[0105] While not limited by theory, it is thought that an object viewer may perceive an object as "three-dimensional" due to a combination of convergence-divergence movements and accommodation. As mentioned above, convergence-divergence movements of two eyes relative to each other (e.g., eye rotations such as pupils moving toward or away from each other, converging the lines of sight and fixing on an object) are closely related to the accommodation of the eye's lens. Under normal conditions, changing the shape of the eye's lens and shifting focus from one object to another at a different distance will automatically produce a consistent change in convergence-divergence movements up to the same distance, under a relationship known as the "accommodation-convergence-divergence reflex." Similarly, changes in convergence-divergence movements will, under normal conditions, induce a consistent change in lens shape.

[0106] Referring now to Figure 4B, embodiments of different accommodation and convergence / divergence states of the eyes are illustrated. Eye pair 222a fixates on an object at optical infinity, while eye pair 222b fixates on an object 221 below optical infinity. It is noteworthy that the convergence / divergence states of each pair of eyes are different, with eye pair 222a pointing straight ahead, while eye pair 222 converges on object 221. The accommodation states of the eyes forming each pair of eyes 222a and 222b are also different, as represented by the different shapes of the lenses 210a and 220a.

[0107] Unfortunately, many users of conventional "3-D" display systems find such systems uncomfortable or completely fail to perceive depth due to the mismatch between the accommodation and convergence / divergence states in these displays. As mentioned earlier, many stereoscopic or "3-D" display systems display scenes by providing slightly different images to each eye. Such systems are uncomfortable for many viewers because they, above all, simply provide different presentations of scenes and cause changes in the convergence / divergence states of the eyes, but without corresponding changes in the accommodation states of those eyes. Rather, the images are presented by the display at a fixed distance from the eyes so that the eyes perceive all image information in a single accommodation state. Such arrangements go against the "accommodation-convergence / divergence reflex" by causing changes in the convergence / divergence state without corresponding changes in the accommodation state. This mismatch is thought to cause viewer discomfort. A display system that provides better integration between distance accommodation and convergence / divergence motion can create a more realistic and comfortable simulation of three-dimensional images.

[0108] While not limited by theory, the human eye is typically thought to be capable of interpreting a finite number of depth planes and providing depth perception. Consequently, a highly realistic simulation of perceived depth can be achieved by providing the eye with different presentations of images corresponding to each of these limited number of depth planes. In some embodiments, the different presentations may provide both cues for convergence-divergence movements and matching cues for accommodation, thereby providing physiologically correct accommodation-convergence-divergence movement matching.

[0109] Continuing with Figure 4B, two depth planes 240 are illustrated, corresponding to different spatial distances from eyes 210 and 220. With respect to a given depth plane 240, condensation-divergence motion cues may be provided by displaying appropriately different viewpoint images for each eye 210 and 220. In addition, with respect to a given depth plane 240, the light forming the image provided to each eye 210 and 220 may have wavefront divergence corresponding to a light field generated by a point at a distance in that depth plane 240.

[0110] In the illustrated embodiment, the distance along the z-axis of the depth plane 240 containing point 221 is 1 m. As used herein, the distance or depth along the z-axis may be measured using a zero point located at the exit pupil of the user's eye. Thus, the depth plane 240 located at a depth of 1 m corresponds to a distance of 1 m from the exit pupil of the user's eye on the optical axis of those eyes, with the eyes pointed toward optical infinity. As an approximation, the depth or distance along the z-axis may be measured from the display in front of the user's eye (e.g., the surface of a waveguide) and a value relating to the distance between the device and the exit pupil of the user's eye may be added. This value is called the pupil distance and may correspond to the distance between the exit pupil of the user's eye and the user-worn display in front of the eye. In practice, the value relating to the pupil distance may generally be a normalized value used for all spectators. For example, the pupil distance may be assumed to be 20 mm, and the depth plane at a depth of 1 m may be at a distance of 980 mm from the front of the display.

[0111] Referring here to Figures 4C and 4D, embodiments of aligned accommodation-convergence-divergence distance and misaligned accommodation-convergence-divergence distance are illustrated, respectively. As shown in Figure 4C, the display system may provide images of virtual objects to each eye 210, 220. The images can cause the eyes 210, 220 to assume a convergence-divergence state in which the eyes converge on point 15 on the depth plane 240. In addition, the images may be formed by light having a wavefront curvature corresponding to a real object in its depth plane 240. As a result, the eyes 210, 220 assume an accommodation state in which the images are in focus on the retinas of their eyes. Thus, the user can perceive the virtual object as being at point 15 on the depth plane 240.

[0112] It should be understood that the accommodation and convergence / divergence states of eyes 210 and 220 are each associated with a specific distance on the z-axis. For example, an object at a specific distance from eyes 210 and 220 will cause those eyes to adopt a specific accommodation state based on the distance of the object. The distance associated with a specific accommodation state can be called the accommodation distance Ad. Similarly, there exists a specific convergence / divergence distance Vd or relative position associated with an eye in a specific convergence / divergence state. When the accommodation distance and convergence / divergence distance are consistent, the relationship between accommodation and convergence / divergence can be said to be physiologically correct. This is considered the most comfortable scenario for the viewer.

[0113] However, in stereoscopic displays, the accommodation distance and the convergence / divergence distance may not always be consistent. For example, as illustrated in Figure 4D, the images displayed to eyes 210 and 220 may be displayed with wavefront divergence corresponding to the depth plane 240, and eyes 210 and 220 may take on a specific accommodation state in which points 15a and 15b on their depth plane are in focus. However, the images displayed to eyes 210 and 220 may provide cues for convergence / divergence movements that cause eyes 210 and 220 to converge on point 15, which is not located on the depth plane 240. As a result, in some embodiments, the accommodation distance corresponds to the distance from the exit pupils of eyes 210 and 220 to the depth plane 240, while the convergence / divergence distance corresponds to a larger distance from the exit pupils of eyes 210 and 220 to point 15. The accommodation distance is different from the convergence / divergence distance. As a result, a mismatch exists between near and far accommodation-convergence / divergence motion. Such mismatches are considered undesirable and can cause discomfort to the user. It should be understood that the mismatch corresponds to distance (e.g., Vd-Ad) and can be characterized using diopters.

[0114] It should be understood that in some embodiments, reference points other than the exit pupils of eyes 210, 220 may also be used to determine distances for determining accommodation-convergence-divergence mismatch, insofar as the same reference points are used for accommodation distance and convergence-divergence distance. For example, distances can be measured from the cornea to the depth plane, from the retina to the depth plane, from the eyepiece (e.g., the waveguide of a display device) to the depth plane, etc.

[0115] While not limited by theory, it is conceivable that users may still perceive accommodative-convergence-divergence motion mismatches of up to approximately 0.25 diopters, up to approximately 0.33 diopters, and up to approximately 0.5 diopters as physiologically correct, without the mismatch itself causing significant discomfort. In some embodiments, the display systems disclosed herein (e.g., display system 250, Figure 6) present images to the viewer having accommodative-convergence-divergence motion mismatches of about 0.5 diopters or less. In some other embodiments, the accommodative-convergence-divergence motion mismatch of images provided by the display system is about 0.33 diopters or less. In yet another embodiment, the accommodative-convergence-divergence motion mismatch of images provided by the display system is about 0.25 diopters or less, including about 0.1 diopters or less.

[0116] Figure 5 illustrates an aspect of an approach to simulating a three-dimensional image by correcting wavefront divergence. The display system includes a waveguide 270 configured to receive light 770 encoded with image information and output the light to the user's eye 210. The waveguide 270 may output light 650 with a defined amount of wavefront divergence corresponding to the wavefront divergence of the light field generated by a point on a desired depth plane 240. In some embodiments, the same amount of wavefront divergence is provided for all objects presented on that depth plane. In addition, the user's other eye may be shown to be provided with image information from a similar waveguide.

[0117] In some embodiments, a single waveguide may be configured to output light with a set wavefront divergence corresponding to one or a limited number of depth planes, and / or the waveguide may be configured to output light with a limited range of wavelengths. As a result, in some embodiments, multiple or stacked waveguides may be used to provide different wavefront divergences for different depth planes, and / or to output light with different ranges of wavelengths. It should be understood that, as used herein, the depth plane may be a plane or follow the contour of a curved surface.

[0118] Figure 6 illustrates an embodiment of a waveguide stack for outputting image information to a user. The display system 250 includes a waveguide stack or stacked waveguide assembly 260, which may be used to provide three-dimensional perception to the eye / brain using a plurality of waveguides 270, 280, 290, 300, 310. It should be understood that in some embodiments, the display system 250 may be considered a light field display. In addition, the waveguide assembly 260 may also be referred to as an eyepiece.

[0119] In some embodiments, the display system 250 may be configured to provide substantially continuous cues for convergence-divergence motion and a plurality of discrete cues for near accommodation. Cues for convergence-divergence motion may be provided by displaying different images to each of the user's eyes, and cues for near accommodation may be provided by outputting light that forms an image with a selectable discrete amount of wavefront divergence. In other words, the display system 250 may be configured to output light with a variable level of wavefront divergence. In some embodiments, each discrete level of wavefront divergence corresponds to a specific depth plane and may be provided by a particular one of waveguides 270, 280, 290, 300, and 310.

[0120] Continuing with Figure 6, the waveguide assembly 260 may also include several features 320, 330, 340, and 350 between the waveguides. In some embodiments, features 320, 330, 340, and 350 may be one or more lenses. Waveguides 270, 280, 290, 300, and 310 and / or several lenses 320, 330, 340, and 350 may be configured to transmit image information to the eye using various levels of wavefront curvature or ray divergence. Each waveguide level may be associated with a specific depth plane and may be configured to output image information corresponding to that depth plane. Image input devices 360, 370, 380, 390, and 400 may function as light sources for the waveguides and may be used to input image information into waveguides 270, 280, 290, 300, and 310, and each may be configured to disperse incident light across each individual waveguide for output toward the eye 210, as described herein. The light exits from the output surfaces 410, 420, 430, 440, and 450 of image input devices 360, 370, 380, 390, and 400 and is input into the corresponding input surfaces 460, 470, 480, 490, and 500 of waveguides 270, 280, 290, 300, and 310. In some embodiments, the input surfaces 460, 470, 480, 490, and 500 may each be the edge of the corresponding waveguide or a portion of the main surface of the corresponding waveguide (i.e., one of the waveguide surfaces that directly faces the world 510 or the viewer's eye 210). In some embodiments, a single beam of light (e.g., a collimated beam) may be injected into each waveguide to output a whole field of cloned collimated beams, which are directed toward the eye 210 at a specific angle (and divergence) corresponding to the depth plane associated with the particular waveguide. In some embodiments, one of the image input devices 360, 370, 380, 390, and 400 may be associated with a plurality (e.g., three) of waveguides 270, 280, 290, 300, and 310 to injected light into them.

[0121] In some embodiments, the image input devices 360, 370, 380, 390, and 400 are discrete displays that generate image information for input into the corresponding waveguides 270, 280, 290, 300, and 310, respectively. In some other embodiments, the image input devices 360, 370, 380, 390, and 400 are output terminals of a single multiplexed display that can send image information to each of the image input devices 360, 370, 380, 390, and 400 via, for example, one or more optical conduits (such as optical fiber cables). It should be understood that the image information provided by the image input devices 360, 370, 380, 390, and 400 may include light of different wavelengths or colors (e.g., different primary colors, as discussed herein).

[0122] In some embodiments, the light introduced into waveguides 270, 280, 290, 300, and 310 is provided by an optical projector system 520, which comprises an optical module 530, which may include an optical emitter such as a light-emitting diode (LED). The light from the optical module 530 may be directed and modified by an optical modulator 540, such as a spatial light modulator, via a beam splitter 550. The optical modulator 540 may be configured to change the perceived intensity of the light introduced into waveguides 270, 280, 290, 300, and 310, thereby encoding the light with image information. Embodiments of the spatial light modulator include liquid crystal displays (LCDs), including liquid crystal on silicon (LCOS) displays. Image input devices 360, 370, 380, 390, and 400 are graphically illustrated, and it should be understood that in some embodiments, these image input devices may represent optical paths and locations within a common projection system, configured to output light into associated waveguides 270, 280, 290, 300, and 310. In some embodiments, the waveguides of waveguide assembly 260 may function as ideal lenses, relaying the light input into the waveguides to the user's eye. In this concept, the object may be a spatial light modulator 540, and the image may be an image on the depth plane.

[0123] In some embodiments, the display system 250 may be a scanning fiber display comprising one or more scanning fibers configured to project light in various patterns (e.g., raster scanning, helical scanning, Lissajous patterns, etc.) into one or more waveguides 270, 280, 290, 300, 310, and ultimately to the viewer's eye 210. In some embodiments, the illustrated image input devices 360, 370, 380, 390, 400 may schematically represent a single scanning fiber or a bundle of scanning fibers configured to input light into one or more waveguides 270, 280, 290, 300, 310. In some other embodiments, the illustrated image input devices 360, 370, 380, 390, 400 may schematically represent a plurality of scanning fibers or a plurality of bundles of scanning fibers, each configured to input light into one of the associated waveguides 270, 280, 290, 300, 310. It should be understood that one or more optical fibers may be configured to transmit light from the optical module 530 to one or more waveguides 270, 280, 290, 300, 310. It should be understood that one or more intervening optical structures may be provided between the scanning fiber or multiple fibers and one or more waveguides 270, 280, 290, 300, 310, for example, to redirect light emitted from the scanning fiber into one or more waveguides 270, 280, 290, 300, 310.

[0124] The controller 560 controls the operation of one or more of the stacked waveguide assemblies 260, including the operation of the image input devices 360, 370, 380, 390, 400, the light source 530, and the optical modulator 540. In some embodiments, the controller 560 is part of the local data processing module 140. The controller 560 includes programming (e.g., instructions in a non-transient medium) to coordinate the timing and provisioning of image information to the waveguides 270, 280, 290, 300, 310, for example, according to any of the various schemes disclosed herein. In some embodiments, the controller may be a single integrated device or a distributed system connected by wired or wireless communication channels. In some embodiments, the controller 560 may be part of the processing module 140 or 150 (Figure 2).

[0125] Continuing with Figure 6, waveguides 270, 280, 290, 300, and 310 may be configured to propagate light within each individual waveguide by total internal reflection (TIR). Waveguides 270, 280, 290, 300, and 310 may each be planar or have another shape (e.g., curved), with major upper and lower surfaces and edges extending between their major upper and lower surfaces. In the illustrated configuration, waveguides 270, 280, 290, 300, and 310 may each include external coupling optical elements 570, 580, 590, 600, and 610, respectively, configured to extract light from the waveguides by redirecting the light, propagating it within each individual waveguide, and outputting image information from the waveguides to the eye 210. The extracted light may also be referred to as external coupling light, and the external coupling optical element light may also be referred to as light extraction optical element. The extracted beam of light can be output by the waveguide at the point where light propagating within the waveguide strikes the light extraction optical element. The external coupling optical elements 570, 580, 590, 600, 610 may be gratings, for example, including diffractive optical features as further discussed herein. For ease of explanation and clarity of the drawings, they are shown positioned on the bottom main surfaces of the waveguides 270, 280, 290, 300, 310, but in some embodiments, the external coupling optical elements 570, 580, 590, 600, 610 may be positioned on the top and / or bottom main surfaces, and / or directly within the volume of the waveguides 270, 280, 290, 300, 310, as further discussed herein. In some embodiments, the external coupling optical elements 570, 580, 590, 600, 610 may be mounted on a transparent substrate and formed within a layer of material that forms the waveguides 270, 280, 290, 300, 310. In some other embodiments, the waveguides 270, 280, 290, 300, 310 may be monolithic material components, and the external coupling optical elements 570, 580, 590, 600, 610 may be formed on and / or inside the material surface of those components.

[0126] Continuing with reference to Figure 6, as discussed herein, each waveguide 270, 280, 290, 300, 310 is configured to emit light and form an image corresponding to a specific depth plane. For example, the waveguide 270 closest to the eye may be configured to deliver collimated light (injected into such waveguide 270) to the eye 210. The collimated light may represent the optical infinity focal plane. The next upper waveguide 280 may be configured to emit collimated light that passes through a first lens 350 (e.g., a negative lens) before reaching the eye 210. Such a first lens 350 may generate some convex wavefront curvature so that the eye / brain interprets the light originating from the next upper waveguide 280 as originating from a first focal plane closer inward from optical infinity toward the eye 210. Similarly, the third upper waveguide 290 passes its output light through both the first lens 350 and the second lens 340 before reaching the eye 210. The combined refractive power of the first lens 350 and the second lens 340 may be configured to generate a different, gradually increasing wavefront curvature so that the eye / brain interprets the light originating from the third waveguide 290 as originating from a second focal plane that is closer inward toward the person from optical infinity than the light originating from the next upper waveguide 280.

[0127] Other waveguide layers 300, 310 and lenses 330, 320 are configured similarly, with the highest waveguide 310 in the stack emitting its output through all the lenses between it and the eye for a convergent focusing force representing the focal plane closest to the person. When viewing / interpreting light originating from the other side world 510 of the stacked waveguide assembly 260, a compensating lens layer 620 may be positioned on top of the stack to compensate for the convergent forces of the lower lens stacks 320, 330, 340, 350 to compensate for the stack of lenses 320, 330, 340, 350. Such a configuration provides the same number of perceived focal planes as there are available waveguide / lens pairs. Both the external coupling optical elements of the waveguides and the focusing sides of the lenses may be static (i.e., not dynamic or electroactive). In some alternative embodiments, one or both may be dynamic using electroactive features.

[0128] In some embodiments, two or more of the waveguides 270, 280, 290, 300, and 310 may have the same associated depth plane. For example, multiple waveguides 270, 280, 290, 300, and 310 may be configured to output images set in the same depth plane, or multiple subsets of waveguides 270, 280, 290, 300, and 310 may be configured to output images set in the same multiple depth planes, with one set for each depth plane. This may offer the advantage of forming tiled images that provide an extended field of view in those depth planes.

[0129] Continuing with Figure 6, the external coupling optical elements 570, 580, 590, 600, and 610 may be configured to redirect light from their respective waveguides for specific depth planes associated with the waveguides and to output the light with an appropriate amount of divergence or collimation. As a result, waveguides with different associated depth planes may have different configurations of the external coupling optical elements 570, 580, 590, 600, and 610, which will output light with different amounts of divergence depending on the associated depth plane. In some embodiments, the light extraction optical elements 570, 580, 590, 600, and 610 may be volumetric or surface features that can be configured to output light at specific angles. For example, the light extraction optical elements 570, 580, 590, 600, and 610 may be stereoscopic holograms, surface holograms, and / or diffraction gratings. In some embodiments, the features 320, 330, 340, and 350 may not be lenses. Rather, they may simply be spacers (e.g., structures for forming cladding layers and / or voids).

[0130] In some embodiments, the external coupling optical elements 570, 580, 590, 600, 610 are diffraction features or “diffractive optical elements” (also referred to herein as “DOEs”) that form a diffraction pattern. Preferably, the DOEs have sufficiently low diffraction efficiency so that only a portion of the beam light is deflected toward the eye 210 at each intersection of the DOEs, while the remainder continues to travel through the waveguide via TIR. The light carrying the image information is therefore split into several associated emission beams that exit the waveguide at various locations, resulting in a very uniform pattern of emission toward the eye 210 with respect to this particular collimated beam bouncing within the waveguide.

[0131] In some embodiments, one or more DOEs may be switchable between an "on" state in which they actively diffract and an "off" state in which they do not significantly diffract. For example, a switchable DOE may comprise a layer of polymer-dispersed liquid crystal, in which microdroplets have a diffraction pattern in the host medium, and the refractive index of the microdroplets may be switched to substantially match the refractive index of the host material (in which case the pattern does not significantly diffract incident light), or the microdroplets may be switched to a refractive index that does not match that of the host medium (in which case the pattern actively diffracts incident light).

[0132] In some embodiments, a camera assembly 630 (e.g., a digital camera including visible light and infrared light cameras) may be provided to capture images of the eye 210 and / or the surrounding tissues, for example, to detect user input and / or monitor the user's physiological state. As used herein, the camera may be any image-capturing device. In some embodiments, the camera assembly 630 may include the image-capturing device and a light source that projects light (e.g., infrared light) onto the eye, which is then reflected by the eye and can be detected by the image-capturing device. In some embodiments, the camera assembly 630 may be mounted on a frame 80 (Figure 9D) and may communicate with processing modules 140 and / or 150 that can process image information from the camera assembly 630. In some embodiments, one camera assembly 630 may be used per eye to monitor each eye separately.

[0133] Referring here to Figure 7, an embodiment of an outgoing beam output by a waveguide is shown. Although one waveguide is illustrated, other waveguides in the waveguide assembly 260 (Figure 6) may function similarly, and it should be understood that the waveguide assembly 260 includes multiple waveguides. Light 640 is introduced into the waveguide 270 at the input surface 460 of the waveguide 270 and propagates through the waveguide 270 by TIR. At the point where the light 640 collides on the DOE 570, a portion of the light exits the waveguide as an outgoing beam 650. The outgoing beam 650 is illustrated as substantially parallel, but may be redirected to propagate towards the eye 210 at a certain angle (e.g., forming a divergent outgoing beam), as discussed herein and depending on the depth plane associated with the waveguide 270. It should be understood that a nearly parallel emitted beam may represent a waveguide with an external coupling optical element that externally couples the light to form an image that appears to be set in the depth plane at a distance from the eye 210 (e.g., optical infinity). Other waveguides or other sets of external coupling optical elements may output a more divergent emitted beam pattern, which would require the eye 210 to adjust to a closer distance and focus on the retina, and would be interpreted by the brain as light from a distance closer to the eye 210 than optical infinity.

[0134] In some embodiments, a full-color image may be formed in each depth plane by overlaying an image onto each of primary colors, for example, three or more primary colors. Figure 8 illustrates an embodiment of a stacked waveguide assembly, where each depth plane includes an image formed using several different primary colors. The illustrated embodiment shows depth planes 240a–240f, but more or fewer depths may also be considered. Each depth plane may have three or more associated primary color images, including a first image of a first color G, a second image of a second color R, and a third image of a third color B. Different depth planes are indicated in the figure by different numbers relating to diopters (dpt) following the letters G, R, and B. As merely an embodiment, the numbers following each of these letters indicate diopters (1 / m), i.e., the inverse distance of the depth plane from the viewer, and each box in the figure represents an individual primary color image. In some embodiments, the precise location of the depth plane for different primary colors may vary to account for differences in the focusing of light of different wavelengths in the eye. For example, different primary color images for a given depth plane may be placed on depth planes corresponding to different distances from the user. Such arrangements may increase visual acuity and user comfort and / or reduce chromatic aberration.

[0135] In some embodiments, each primary color light may be output by a single dedicated waveguide, and as a result, each depth plane may have multiple waveguides associated with it. In such embodiments, each box in the figure, including the letters G, R, or B, can be understood to represent an individual waveguide, and three waveguides may be provided for each depth plane, and three primary color images are provided for each depth plane. The waveguides associated with each depth plane are shown adjacent to each other in this drawing for ease of explanation, but it should be understood that in a physical device, all waveguides may be arranged in a stack with one waveguide per level. In some other embodiments, multiple primary colors may be output by the same waveguide, for example, so that only a single waveguide may be provided for each depth plane.

[0136] Continuing to refer to Figure 8, in some embodiments, G is green, R is red, and B is blue. In some other embodiments, other colors associated with other wavelengths of light, including magenta and cyan, may be used in addition to or replace one or more of red, green, or blue.

[0137] Throughout this disclosure, any reference to a given color of light should be understood to encompass light of one or more wavelengths within a range of wavelengths that is perceived by the viewer as that given color. For example, red light may include light of one or more wavelengths within the range of approximately 620–780 nm, green light may include light of one or more wavelengths within the range of approximately 492–577 nm, and blue light may include light of one or more wavelengths within the range of approximately 435–493 nm.

[0138] In some embodiments, the light source 530 (Figure 6) may be configured to emit light of one or more wavelengths outside the viewer's visual perception range, such as infrared and / or ultraviolet wavelengths. In addition, internal coupling, external coupling, and other light redirection structures of the waveguide of the display 250 may be configured to direct and emit this light from the display toward the user's eye 210, for example, for imaging and / or user stimulation applications.

[0139] Referring here to Figure 9A, in some embodiments, light impacting a waveguide may need to be redirected to internally couple that light into the waveguide. Internal coupling optical elements may be used to redirect and internally couple the light into its corresponding waveguide. Figure 9A illustrates cross-sectional side views of embodiments of multiple or set 660 stacked waveguides, each including an internal coupling optical element. Each waveguide may be configured to output light of one or more different wavelengths or one or more different wavelength ranges. Stack 660 may correspond to stack 260 (Figure 6), and the illustrated waveguides of stack 660 may correspond to some of the multiple waveguides 270, 280, 290, 300, 310, but it should be understood that light from one or more of the image input devices 360, 370, 380, 390, 400 is input into the waveguide from a position where the light is required to be redirected for internal coupling.

[0140] The illustrated set of stacked waveguides 660 includes waveguides 670, 680, and 690. Each waveguide includes associated internal coupling optical elements (which may also be referred to as optical input areas on the waveguide), for example, internal coupling optical element 700 is located on the main surface of waveguide 670 (e.g., the upper main surface), internal coupling optical element 710 is located on the main surface of waveguide 680 (e.g., the upper main surface), and internal coupling optical element 720 is located on the main surface of waveguide 690 (e.g., the upper main surface). In some embodiments, one or more of the internal coupling optical elements 700, 710, and 720 may be located on the bottom main surfaces of individual waveguides 670, 680, and 690 (in particular, one or more internal coupling optical elements are reflective deflection optical elements). As illustrated, the internally coupled optical elements 700, 710, and 720 may be located on the upper main surface of their respective waveguides 670, 680, and 690 (or on the upper part of the following lower waveguide), and in particular, these internally coupled optical elements are transmissive deflection optical elements. In some embodiments, the internally coupled optical elements 700, 710, and 720 may be located within the body of the respective waveguides 670, 680, and 690. In some embodiments, as discussed herein, the internally coupled optical elements 700, 710, and 720 are wavelength-selective, selectively redirecting one or more wavelengths of light while transmitting other wavelengths of light. Although illustrated on one side or corner of their respective waveguides 670, 680, and 690, it should be understood that in some embodiments, the internally coupled optical elements 700, 710, and 720 may be located within other areas of their respective waveguides 670, 680, and 690.

[0141] As illustrated, the internally coupled optical elements 700, 710, and 720 may be offset laterally from one another. In some embodiments, each internally coupled optical element may be offset so that its light does not pass through another internally coupled optical element before receiving light. For example, each internally coupled optical element 700, 710, and 720 may be configured to receive light from different image input devices 360, 370, 380, 390, and 400, as shown in Figure 6, and may be separated from the other internally coupled optical elements 700, 710, and 720 (e.g., separated laterally) so that it does not substantially receive light from the other internally coupled optical elements 700, 710, and 720.

[0142] Each waveguide also includes associated optical dispersion elements, for example, optical dispersion element 730 is located on the main surface (e.g., upper main surface) of waveguide 670, optical dispersion element 740 is located on the main surface (e.g., upper main surface) of waveguide 680, and optical dispersion element 750 is located on the main surface (e.g., upper main surface) of waveguide 690. In some other embodiments, optical dispersion elements 730, 740, and 750 may be located on the bottom main surfaces of the associated waveguides 670, 680, and 690, respectively. In some other embodiments, optical dispersion elements 730, 740, and 750 may be located on both the top and bottom main surfaces of the associated waveguides 670, 680, and 690, respectively, or optical dispersion elements 730, 740, and 750 may be located on different top and bottom main surfaces within different associated waveguides 670, 680, and 690, respectively.

[0143] Waveguides 670, 680, and 690 may be separated and isolated by, for example, gaseous, liquid, and / or solid layers of material. For example, as shown, layer 760a may separate waveguides 670 and 680, and layer 760b may separate waveguides 680 and 690. In some embodiments, layers 760a and 760b are formed from a low refractive index material (i.e., a material having a lower refractive index than the material forming the immediate vicinity of waveguides 670, 680, and 690). Preferably, the refractive index of the material forming layers 760a and 760b is 0.05 or greater, or 0.10 or less, than the refractive index of the material forming waveguides 670, 680, and 690. Advantageously, the lower refractive index layers 760a, 760b may function as cladding layers that promote total internal reflection (TIR) ​​of light through the waveguides 670, 680, 690 (e.g., TIR between the upper and lower main surfaces of each waveguide). In some embodiments, layers 760a, 760b are formed from air. It should be understood that, although not shown, the upper and lower parts of the illustrated set 660 waveguides may also include an immediate cladding layer.

[0144] Preferably, to facilitate manufacturing and other considerations, the materials forming waveguides 670, 680, and 690 are similar or identical, and the materials forming layers 760a and 760b are similar or identical. In some embodiments, the materials forming waveguides 670, 680, and 690 may differ between one or more waveguides, and / or the materials forming layers 760a and 760b may differ, while still maintaining the various refractive index relationships described above.

[0145] Continuing to refer to Figure 9A, rays 770, 780, and 790 are incident on the waveguide set 660. It should be understood that rays 770, 780, and 790 may also be introduced into waveguides 670, 680, and 690 by one or more image input devices 360, 370, 380, 390, and 400 (Figure 6).

[0146] In some embodiments, the rays 770, 780, and 790 may have different properties, such as different wavelengths or different wavelength ranges, which may correspond to different colors. The internal coupling optical elements 700, 710, and 720 each deflect the incident light so that the light propagates through one of the waveguides 670, 680, and 690 by TIR. In some embodiments, the internal coupling optical elements 700, 710, and 720 each selectively deflect one or more specific wavelengths of light while allowing other wavelengths to pass through the lower waveguide and associated internal coupling optical elements.

[0147] For example, the internally coupled optical element 700 may be configured to selectively deflect a ray 770 having a first wavelength or wavelength range, while transmitting rays 780 and 790 having different second and third wavelengths or wavelength ranges, respectively. The transmitted ray 780 collides with an internally coupled optical element 710 configured to selectively deflect light of the second wavelength or wavelength range, and is deflected by it. The ray 790 is deflected by an internally coupled optical element 720 configured to selectively deflect light of the third wavelength or wavelength range.

[0148] Continuing with Figure 9A, the deflected rays 770, 780, and 790 are deflected so that they propagate through the corresponding waveguides 670, 680, and 690. That is, the internal coupling optical elements 700, 710, and 720 of each waveguide deflect the light into its corresponding waveguide 670, 680, and 690, and internally couple the light into the corresponding waveguide. The rays 770, 780, and 790 are deflected at an angle that causes the light to propagate through the individual waveguides 670, 680, and 690 by TIR. The rays 770, 780, and 790 propagate through the individual waveguides 670, 680, and 690 by TIR until they collide with the corresponding optical dispersion elements 730, 740, and 750 of the waveguide.

[0149] Referring now to Figure 9B, a perspective view of an embodiment of the multiple stacked waveguides shown in Figure 9A is illustrated. As previously mentioned, the internally coupled rays 770, 780, and 790 are deflected by the internally coupled optical elements 700, 710, and 720, respectively, and then propagate by TIR within waveguides 670, 680, and 690, respectively. The rays 770, 780, and 790 then collide with the optical dispersion elements 730, 740, and 750, respectively. The optical dispersion elements 730, 740, and 750 deflect the rays 770, 780, and 790 so that they propagate toward the externally coupled optical elements 800, 810, and 820, respectively.

[0150] In some embodiments, the optical dispersion elements 730, 740, 750 are orthogonal pupil expanders (OPEs). In some embodiments, the OPE deflects or disperses light to the external coupling optical elements 800, 810, 820, and in some embodiments, also increases the beam or spot size of the light as it propagates to the external coupling optical elements. In some embodiments, the optical dispersion elements 730, 740, 750 may be omitted, and the internal coupling optical elements 700, 710, 720 may be configured to deflect light directly to the external coupling optical elements 800, 810, 820. For example, referring to FIG. 9A, the optical dispersion elements 730, 740, 750 may be replaced by the external coupling optical elements 800, 810, 820, respectively. In some embodiments, the external coupling optical elements 800, 810, 820 are an exit pupil (EP) or an exit pupil expander (EPE) that directs light to the viewer's eye 210 (FIG. 7). It should be understood that the OPE may be configured to increase the size of the eyebox in at least one axis, and the EPE may increase the eyebox in an axis that intersects, for example, is orthogonal to, the axis of the OPE. For example, each OPE may be configured to redirect a portion of the light impinging on the OPE to the EPE of the same waveguide while allowing the remaining portion of the light to continue to propagate along the waveguide. In response to the collision with the OPE, again, another portion of the remaining light is redirected to the EPE, and the remaining portion of that portion continues to propagate further along the waveguide and the like. Similarly, in response to the collision with the EPE, a portion of the colliding light is directed from the waveguide towards the user, and the remaining portion of that light continues to propagate through the waveguide until it impinges again on the EP, at which point, another portion of the colliding light is directed from the waveguide, etc. As a result, a single beam of internally coupled light is "replicated" each time a portion of that light is redirected by the OPE or the EPE, thereby forming a beam field of cloned light as shown in FIG. 6. In some embodiments, the OPE and / or the EPE may be configured to modify the size of the beam of light.

[0151] Therefore, referring to Figures 9A and 9B, in some embodiments, the set of waveguides 660 includes, for each primary color, waveguides 670, 680, 690, internally coupled optical elements 700, 710, 720, optical dispersion elements (e.g., OPE) 730, 740, 750, and externally coupled optical elements (e.g., EP) 800, 810, 820. Waveguides 670, 680, 690 may be stacked with air gaps / cladding layers between each one. The internally coupled optical elements 700, 710, 720 redirect or deflect the incident light into their waveguides (using different internally coupled optical elements that receive light of different wavelengths). The light then propagates within the individual waveguides 670, 680, 690 at angles that will result in a TIR. In the embodiment shown, a ray 770 (e.g., blue light) is polarized by the first internal coupling optical element 700 in the manner described above, and then continues to bounce along the waveguide, interacting with the optical dispersion element (e.g., OPE) 730 and then the external coupling optical element (e.g., EP) 800. Rays 780 and 790 (e.g., green and red light, respectively) pass through waveguide 670, with ray 780 colliding with the internal coupling optical element 710, thereby being deflected. Ray 780 will then bounce along waveguide 680 via TIR, proceeding to its optical dispersion element (e.g., OPE) 740 and then the external coupling optical element (e.g., EP) 810. Finally, ray 790 (e.g., red light) passes through waveguide 690 and colliding with the optical internal coupling optical element 720 of waveguide 690. The internal optical coupling element 720 deflects the ray 790 so that it propagates by TIR to the optical dispersion element (e.g., OPE) 750, and then by TIR to the external coupling optical element (e.g., EP) 820. The external coupling optical element 820 then finally externally couples the ray 790 to the viewer, who also receives externally coupled light from the other waveguides 670, 680.

[0152] FIG. 9C illustrates top and bottom plan views of an embodiment of the plurality of stacked waveguides of FIGS. 9A and 9B. As shown, waveguides 670, 680, 690 may be vertically aligned with associated optical dispersion elements 730, 740, 750 and associated external coupling optical elements 800, 810, 820 of each waveguide. However, as discussed herein, internal coupling optical elements 700, 710, 720 are not vertically aligned. Rather, the internal coupling optical elements are preferably non-overlapping (e.g., laterally spaced as seen in the top and bottom views). As further discussed herein, this non-overlapping spatial arrangement facilitates the injection of light from different resources into different waveguides on a one-to-one basis, thereby enabling a specific light source to be uniquely coupled to a specific waveguide. In some embodiments, an array including non-overlapping spatially separated internal coupling optical elements may be referred to as a deflected pupil system, and the internal coupling optical elements within these arrays may correspond to sub-pupils.

[0153] FIG. 9D illustrates an embodiment of a wearable display system 60 in which various waveguides and related systems disclosed herein may be integrated. In some embodiments, display system 60 is the system 250 of FIG. 6, and FIG. 6 schematically shows some parts of that system 60 in more detail. For example, the waveguide assembly 260 of FIG. 6 may be part of display 70.

[0154] Continuing with reference to Figure 9D, the display system 60 includes a display 70 and various mechanical and electronic modules and systems to support the functions of the display 70. The display 70 may be coupled to a frame 80, which is wearable by the display system user or viewer 90 and configured to position the display 70 in front of the user 90's eyes. In some embodiments, the display 70 may be considered an eyepiece. In some embodiments, a speaker 100 is coupled to the frame 80 and configured to be positioned adjacent to the user 90's ear canal (in some embodiments, another speaker, not shown, may also be optionally positioned adjacent to the user's other ear canal to provide stereo / shapeable sound control). The display system 60 also includes one or more microphones 110 or other devices to detect sound. In some embodiments, the microphones may be configured to allow the user to provide input or commands to the system 60 (e.g., selection of voice menu commands, natural language questions, etc.) and / or enable audio communication with other persons (e.g., other users of a similar display system). The microphone may also be configured as a peripheral sensor to collect audio data (e.g., sounds from the user and / or the environment). In some embodiments, the display system may also include a peripheral sensor 120a, which is separate from the frame 80 and may be mounted on the user 90's body (e.g., the user 90's head, torso, limbs, etc.). In some embodiments, the peripheral sensor 120a may be configured to obtain data characterizing the user 90's physiological state. For example, the sensor 120a may be an electrode.

[0155] Continuing to refer to Figure 9D, the display 70 is operably coupled to the local data processing module 140 by a communication link 130, such as a wired cable or wireless connectivity, which may be mounted in various configurations, such as being fixedly attached to the frame 80, fixedly attached to a helmet or hat worn by the user, embedded in headphones, or otherwise removable by the user 90 (e.g., in a backpack configuration, in a belt-mounted configuration). Similarly, the sensor 120a may be operably coupled to the local processor and data module 140 by a communication link 120b, such as a wired cable or wireless connectivity. The local processing and data module 140 may include a hardware processor and digital memory such as non-volatile memory (e.g., flash memory or a hard disk drive), both of which may be used to assist in data processing, caching, and storage. Optionally, the local processing and data module 140 may include one or more central processing units (CPUs), graphics processing units (GPUs), dedicated processing hardware, etc. The data may include a) data captured from sensors (image capture devices (such as cameras), microphones, inertial measurement units, accelerometers, compasses, GPS units, wireless devices, gyroscopes, and / or other sensors disclosed herein (e.g., operably coupled to frame 80 or otherwise attached to user 90)), and / or b) data acquired and / or processed using the remote processing module 150 and / or remote data repository 160 (including data related to virtual content) for passing to display 70 after processing or reading, as possible. The local processing and data module 140 may be operably coupled to the remote processing module 150 and the remote data repository 160 by communication links 170, 180, such as via wired or wireless communication links, so that these remote modules 150, 160 are operably coupled to each other and available as resources to the local processing and data module 140.In some embodiments, the local processing and data module 140 may include one or more of the following: an image acquisition device, a microphone, an inertial measurement unit, an accelerometer, a compass, a GPS unit, a wireless device, and / or a gyroscope. In some other embodiments, one or more of these sensors may be mounted on the frame 80 or may be a standalone structure communicating with the local processing and data module 140 via a wired or wireless communication path.

[0156] Continuing with Figure 9D, in some embodiments, the remote processing module 150 may comprise one or more processors configured to analyze and process data and / or image information, for example, one or more central processing units (CPUs), graphics processing units (GPUs), dedicated processing hardware, etc. In some embodiments, the remote data repository 160 may comprise digital data storage facilities that may be available through the internet or other networking configurations in a “cloud” resource configuration. In some embodiments, the remote data repository 160 may comprise one or more remote servers that provide information, for example, augmented reality content, for generating to the local processing and data modules 140 and / or the remote processing module 150. In some embodiments, all data is stored, and all calculations are performed within the local processing and data modules, enabling fully autonomous use from the remote modules. Optionally, an external system (e.g., one or more processors, one or more computer systems), including a CPU, GPU, etc., may perform at least part of the processing (e.g., generating image information, processing data) and provide information to modules 140, 150, and 160, and receive information from them, for example, via a wireless or wired connection. (Liquid crystal materials for broadband adaptive waveplate lens assemblies)

[0157] Generally, liquid crystals possess physical properties that can be intermediate between conventional fluids and solids. While liquid crystals are fluid in some respects, unlike most fluids, the arrangement of molecules within a liquid crystal exhibits a certain structural order. Different types of liquid crystals include thermotropic, lyotropic, and polymeric liquid crystals. The thermotropic liquid crystals disclosed herein can be implemented in various physical states, e.g., phases, including nematic states / phases, smectic states / phases, chiral nematic states / phases, or chiral smectic states / phases.

[0158] As described herein, liquid crystals in a nematic state or phase may have calamistic (rod-shaped) or discotic (disk-shaped) organic molecules that have relatively little positional order but possess long-range directional order, with their long axes being substantially parallel. Thus, the organic molecules can flow freely, and their centers of mass are randomly dispersed as in a liquid, while still maintaining their long-range directional order. In some implementations, liquid crystals in a nematic phase can be uniaxial, i.e., the liquid crystal has one longer, preferred axis, and the other two are substantially equal. In some implementations, liquid crystal molecules are oriented along their long axes. In other implementations, liquid crystals can be biaxial, i.e., in addition to oriented along their long axes, the liquid crystal can also be oriented along secondary axes.

[0159] As described herein, liquid crystals in a smectic state or phase may have organic molecules forming relatively clearly defined layers that can slide across each other. In some implementations, liquid crystals in the smectic phase can be positionally ordered along one direction. In some implementations, the long axes of the molecules can be oriented along a direction approximately normal to the plane of the liquid crystal layer, while in other implementations, the long axes of the molecules may be tilted with respect to the direction normal to the plane of the layer.

[0160] Here, and throughout this disclosure, nematic liquid crystals consist of rod-shaped molecules, and the long axes of neighboring molecules are substantially aligned with one another. To describe this anisotropic structure, a dimensionless unit vector n, called an orientor, may be used to describe the preferred orientation of the liquid crystal molecules.

[0161] Here, and throughout this disclosure, the azimuthal angle or rotation angle φ is used to describe the rotation angle of the liquid crystal molecules about the axis normal to the main surface of the liquid crystal layer, measured in a plane parallel to the main surface of the liquid crystal layer or substrate, for example, the xy plane, and between the alignment direction, for example, the elongation direction or orientation direction, and the direction parallel to the main surface, for example, the y-direction.

[0162] Here, and throughout this disclosure, when angles such as rotation angles φ are referred to as substantially the same or different between different regions, the average angle may be, for example, within about 1%, 5%, or 10% of each other, but it should be understood that in some cases the average angle may be larger.

[0163] As described herein, some liquid crystals in the nematic or smectic state can also exhibit torsion in the layer normal direction. Such liquid crystals are referred to as torsioned nematic (TN) liquid crystals or torsioned smectic (SN) liquid crystals. TN or SN liquid crystals may exhibit molecular torsion about an axis perpendicular to the aligner, where the molecular axis is parallel to the aligner. When the degree of torsion is relatively large, the torsioned liquid crystal may be referred to as chiral or cholesteric.

[0164] As described herein, TN or SN liquid crystals may be described as having a torsion angle or net torsion angle (φ), which may refer, for example, to the relative azimuthal rotation between the uppermost and lowermost liquid crystal molecules across a defined length, e.g., the thickness of the liquid crystal layer.

[0165] As described herein, “polymerizable liquid crystal” may refer to a liquid crystal material that can be polymerized, for example, by photopolymerization in situ, and which may be described herein as a reactive mesogen (RM).

[0166] In some embodiments, liquid crystal molecules may be polymerizable, and once polymerized, they can form a large network with other liquid crystal molecules. For example, liquid crystal molecules may be linked by chemical bonds or by linking chemical species to other liquid crystal molecules. Once polymerized together, the liquid crystal molecules can form liquid crystal domains having substantially the same orientation and location as before they were linked together. The term “liquid crystal molecule” as used herein may refer to both the liquid crystal molecules before polymerization and the liquid crystal domains formed by these molecules after polymerization. Once polymerized, the polymerized network may be referred to as a liquid crystal polymer (LCP).

[0167] In some embodiments, the unpolymerized or polymerizable liquid crystal molecules prior to the polymerization step may have at least limited rotational degrees of freedom. These unpolymerized liquid crystal molecules may rotate or tilt, for example, under electrical stimulation, which results in a modification of optical properties. For example, by applying an electric field, several liquid crystal layers containing unpolymerized liquid crystal molecules may be switched between one or more states having different diffraction or polarization modification properties.

[0168] The inventors recognize that the properties of liquid crystals or reactive mesogens (RMs) described above are advantageously applicable to various components of broadband switchable waveplates and waveplate lenses disclosed herein. For example, in some unpolymerized RMs, the orientation of LC molecules can be modified after deposition, for example, by external stimuli, such as the application of an electric field. Based on this recognition, the inventors disclose herein waveplates and waveplate lenses that can be switched between multiple states by the application of external stimuli.

[0169] In addition, the inventors recognize that, when not polymerized, the orientation of LC molecules at the surface or interface of several LC or RM can be matched by controlling the surface or interface on which the LC molecules are formed. For example, a stack of multiple LC layers can be formed, and by controlling the orientation of the LC molecules closest to the surface of the LC layer, the orientation of directly adjacent LCs in the next LC layer can be controlled to have the same orientation as, for example, the LC molecules closest to the surface in the previous LC layer or the same orientation as the extended microstructure in the adjacent layer. In addition, the LC molecules between LC molecules at the surface or interface can be controlled to have a predetermined amount of torsion. Based on the recognition of these and other attributes, including birefringence, chirality, and ease for multiple coatings, the inventors disclose herein waveplates and waveplate lenses having useful properties such as broadband capability with tuned optical properties, for example, diffraction efficiency, refractive power, and polarization. (A display device having a switchable broadband adaptive waveplate lens assembly.)

[0170] As described above with reference to Figure 6, several display systems according to embodiments include a waveguide assembly 260 configured to form images on a plurality of virtual depth planes. The waveguide assembly 260 includes waveguides 270, 280, 290, 300, and 310, each configured to propagate light by total internal reflection (TIR), and each includes external coupling optical elements 570, 580, 590, 600, and 610, each configured to extract light out of the individual waveguides 270, 280, 290, 300, and 310 by redirecting the light. Waveguides 270, 280, 290, 300, and 310 are each configured to output light and form images corresponding to a particular depth plane. The waveguide assembly 260 may also optionally include a plurality of lenses 320, 330, 340, 350 between the waveguides to provide different refractive forces for forming images on different virtual depth planes.

[0171] In the illustrated embodiment of the waveguide assembly 260 in Figure 6, the number of depth planes may be directly proportional to the number of waveguides and lenses. However, the inventors recognize various challenges associated with the step of implementing a waveguide assembly configured to display an image in multiple depth planes by having a proportional number of waveguides and lenses. For example, a large number of waveguides 270, 280, 290, 300, 310 and a large number of corresponding lenses 320, 330, 340, 350 can undesirably increase the overall thickness, weight, cost, and manufacturing challenges of the waveguide assembly 260. For example, when formed from conventional lens materials, such as glass, lenses 320, 330, 340, 350 can each add several millimeters or tens of millimeters of thickness and corresponding weight to the display. In addition, a large number of waveguides and lenses can produce optical effects undesirable to the user, such as relatively high absorption loss. Therefore, in one respect, the inventors recognize the potential advantages for a display system that, in some cases, can generate images in multiple depth planes using fewer waveguides, fewer lenses, thinner and lighter waveguides and lenses, and / or fewer lenses per waveguide.

[0172] Referring still to Figure 6, it should be understood that lenses 320, 330, 340, and 350 can be configured to form images in different depth planes by imparting individual refractive powers to the light from waveguides 310, 300, 290, and 280. In various embodiments, the light externally coupled from the waveguide may have polarization, for example, circular polarization. However, when the polarized light externally coupled from the waveguide passes through a waveplate lens or waveplate formed from liquid crystal, less than 100% of the externally coupled light transmitted through it may be optically affected, for example, diffracted, focused, or its polarization altered, resulting in some of the externally coupled light passing through without optical effect. Light that passes through the lens in this way without optical effect is sometimes referred to as leak light. Leak light is undesirably focused, defocused, or its polarization altered, or it is not affected at all, in the downstream optical path. When a significant portion of light passing through a waveplate or waveplate lens constitutes leaked light, the user may experience undesirable effects such as "afterimage" images, which are images visible to the user in unintended depth planes or images in unintended depth planes. The inventors recognize that such leaked light may result from the fact that the waveplate lens or waveplate is formed from liquid crystal, configured to have relatively high diffraction efficiency within a relatively narrow wavelength range in the visible spectrum, among other causes. Thus, on another level, the inventors recognize the need for a broadband adaptive waveplate lens assembly that can generate images in multiple depth planes with little to no undesirable effects resulting from leaked light over a wide range of wavelengths in the visible spectrum. To address these and other needs, various embodiments include a broadband adaptive waveplate lens assembly comprising a switchable waveplate lens or switchable waveplate based on liquid crystal, configured to provide variable refractive power. Waveplate lenses and waveplates formed from liquid crystal can offer various advantages toward achieving these objectives, including thin thickness, light weight, and high configurability at the molecular level.In various embodiments described herein, a display device is configured to form an image in different virtual depth planes using a waveguide assembly that guides light in a lateral direction parallel to an output surface of the waveguide and externally couples the light guided through the output surface to one or more broadband adaptive waveplate lens assemblies. In various embodiments, the broadband adaptive waveplate lens assembly is configured to internally couple and diffract the externally coupled light from the waveguide. The broadband adaptive lens assembly includes a first waveplate lens comprising a liquid crystal (LC) layer arranged such that the waveplate lens has a birefringence (Δn) that varies in a radially outward direction from a central region of the first waveplate lens, and is configured to diffract externally coupled light within a broadband wavelength range including at least 450 nm to 630 nm at a diffraction efficiency of greater than 90%, greater than 95%, or even greater than 99%. In some embodiments, the broadband adaptive waveplate lens assembly according to the embodiments is significantly lighter and thinner (a few microns) compared to conventional lenses and, advantageously, can provide a variable refractive power over a broadband wavelength range. Advantageously, such a broadband adaptive lens assembly can reduce the number, thickness, and weight of a waveguide assembly such as waveguide assembly 260 (FIG. 6) and can reduce or eliminate undesirable effects resulting from leaked light.

[0173] As used herein, refractive power (P, also referred to as refractive power, focusing power, or converging power) refers to the degree to which a lens, mirror, or other optical system converges or diverges light. This is equal to the reciprocal of the focal length of the device: P = 1 / f. That is, a high refractive power corresponds to a short focal length. The SI unit for refractive power is per meter (m -1 ), which is generally referred to as a diopter (D).

[0174] As described herein, a converging lens, which focuses the light passing through it, is described as having a positive refractive power, while a diverging lens, which defocuses the light passing through it, is described as having a negative power. Although not constrained by theory, when light passes through two or more thin lenses that are relatively close to each other, the refractive power of the combined lenses can be approximated as the sum of the refractive powers of the individual lenses. Thus, when light passes through a first lens having a first refractive power P1 and then through a second lens having a second refractive power P2, the light can be understood to converge or diverge according to the sum of refractive powers Pnet = P1 + P2.

[0175] A medium having a refractive index that depends on the polarization and propagation direction of light is called a birefringent (or double-refractive) medium. As described throughout this specification and as understood in the related industries, light whose polarization is perpendicular to the optical axis of the birefringent medium has a normal refractive index (n o It is described that the light has an anomalous refractive index (n) and its polarization is parallel to the optical axis of the birefringent medium. e It is described as having the difference in refractive index n observed in birefringent media materials. e -n o It is described as having birefringence Δn. The phase delay of light in a material medium having birefringence Δn can be expressed as Γ = 2πΔnd / λ for different λ, where d is the thickness of the medium.

[0176] Generally, optically anisotropic materials, such as liquid crystals, exhibit a positive dispersion of birefringence (Δn), which decreases with longer wavelengths of light λ. This positive dispersion of Δn results in different phase delays Γ = 2πΔnd / λ at different λ values, where d is the thickness of the medium. Anisotropic materials exhibiting a negative dispersion of birefringence (Δn), as disclosed herein, refer to materials in which birefringence increases with longer wavelengths of light λ.

[0177] As described above, the wavelength dependence of the diffraction efficiency of a waveplate lens or waveplate can be an important consideration when reducing or minimizing various undesirable optical effects. As described herein, the diffraction efficiency (η) of a birefringent medium such as a liquid crystal layer is given by η = sin 2 It can be expressed as (πΔnd / λ), where Δn is the birefringence, λ is the wavelength, and d is the thickness. As light propagates through the diffracting component, the phase delay varies with wavelength with respect to conventional birefringent media. Therefore, some diffracting components, including waveplate lenses and waveplates, exhibit a relatively narrow wavelength or bandwidth in the visible spectrum where the diffraction efficiency is sufficiently high. In contrast, according to embodiments, waveplate lenses and waveplates exhibit a relatively wide wavelength or bandwidth in the visible spectrum where the diffraction efficiency is sufficiently high for the various applications described herein.

[0178] According to various embodiments, a broadband waveplate lens or waveplate has a normalized bandwidth (Δλ / λ o It can be explained that it has ), in the formula, λ o λ is the central wavelength in the visible spectrum extending to a wavelength range of approximately 400-800 nm, including one or more of the following: the red spectrum having a wavelength range of approximately 620-780 nm, the green spectrum having a wavelength range of approximately 492-577 nm, and the blue spectrum having a wavelength range of approximately 435-493 nm, wherein Δλ is the diffraction efficiency that exceeds 70%, 80%, 90%, 95%, 99%, or any value within the range defined by these values. o This is the wavelength range centered around [a specific point].

[0179] According to various embodiments, when a waveplate lens or waveplate is described as a broadband waveplate lens or broadband waveplate, it will be understood that it has an average, instantaneous, mean, median, or minimum diffraction efficiency exceeding 70%, 80%, 90%, 95%, 99%, or any percentage within these values, in at least a portion of the visible spectrum extending to a wavelength range of about 400–800 nm, including one or more of the wavelength ranges defined by a red spectrum including a wavelength range of about 620–780 nm, a green spectrum including a wavelength range of about 492–577 nm, a blue spectrum including a wavelength range of about 435–493 nm, or one or more of the wavelength ranges defined by any wavelength in the visible spectrum within the visible spectrum within the wavelength range of about 400–800 nm, for example, 400–700 nm, 430–650 nm, or 450–630 nm.

[0180] The relationship η = sin, as explained above, is related to diffraction efficiency. 2 Based on (πΔnd / λ), a broadband waveplate lens or waveplate can have efficiency with respect to a fixed d when the ratio of Δn / λ has a positive and relatively constant value. As described herein, a medium having a positive ratio value of Δn / λ is said to have negative dispersion. According to embodiments, the broadband waveplate lens or broadband waveplate described herein has negative dispersion, i.e., a birefringence (Δn) that increases with increasing wavelength (λ) within the wavelength range described above.

[0181] According to various embodiments, a broadband waveplate lens or waveplate can be described as having an instantaneous, mean, median, minimum, or maximum value of the ratio Δn / λ, which is a positive value within any range of the visible spectrum described above. In addition, the broadband waveplate lens or waveplate has a ratio of Δλ / λ o It has a relatively high ratio, and Δλ is a wavelength range within any range of the visible spectrum described above, λ o Δλ is the central wavelength within Δλ. According to various embodiments, the high normalized bandwidth Δλ / λ oThe ratio Δn / λ can have values ​​of approximately 0.3-1.0, approximately 0.3-0.7, 0.4-0.7, 0.5-0.7, 0.6-0.7, or any range defined by these values. In addition, broadband waveplate lenses or waveplates have a ratio Δn / λ that is relatively constant within the various wavelength ranges in the visible spectrum described above. For example, the ratio Δn / λ can have a deviation from the mean, median, minimum, or maximum value of the ratio Δn / λ, e.g., a standard deviation, which does not exceed a percentage within 30%, 20%, 10%, 5%, 1%, or any of these values.

[0182] As described herein, a “transmissive” or “transparent” structure, such as a transparent substrate, may allow at least a portion of incident light, for example, at least 20, 30, 50, 70, or 90%, to pass through it. Thus, the transparent substrate may, in some embodiments, be glass, sapphire, or a polymer substrate. In contrast, a “reflective” structure, such as a reflective substrate, may reflect at least a portion of incident light, for example, at least 20, 30, 50, 70, 90%, or more, to be reflected from it.

[0183] Figure 10 illustrates an embodiment of a display device 1000, such as a wearable display device, comprising one or more broadband adaptive lens assemblies, for example, a pair of broadband adaptive lens assemblies 1004, 1008 interposed by a waveguide assembly 1012 within an optical path 1016. As described above, the waveguide assembly includes a waveguide configured to propagate light (e.g., visible light) under total internal reflection and to externally couple the light in an optical axis extending from the optical output surface of the waveguide (e.g., the main surface of the waveguide) (e.g., in the direction normal thereto). In some embodiments, the light may be externally coupled by a diffraction grating. Each of the broadband adaptive lens assemblies 1004, 1008 may be configured, at least partially, to transmit the externally coupled light through it. In the illustrated embodiment, each of the broadband adaptive lens assemblies may receive the externally coupled light from the waveguide assembly 1012 and be configured to focus or diverge the externally coupled light in the optical axis direction. Broadband adaptive lens assemblies 1004 and 1008 each comprise a waveplate lens with liquid crystal, arranged such that the waveplate lens has a birefringence (Δn) that varies radially from the central region of the waveplate lens and decreases with increasing wavelength (λ) within the visible spectrum. The broadband adaptive lens assemblies are configured to be selectively switched between multiple states having different refractive powers. When activated (e.g., electrically activated), the broadband adaptive lens assemblies are configured to modify the polarization state of externally coupled light passing through them.

[0184] As used herein, an adaptive lens assembly refers to a lens assembly having at least one optical property that can be tuned, for example, reversibly activated and deactivated using an external stimulus. Exemplary optical properties that can be reversibly activated and deactivated include, among other properties, refractive power (focal length), phase, polarization, polarization selectivity, transmittance, reflectance, birefringence, and diffractive properties. In various embodiments, an adaptive lens assembly is capable of electrically varying the refractive power and polarization state of light passing through it.

[0185] In the illustrated embodiment, the pair of broadband adaptive lens assemblies 1004 and 1008 are each configured to be selectively switchable between at least two states, in the first state each is configured to allow externally coupled light to pass through without altering its polarization state, while in the second state each is configured to alter the polarization state of the externally coupled light passing through it. For example, in the second state, the broadband adaptive lens assemblies 1004 and 1008 each reverse the circular polarization palmarity, while in the first state, the broadband adaptive lens assemblies 1004 and 1008 each preserve the circular polarization palmarity.

[0186] Still referring to Figure 10, the display device 1000 further comprises a waveguide assembly 1012 interposed between a pair of adaptive lens assemblies 1004, 1008. Waveguide assembly 1012 may be analogous to waveguide assembly 260 described above with respect to Figure 6, which comprises one or more waveguides analogous to one or more waveguides 270, 280, 290, 300, 310 in Figure 6. For example, as described above with respect to Figures 6 and 7, the waveguide may be configured to propagate light in a lateral direction parallel to the main surface of the waveguide under total internal reflection. The waveguide may further be configured to externally couple light in a direction normal to the main surface of the waveguide, for example.

[0187] Still referring to Figure 10, the first adaptive lens assembly 1004 of the paired adaptive lens assembly is positioned on the first side of the waveguide assembly 1012, for example, on the side of the world 510 observed by the user, and the second adaptive lens assembly 1008 of the paired lens assembly is positioned on the second side of the waveguide assembly 1012, for example, on the side of the user's eye 210. The paired adaptive lens assembly, configured as described below, provides the user with virtual content from the waveguide assembly 1012 along with a view of the real world in multiple virtual depth planes. In some embodiments, there is little to no distortion due to the presence of the adaptive lens assemblies. The virtual content and the view of the real world are provided to the user in response to the activation of the first and second adaptive lens assemblies 1004, 1008, as described below with respect to Figures 11A and 11B.

[0188] Figures 11A and 11B illustrate embodiments of the display devices 1100A / 1100B, each comprising an adaptive lens assembly that, when in operation, outputs image information to the user. Display devices 1100A and 1100B are structurally identical in the unpowered state. Display device 1100A is used herein to illustrate the output of a virtual image to the user, while display device 1100B is used herein to illustrate the transmission of a real-world image to the user through the display device 1100B. The display devices 1100A / 1100B include a pair of switchable lens assemblies 1004, 1008 configured to be electrically activated, for example, by the application of voltage or current. In some embodiments, for example, in the deactivated state, where no voltage or current is applied, the first and second switchable lens assemblies 1004, 1008 each have low, e.g., about zero refractive power. In some embodiments, for example, in an activated state where a voltage or current is applied, the first adaptive lens assembly 1004 on the world side may provide a first net refractive power (Pnet1) having a first sign, e.g., a positive refractive power. When in an activated state, the second adaptive lens assembly 1008 on the user side may provide a second net refractive power (Pnet2) having a second sign, e.g., a negative refractive power.

[0189] Figure 11A illustrates an embodiment of the display system of Figure 10 for displaying virtual content to a user in a virtual depth plane, according to several embodiments. As described above, a waveguide assembly 1012 interposed between a pair of adaptive lens assemblies 1004, 1008 comprises a waveguide configured to receive light containing virtual image information and propagate the light under total internal reflection. The waveguide assembly 1012 is further configured to externally couple the light toward the eye 210, for example, through a diffraction grating. The externally coupled light passes through a second adaptive lens assembly 1008 prior to entering the eye 210. When activated, the second adaptive lens assembly 1008 has a second net refractive power Pnet2, which may have a negative value so that the user can see a virtual image in the virtual depth plane 1104.

[0190] In some embodiments, the second net refractive power Pnet2 may be electrically tuned to adjust the second net refractive power (Pnet2) of the second adaptive lens assembly 1008, thereby adjusting the distance to the virtual depth plane 1104. For example, as a virtual object "moves" closer to and further away from the eye 210 in virtual three-dimensional space, the second net refractive power Pnet2 of the second adaptive lens assembly 1008 may also be tuned accordingly so that the virtual depth plane 1104 adjusts to track the virtual object. Thus, the user will experience little to no accommodation / convergence-divergence motion mismatch that exceeds a relatively acceptable threshold. In some embodiments, the magnitude of the distance to the virtual depth plane 1104 may be tuned in discrete steps, while in some other embodiments, the magnitude of the distance to the virtual depth plane 1104 may be tuned continuously.

[0191] Figure 11B illustrates an embodiment of the display system of Figure 10 that provides a user with a view of real-world content, according to several embodiments. When the second adaptive lens assembly 1008 is activated to have a second net refractive power (Pnet2) for displaying virtual content on the virtual depth plane 1104, light from the real world passing through the second adaptive lens assembly 1008 may also converge or diverge according to the Pnet2 of the activated second adaptive lens assembly 1008. Thus, objects in the real world may appear out of focus. To mitigate such distortion, according to the embodiment, the first and second adaptive lens assemblies 1004, 1008 may be configured to have refractive powers with opposite signs when activated. In some embodiments, light passing through the first and second adaptive lens assemblies 1004, 1008 converges or diverges according to a combined refractive force having a magnitude that is approximately the difference between the magnitudes of the first and second net refractive forces Pnet1, Pnet2 of the first and second adaptive lens assemblies 1004, 1008, respectively. In some embodiments, the waveguide assembly 1012 may also have refractive force, and the adaptive lens assembly 1008 may be configured to account for distortion caused by both the lens assembly 1004 and the waveguide assembly 1012. For example, the refractive force of the adaptive lens assembly 1008 may have the opposite sign to the sum of the refractive forces of the lens assembly 1004 and the waveguide assembly 1012.

[0192] In some embodiments, the first adaptive lens assembly 1004 is configured to have a first net refractive power Pnet1, which is close to or identical in size to the second net refractive power Pnet2 of the second adaptive lens assembly 1008. As a result, when both the first and second adaptive lens assemblies 1004 and 1008 are activated simultaneously, objects in the real world appear relatively unaffected by the refractive power of the second adaptive lens assembly 1008 provided for displaying virtual content.

[0193] In some embodiments, the first adaptive lens assembly 1004 may be configured, when activated, to dynamically match the first net refractive power Pnet1 of the second adaptive lens assembly 1008 to the second net refractive power Pnet2 of the second adaptive lens assembly 1008. For example, as the second net refractive power Pnet1 of the second switchable assembly 1008 is adjusted to track a moving virtual object in a virtual three-dimensional space, the first net refractive power Pnet1 of the first adaptive lens assembly 1004 may be dynamically adjusted so that the magnitude of the combined refractive power P = Pnet1 + Pnet2 is kept below a predetermined value. Thus, according to the embodiment, an object in the real world will have a combined refractive power P = Pnet1 + Pnet2 that is small, for example, about 0 m. -1 To prevent unacceptable focus shifts, the second net refractive power (Pnet2) of the second adaptive lens assembly 1008, which may have a negative value, can be compensated for by the first net refractive power (Pnet1) of the first adaptive lens assembly 1004. (Switchable waveplates and switchable waveplate lenses for broadband adaptive waveplate lens assemblies)

[0194] As discussed above, one of the advantages of forming images in multiple depth planes using fewer waveguides is the overall reduction in the thickness and weight of the display device (e.g., display device 1000 in Figure 10). Accordingly, the various embodiments described herein provide adaptive waveplate lens assemblies that are compact and lightweight and provide various optical functionalities, such as high bandwidth capability and variable refractive power. In addition, the various embodiments described herein provide adaptive lens assemblies with relatively low light leakage.

[0195] To provide images to multiple depth planes with high efficiency over a wide visible spectrum, broadband adaptive lens assemblies, according to various embodiments, include waveplate lenses (1154A and 1154B in Figures 12A and 12B, respectively) comprising liquid crystals, arranged such that the waveplate lenses have a birefringence (Δn) that varies radially from the central region of a first waveplate lens and decreases with increasing wavelength (λ) within the visible spectrum. As described above, according to various embodiments, broadband adaptive waveplate lens assemblies can generate images to multiple depth planes by being configured to selectively switch between multiple states with different refractive powers. Selective switching of a broadband lens assembly can, by extension, be performed by switching waveplate lenses or waveplates contained within a broadband adaptive waveplate lens assembly, as discussed herein.

[0196] Referring to Figure 12A, in some embodiments, the broadband adaptive lens assembly 1150A is configured to switch between different refractive power states by employing a switchable waveplate 1158 with liquid crystal in the same optical path as the waveplate lens 1154A. The waveplate lens 1154A may be a passive lens, and the broadband adaptive lens assembly 1150A may be selectively switched between different states by electrically activating and deactivating the switchable waveplate 1158.

[0197] Referring still to Figure 12A, during operation, the waveplate lens 1154A is configured, according to various embodiments, to diverge or converge the incident light 1162A, 1162B passing through it, depending on the polarization of the light, for example, circular polarization. When configured as a half-waveplate (HWP) lens, the illustrated waveplate lens 1154A, which can be a passive waveplate lens, is configured to converge a right-circularly polarized (RHCP) light beam 1162B incident on the waveplate lens 1154A into a left-circularly polarized (LHCP) light beam 1166A. On the other hand, the waveplate lens 1154A is configured to diverge an LHCP light beam 1162A incident on the waveplate lens 1154A into a right-circularly polarized (RHCP) light beam 1166B.

[0198] Still referring to Figure 12A, the LHCP light beam 1166A or RHCP light beam 1166B is incident on the switchable waveplate 1158 after being focused or defocused by the waveplate lens 1154A depending on the circular polarization of the light incident on it. The liquid crystal of the switchable waveplate 1158 is configured such that, when activated, for example electrically, the polarization of the circularly polarized light passing through it is preserved (not shown). That is, the LHCP light beam 1166A and RHCP light beam 1166B pass through the switchable waveplate 1158 unaffected. On the other hand, when deactivated, for example electrically, the polarization of the circularly polarized light passing through it is converted (illustrated). That is, the LHCP light beam 1166A is converted to the RHCP light beam 1170A, and the RHCP light beam 1166B is converted to the LHCP light beam 1170B.

[0199] Referring to Figure 12B, in some other embodiments, the broadband adaptive lens assembly 1150B is configured to switch between different refractive power states by employing a switchable waveplate lens 1154B having liquid crystal. The adaptive lens assembly 1150B may be selectively switched between different states by electrically activating and deactivating the switchable waveplate lens 1154B.

[0200] During operation, the liquid crystal of the waveplate lens 1154B is configured, according to various embodiments, to diverge or converge the incident light 1162A, 1162B passing through it, depending on its polarization, for example, circular polarization. When configured as a half-waveplate lens, when deactivated, for example electrically, the illustrated waveplate lens 1154B is configured to converge the RHCP light beam 1162B incident on the waveplate lens 1160B into the LHCP beam 1166A. Conversely, when deactivated, the waveplate lens 1154B is configured to diverge the left-handed polarized (LHCP) light beam 1162A incident on the waveplate lens 1154B into the RHCP beam 1166B. On the other hand, when activated, for example electrically, the polarization of circularly polarized light passing through it is preserved (not shown), and the LHCP light beam 1162A and RHCP light beam 1162B incident on it pass through the waveplate lens 1154B without substantially converging or diverging. In various embodiments, the waveplate lens assemblies 1150A and 1150B may be activated or deactivated, converging or diverging, and the polarization of circularly polarized light may be converted or preserved depending on its polarization, by configuring the liquid crystal to rearrange in response to a switching signal, for example, an electric field. (Broadband switchable waveplate)

[0201] As described above, according to various embodiments, a broadband adaptive waveplate lens assembly can be used to generate images in multiple depth planes by selectively switching the broadband waveplate lens assembly between multiple lens states having different refractive powers. As described above, in some embodiments, the broadband adaptive waveplate lens assembly may be configured to be selectively switched between multiple lens states by electrically activating a broadband switchable waveplate contained within the broadband adaptive waveplate lens assembly. Embodiments of broadband switchable waveplates are disclosed below.

[0202] In some embodiments, a broadband switchable waveplate comprises a layer of unpolymerized, twisted nematic (TN) liquid crystal (LC) and is configured to switch in response to the application of an electric field across the thickness of the TN LC layer. Although not constrained by any theory, the switching may be achieved by altering the orientation of the unpolymerized LC molecules across the thickness of the TN LC layer.

[0203] Referring to Figures 13A-13F, according to various embodiments, a broadband switchable waveplate comprises a layer of twisted nematic (TN) liquid crystal (LC). Figure 13A illustrates a cross-sectional view of an embodiment of a switchable waveplate comprising a layer of TN LC. The TN LC switchable waveplate 1300A comprises a layer of TN LC 1302 disposed between a pair of transparent substrates 1312. The transparent substrates 1312 are formed on the inner surfaces of conductive transparent electrodes 1316, 1320, respectively.

[0204] The surfaces of the transparent electrodes 1316, 1320 and / or the substrate 1312 may be configured such that TN LC molecules in contact with or directly adjacent to the upper electrode 1316 tend to be oriented with their long axes extending in a first lateral direction, while TN LC molecules in contact with or directly adjacent to the lower electrode 1320 tend to be oriented with their long axes extending in a second lateral direction, which may intersect, for example, at an angle of about 90 degrees with respect to the first lateral direction. TN LC molecules between those directly adjacent to the lower electrode 1320 and those directly adjacent to the upper electrode 1316 undergo torsion. As configured, the switchable waveplate 1300A of TN LC is configured as a broadband waveplate.

[0205] Referring again to Figure 13A, during operation, in the absence of an electric field across the TN LC layer 1302 (deactivation state), the nematic orienters of the TN LC molecules undergo a smooth 90-degree twist across the thickness of the TN LC layer 1302. In this state, incident light 1308 polarized in a first direction (the same direction as the LC molecule closest to the lower electrode 1312) is incident on the TN LC layer 1302. The twisted arrangement of TN LC molecules within the TN LC layer 1302 then acts as an optical waveguide, rotating the plane of polarization by a quarter-degree change (90 degrees) before reaching the upper electrode 1316. In this state, the TN LC layer 1302 plays a role in shifting the polarization direction of linearly polarized light passing through it from one linear polarization direction to another. Therefore, the transmitted light 1304 is polarized in a second direction opposite to the first direction (in the same direction as the LC molecule adjacent to the upper electrode 1316).

[0206] On the other hand, when a voltage exceeding the threshold voltage (V>Vth) of the switchable waveplate 1300A of the TN LC is applied across electrodes 1316 and 1320 (activated state), the TN The TN LC molecules within the LC layer 1306 tend to match the resulting electric field, and the optical wave inductive properties of the TN LC layer 1304, as described above, are lost in the deactivation state. In this state, the TN LC layer 1306 plays a role in preserving the polarization direction of the light passing through it. Therefore, the incident light 1308 and the transmitted light 1304B are polarized in the same first direction (the same direction as the LC molecule closest to the lower electrode 1312).

[0207] When the voltage or electric field is turned off, the TN LC molecules relax and return to their twisted state, and the TN LC molecules of TN LC layer 1306 in the activated state return to the configuration of the TN LC molecules of TN LC layer 1302 in the deactivated state.

[0208] As described above, the switchable waveplate 1300A of the TN LC described with respect to Figure 13A serves to shift the polarization direction of linearly polarized light. However, the various broadband waveplate lens assemblies described herein include switchable waveplates configured as switchable half-waveplates for reversing the polarity of circularly polarized light. Accordingly, in the following with respect to Figures 13B-13D, switchable waveplates configured as switchable half-waveplates are described according to embodiments.

[0209] Figure 13B illustrates a cross-sectional view of a switchable broadband waveplate 1300B configured as a half-waveplate according to an embodiment. The switchable broadband waveplate 1300B includes a switchable waveplate 1300A of TN LC as shown with respect to Figure 13A. In addition, to serve as a broadband half-waveplate for circular polarization, the switchable broadband waveplate 1300B also includes a pair of achromatic quarter-waveplates (QWPs) 1324, 1326.

[0210] During operation, when the switchable broadband waveplate 1300B is activated, an incident circularly polarized beam 1324 having a first polarity, for example, a left-circularly polarized (LHCP) light beam, passes through the first QWP 1324, which converts the circularly polarized beam 1324 into a first linearly polarized beam 1328 having a first linear polarization. Subsequently, as it passes through the switchable waveplate 1300A of the activated TN LC, the first linearly polarized beam 1328 is converted into a second linearly polarized beam 1332 having a second linear polarization. Subsequently, as it passes through the second QWP 1326, the second linearly polarized beam 1332 is converted into an outgoing circularly polarized beam 1340, for example, an RHCP light beam, having a second polarity opposite to the first polarity. Therefore, when activated, the switchable broadband waveplate 1300B acts as a half-waveplate, reversing the polarization of the circularly polarized beam.

[0211] On the other hand, when the switchable broadband waveplate 1300B is deactivated, the incident circularly polarized beam 1324 passes through the first QWP 1324 as described above, and then through the deactivated TN LC switchable waveplate 1300A, after which the polarization of the first linearly polarized beam 1328 is preserved. Subsequently, as it passes through the second QWP 1326, the first linearly polarized beam 1328 is converted into an outgoing circularly polarized beam 1340, for example, an LHCP light beam, having first polarity. Thus, when deactivated, the broadband waveplate 1300B acts as a transparent medium, which preserves the polarization of the circularly polarized beam.

[0212] In the various embodiments described herein, the first and / or second QWPs 1324, 1326 are broadband quarter-wave plates having a similar bandwidth to the TN LC switchable waveplate 1300A. According to the embodiments, the quarter-wave plates can be formed using polymerized TN LC layers. To provide broadband capability, according to the various embodiments, the QWP comprises multiple TN LC layers. When each TN LC layer is formed on its own substrate, the optical absorption of the resulting broadband quarter-wave plate and / or the resulting stack can become unacceptably thick. Therefore, embodiments of the QWP comprising multiple TN LC layers formed on a single substrate are described below in relation to efficient integration with the TN LC switchable waveplate 1300A.

[0213] Figure 13C illustrates a cross-sectional view of a broadband QWP 1300C, which may be the first and / or second QWPs 1324, 1326, as illustrated above with respect to Figure 13B, comprising a plurality (M) of TN LC layers 1302-1, 1302-2, ..., 1302-M stacked on a matching layer 1302-0 formed on a substrate 1312. As described in more detail elsewhere in this specification, the matching layer 1302-0 is configured to induce the elongation direction of LC molecules in the first TN LC layer 1302-1 directly adjacent to the matching layer 1302-0 to be aligned in a first direction. The LC molecules above the LC molecules aligned by the matching layer 1302-0 undergo a first twist so that the LC molecules in the first TN LC layer 1302-1 directly adjacent to the second TN LC layer 1302-2 are elongated in a second direction. The alignment of LC molecules within each of the subsequent TN LC layers 1302-2 to 1302-M is such that the LC molecule closest to the previous layer is aligned in the same direction as the topmost LC molecule of the previous layer, except that the first TN Alignment occurs in a manner similar to that of LC layer 1302-1. For example, the uppermost LC molecules in the first TN LC layer 1302-1 and the lowermost LC molecules in the second TN LC layer 1302-1 are aligned in the same second direction. The LC molecules in the second TN LC layer 1302-2 undergo a second twist such that the uppermost LC molecules in the second TN LC layer 1302-2 are stretched in a third direction. A given TN is formed as a result of the alignment of LC molecules in adjacent layers that are in contact with it. Such alignment of LC molecules within an LC layer is sometimes referred to as self-alignment because no intervening matching layer is present between them. Therefore, in some embodiments, a broadband QWP comprises multiple TN LC layers, each having two or more self-aligned TN LC layers with non-zero torsion.

[0214] In the embodiment, the TN LC layer comprises polymerized LC molecules (LCPs) formed, for example, using a reactive mesogen. As described above, the reactive mesogen is initially a low molecular weight LC, which can be matched by surface and torsion to have a complex profile, similar to conventional LCs, and then cured into a solid polymer film by photopolymerization.

[0215] Figure 13D illustrates a cross-sectional view of an integrated switchable broadband waveplate 1300D, in which a switchable waveplate 1300A of a TN LC, similar to that described above with respect to Figure 13A, is integrated into a single stack with a pair of broadband QWPs 1324, 1326, similar to those described above with respect to Figure 13C. In the illustrated embodiment, the switchable waveplate 1300A of the TN LC is integrated into a single stack by using an adhesive layer 1348 to attach the pair of broadband quarter-waveplates 1324, 1326 to its opposite side.

[0216] Figure 13E shows a cross-sectional view of an integrated switchable broadband waveplate 1300E, in which a switchable TN LC waveplate 1300A, similar to that described above with respect to Figure 13A, is integrated into a single stack together with a pair of broadband quarter-waveplates 1324, 1326, in a manner similar to that described above with respect to Figure 13D, except that instead of using adhesive to form an integrated stack, one of a pair of broadband quarter-waveplates 1324, 1326 serves as a substrate on which the switchable TN LC waveplate 1300A (Figure 13A) can be directly formed. For example, different layers of the switchable TN LC waveplate 1300A may be directly formed on one surface of the QWP 1324, 1326. Advantageously, one or both of the substrates 1312 of the switchable TN LC waveplate 1300A may be omitted. Therefore, the switchable waveplate 1300A of the TN LC is integrated into a compact single stack by forming it directly on one of the pair of broadband QWP 1324, 1326 and forming the other of the pair of broadband QWP 1324, 1326 on top of it.

[0217] In each of the embodiments illustrated above with respect to Figures 13D and 13E, the broadband QWP can be formed from, for example, a liquid crystal-based material such as quartz and MgF2, or other non-liquid crystal-based materials. In the embodiments below with respect to Figure 13F, the broadband QWP comprises a liquid crystal, which is particularly advantageous as it is integrated into a single stack together with a switchable waveplate of TN LC, serving not only as a QWP but also as a matching layer for the switchable waveplate of TN LC.

[0218] Figure 13F illustrates a cross-sectional view of an integrated switchable broadband waveplate 1300F that integrates a switchable waveplate 1300A of TN LC similar to that described above with respect to Figure 13A. The switchable broadband waveplate 1300F includes a pair of broadband QWPs 1324, 1326 arranged in a manner similar to that described above with respect to Figure 13E, except that the broadband QWPs 1324, 1326 are arranged in a manner similar to that described above with respect to Figure 13E, except that instead of broadband QWPs 1324, 1326 as substrates for the TN LC layer 1302, the broadband QWPs 1324, 1326 comprise thin polymerized LC layers formed on separate surfaces of the substrate 1312, and the LC molecules of the TN LC layer 1302 are inserted into gaps formed between the opposing surfaces of the broadband QWPs 1324, 1326 by spacers 1350 that define the thickness of the TN LC layer 1302. The method of inserting the LC molecules is described elsewhere in this specification. In addition, the different layers of the switchable waveplate 1300A of the TN LC and the different layers of the broadband QWPs 1324 and 1326 are integrally formed within a single stack. For example, the first broadband QWP 1324 includes a substrate 1312 on which a lower transparent electrode 1316 is formed, followed by a matching layer 1302-2 and multiple TN LC layers 1302-1 and 1302-2. Similarly, the second broadband QWP 1326 includes a substrate 1312 on which an upper transparent electrode 1320 is formed, followed by a matching layer 1302-0 and multiple TN LC layers 1302-1 and 1302-2.

[0219] Referring still to Figure 13F, it is advantageous that the outermost LC molecules of the TN LC layer 1302-2 of the first broadband QWP 1324 facing the gap and the outermost LC molecules of the TN LC layer 1302-2 of the second broadband QWP 1326 facing the gap are arranged to serve as matching layers for the switchable TN LC layer 1302, in a manner similar to that described above with respect to Figure 13C, such that the outermost LC molecules of the TN LC layer 1302 are self-aligned. In addition, by integrally stacking the different layers of the switchable waveplate 1300A of the TN LC and the different layers of the broadband QWPs 1324 and 1326, the total thickness of the entire stack can be substantially reduced. For example, mechanically joining a switchable waveplate 1300A of TN LC as shown in Figure 13A and broadband quarter-waveplates 1324 and 1326 as shown in Figure 13C would result in four substrates, whereas the entire stack of switchable broadband waveplates 1300F has only two substrates.

[0220] Referring to Figure 13F and the various embodiments described throughout this specification, the switchable LC layers, for example, the TN LC layer 1302 inserted into the gap, have thicknesses of approximately 1 μm to 50 μm, 1 to 10 μm, 10 to 20 μm, 20 to 30 μm, 30 to 40 μm, 40 to 50 μm, or any range defined by these values. In addition, the passive LC layers, for example, the TN LC layers 1302-1, 1302-2, can have thicknesses of approximately 0.1 μm to 50 μm, 0.1 to 1 μm, 1 to 10 μm, 10 to 20 μm, 20 to 30 μm, 30 to 40 μm, 40 to 50 μm, or any range defined by these values.

[0221] In various embodiments described herein, matching layers (e.g., 1302-2 in Figures 13C and 13F) are used to align LC molecules, for example, to align the elongation direction of LC molecules along a specific direction. For example, as described above with respect to Figures 13A-13F, matching layers can be used to define an orienting element (n), i.e., the locally average elongation direction of elongated LC molecules in a given direction. In some other embodiments, matching layers may be formed from organic polymers such as polyimides and polyamides that are mechanically abraded, obliquely deposited inorganic oxides such as SiO2, or long-chain aliphatic siloxanes. In some embodiments, non-contact matching layers may be formed from organic polymers using plane-polarized light to generate surface anisotropy, which in turn defines the orienting element. For example, the use of cis-trans photoisomerization of azo dyes, which are directly deposited or can be dissolved in a standard orienting layer (e.g., polyimide) or LC mixture, can produce an orienting effect within the matching layer without abrasion. Non-contact matching layers using azo chromophores sometimes employ high-intensity laser light to induce isomerization of dye molecules.

[0222] In some other embodiments, the nanostructure pattern can serve as a matching layer for matching LC molecules. Advantageously, in some embodiments, the nanostructure pattern can be formed as part of an electrode layer, improving optical transmittance, reducing process steps, and further reducing the overall thickness of the broadband waveplate, for example, as described above with respect to Figures 13A–13F. To achieve this objective, Figure 14A illustrates a perspective view of a nanostructure 1400A pattern, for example, a nanowire formed on a transparent substrate 1312, which serves a dual function as both a matching layer and an electrode layer according to an embodiment. The nanostructure 1400A pattern can be patterned on the substrate 1312 using, for example, lithography or nanoimprint techniques, as described in detail elsewhere in this specification. The nanostructure can be formed from a sufficiently thin conductive material, which is patterned as elongated metallic wires. For example, the conductive material can be gold, silver, copper, aluminum, or ITO, or any suitable conductive material, having thickness and electrical resistivity such that the pattern resulting from the nanostructure can simultaneously serve as a matching layer and an electrode layer. In the illustrated embodiment, the pattern of the nanostructure 1400A comprises periodic conductive lines 1404A extending in a first direction, e.g., the x-direction, connected to rail 1408A to supply current or voltage to the periodic conductive lines 1404A. In various embodiments, the periodic conductive lines 1404A can have a pitch of 1 μm to 1,000 μm, 5 μm to 500 μm, 10 μm to 100 μm, or any value within the range defined by these values. The conductive lines 1404 can have a width of 10 nm to 1 μm, 100 nm to 1,000 nm, 100 nm to 500 nm, 200 nm to 300 nm, or any value within the range defined by these values. The periodic conductive line 1404 can have a thickness of 10 nm to 1 μm, 100 nm to 1000 nm, 100 nm to 500 nm, 400 nm to 500 nm, or any value within the range defined by these values.The material, thickness, and width combinations for the periodic conductive line 1404A can be selected so that the resulting sheet resistance of the periodic conductive line 1404A is approximately 1 ohm / square to 100 ohms / square, 2 ohms / square to 50 ohms / square, 5 ohms / square to 20 ohms / square, or any value within the range defined by these values, e.g., approximately 10 ohms / square. In addition, the material and thickness combinations for the conductive line 1404A can be selected so that the resulting transmittance in the visible spectrum is 80% to 99%, 90% to 99%, 95% to 99%, 97% to 99%, or any value within the range defined by these values, e.g., approximately 98%. Other dimensions, configurations, and values ​​are also possible.

[0223] Figure 14B shows a perspective view of the pattern of nanostructure 1400B, which is similar to the pattern of nanostructure 1400A described above with respect to Figure 14A, except that the pattern of nanostructure 1400B includes a periodic conductive line 1404B extending in a second direction, for example, the y-direction, which is connected to a rail 1408B for supplying current to the periodic conductive line 1404B.

[0224] Figure 14C illustrates a perspective view of a pair of electrodes 1400C according to an embodiment. The pair of electrodes 1400C includes patterns of nanostructures 1400A and 1400B, in which periodic conductive lines 1404A and 1404B are arranged to face each other, intersect, and be separated by gaps 1412, in which one or more LC layers, such as TN LC layers, are configured to be placed. Advantageously, it has been found that the patterns of nanostructures 1400A and 1400B can each serve as matching layers similar to the matching layers 1302-0 described above with respect to Figures 13C and 13F, such that when nematic LC molecules, such as reactive mesogens, are formed on them, the LC molecules directly adjacent to each of the patterns of nanostructures 1400A and 1400B can be aligned with the orientation of the nematic LC molecules, for example, generally aligned in the same direction as the extension direction of the periodic conductive lines 1404A and 1404B. In addition, the LC molecules between LC molecules directly adjacent to the periodic conductive lines 1404A and 1404B can be configured to undergo torsion using a torsion agent so that unpolymerized TN LC layers similar to TN LC layer 1302 described above with respect to Figure 13A and polymerized TN LC layers similar to TN LC layers 1302-1, 1302-2, ..., 1302-M described above with respect to Figure 13C can be formed.

[0225] Referring back to Figure 13F, it should be understood that in some embodiments, by combining the functionality of the electrodes and matching layers, the pattern of nanostructure 1400A can replace the combination of transparent electrode 1316 and matching layer 1302-0 of broadband QWP 1324, and the pattern of nanostructure 1400B can replace the combination of transparent electrode 1320 and matching layer 1302-0 of broadband QWP 1326, thereby enabling a more compact overall stack.

[0226] Referring still to Figure 14C, the corresponding effects on the arrangement of LC molecules and the polarization of light, with and without an electric field, during operation are similar to those described above with respect to Figure 13A.

[0227] Figures 15A and 15B illustrate plan and cross-sectional views of a switchable broadband waveplate 1500 of a TN LC according to an embodiment. Unlike the broadband waveplate illustrated above with respect to Figures 13A and 13F, which has vertically separated electrodes for switching, the switchable broadband waveplate of a TN LC includes electrodes separated laterally in-plane for switching. The switchable broadband waveplate 1500 of a TN LC includes a matched electrode stack 1524 and a matched layer stack 1526. Similarly, as described above with respect to Figure 13F, LC molecules are inserted into the gap formed by a spacer 1350 between the opposing surfaces of the matched electrode stack 1524 and the matched layer stack 1526. A method for inserting LC molecules is described elsewhere in this specification. The matched electrode stack 1524 includes first and second electrodes 1500A and 1500B formed on an upper transparent substrate 1312, and further includes an optional upper matched layer 1302-0. The matching layer stack 1526 includes a lower matching layer 1302-0 formed on the lower transparent substrate 1312.

[0228] Referring to Figure 15A, the matched electrode stack 1524 includes first and second electrodes 1500A and 1500B, each containing separate first and second periodic conductive lines 1504A and 1504B. Periodic conductive line 1504A is interlocked or interwoven with periodic conductive line 1504B. The first and second periodic conductive lines 1504A and 1504B are strapped to rails 1508A and 1508B, respectively, in a manner similar to that described above with respect to patterned nanostructures 1400A (Figure 14A) and 1400B (Figure 14B). The material, thickness, width, and pitch of the alternating periodic conductive lines 1504A and 1504B can be analogous to those described above with respect to the patterned nanostructures 1400A (Figure 14A) and 1400B (Figure 14B). However, unlike the pair of electrodes 1400C described above with respect to Figure 14C, which are vertically separated, periodic conductive line 1504A alternates with periodic conductive line 1504B in a lateral direction, e.g., in the x-direction, such that the electric field between periodic conductive line 1504A and periodic conductive line 1504B is directed in a lateral direction.

[0229] Referring to the cross-sectional view of the switchable cell 1500 of the TN LC in Figure 15B, in a manner similar to that described above with respect to Figure 13F, the LC molecules are inserted into a gap formed between the opposing surfaces of the matching electrode stack 1524 and the matching layer stack 1526 so that a TN LC layer (not shown) similar to the TN LC layer 1302 (Figure 13A) can be formed. The method of inserting the LC molecules is described elsewhere in this specification.

[0230] In some embodiments, in a manner similar to that described above with respect to Figure 14C, the alternating periodic conductive lines 1504A, 1504B and / or the upper matching layer 1302-0 within the matching electrode stack 1524 can serve as matching layers for the outermost LC molecules of the TN LC layer 1302 formed within the gap 1412, in a manner similar to the matching layer 1316 described above with respect to Figure 13A and the conductive line 1404B described above with respect to Figure 14C. When the alternating periodic conductive lines 1504A and 1504B serve as matching layers, in some embodiments, the upper matching layer 1302-0 may be omitted. Similar to the matching layer 1320 described above with respect to Figure 13A and the conductive line 1404A described above with respect to Figure 14C, the lower matching layer 1302-0 can serve to match the LC molecules within the gap 1412 that are directly adjacent to it.

[0231] Although not shown, in some embodiments, the illustrated TN LC switchable broadband waveplate 1500 integrates multiple TN LC layers similar to TN LC layers 1302-1, 1302-2, ... 1302-M (Figure 13F, not shown) between alternating periodic conductive lines 1504A, 1504B and LC molecules in the gap 1412 and / or between the lower matching layer 1302-0 and LC molecules in the gap 1412, thereby providing integrated QWP functionality in a manner similar to that described above with respect to Figure 13F.

[0232] Referring still to Figures 15A and 15B, during operation, in the absence of an electric field, the alternating periodic conductive lines 1504A and 1504B act as matching layers for LC molecules directly adjacent to the periodic conductive lines 1504A and 1504B, such that the LC molecules generally have orienters extending parallel to the periodic conductive lines 1504A and 1504B. In the deactivated state, in a manner similar to that described above with respect to Figure 13A, the switchable broadband waveplate 1500 is configured to reverse the polarization of linearly polarized light. On the other hand, when an electric field is applied laterally between periodic conductive lines 1504A and 1504B, for example in the y-direction, the LC molecules between directly adjacent periodic conductive lines 1504A and 1504B align their extension direction, for example, in a direction away from parallel between parallel and perpendicular, or perpendicular to the periodic conductive lines 1504A and 1504B. In the activated state, the switchable broadband waveplate 1500 is configured to preserve the polarization of linearly polarized material, in a manner similar to that described above with respect to Figure 13A.

[0233] In some embodiments, in addition to combining the functionality of electrodes and matching layers, the first and second electrodes 1500A and 1500B can replace, for example, the combination of transparent electrodes 1316 and 1320 and upper and lower matching layers 1302-0 of the broadband waveplate 1300F (Figure 13F), thereby enabling a more compact overall stack and even more improved transparency due to halving the electrode layer. (Liquid crystal-based waveplate lens)

[0234] As described above with respect to Figure 12A, several broadband adaptive waveplate lens assemblies, according to embodiments, include a switchable waveplate and one or more waveplate lenses, which may be passive or switchable, formed from a thin film of birefringent liquid crystal, in order to provide images to multiple depth planes with high efficiency over a wide range of the visible spectrum. Hereinafter, exemplary waveplate lenses are disclosed, which include liquid crystal, the orientation of the waveplate in the plane of which is adapted to focus and / or modify the polarization state of light transmitted through it. Hereinafter, various embodiments of the lenses and waveplates are formed from liquid crystal.

[0235] An embodiment of a liquid crystal-based waveplate lens is illustrated with reference to Figures 16A and 16B.

[0236] Figures 16A and 16B illustrate embodiments of waveplate lenses 1200A and 1200B, respectively, each comprising a transparent substrate 1204, for example, a glass substrate on which liquid crystal molecules 1208 are formed, stretched along different stretching directions with respect to the axial direction (e.g., x-direction or y-direction) and the direction parallel to the main surface of the substrate 1204. That is, the liquid crystal molecules 1208 are rotated by different rotation angles (φ) about the direction normal to the main surface of the substrate 1204 (e.g., z-direction), where φ is described as the angle between the stretching directions of the liquid crystal molecules with respect to the direction parallel to the layer normal (e.g., x-direction or y-direction).

[0237] In the illustrated implementation, the liquid crystal molecules 1208 at a given radius from the central axis C or the center of the lens have substantially the same rotation angle (φ). The liquid crystal molecules 1208 are arranged to focus a collimated beam of light to a point at a certain focal length. While not constrained by any theory, the rotation angle (φ) of the liquid crystal molecules 1208 can be proportional to a power of r, where r is the radial distance from C and has a value of approximately 1 to 3, e.g., 2. In one implementation, the angle (φ) is + / -k0r 2The value can be proportional to / f, where r is the radial distance from C, k0 = 2π / λ is the wavenumber of the light that will be focused by the diffractive waveplate lens, λ is the wavelength of the light, and f is the focal length of the waveplate lenses 1200A and 1200B. The + and - signs can correspond to the rotation direction of the liquid crystal molecule 1208 with respect to the liquid crystal molecule 1208 closest to the center C of the waveplate lenses 1200A and 1200B.

[0238] It should be understood that the patterns of liquid crystal molecules 1208 in waveplate lenses 1200A and 1200B represent inverted images of each other. That is, one of the waveplate lenses 1200A and 1200B can be obtained by rotating the other waveplate lens 1200B by 180 degrees around the axial direction (e.g., x-direction or y-direction). As configured, the focal lengths and refractive powers of waveplate lenses 1200A and 1200B are the same in magnitude but opposite in sign.

[0239] In some implementations, the waveplate lenses 1200A and 1200B can each function as half-waveplate lenses. When configured as half-waveplate lenses, the waveplate lenses 1200A and 1200B each rotate the plane of linear polarization by an angle of 2α with respect to the polarization of the input beam, where α is the angle between the input polarization direction and the waveplate axis. With respect to a circularly polarized beam, this change in angle is converted into a phase shift and a reversal of polarization palmarity. Thus, a ±2α phase shift can be generated in the circularly polarized beam, with the sign of the phase shift depending on the polarization palmarity.

[0240] Figure 16C illustrates embodiments of a waveplate lens that diverges or focuses light passing through it, depending on the polarization of the light and the side from which the light is incident, according to several embodiments. When configured as a half-waveplate lens, the illustrated waveplate lens 1200A may be configured to diverge a right-circularly polarized (RHCP) light beam 1212 incident on the first side into a left-circularly polarized (LHCP) beam 1216. On the other hand, the waveplate lens 1200A may be configured to focus an RHCP light beam 1220 incident on a second side opposite to the first side into a left-circularly polarized (LHCP) beam 1224.

[0241] With respect to the waveplate lens 1200B, the situation is reversed. As shown in Figure 16D, when configured as a half-waveplate, the waveplate lens 1200B may be configured to focus the LHCP light beam 1228 incident on the first side into the RHCP beam 1232. On the other hand, the waveplate lens 1200B may be configured to diverge the LHCP light beam 1236 incident on the second side opposite to the first side into the RHCP beam 1240.

[0242] Therefore, by controlling the rotational angular and radial distribution of the liquid crystal 1208, the waveplate lens can be configured to focus or diverge circularly polarized light having either palpable or ambiguous properties. It should be understood that the refractive power can be increased or decreased based on the relationship between the rotational angles of the liquid crystal. In addition, in some embodiments, the liquid crystal may be matched and mismatched by applying an electric field. Therefore, it should be understood that at the limit where the refractive power is approximately zero, the waveplate lens may be used as a waveplate, for example, a switchable waveplate. (Broadband adaptive waveplate lens assembly including switchable waveplates)

[0243] As described above with respect to Figure 12A, in order to provide images to multiple depth planes with high efficiency over a wide range of the visible spectrum, some broadband adaptive waveplate lens assemblies according to embodiments include a switchable waveplate and one or more waveplate lenses, which may be passive or switchable, formed from a thin film of a birefringent material, such as liquid crystal. Embodiments of broadband adaptive waveplate lens assemblies comprising a switchable broadband waveplate are disclosed below. For example, the switchable broadband waveplate may be one of the broadband switchable waveplates described above with respect to Figures 13A-13F, 14A-14C and 15A-15B.

[0244] Figure 17A illustrates an embodiment of a broadband adaptive waveplate lens assembly 1700, comprising a waveplate lens, for example, a passive waveplate lens, and a switchable waveplate, according to several embodiments. The broadband adaptive waveplate lens assembly 1700 may be configured as one of the pairs of switchable waveplate assemblies 1004, 1008 described above with respect to Figures 10, 11A, and 11B, for example. Figure 17B illustrates the broadband adaptive waveplate lens assembly 1700A when the switchable waveplate of the adaptive lens assembly 1700 illustrated in Figure 17A is activated during operation, while Figure 17C illustrates the broadband adaptive waveplate lens assembly 1700B when the switchable waveplate of the adaptive lens assembly 1700 illustrated in Figure 17A is deactivated during operation. The adaptive lens assembly 1700 is configured to couple and transmit light externally coupled from the waveguide assembly 1012 (Figures 10, 11A, 11B). The adaptive lens assembly 1700 comprises a first waveplate lens (L1 / HWP1) 1704, for example, a first half-waveplate lens; a second waveplate lens (L2 / HWP2) 1708, for example, a second half-waveplate lens; and a switchable waveplate (HWP3) 1712, for example, a switchable half-waveplate.

[0245] In various embodiments, L1 / HWP1 1704 and L2 / HWP2 1708 are configured to function as a lens and a half-wave plate, respectively. As described above with respect to Figures 12A and 12B, when configured as half-wave plates, L1 / HWP1 1704 and L2 / HWP2 1708 are configured to convert light having a first degree of circular polarization (first HCP) to light having a second degree of circular polarization (second HCP), respectively. That is, L1 / HWP1 1704 and L2 / HWP2 1708 are configured to convert the light passing through them, converting light having LHCP or RHCP to light having RHCP or LHCP, respectively.

[0246] In various embodiments, L1 / HWP1 1704 and L2 / HWP2 1708 are configured to act as lenses, each having either a first lens effect or a second lens effect opposite to the first lens effect with respect to a given polarization. That is, L1 / HWP1 1704 and L2 / HWP2 1708 are configured to either converge or diverge the light passing through them. In various embodiments, L1 / HWP1 1704 and L2 / HWP2 1708 may each be configured to have opposite lens effects depending on the polarization state of the incident light. For example, L1 / HWP1 1704 and L2 / HWP2 1708 may each be configured to focus light incident on them having a first HCP, while each is configured to defocus light incident on them having a second HCP.

[0247] In some embodiments, L1 / HWP1 1704 and L2 / HWP2 1708 are configured to have the same lensing effect with respect to light having a given HCP. That is, both L1 / HWP1 1704 and L2 / HWP2 1708 may be configured to focus light having LHCP, focus light having RHCP, defocus light having LHCP, or defocus light having RHCP.

[0248] In some embodiments, L1 / HWP1 1704 and L2 / HWP2 1708 may each comprise liquid crystal molecules that are stretched and rotated such that the liquid crystals at a given radius from the central axis of the individual waveplate lenses 1704, 1708 have the same rotation angle (φ), as described above with respect to Figures 12A and 12B. The first and second waveplate lenses 1704, 1708 are each configured to alter the polarization state, for example, to reverse the polarization state of light passing through them. The switchable waveplate 1712 is configured to alter the polarization state, for example, to reverse the polarization state of light passing through it, when electrically deactivated, while being configured to substantially allow light to pass through it without altering the polarization state of the light passing through it. An electrical signal, for example, a current signal or a voltage signal for switching the switchable waveplate 1712, may be provided by a switching circuit 1716 electrically connected thereto.

[0249] In various embodiments, the HWP3 is deactivated electrically, for example, by using a voltage or current signal provided by the switching circuit 1716. 1712B (Figure 17C) acts as a half-wave plate. That is, when deactivated, HWP3 1712B (Figure 17C) acts as a half-wave plate configured to convert the light passing through it from light having LHCP or RHCP to light having RHCP or LHCP. Thus, L1 / HWP1 1704, L2 / HWP2 1708, and HWP3 1712B, when deactivated (Figure 17C), are configured to convert light having a first circumferential circular polarization (first HCP) to light having a second circumferential circular polarization (second HCP).

[0250] In various embodiments, when electrically activated, for example by using a voltage or current signal provided by a switching circuit 1716, or by removing a voltage or current signal, the HWP3 1712A (Figure 17B) acts as a light-transmitting medium without affecting the provision of polarization or any lensing effect.

[0251] In some embodiments, the single-waveplate lenses 1704 and / or 1708 may function as both a waveplate lens and a switchable half-waveplate. In such embodiments, the dedicated switchable half-waveplate 1712 may be omitted.

[0252] Figure 17B illustrates an embodiment of the adaptive lens assembly of Figure 17A in which a switchable waveplate is activated during operation, according to several embodiments. The adaptive lens assembly 1700A may be activated when the switchable waveplate 1712 is activated, for example, when no current or voltage is applied to the switchable waveplate 1712 by the switching circuit 1716. The adaptive lens assembly 1700A may correspond to a first adaptive lens assembly 1004 (world side) or a second adaptive lens assembly 1008 (user side). For example, the adaptive lens assembly 1700A will be described as corresponding to the first adaptive lens assembly 1004 or the second adaptive lens assembly 1008 as part of a display device 1000 (Figure 10) that displays a real-world view to the user without displaying a virtual image. For example, the display device 1000 (Figure 10) may be used as ordinary eyeglasses or ordinary goggles. L1 / HWP1 1704 and L2 / HWP2 1708 may each be configured to exert a first lens effect, such as a divergent effect, on light having a first HCP, such as an LHCP passing through it. L1 / HWP1 1704 and L2 / HWP2 1708 may also each be configured to exert a second lens effect, such as a converging effect, opposite to the first lens effect, on light having an opposite HCP, such as an RHCP passing through it.

[0253] In the illustrated embodiment, the light beam 1720 may represent a light beam from the world that is incident on either the first adaptive lens assembly 1004 (world side) or the second adaptive lens assembly 1008 (user side) while the display device 1700A is being used as ordinary glasses or goggles without displaying virtual content. For example, a light beam 1720 having a first HCP, e.g., an LHCP, travels, for example, in the positive z-direction until the beam 1720 collides on the L1 / HWP 1704 for transmission through it. The L1 / HWP 1704 converts the light beam 1720 having an LHCP into a light beam 1724 having an RHCP. Since the L1 / HWP 1704 is also configured as a lens, the L1 / HWP 1704 also diverges the light beam 1720 according to a first refractive power P1 of the L1 / HWP 1704.

[0254] The optical beam 1724 having RHCP is subsequently incident on the HWP3 1712A in an activated state. Because HWP3 1712A is activated, the optical beam 1724 having RHCP is transmitted through HWP3 1712A substantially unaffected in terms of polarization or lensing effects and incident on L2 / HWP2 1708 as the optical beam 1728A having RHCP. When configured as a user-side adaptive lens assembly (e.g., the second adaptive lens assembly 1004 in Figure 10) as described above, L2 / HWP2 1708 is configured, in the illustrated embodiment, similar to L1 / HWP1 1704, i.e., to change the polarization and diverge the light having LHCP while focusing the light having RHCP. Thus, the optical beam 1728A having RHCP is inversely converted to the optical beam 1732 having LHCP. Therefore, when HWP3 1712A is activated, L1 / HWP1 1704 and L2 / HWP2 1704 transmit a light beam having opposite polarization such that L1 / HWP1 1704 and L2 / HWP2 1708 exert an opposite lens effect on the light passing through them. That is, the light beam 1728A incident on L2 / HWP2 1704 has RHCP, so the light beam 1732A exiting L2 / HWP2 1708 diverges according to a first refractive power P1, unlike the light beam 1724 exiting L1 / HWP1 1704, which is focused according to a second refractive power P2. Subsequently, depending on the exit from the adaptive lens assembly 1700A in the activated state, the light beam 1732A can be seen by the eye.

[0255] In some embodiments, when HWP3 1712A is activated, the first refractive power P1 of L1 / HWP1 1704, which may be negative (i.e., divergent), and the second refractive power P2 of L2 / HWP2 1708, which may be positive (i.e., convergent), may have substantially identical or matching magnitudes. In these embodiments, the net refractive power Pnet of the adaptive lens assembly 1700A, which may be about -P1+P2, may be substantially zero to compensate for the lens effects of L1 / HWP1 1704 and L2 / HWP2 1708. However, embodiments are not limited in this way, and the first and second refractive powers P1 and P2 may have different magnitudes so that the net refractive power Pnet may have a non-zero value. For example, in some embodiments, the non-zero Pnet may be equal to the user's eyeglass prescription, thereby allowing correction of the user's eye focusing error (e.g., refractive focusing error).

[0256] In the illustrated embodiment, the incident light beam 1720 has an LHCP, but it should be understood that similar results would be obtained when the incident light beam 1720 has an RHCP. That is, when the light beam 1720 has an RHCP, the light beams 1724 and 1728A have an LHCP, and unlike the illustrated embodiment, the light beams 1724 and 1728A are focused relative to the light beam 1720. Similarly, L2 / HWP2 1708 diverges the light beam 1728A, which is focused by L1 / HWP1 1704, so that the net refractive power Pnet can be substantially zero.

[0257] Regarding Figure 17B, L1 / HWP1 1704 and L2 / HWP2 are described above. The lens effect of 1708 and its selectivity for the polarization state of the incident light beam serve only as one embodiment, and it should be understood that other configurations are also possible. For example, in Figure 17B, L1 / HWP1 1704 and L2 / HWP2 1708 are configured to diverge light with LHCP while converging light with RHCP, but in other embodiments, L1 / HWP1 1704 and L2 / HWP2 1708 may be configured to converge light with LHCP while diverging light with RHCP.

[0258] In short, in some embodiments, when the HWP3 1712A of the adaptive lens assembly 1700A is activated, the output light beam 1732A has the same HCP as the incident light beam 1720 and can be substantially matched to the incident light beam 1720 in terms of lens effect, in order to compensate for the lens effect between P1 of L1 / HWP1 1704 and P2 of L2 / HWP2 1708. As a result, when the user is not viewing virtual content, the view of the world is relatively unaffected by the presence of the adaptive lens assembly (1004, 1008 in Figures 10, 11A, 11B).

[0259] Figure 17C illustrates an embodiment of the adaptive lens assembly of Figure 17A in which the switchable waveplate is deactivated during operation, according to several embodiments. The adaptive lens assembly 1700B may be deactivated when the switchable waveplate 1712B is deactivated, for example, when a current or voltage is applied to the switchable waveplate 1712B by the switching circuit 1716. The adaptive lens assembly 1700B may correspond to, for example, a first adaptive lens assembly 1004 (world side) or a second adaptive lens assembly 1008 (user side). Hereinafter, as an example, the adaptive lens assembly 1700B will be described as being configured first as a second adaptive lens assembly 1008 on the user side, as part of a display device (for example, display device 1100A in Figure 11A) that outputs a virtual image to the user. Next, it will be described that the adaptive lens assembly 1700B is configured as the world-side first adaptive lens assembly 1004, as part of a display device 1100B (Figure 11B), which simultaneously outputs a virtual image to the user while transmitting a real-world view, and reduces or essentially eliminates distortion of the real-world view resulting from the lens effect of the second adaptive lens assembly 1008.

[0260] When configured as a second adaptive lens assembly 1008 on the user side (Figure 11A), L1 / HWP1 1704 and L2 / HWP2 1708 may each be configured to diverge light having one of the HCPs, for example, an LHCP passing through it. L1 / HWP1 1704 and L2 / HWP2 1708 may also each be configured to focus light having another HCP, for example, an RHCP passing through it.

[0261] As described above with respect to Figure 11A, a portion of the light propagating in the waveguide assembly 1012 in the x-direction, for example by total internal reflection, may be redirected or externally coupled in the z-direction. The light externally coupled from the waveguide assembly 1012 (Figure 11A) may be incident on the switchable lens assembly 1700B as a circularly polarized beam 1720 having an LHCP. The light beam 1720 propagates, for example, in the positive z-direction until the light beam 1720 collides with and is transmitted through the L1 / HWP 1704. 1704 converts the light beam 1720 having LHCP into a light beam 1724 having RHCP. Since L1 / HWP1 1704 is configured to diverge the light having LHCP, the light beam 1724 is also diverged according to the first refractive power P1 of L1 / HWP1 1704.

[0262] The optical beam 1724, which has RHCP, is then incident on HWP3 1712B, which is in a deactivated state. Unlike the activated HWP1712A shown above with respect to Figure 17B, HWP3 1712B is deactivated, so the optical beam 1724, which has RHCP, transmitted through HWP3 1712B is converted into an optical beam 1728B, which has LCHP. Subsequently, the optical beam 1728B, which has LHCP, is incident on L2 / HWP2 1708. Unlike the optical beam 1728A shown above with respect to Figure 17B, the optical beam 1728B incident on L2 / HWP2 1708 has LHCP, so L2 / HWP2 1708 further diverges the optical beam 1728B into an optical beam 1732B, which has RHCP, according to a second refractive force P2. In other words, unlike the activated state of HWP1712A illustrated in Figure 17B, HWP1712B is deactivated, so L1 / HWP1 1704 and L2 / HWP1 1704 are configured to transmit light beams having the same polarization LHCP. Therefore, L1 / HWP1 has the compensation effect illustrated in Figure 17B. Unlike 1704 and L2 / HWP2 1708, L1 / HWP1 in Figure 17C 1704 and L2 / HWP2 1708 exert an additional lensing effect on the light passing through them. That is, since both the light beam 1720 incident on L1 / HWP1 and the light beam 1728B incident on L2 / HWP2 1704 have LHCPs, the light beam 1732B emanating from L2 / HWP2 1708 will be further diverged in addition to the divergence caused by L1 / HWP1 1704. Subsequently, depending on the emission from the adaptive lens assembly 1700B in the deactivated state, the light beam 1732A may be visible to the eye.

[0263] In some embodiments, the first refractive power P1 of L1 / HWP1 1704 and the second refractive power P2 of L2 / HWP2 1708 may both be negative (i.e., divergent) and may have substantially the same or matching magnitudes. In these embodiments, the net refractive power Pnet of the adaptive lens assembly 1700B, which may be about P1 + P2, may be substantially twice that of P1 or P2 due to the additional lens effect of the combination of L1 / HWP1 1704 and L2 / HWP2 1708. However, embodiments are not limited in this way, and the first and second refractive powers P1 and P2 may have different magnitudes.

[0264] In the illustrated embodiment, the incident light beam 1720 has an LHCP, but it should be understood that similar results would also be obtained when the incident light beam 1720 has an RHCP. That is, when the light beam 1720 has an RHCP, unlike in the illustrated embodiment, the resulting light beam 1732B has an LHCP and is focused by L1 / HWP1 1704 and L2 / HWP2 1708 according to a net refractive power Pnet having a magnitude that is approximately the sum of the magnitudes of the first and second refractive powers P1 and P2.

[0265] Regarding Figure 17C, L1 / HWP1 1704 and L2 / HWP2 are described above. It should be understood that the lens effect of 1708 and its dependence on the polarization state of the incident light beam serve only as one embodiment, and other configurations are also possible. For example, in Figure 17B, L1 / HWP1 1704 and L2 / HWP2 1708 are configured to diverge light with LHCP while converging light with RHCP, but in other embodiments, L1 / HWP1 1704 and L2 / HWP2 1708 may be configured, conversely, to diverge light with LHCP while converging light with RHCP.

[0266] As a result, in some embodiments, when the switchable half-wave plate 1712B of the adaptive lens assembly 1700B is in the deactivation state, the emitted light beam 1732B may have an opposite HCP to the incident light beam 1720 and diverge according to the additional refractive powers P1 of L1 / HWP1 1704 and P2 of L2 / HWP2 1708. Consequently, when the user views virtual content, the virtual content is focused into the eye 210 according to the net refractive power, the value of which is approximately Pnet = P1 + P2.

[0267] The above describes the case where the adaptive lens assembly 1700B in the deactivated state is configured as the second adaptive lens assembly 1008 on the user side in the display device 1100A as described above with respect to Figure 11A. However, as described above with respect to Figure 11B, activating the second adaptive lens assembly 1008 and displaying virtual content to the user's eye 210 without any compensatory effect may result in a focus shift or distortion of the real-world view, which is undesirable. Therefore, it may be desirable to configure the first adaptive lens assembly 1004 on the world side to, at least partially, compensate for or disable the lens effect of the second adaptive lens assembly 1008 when deactivated to display virtual content.

[0268] Referring back to Figure 17C, when the first adaptive lens assembly 1004 (Figure 11B) on the world side is configured to neutralize the lens effect of the second adaptive lens assembly 1008 (Figure 11B) on the user side, the components of the adaptive lens assembly 1700B may be configured similarly as described above with respect to Figure 11B. That is, as light transmitted from the world 510 to the eye 210 passes through the first and second adaptive lens assemblies 1004 and 1008, they may be configured as described above with respect to the adaptive lens assembly 1700B as described with respect to Figure 17C. During operation, as described above, the polarization of the light transmitted from the world through the first adaptive lens assembly 1004 is converted from a first polarization state to a second polarization state, e.g., from RHCP to LHCP. Subsequently, the polarization of the light transmitted through the second adaptive lens assembly 1008 is converted inversely from the second polarization state to the first polarization state, e.g., from LHCP to RHCP. Furthermore, as explained above with respect to Figure 11B, light transmitted from the world through the first adaptive lens assembly 1004 undergoes a first lens effect, e.g., a converging effect, according to a first net refractive power Pnet1 = P1 + P2, which has a first sign, e.g., a positive sign. Subsequently, light transmitted through the second adaptive lens assembly 1008 undergoes a second lens effect, e.g., a diverging effect, which is the opposite of the first lens effect, according to a second net refractive power Pnet2 = P1' + P2', which has a second sign, e.g., a negative sign, because the light incident on the second adaptive lens assembly 1008 has opposite polarization to the light incident on the first adaptive lens assembly 1004. When Pnet1 and Pnet2 have substantially similar magnitudes, the overall lens effect, approximated by P = Pnet1 + Pnet2, can be substantially zero. As a result, when a user views virtual content and real objects in the surrounding world by activating the second lens assembly 1008, the view of the world is relatively unaffected by the compensatory effect of the first lens assembly 1004.

[0269] In various embodiments, when deactivated, the first and second adaptive lens assemblies 1004 and 1008 may provide a net refractive power (positive or negative) within the ranges of approximately ±5.0 diopters to 0 diopters, ±4.0 diopters to 0 diopters, ±3.0 diopters to 0 diopters, ±2.0 diopters to 0 diopters, and ±1.0 diopters to 0 diopters (including any range defined by these values, e.g., ±1.5 diopters). (A display device including an adaptive lens assembly having a switchable half-wave plate and a waveplate lens)

[0270] In the following, embodiments of the display device described above with respect to Figures 10, 11A, and 11B are described, in which an adaptive lens assembly comprising a waveplate lens and a switchable waveplate, for example, an adaptive lens assembly 1300 described above with respect to Figures 17A-17C, is integrated according to several embodiments. The switchable waveplate may be, for example, one of the broadband switchable waveplates described above with respect to Figures 13A-13F, 14A-14C, and 15A-15B.

[0271] Figures 18A and 18B illustrate exemplary display devices 1800A / 1800B, each including a waveguide assembly 1012 interposed between a first broadband adaptive waveguide lens assembly 1004 and a second broadband adaptive waveguide lens assembly 1008. Display device 1800A is similar to display devices 1100A / 1100B described above with respect to Figures 11A / 11B, and the first and second adaptive lens assemblies 1004, 1008 each comprise a first waveplate lens (L1 / HWP1) 1704, e.g., a first half-waveplate lens, a second waveplate lens (L2 / HWP2) 1708, e.g., a second half-waveplate lens, and a switchable waveplate (HWP3) 1712, e.g., a switchable half-waveplate.

[0272] Referring to Figure 18A, the display device 1800A is described as being activated when both the first and second adaptive lens assemblies 1004, 1008, as described above with respect to Figure 17A, are activated during operation. The first and second adaptive lens assemblies 1004, 1008 may also be activated when the switchable waveplate 1712 (Figure 17A) is activated, for example, when no current or voltage is applied to the switchable waveplate 1712 by the switching circuits 1816, 1816'. The display device 1800A may be configured, for example, to display a real-world view to the user without displaying a virtual image. For example, the display device 1800A may be configured to be used as ordinary eyeglasses or ordinary goggles, as described in detail with respect to Figure 17B. Similar to Figure 17A, the first and second adaptive lens assemblies 1004, 1008 each include a first waveplate lens (L1 / HWP1) 1804, e.g., a first half-waveplate lens, a second waveplate lens (L2 / HWP2) 1808, e.g., a second half-waveplate lens, and a switchable waveplate (HWP3) 1812, e.g., a switchable half-waveplate. As described with respect to Figure 17A, L1 / HWP1 1804 and L2 / HWP2 1808 may each be configured to exert a first lensing effect, e.g., a divergent effect, on a first HCP, e.g., light having an LHCP passing through it. In addition, L1 / HWP1 1804 and L2 / HWP2 1808 may also be configured to exert a second lensing effect opposite to the first lensing effect, such as a focusing effect, on light having an opposite HCP, such as an RHCP passing through it. When deactivated, for example, electrically deactivated using a voltage or current signal provided by switching circuits 1816, 1816', HWP3 1712B (Figure 17C) acts as a waveplate, such as a half-waveplate.As described above with respect to Figure 17C, when deactivated, HWP3 1712B (Figure 17C) acts as a half-wave plate, configured to convert the light passing through it from light having LHCP or RHCP to light having RHCP or LHCP. On the other hand, when activated, for example using a voltage or current signal provided by switching circuits 1816, 1816', and when electrically activated, for example by removing a voltage or current signal, HWP3 1712A (Figure 17B) acts as a light-transmitting medium without affecting polarization. The detailed operating principles of the first and second adaptive lens assemblies 1004, 1008, including L1 / HWP1 1804, L2 / HWP2 1808, and HWP3, 1812A, are provided above with respect to Figures 17A and 17B and are therefore omitted here.

[0273] Based on the operating principle described in detail with respect to Figures 17B and 17C, when the first and second adaptive lens assemblies 1004 and 1008 are in the activated state, the light beams (e.g., 1732A in Figure 17B) emanating from each of the first and second adaptive lens assemblies 1004 and 1008 have the same HCP as the incident light beam (e.g., 1720 in Figure 17B). In addition, the incident light beam 1720 and the outgoing light beam 1732A can be substantially matched in terms of the magnitude of the lens refractive power to compensate for the net refractive power of the first and second lens assemblies 1004 and 1008, as described above with respect to Figure 13B.

[0274] Figure 18B illustrates an embodiment of the display device of Figure 18A in which the switchable waveplates are deactivated during operation, according to several embodiments. The first and second adaptive lens assemblies 1004, 1008 activate individual switchable waveplates 1712 (Figure 17A) by applying current or voltage to the switchable waveplates 1712, for example, using switching circuits 1816, 1816'. The operation of the display device 1800B, which outputs a virtual image to the user while transmitting light from objects in the real world, with distortion resulting from the lens effects of the adaptive lens assemblies 1004, 1008 reduced or essentially eliminated.

[0275] When displaying a virtual image, as described above with respect to Figures 11A and 17C, some of the light propagating in the waveguide within the waveguide assembly 1012 in the x-direction may be redirected or externally coupled in the z-direction. The light beam 1720 propagates, for example, in the positive z-direction until the light beam 1720 collides with the L1 / HWP 1804 of the second adaptive lens assembly 1008. Based on the operating principle of the second adaptive lens assembly 1008 as described above with respect to Figure 17C, in the deactivated state, the second adaptive lens assembly 1008 has an outgoing light beam (e.g., 1732B in Figure 17C) opposite the incident light beam (e.g., 1720 in Figure 17C) and diverges according to a second net refractive power Pnet2 to display the virtual content on the corresponding virtual depth plane.

[0276] In various embodiments, when deactivated, the first and second adaptive lens assemblies 1004, 1008 may provide net refractive power (positive or negative) within the ranges of approximately ±5.0 diopters to 0 diopters, ±4.0 diopters to 0 diopters, ±3.0 diopters to 0 diopters, ±2.0 diopters to 0 diopters, and ±1.0 diopters to 0 diopters (including any range defined by these values, e.g., ±1.5 diopters). In some embodiments, the first adaptive lens assembly 1004 between the waveguide assembly 1012 and the world may have positive refractive power, while the second adaptive lens assembly 1008 between the waveguide assembly 1012 and the user may have negative refractive power, so that the refractive powers of the first and second switchable assemblies 1004, 1008 compensate for each other when viewing the world.

[0277] As a result, still referring to Figures 18A and 18B, the display device 1800A / 1800B comprises a pair of adaptive lens assemblies 1004, 1008 in the optical path between the world 510 and the eye 210, each of which comprises a switchable waveplate (e.g., 1712A / 1712B in Figures 17A / 17B) configured to alter the polarization state of light passing through it when electrically deactivated. When electrically deactivated, the pair of adaptive lens assemblies have net refractive powers (Pnet1, Pnet2) with opposite signs such that light passing through the pair of adaptive lens assemblies converges or diverges according to a combined refractive power having a magnitude approximately the difference between the magnitudes of the refractive powers of the pair of adaptive lens assemblies. Virtual content can be negative, and can be observed by the user in a certain depth plane according to Pnet2, while the view of the world is relatively, at least partially, positive, compensated by Pnet1, and unaffected by Pnet2.

[0278] In some embodiments, each pair of adaptive lens assemblies has individual net refractive powers (Pnet1, Pnet2) that are electrically adjustable or tuned to one of several values ​​using switching circuits 1816, 1816'. As described above, as the image of a virtual object produced by light externally coupled by waveguide assembly 1012 moves in 3D, the second net refractive power (Pnet2) of the second adaptive lens assembly 1008 on the user side is adjusted to conform to the changing depth of the virtual depth plane. Simultaneously, according to embodiments, the first net refractive power (Pnet1) of the first adaptive lens assembly 1004 is also adjusted accordingly using switching circuits 1816, 1816' so that the real-world view is not undesirably out of focus or distorted. To address this and other needs, in some embodiments, the display device 1800A / 1800B includes a controller 1804 configured such that when the first net refractive power (Pnet1) of the first of a pair of adaptive lens assemblies 1004, 1008 is electrically adjusted, the second refractive power (Pnet2) of the second of the pair of adaptive lens assemblies is adjusted in correspondence, such that the combined refractive power (Pnet1 + Pnet2) remains substantially constant, for example, about zero. The controller circuit and the switchable waveplate 1812 are configured, as described herein, to switch between first and second net refractive powers Pnet, Pnet2, to adjust the virtual depth plane using the second adaptive lens assembly 1008, and to compensate for the real-world view using the first adaptive lens assembly 1004, such that the time is less than about 100 milliseconds, less than about 50 milliseconds, approximately less than 10 milliseconds, less than about 5 milliseconds, less than 1 millisecond, or within the range defined by any of these values. (Broadband switchable waveplate lens)

[0279] As described above, according to various embodiments, a broadband adaptive waveplate lens assembly can generate images in multiple depth planes by selectively switching between multiple states having different refractive powers. In some embodiments described above, the broadband capability of the broadband adaptive waveplate lens assembly can be enabled by one or more broadband passive waveplate lenses (e.g., 1154A in Figure 12A) coupled with a broadband switchable waveplate (e.g., 1158 in Figure 12A). In some other embodiments, the broadband capability of the broadband adaptive waveplate lens assembly can be enabled by a broadband switchable waveplate lens without a broadband switchable waveplate (e.g., 1154B in Figure 12B). Below, the structure and configuration of the liquid crystal layer of the broadband switchable waveplate lens and the broadband adaptive lens assembly having it will be described according to embodiments.

[0280] Figure 19A illustrates plan views of broadband waveplate lenses 1900 comprising layers of LC molecules formed on a transparent substrate, according to various embodiments. The elongation direction of the bottommost LC molecules or the LC molecules closest to the substrate and / or the spatial distribution of local LC molecule orientors resulting therefrom can be dispersed according to the arrow pattern depicted in Figure 19A. In the illustrated embodiments, the LC molecules closest to the substrate at a given radius from the central region generally have the same elongation direction.

[0281] In some embodiments, the waveplate lens 1900 is a polarizing Fresnel zone plate (FZP) lens having a radially symmetric and radially modulated birefringence profile. In some embodiments, the elongation orientation or local oriented element of the LC molecules may vary as a function of radius according to a mathematical function. In the illustrated embodiments, the azimuthal angle φ of the local oriented element of the LC molecules may have discrete values ​​in different zones located at different radii from the center of the waveplate lens 1900. For example, φ in the m-th zone may be expressed as follows: [ka] In the formula, f is the focal length and r is the distance from the center of the waveplate lens 1900.

[0282] In some other embodiments, the elongation direction of the LC molecules or the spatial distribution of local orientors or the resulting local birefringence may be similar to those described above with respect to Figures 16A and 16B.

[0283] In some embodiments, the local orientation direction of LC molecules above the bottommost LC molecule, for example, the elongation direction, may generally be the same as that of the bottommost LC molecule closest to the substrate. In some other embodiments, the local orientation direction of LC molecules above the bottommost LC molecule may generally differ from that of the bottommost LC molecule closest to the substrate. For example, the local orientation direction of LC molecules above the bottommost LC molecule may be continuously twisted, as described below (e.g., Figures 20A, 20B).

[0284] During operation, in a manner similar to the waveplate lenses described above with respect to Figures 16A and 16B, the broadband waveplate lens 1900 has a polarization-selective lensing effect, functioning as a convex (or positive) lens (Figure 19B) for incident light 1162B having a first polarization, e.g., right-handed circularly polarized light (RHCP), while functioning as a concave (or negative) lens (Figure 19C) for incident light 1162A having a second polarization, e.g., left-handed circularly polarized light (LHCP). In addition, the broadband waveplate lens 1900 converts the polarization of the diffracted light. That is, incident light 1162B having RHCP is converted by the broadband waveplate lens 1900 to light 1166A having LHCP, as shown in Figure 19B, while incident light 1162A having LHCP is converted by the waveplate lens 1900 to light 1166B having RHCP, as shown in Figure 19C. The relative proportion of undiffracted leaked light 1904 determines the diffraction efficiency, as explained above.

[0285] The inventors have found that further improvements in the high bandwidth capability of waveplate lenses can be achieved, in particular, by arranging the twisted arrangement of LC molecules vertically within one or more LC layers (e.g., Figures 20A, 20B), or by employing negatively dispersed LC materials (Figure 21), which can further reduce undiffractioned leaked light 1904 and increase diffraction efficiency, which in turn further reduces undesirable visual effects such as afterimages, as described below.

[0286] Figures 20A and 20B schematically illustrate plan and cross-sectional views of a broadband waveplate lens 2000 comprising multiple LC layers of a crystal according to an embodiment. The illustrated broadband waveplate lens 2000 comprises a stack of two LC layers 2004, 2008, each having LC molecules with opposite torsional orientations, such that the light delay caused by one of the LC layers 2004, 2008 is compensated by the other LC layer 2004, 2008. For illustrative purposes only, Figures 20A and 20B depict the relative orientation of the LC molecules, which schematically varies laterally in a particular manner. However, it should be understood that the lateral arrangement of LC molecules across the xy plane at a given depth in the z direction can also have any of the various arrangements described above, including those illustrated above with respect to Figures 16A and 16B and Figure 19A. For example, in some embodiments, the LC molecules closest to the substrate generally have the same local orientation direction, e.g., a local extension direction or local orienter at a given radius from the central region, and / or an orientation direction that varies as a function of radius, similar to that described above with respect to Figure 19A. In addition, the arrangement of LC molecules in a given columnar region within two LC layers 2004, 2008 can be represented as having a nematic orienter n, which varies as a function of the vertical location within the LC layer, according to the following: [ka] In the formula, φ is the azimuthal angle of the orientor n in the xz plane. That is, with respect to a given row of LC molecules having a first orientation of twist in one of the LC layers 2004, 2008, the corresponding row of LC molecules in the other LC layer 2004, 2008 has the opposite orientation of twist. In other words, the LC molecules in the two LC layers 2004, 2008 are mirror images of each other with respect to the interface between the two LC layers 2004, 2008.

[0287] According to the embodiment, a reactive mesogen can be used to create an arrangement of LC molecules within two LC layers 2004, 2008. For example, by suitably configuring a matching layer 1302-0 on the substrate 1312, the bottommost LC molecules in the first LC layer 2004 closest to the matching layer 1302-0 can be arranged to have a first azimuthal angle.

[0288] The first azimuthal angle can be defined according to the alignment of the LC molecules in the extensional direction, for example, as described above with respect to any one of Figures 16A, 16B, and 19A. In addition, the LC molecules above the bottommost LC molecules in the first LC layer 2004 can be configured to have a first twist by adding a chiral agent to the first LC layer 2004 such that the topmost LC molecules closest to the surface of the first LC layer 2004 have a second azimuthal angle. Subsequently, by suitably configuring the surface region of the first LC layer 2004, the bottommost LC molecules in the second LC layer 2008 closest to the first LC layer 2004 can be aligned to have a second azimuthal angle. In addition, the LC molecules above the bottommost LC molecule in the second LC layer 2008 can be configured to have a second chiral torsion by adding a chiral agent to the second LC layer 2008 such that the topmost LC molecule closest to the surface of the second LC layer 2008 has a third azimuthal angle. In some embodiments, the first and second chiral torsions are substantially identical such that the bottommost LC molecule of the first LC layer 2004 and the topmost LC molecule of the second LC layer 2008 have the same first azimuthal angle.

[0289] In one exemplary configuration, by configuring the LC layers 2004 and 2008 to have a suitable thickness, for example, about 1 μm to 2 μm or about 1.5 μm to 2 μm, for example, about 1.7 μm, and a suitable chiral twist of about 50 to 90 degrees or about 60 to 80 degrees, for example, about 70 degrees, the diffraction efficiency wavelength range can be greater than 99%, with a relative bandwidth Δλ / λ greater than 40%, 50%, or 60%, for example, about 56%. o However, this can be achieved according to the embodiments.

[0290] As explained above, the diffraction efficiency (η) is given by η = sin 2 It can be expressed as (πΔnd / λ), where Δn is the birefringence, λ is the wavelength, and d is the thickness. Generally, optically anisotropic materials exhibit a Δn that decreases with increasing λ (referred herein to as the positive dispersion of Δn). However, the positive dispersion of Δn results in different phase delays Γ = 2πΔnd / λ at different λ. The inventors recognize that by employing an optically anisotropic material that exhibits a Δn that increases with increasing λ (referred herein to as the negative dispersion of Δn), the phase delay Γ can be kept relatively constant at different λ, according to the embodiment, and the diffraction efficiency η can be kept relatively high and relatively constant over a relatively wide wavelength range.

[0291] Figure 21 illustrates a cross-sectional view of a broadband waveplate lens 2100 according to an embodiment, comprising a negative dispersion (ND) liquid crystal (LC) layer 2104 formed on a substrate 1312 and a matching layer 1312-0. Similar to the broadband waveplate lenses described above with respect to Figures 19A and 20A / 20B, the ND LC layer 2104 can be arranged, for example, by suitably arranging the matching layer 1312-0 such that the waveplate lens 2100 has birefringence (Δn) that varies radially from the central region. In addition, in some embodiments, the bottommost LC molecules closest to the substrate 1312 can be arranged, for example, using the matching layer 1312-0, which is suitably configured as discussed elsewhere herein, in a manner similar to that described above with respect to Figures 16A, 16B, and 19A, generally having the same orientation direction at a given radius from the central region and generally having an orientation direction that varies as a function of radius.

[0292] In various embodiments, the negative dispersion (ND) liquid crystal (LC) layer 2104 may have an average, local, mean, median, maximum, or minimum birefringence (Δn) within a range defined by 0.05-0.10, 0.15-0.20, 0.20-0.25, 0.25-0.30, 0.30-0.35, 0.35-0.40, 0.40-0.45, 0.45-0.50, 0.50-0.55, 0.55-0.60, 0.60-0.65, 0.65-0.70, or any of these values. In addition, the negative dispersion (ND) liquid crystal (LC) layer 2104 may have an intralayer birefringence (Δn) in the range of 0.01-0.05, 0.05-0.10, 0.15-0.20, 0.20-0.25, 0.25-0.30, 0.30-0.35, 0.35-0.40, or within the range defined by any of these values.

[0293] Still referring to Figure 21, unlike the LC molecules described above with respect to Figures 20A and 20B, the ND LC layer 2104 may be vertically homogeneous. For example, in the ND LC layer 2104, the LC crystals formed above the bottommost LC molecules may not be twisted. Instead, in some embodiments, within a given columnar region, the local orientors n may be substantially constant across the thickness of the ND LC layer 2104. In some other embodiments, within a given columnar region, the local orientors n may be substantially random across the thickness of the LC layer 2104.

[0294] According to various embodiments, the ND LC layer 2104 may be formed from a material, such as a reactive mesogen, having material properties that increase with increasing wavelength (λ) within at least a portion of the visible spectrum between 400 and 800 nm, including one or more of the wavelength ranges defined by the red spectrum including wavelengths in the range of about 620 to 780 nm, the green spectrum including wavelengths in the range of about 492 to 577 nm, and the blue spectrum in the range of about 435 to 493 nm, or one or more of the wavelength ranges defined by any wavelength in the visible spectrum between 400 and 800 nm, for example, 400 to 700 nm, 430 to 650 nm, or 450 to 630 nm. In some embodiments, within any of these wavelength ranges, the NC LC layer 2104 has a normal refractive index n o Smaller anomalous refractive index n than that of e It has a variance of .

[0295] In some embodiments, the ND LC layer 2104 includes a smectic liquid crystal (LC), such as a smectic LC polymer synthetic material.

[0296] Advantageously, in some embodiments, the broadband waveplate lens 2100 has a single ND LC layer 2104 having birefringence, unlike the broadband waveplate lens 2000 described above with respect to Figures 20A and B, which has multiple layers, for example.

[0297] In various embodiments of broadband waveplate lenses described above with respect to Figures 16A, 16B, 19A, 20A / 20B, and 21, the LC layer can be configured to be passive or switchable according to the embodiment. When configured as a passive lens, the layer of LC molecules can be formed from polymerized LC (LCP), while when configured as a switchable lens, the layer of LC molecules can be formed from unpolymerized LC molecules or reactive mesogens. When configured as a switchable lens, the waveplate lenses described above with respect to Figures 16A, 16B, 19A, 20A / 20B, and 21 further include transparent electrodes on both sides (e.g., Figure 14C) or on the same side (e.g., Figure 15A / 15B) of the layer of LC molecules, in a manner similar to that described above with respect to the various embodiments described above.

[0298] Figures 22A–22C illustrate a switchable broadband waveplate lens 2200, which may, in operation, be similar to any of the broadband waveplate lenses described above with respect to Figures 16A, 16B, 19A, 20A / 20B, and 21. Figures 22A, 22B, and 22C illustrate a deactivated switchable broadband waveplate lens 2200 having an LHCP light beam incident thereon, a deactivated switchable broadband waveplate lens 2200 having an RHCP light beam incident thereon, and an activated switchable broadband waveplate lens 2200 having an LHCP light beam 1162A or an RHCP light beam 1162B incident thereon.

[0299] Referring to Figure 22A, the switchable broadband waveplate lens 2200 is arranged as described above with respect to Figures 16A, 16B, 19A, 20A / 20B, and 21 and comprises liquid crystals configured to be selectively switched between different lens states by electrically activating and deactivating. During operation, the switchable broadband waveplate lens 2200 is configured, according to various embodiments, to diverge the light according to the refractive power -P and to focus the light according to the refractive power P, depending on the polarization of the incident light 1162A, 1162B, for example, circular polarization.

[0300] Referring to Figure 22A, when deactivated, the switchable broadband waveplate lens 2200 is configured to diverge the LHCP light beam 1162A incident on it into the RHCP light beam 1166B according to the refractive power -P. Conversely, referring to Figure 22B, when deactivated, for example electrically, the switchable broadband waveplate lens 2200 is configured to converge the RHCP light beam 1162B incident on it into the LHCP light beam 1166A according to the refractive power P. On the other hand, referring to Figure 22C, when activated, for example electrically, the polarization of circularly polarized light passing through it is preserved (not shown), and the RHCP light beam 1162B and LHCP light beam 1162A incident on it pass through the switchable broadband waveplate lens 2200 without substantially converging or diverging (i.e., refractive power P about 0). (Broadband adaptive waveplate lens assembly with switchable waveplate lenses)

[0301] As described above with respect to Figures 22A-22C, a switchable broadband waveplate lens according to the embodiment can be configured to impart a refractive power P or -P depending on the polarization of the incident light when deactivated, while substantially unable to impart refractive power when activated. The inventors recognize that by combining two or more switchable broadband waveplate lenses, more lens states can be obtained to display virtual images at many different depths of focus. Below, a broadband adaptive lens assembly comprising multiple switchable broadband waveplate lenses is described, and by configuring the broadband waveplate lenses to have different refractive powers, 2 n Different refractive power states can be obtained with respect to incident light having a given polarization.

[0302] Figures 23A–23D illustrate a broadband adaptive lens assembly 2300 comprising a first switchable broadband waveplate lens 2204 and a second switchable broadband waveplate lens 2208, each capable of operating in a manner similar to the switchable waveplate lenses described above with respect to Figures 22A–22C. The switchable broadband waveplate lenses 2204 and 2208 may each be arranged in a manner similar to any of the broadband waveplate lenses described above with respect to Figures 16A, 16B, 19A, 20A / 20B, and 21. Figures 23A, 23B, 23C, and 23D illustrate the state combinations of the first switchable broadband waveplate lens 2304 / second switchable broadband waveplate lens 2308, respectively: deactivated / deactivated, deactivated / activated, activated / deactivated, and activated / activated.

[0303] In the illustrated embodiment, the first switchable broadband waveplate lens 2304 is configured in a similar manner to the broadband waveplate lens 2200 described above with respect to Figures 22A-22C. That is, when deactivated, the first switchable broadband waveplate lens 2304 is configured to diverge the LHCP light beam 1162A incident on it into the RHCP beam 1166B according to the refractive power -P1. In addition, although not shown, when deactivated, the first switchable broadband waveplate lens 2304 is configured to converge the RHCP light beam incident on it into the LHCP beam according to the refractive power +P1. On the other hand, when activated, the first switchable broadband waveplate lens 2304 is configured to substantially preserve the polarization of circularly polarized light passing through it without substantially converging or diverging (i.e., refractive power P1 about 0).

[0304] On the other hand, when deactivated, the second switchable broadband waveplate lens 2308 is configured to operate in the opposite manner to the broadband waveplate lens 2200 described above with respect to Figures 22A-22C, with respect to the sign of the applied refractive power. That is, when deactivated, the second switchable broadband waveplate lens 2308 is configured to focus the LHCP light beam 1162A incident on it into the RHCP beam 1166B according to the refractive power +P2. In addition, although not shown, when deactivated, the second switchable broadband waveplate lens 2308 is configured to diverge the RHCP light beam incident on it into the LHCP beam according to the refractive power -P2. On the other hand, when activated, the second switchable broadband waveplate lens 2308 is configured to substantially preserve the polarization of circularly polarized light passing through it without substantially focusing or diverging it (i.e., refractive power P2 about 0).

[0305] Referring to Figure 23A, the first switchable broadband waveplate lens 2304 is deactivated, diverting the LHCP light beam 1162A incident on it into the RHCP light beam 1166B according to the refractive power -P1. Subsequently, the second switchable broadband waveplate lens 2208 is deactivated, diverting the RHCP light beam 1166B incident on it into the LHCP light beam 1170A according to the refractive power -P2. In short, the LHCP light beam 1162A incident on the broadband adaptive lens assembly 2300 is diverted into the LHCP light beam 1170A according to a net refractive power of -(P1+P2).

[0306] Referring to Figure 23B, the first switchable broadband waveplate lens 2304 is deactivated, causing the LHCP light beam 1162A incident on it to diverge into the RHCP light beam 1166B according to the refractive power -P1. Subsequently, the second switchable broadband waveplate lens 2208 is activated, preserving the polarization of the RHCP light beam 1166B passing through it without substantially converging or further diverging. In short, the LHCP light beam 1162A incident on the broadband adaptive lens assembly 2300 is diverged into the RHCP light beam 1166BA according to the net refractive power of -P1.

[0307] Referring to Figure 23C, the first switchable broadband waveplate lens 2304 is activated and preserves the polarization of the LHCP light beam 1162A passing through it without substantially converging or diverging. Subsequently, the second switchable broadband waveplate lens 2308 is deactivated and focuses the LHCP light beam 1162A incident on it into the RHCP light beam 1170B according to the refractive power +P2. In short, the LHCP light beam 1162B incident on the broadband adaptive lens assembly 2300 is focused into the RHCP light beam 1170B according to the net refractive power of +P2.

[0308] Referring to Figure 23D, both the first and second switchable broadband waveplate lenses 2304 and 2308 are activated and preserve the polarization of the LHCP light beam 1162A passing through them without substantially converging or diverging. Thus, the LHCP light beam 1162A incident on the broadband adaptive lens assembly 2300 appears as the LHCP light beam 1162A, substantially unaffected.

[0309] In short, as illustrated in Figures 23A-23D, by selectively switching between the first and second switchable broadband waveplate lenses 2304 and 2308, the broadband adaptive lens assembly 2300 can have four different refractive power states, according to the embodiment: 0, -P1, +P2, and -(P1+P2).

[0310] In addition, although not shown, in a similar configuration, when the incident light is an RHCP light beam, the broadband adaptive lens assembly 2300 can have four different refractive power states, which will be 0, +P1, -P2, and +(P1+P2), by selectively switching the first and second switchable broadband waveplate lenses 2304, 2308.

[0311] In addition, although not shown, in some embodiments, the second switchable broadband waveplate lens 2308 can be configured to operate in the same manner as the first switchable broadband waveplate lens 2304 in terms of the sign dependence of the refractive power on the polarization of the incident light. In these embodiments, for example, when the incident light is an LHCP light beam, the resulting four different refractive power states would be 0, -P1, -P2, and -(P1-P2). In addition, if the second switchable broadband waveplate lens 2308 is configured to operate in the same manner as the first broadband waveplate lens 2304 in terms of the sign dependence of the refractive power on the polarization of the incident light when the incident light is an RHCP light beam, the resulting four different refractive power states would be 0, P1, P2, and (P1-P2).

[0312] In Figures 23A-23D, the illustrated broadband adaptive lens assembly 2300 is configured to achieve variable refractive power by independently switching the lenses themselves (e.g., the first and second switchable broadband waveplate lenses 2304, 2308). However, other embodiments are also possible in which one or both of the first and second switchable broadband waveplate lenses 2204, 2208 may be replaced by a combination of a passive waveplate lens and a switchable waveplate, similar to the combination of a passive waveplate lens 1154A and a switchable waveplate 1158 as described above with respect to Figure 12A.

[0313] Figure 24A illustrates an integrated broadband adaptive lens assembly 2400 comprising a switchable layer of LC molecules, similar to those described above with respect to Figures 19A, 20A / 20B, and 21, according to an embodiment. The integrated broadband adaptive lens assembly 2400 includes a switchable LC layer 2304, which can be similar to those described above with respect to Figures 19A, 20A / 20B, and 21, except that the switchable LC layer 2304 is interposed between a pair of passive waveplate lens stacks 2308, 2312. Similarly, as described above with respect to Figure 13F, the LC molecules are inserted into a gap formed between the surfaces of the passive waveplate lens stacks 2308, 2312, which face each other by a spacer 1350, the method of which is described elsewhere in this specification. The first passive waveplate lens stack 2308 includes a substrate 1312, on which a lower transparent electrode 1316 is formed, followed by a matching layer 2302 and a lower polymerized LC(LCP) layer 2302-1. Similarly, the second passive waveplate lens stack 2312 includes a substrate 1312, on which an upper transparent electrode 1320 is formed, followed by a matching layer 2302 and an upper polymerized LC(LCP) layer 2302-2.

[0314] The first and second passive waveplate lens stacks 2308 and 2312 each serve as matching layers for matching the waveplate lens and LC molecules within the switchable LC layer 2304. Similarly, as described above with respect to Figure 13F, the LC molecules of the lower LCP layer 2302-1 closest to the gap and the LC molecules of the upper LCP layer 2302-2 closest to the gap are arranged in a manner described above with respect to Figure 13C such that the outermost LC molecules of the switchable LC layer 2304 are self-aligned. However, embodiments are not limited thereto, and in some other embodiments, the outermost LC molecules of the switchable LC layer 2204 may be sufficiently aligned by matching layers 2302, 2302 such that one of the first and second LCP layers 2302-1 and 2302-2 is omitted.

[0315] Referring to Figure 24A and the various embodiments described throughout this specification, the switchable LC layers, for example, the switchable LC layer 2304 inserted into the gap, have thicknesses of approximately 1 μm to 50 μm, 1 to 10 μm, 10 to 20 μm, 20 to 30 μm, 30 to 40 μm, 40 to 50 μm, or any range defined by these values. In addition, the passive LC layers, for example, the LCP layers 2302-1, 2302-2, can have thicknesses of approximately 0.1 μm to 50 μm, 0.1 to 1 μm, 1 to 10 μm, 10 to 20 μm, 20 to 30 μm, 30 to 40 μm, 40 to 50 μm, or any range defined by these values.

[0316] In the illustrated embodiment, the LCP layers 2302-1 and 2302-2 may each have LC molecules with a net twist of 30-90 degrees, 40-80 degrees, 50-70 degrees, and, for example, about 60 degrees.

[0317] In some embodiments, the switchable LC layer 2304 may be a single layer, similar to the LC layer described above with respect to Figure 21. However, embodiments are not limited thereto. For example, the switchable LC layer 2204 may include multiple LC layers in a manner similar to that described above with respect to Figures 20A / 20B.

[0318] During operation, the integrated broadband adaptive lens assembly 2400, as described herein with respect to Figure 24A, may be similar to the switchable waveplate 1300F described above with respect to Figure 13F, sharing several properties. For example, in both embodiments, the switchable waveplate element (switchable TN LC layer 1302 in Figure 13F and switchable LC layer 2304 in Figure 24A) is interposed between a pair of passive waveplate elements (a plurality of TN LC layers 1302-1, 1302-2 and polymerized LC (LCP) layers 2302-1, 2302-2 in Figure 13F). In both embodiments, the switchable waveplate element is configured to change the polarization of light passing through it to orthogonal polarization. Similarly, in both embodiments, the passive waveplate element is also matched by separate matching layers such that when the switchable waveplate element is electrically activated and allows light to pass through it without diffraction, the passive waveplate element has a mutually canceling effect. On the other hand, when the switchable waveplate element is electrically deactivated and diffracts the light passing through it, the passive waveplate element has a complementary effect. In certain embodiments, when the passive waveplate element has the same refractive power and the switchable waveplate element is activated, the net refractive power of the assembly is approximately zero and the polarization of the light is not altered. On the other hand, when the switchable waveplate element is deactivated, the net refractive power of the assembly is the net sum of the refractive powers of the switchable and passive waveplate elements, which have different signs. Below, with reference to Figures 24B-24D, one particular embodiment is described in which the passive waveplate element is a half-waveplate lens and the switchable waveplate element is also a half-waveplate.

[0319] Figures 24B–24D illustrate the integrated broadband adaptive lens assembly 2400 in operation, which is similar to the adaptive lens assembly described above with respect to Figures 17A–17C, except that a switchable half-wave plate in the center is configured as a lens that imparts refractive power.

[0320] Figure 24B illustrates the integrated broadband adaptive lens assembly 2400, as described above with respect to Figure 24A, from the viewpoint of optical functionality. Figure 24C illustrates the integrated broadband adaptive lens assembly 2400A (Figure 24A) when the switchable waveplate lens 2304 of the adaptive lens assembly 2400 illustrated in Figure 24B is activated during operation, while Figure 24D illustrates the switchable assembly 2400B when the switchable waveplate lens 2304 of the integrated broadband adaptive lens assembly 2400 illustrated in Figure 24B is deactivated during operation. The integrated broadband adaptive lens assembly 2400 is configured to couple and transmit light externally coupled from the waveguide assembly 1012 (Figures 10, 11A, 11B) through it. The integrated broadband adaptive lens assembly 2400 comprises a first waveplate lens (L1 / HWP1) 2308 (Figure 24A) corresponding to the passive waveplate lens stack 2308, for example, a first half-waveplate lens; a second waveplate lens (L2 / HWP2) 2312 (Figure 24A) corresponding to the passive waveplate lens stack 2312, for example, a second half-waveplate lens; and a switchable half-waveplate (L3 / HWP3) 2304 (Figure 24A) corresponding to the switchable LC layer 2304.

[0321] In Figures 24B-24D, L3 / HWP2304B (Figure 24D), L1 / HWP1 2308, and L2 / HWP2 2312 in the deactivated state act as passive half-waveplate lenses, each configured to impart refractive powers P3, P1, and P2, respectively, and to convert the palmarity of the circularly polarized light passing through them from a first palmarity (first HCP) to a second palmarity (second HCP). On the other hand, L3 / HWP2304A (Figure 24C) in the activated state is configured to preserve the palmarity of the circularly polarized light passing through it.

[0322] In addition, when deactivated, for example using a voltage or current signal provided by the switching circuit 1716, L3 / HWP3 2304B (Figure 24D) functions as a half-wave plate lens with refractive power P3. On the other hand, when activated using the switching circuit 1716, for example by removing a voltage or current signal, L3 / HWP3 2304A (Figure 24C) functions as a light-transmitting medium without affecting polarization or providing any substantial lensing effect.

[0323] Figure 24C illustrates the integrated broadband adaptive lens assembly 2400B when L3 / HWP2304A is activated during operation. The integrated broadband adaptive lens assembly 2400B may correspond to a first adaptive lens assembly 1004 (Figure 10, world side) or a second adaptive lens assembly 1008 (Figure 10, user side). For example, the integrated broadband adaptive lens assembly 2400A may be described as corresponding to the first adaptive lens assembly 1004 or the second adaptive lens assembly 1008 as part of a display device 1000 (Figure 10) that displays a real-world view to the user without displaying a virtual image. For example, the display device 1000 (Figure 10) may be used as ordinary eyeglasses or ordinary goggles. L1 / HWP1 2308 and L2 / HWP2 2312 may each be configured to exert a first lensing effect, such as a divergent effect, on light having a first HCP, such as an LHCP, passing through it. Although not shown, L1 / HWP1 2308 and L2 / HWP2 2312 may also each be configured to exert a second lensing effect opposite to the first lensing effect, such as a converging effect, on light having an opposite HCP, such as an RHCP, passing through it.

[0324] In the illustrated embodiment, the light beam 1720 may represent a light beam from the world that is incident on either the first adaptive lens assembly 1004 (world side) or the second adaptive lens assembly 1008 (user side) while the display device 1000 (Figure 10) is used as ordinary glasses or goggles without displaying virtual content. For example, the light beam 1720 having a first HCP, e.g., an LHCP, travels in the positive z-direction until, for example, the beam 1720 passes through L1 / HWP2308, is transmitted through it, and is converted into a light beam 1724 having an RHCP, while the light beam 1720 diverges according to a first refractive force -P1.

[0325] Still referring to Figure 24C, L3 / HWP3 2304A is then activated, so that the light beam 1724 with RHCP is transmitted through L3 / HWP3 2304A substantially unaffected in terms of polarization or lensing effects and incident onto L2 / HWP2 2312 as the light beam 1728A with RHCP. As described above, when configured as an adaptive lens assembly on the user side (e.g., the second adaptive lens assembly 1004 in Figure 10), L2 / HWP2 2312 is configured to be similar to L1 / HWP1 1704 (Figure 17B), i.e., to change the polarization and diverge the light with LHCP while focusing the light with RHCP. Thus, the light beam 1728A with RHCP is inversely converted to the light beam 1732A with LHCP. Therefore, when L3 / HWP3 2304A is activated, L1 / HWP1 2308 and L2 / HWP2 2312 transmit a light beam having opposite polarization such that L1 / HWP1 2308 and L2 / HWP2 2312 exert an opposite lens effect on the light passing through them. That is, since the light beam 1728A incident on L2 / HWP2 2312 has RHCP, the light beam 1732A exiting L2 / HWP2 2312 diverges according to a first refractive power -P1, unlike the light beam 1724 exiting L1 / HWP1 1704, which is focused according to a second refractive power +P2. Subsequently, depending on the emission from the adaptive lens assembly 1700A in the activated state, the light beam 1732A can be seen by the eye.

[0326] In some embodiments, when L3 / HWP3 2304A is activated, the first refractive power -P1 of L1 / HWP1 2308 and the second refractive power +P2 of L2 / HWP2 2312 may have opposite signs but substantially identical or matching magnitudes. In these embodiments, the net refractive power Pnet of the integrated broadband adaptive lens assembly 2400, which may be about -P1+P2, may be substantially zero so as not to substantially affect the view of the world to the viewer. However, embodiments are not limited thereto, and the first and second refractive powers -P1, +P2 may have different magnitudes so that the net refractive power Pnet may have a non-zero value. For example, in some embodiments, the non-zero Pnet may be equal to the user's eyeglass prescription, thereby allowing correction of the user's eye focusing error (e.g., refractive focusing error).

[0327] In the illustrated embodiment, the incident light beam 1720 has an LHCP, but similar results would be obtained when the incident light beam 1720 has an RHCP. That is, when light beam 1720 has an RHCP, light beams 1724 and 1728A have an LHCP, and unlike the illustrated embodiment, light beams 1724 and 1728A are focused according to the refractive power +P1. Similarly, light beam 1728A diverges according to the refractive power -P2 such that the net refractive power Pnet can be +P1-P2, which may be substantially zero.

[0328] With respect to Figure 24C, the lensing effect of L1 / HWP1 2308 and L2 / HWP2 2312 and the selectivity of the lensing effect on the polarization state of the incident light beam, as described above, serve only as one embodiment, and it should be understood that other configurations are also possible. For example, in Figure 24C, L1 / HWP1 2408 and L2 / HWP2 2312 are configured to diverge light with LHCP while converging light with RHCP, but in other embodiments, L1 / HWP1 2308 and L2 / HWP2 2312 may be configured to converge light with LHCP while diverging light with RHCP.

[0329] In short, in some embodiments, when L3 / HWP3 2304A is activated, the outgoing light beam 1732A has the same HCP as the incident light beam 1720 and can be substantially matched to the incident light beam 1720 in terms of lens effect, in order to compensate for the lens effect between P1 of L1 / HWP1 2308 and P2 of L2 / HWP2 2312. As a result, when the user is not viewing virtual content, the view of the world is relatively unaffected by the presence of the adaptive lens assembly (1004, 1008 in Figures 10, 11A, 11B).

[0330] Figure 24D illustrates an embodiment of the adaptive lens assembly of Figure 24B when the L3 / HWP3 2304B is deactivated during operation. The integrated broadband adaptive lens assembly 2400B may correspond, for example, to a first adaptive lens assembly 1004 (world side) or a second adaptive lens assembly 1008 (user side). Hereinafter, as an example, the integrated broadband adaptive lens assembly 2400B will be described as being configured first as a second adaptive lens assembly 1008 on the user side, as part of a display device (e.g., display device 1100A in Figure 11A) that outputs a virtual image to the user. Next, the integrated broadband adaptive lens assembly 2400B will be described as being configured as the world-side first adaptive lens assembly 1004, as part of a display device 1100B (Figure 11B), which simultaneously outputs a virtual image to the user while transmitting a real-world view, and reduces or essentially eliminates distortion of the real-world view resulting from the lens effect of the second adaptive lens assembly 1008.

[0331] When configured as a second adaptive lens assembly 1008 on the user side (Figure 11A), L1 / HWP1 2308 and L2 / HWP2 2312 may each be configured to diverge light having one of the HCPs, for example, an LHCP passing through it. L1 / HWP1 2308 and L2 / HWP2 2312 may also each be configured to focus light having another HCP, for example, an RHCP passing through it.

[0332] With respect to Figure 11A, as described above, a portion of the light propagating in the waveguide assembly 1012 in the x-direction, for example by total internal reflection, may be redirected or externally coupled in the z-direction. The light externally coupled from the waveguide assembly 1012 (Figure 11A) may be incident on the integrated broadband adaptive lens assembly 2400B as a circularly polarized beam 1720 having LHCP. The light beam 1720 propagates in the positive z-direction until, for example, the light beam 1720 is transmitted through L1 / HWP 2308 and converted into a light beam 1724 having RHCP, while also diverging according to the first refractive power -P1 of L1 / HWP 2308.

[0333] Next, L3 / HWP3 2304B is deactivated, and the optical beam 1724 with RHCP, which is transmitted through L3 / HWP3 2304B, is converted to optical beam 1728B with LCHP, while also diverging or converging according to the third refractive power - / +P3. Subsequently, the optical beam 1728B with LHCP is converted to L2 / HWP2 The light beam 1728B is incident on L2 / HWP2 2312. Unlike the light beam 1728A illustrated above with respect to Figure 24C, the light beam 1728B incident on L2 / HWP2 2312 has LHCP, so L2 / HWP2 2312 further diverges the light beam 1728B to the light beam 1732B, which has RHCP, according to a second refractive power -P2. Thus, unlike the configuration illustrated with respect to Figure 24C, L1 / HWP1 2308, L2 / HWP2 2312, and L3 / HWP3 2304B in Figure 24D can have an additional lens effect. Subsequently, the light beam 1732A can be seen by the eye as it exits from the adaptive lens assembly 1700B in the deactivated state.

[0334] In some embodiments, the first refractive power -P1 of L1 / HWP1 2308 and the second refractive power -P2 of L2 / HWP2 2312 may both be negative (i.e., divergent) and may have substantially the same or matching magnitudes. In addition, L3 / HWP3 The third refractive power -P3 of 2304B may also be negative. In these embodiments, the net refractive power Pnet of the integrated broadband adaptive lens assembly 2400B may be approximately -(P1+P2+P3). However, embodiments are not limited in this way, and in some other embodiments, the third refractive power +P3 of L3 / HWP3 2304B may be positive. In these embodiments, the net refractive power Pnet of the integrated broadband adaptive lens assembly 2400B may be approximately -(P1+P2)+P3. In addition, the first and second refractive powers P1 and P2 may have different magnitudes.

[0335] In the illustrated embodiment, the incident light beam 1720 has an LHCP, but equivalent results would also be obtained when the incident light beam 1720 has an RHCP. That is, when the light beam 1720 has an RHCP, unlike in the illustrated embodiment, the resulting light beam 1732B has an LHCP and can be focused by L1 / HWP1 2308, L2 / HWP2 2312, and L3 / HWP3 2304B according to the net refractive power Pnet = +(P1 + P2 + P3).

[0336] With respect to Figure 24D, the lensing effects of L1 / HWP1 2308, L2 / HWP2 2312, and L3 / HWP2 304B described above, and the dependence of the lensing effects on the polarization state of the incident light beam, serve only as one embodiment, and other configurations are possible. For example, unlike the illustrated embodiment, L1 / HWP1 2308, L2 / HWP2 2312, and the deactivated L3 / HWP3 2304B may each be configured to focus light with LHCP while diverging light with RHCP.

[0337] The above describes the case where the integrated broadband adaptive lens assembly 2400B in the deactivated state is configured as the user-side second adaptive lens assembly 1008 in the display device 1100A as described above with respect to Figure 11A. However, as described above with respect to Figure 11B, activating the second adaptive lens assembly 1008 without any compensatory effect and displaying virtual content to the user's eye 210 may result in a focus shift or distortion of the real-world view, which is undesirable. Therefore, it may be desirable to configure the world-side first adaptive lens assembly 1004, when deactivated to display virtual content, to at least partially compensate for or disable the lens effect of the second adaptive lens assembly 1008.

[0338] Referring back to Figure 24D, when the first adaptive lens assembly 1004 (Figure 11B) on the world side is configured to neutralize the lens effect of the second adaptive lens assembly 1008 (Figure 11B) on the user side, the components of the adaptive lens assembly 1700B may be configured similarly as described above with respect to Figure 11B. That is, as light transmitted from the world 510 to the eye 210 passes through the first and second adaptive lens assemblies 1004 and 1008, they may be configured as described above with respect to the integrated broadband adaptive lens assembly 2400B described with respect to Figure 24D, respectively. During operation, as described above, the polarization of the light transmitted from the world through the first adaptive lens assembly 1004 is converted from a first polarization state to a second polarization state, e.g., from RHCP to LHCP. Subsequently, the polarization of the light transmitted through the second adaptive lens assembly 1008 is converted inversely from the second polarization state to the first polarization state, e.g., from LHCP to RHCP. Furthermore, as explained above with respect to Figure 11B, light transmitted from the world through the first adaptive lens assembly 1004 undergoes a first lens effect, e.g., a converging effect, according to a first net refractive power Pnet1=(P1+P2+P3) having a first sign, e.g., a positive sign. Subsequently, light transmitted through the second adaptive lens assembly 1008 undergoes a second lens effect, e.g., a diverging effect, opposite to the first lens effect, according to a second net refractive power Pnet2=-(P1'+P2'+P3') having a second sign, e.g., a negative sign, because the light incident on the second adaptive lens assembly 1008 has opposite polarization to the light incident on the first adaptive lens assembly 1004. When Pnet1 and Pnet2 have substantially similar magnitudes, the overall lens effect, approximated by P=Pnet1+Pnet2, can be substantially zero. As a result, when a user views virtual content and real objects in the surrounding world by activating the second lens assembly 1008, the view of the world is relatively unaffected by the compensatory effect of the first lens assembly 1004.

[0339] In various embodiments, when deactivated, the first and second adaptive lens assemblies 1004 and 1008 may provide a net refractive power (positive or negative) within the ranges of approximately ±5.0 diopters to 0 diopters, ±4.0 diopters to 0 diopters, ±3.0 diopters to 0 diopters, ±2.0 diopters to 0 diopters, and ±1.0 diopters to 0 diopters (including any range defined by these values, e.g., ±1.5 diopters).

[0340] Figures 25A and 25B are graphs 2500A and 2500B illustrating the transmission spectra corresponding to the integrated broadband adaptive lens assembly 2400 (Figures 24A and 24B) when the L3 / HWP3 2304 is deactivated (Figure 24C) and activated (Figure 24D), respectively. The simulation corresponds to an integrated broadband adaptive lens assembly 2400 in which L3 / HWP3 2304 is formed from an unpolymerized LC layer with a thickness of 10 μm (e.g., the switchable LC layer 2304 in Figure 23) and has a Δn of 0.2, while L1 / HWP1 2308 and L2 / HWP2 2312 are polymerized LC layers (e.g., the upper and lower polymerized LC(LCP) layers 2302-1 and 2303-2 in Figure 24A) formed from polymerized twisted LC molecules with a twist angle of 60 degrees. As shown in Graph 2500A, when L3 / HWP3 2304A is deactivated (Figure 24C), the diffraction efficiency is high, resulting in low leakage (maximum approximately 20%), indicating that the incident light is efficiently diffracted by the integrated broadband adaptive lens assembly 2400A with virtually no leakage through 400nm to 800nm. On the other hand, as shown in Graph 2500B, when L3 / HWP3 2304B is activated (Figure 24D), the diffraction efficiency is very high, indicating that most of the incident light is transmitted without diffraction (approximately 100%), and that most of the incident light is not diffracted by the integrated broadband adaptive lens assembly 2400A in the 400nm to 800nm ​​range. (Chromatic aberration reduction in broadband adaptive lens assemblies)

[0341] While some broadband adaptive lens assemblies exhibit high efficiency across a wide range of wavelengths, they may possess a focal length or refractive power that is substantially dependent on the wavelength of light, thereby leading to significant chromatic aberration. This is because, for relatively large focal lengths, the refractive power of the lens is proportional to the corresponding wavelength. That is, the dependence of the refractive power P(λ) of a waveplate lens at different wavelengths is given by P(λ). B )=P(λ G )λ B / λ G and P(λ R )=P(λ G )λ R / λ G It can be approximated as follows, where B, G, and R correspond to wavelengths in the blue spectrum, the green spectrum, and the red spectrum, respectively. Therefore, it is necessary to reduce chromatic aberration in broadband adaptive lens assemblies. Methods for reducing chromatic aberration are described below according to embodiments.

[0342] In the above, for example with respect to Figures 23A-23D, an embodiment of a broadband adaptive lens assembly having two switchable broadband waveplate lenses is disclosed, which has two with respect to circularly polarized light. 2 This leads to a refractive power state of =4. Furthermore, a stack is formed with more than two (N) switchable broadband waveplate lenses, and 2 N It is possible to have eight refractive power states. For example, with respect to a broadband adaptive lens assembly having three switchable broadband waveplate lenses (N=3), eight refractive power states can be achieved. Table 1 illustrates the calculated refractive powers of a broadband adaptive assembly having three switchable broadband waveplate lenses, each switchable broadband waveplate lens being similar to, for example, the switchable broadband waveplate lenses described above with respect to Figures 22A-22C. [Table 1]

[0343] Regarding a broadband adaptive assembly having three switchable broadband waveplate lenses, the net lens refractive power is P net =((S1 * P1+P2) * S2+P3) * It can be expressed as S3, where P i and S i =±1(i=1, 2, 3) represents the refractive power and refractive power state of the individual switchable broadband waveplate lenses. For example, the activated state may be represented as S=+1, while the deactivated state may be represented as S=-1. Referring to Table 1, the columns labeled State 1-State 8 correspond to the different lens states for each of the three lenses, and the blue, green, and red rows represent the calculated refractive powers for wavelengths of 450 nm, 525 nm, and 632 nm, representing the blue, green, and red colors of light, respectively. The calculations assume that only light with one polarization, e.g., the first circularly polarized light, reaches the eye, while the others are either reused or reflected. For illustrative purposes, the refractive powers of the three individual broadband waveplate lenses are calculated to be 0.5D, 0.5D, and 1.5D at the green wavelength (525 nm). Based on Table 1, it can be seen that lens states 3, 5, and 1 can be selected to obtain target net refractive powers of 0.5D, 1.5D, and 2.5D. However, it is observed that the net refractive power at blue and red wavelengths (450nm-632nm) can cause significant chromatic aberration, for example, 0.51D for a target net refractive power of 2.5D for red wavelengths.

[0344] However, the inventors recognize that chromatic aberration can be substantially reduced if, instead of using one state to achieve one target net refractive power for three colors, more than one state is used to achieve a given target net refractive power for different colors, as illustrated in Table 1. This approach is illustrated in Table 2. [Table 2]

[0345] Referring to Table 2, chromatic aberration can be substantially reduced by using one above state to achieve a given target net refractive power for different colors and slightly different target lens refractive powers. Here, the refractive powers of three individual broadband waveplate lenses are 0.4D, 0.7D, and 1.6D at the green wavelength (525nm). Based on Table 2, it can be seen that single lens state 3 can be selected to obtain a target net refractive power of 0.5D. However, to reduce chromatic aberration, states 5 and 7 can be selected for a target net refractive power of 1.5D, and states 1 and 5 can be selected for a target net refractive power of 2.5D. Compared to the chromatic aberration of 0.51D for a target net refractive power of 2.5D shown in Table 1, the chromatic aberration for a target net refractive power of 2.5D for the red wavelength can be reduced to 0.2 by using one above state for different colors.

[0346] Figures 26A, 26B, and 26C are graphs 2600A, 2600B, and 2600C illustrating the calculated target refractive power versus actual refractive power for blue, green, and red wavelengths, respectively, according to the embodiment, and illustrating the improved chromatic aberration performance achieved by using a method that uses different lens states for different color wavelengths to achieve the target refractive power. In graphs 2600A, 2600B, and 2600C, respectively, the solid black lines 2612, 2622, and 2632 represent the target net refractive power; the dotted lines 2604, 2614, and 2624 represent the calculated refractive power when a method is used to obtain a given refractive power using a single lens state, as described above with respect to Table 1; and the solid gray lines 2608, 2618, and 2628 represent the calculated refractive power when a method is used to obtain a given refractive power using multiple lens states, as described above with respect to Table 2. As observed, the actual refractive power is closer to the target refractive power when multiple lens states are used to obtain a given refractive power. (Processing of broadband waveplates and waveplate lenses using optical matching)

[0347] Figures 27A-27C illustrate exemplary methods for fabricating broadband waveplates or broadband waveplate lenses. Referring to intermediate structure 2700A in Figure 27A, a transparent substrate 1312 is provided on which a matching layer 1302-0 is formed. The transparent substrate 1312 may include, for example, silicon dioxide, sapphire, or any suitable transparent material. It should be understood that additional structures and layers, not shown but according to various embodiments described herein, may be present on the substrate 1312 leading to the formation of the matching layer 1302-0. For example, when forming a switchable waveplate 1300F (Figure 13F), a first transparent electrode layer 1316, 1320 may be present on the substrate 1312 prior to the step of forming the matching layer 1302-0.

[0348] In some embodiments, the matching layer 1302-0 can be an optical matching layer, on which LC molecules are deposited, and the LC molecules may be oriented along a preferred direction due to, for example, the anchoring energy imparted to the liquid crystal molecules by the optical matching layer. Examples of optical matching layers include, to name a few, polyimides, linearly polarizing polymerizable polymers (LPPs), azo-containing polymers, coumarin-containing polymers, and cinnamic acid-containing polymers, and other composites described above with respect to Figures 13C and 13F.

[0349] The matching layer 1302-0 may be formed by dissolving a precursor, such as a monomer, in a suitable solvent and coating the substrate 1312 with the solution using a suitable process, such as spin coating, slot coating, doctor blade coating, spray coating, and jet (inkjet) coating, among other deposition processes. The solvent can then be removed from the coated solution. The matching layer 1302-0 may also be cured, for example, using a polarizer, such as UV curing, in preparation for subsequent matching of LC molecules onto it.

[0350] Referring to the intermediate structure 2700B in Figure 27B, after coating with matching layer 1302-0, the matching layer 1302-0 is optically patterned or recorded. Optical patterning can be performed using a holographic two-beam exposure process (Figure 28) or an optical replication process using a master lens and a one-beam exposure process (Figures 29A, 29B).

[0351] Referring to intermediate structure 2700C or Figure 27C, after coating the matching layer 1302-0, the LC layer 2704 is formed thereon. The LC layer 2704 may be formed by depositing a reactive mesogen mixture (e.g., containing liquid crystal monomers, solvents, photoinitiators, and surfactants) on the matching layer 1302-0 using a preferred process, for example, including, among other deposition processes, spin coating, slot coating, doctor blade coating, spray coating, and inkjet coating.

[0352] When the LC layer 2704 is integrated as part of a passive waveplate lens or a switchable waveplate, the LC layer 2704 may be cured, for example, UV cured, and photopolymerized so that the LC molecules can be fixed and oriented as described above.

[0353] In contrast, when the LC layer 2704 is integrated as part of a switchable waveplate lens or a switchable waveplate, the LC layer 2704 may be further treated without polymerization so that the LC molecules can reorient themselves in response to a switching signal, as described above.

[0354] Depending on the deposition, at least the bottommost LC molecules of the liquid crystal (LC) layer 2704 directly above the matching layer 1302-0 may self-organize according to the configuration of the matching layer 1302-0, depending on the various applications described herein. For example, when the LC layer 2704 forms part of a broadband waveplate lens, the matching layer 1302-0 is configured such that the bottommost LC molecules have local orientations or aligners that vary along the radius of the LC layer 2704, radially outward from the central region, as described above, for example with respect to Figures 16A, 16B, and 19A. In addition, when the LC layer 2704 forms part of a broadband waveplate, the matching layer 1302-0 is configured such that the bottommost LC molecules have local orientations or aligners, such that their long axes are generally oriented in a first lateral direction, as described above, for example with respect to Figures 13A and 13C. Still referring to Figure 27C, in some embodiments, the LC layer 2704 may be configured such that the LC molecules above the bottommost LC molecule in the LC layer 2704 are arranged differently from the bottommost LC molecule in the LC layer 2704, as described elsewhere in this application. For example, the topmost LC molecules in the LC layer 2704 may be aligned differently from the second matching layer formed on the LC layer 2704. In addition, the LC molecules between the topmost and bottommost LC molecules may have torsion, as described with respect to various embodiments, including Figures 13C and 20A / 20B.

[0355] After depositing the LC layer 2704, the intermediate structure 2700C may optionally be further processed after polymerization to form additional structures and / or layers, as described in the various embodiments described herein. For example, when forming a switchable waveplate 1300F (Figure 13F), after forming the LC layer 2704, the intermediate structure 2700C may be further processed to form, for example, a second matching layer 1302-0 on top of the LC layer 2704 and the second transparent electrode layers 1316, 1320. In addition, in some embodiments, the additional LC layer may be formed on the LC layer 2704, and the bottommost LC molecules of the subsequent LC layer match the topmost LC molecules of the previous LC layer, as described in Figures 13F and 24A.

[0356] Figure 28 illustrates an exemplary method for constructing a matching layer, as described above with respect to Figure 27C, to match LC molecules within a broadband waveplate or broadband waveplate lens using a two-beam exposure process, sometimes also referred to as polarization holography. While most conventional holography uses intensity modulation, polarization holography involves modulation of polarization states as a result of the interference of light with different polarizations. Referring to the intermediate structure 2800 in Figure 28, the illustrated method includes the step of forming an unpolymerized optical matching layer 1302-0 on a substrate 1312, as described above with respect to Figure 27A. Thereafter, multiple coherent light beams having different polarizations, e.g., an RHCP light beam 2808 and an LHCP light beam 2804, are directed onto the matching layer 1302-2. In the illustrated embodiment, the RHCP light beam 2808 and the LHCP light beam 2804 are orthogonal circularly polarized beams. One of the RHCP light beam 2808 and LHCP light beam 2804, which may be the recording beam, can converge or diverge, while the other of the RHCP light beam 2808 and LHCP light beam 2804, which may be the reference beam, can collimate. However, embodiments are not so limited. For example, the orthogonal polarized beams can include linear vertically polarized and linear horizontally polarized beams or linearly polarized beams at ±45 degrees. In some implementations, two-beam exposure to the polarized hologram of matching layer 1302-0 may be performed using a UV laser with orthogonal circular polarization (e.g., HeCd, 325 nm). A typical recording dose is about several J·cm, depending on the liquid crystal material and lattice parameters (e.g., thickness d). -2 This is possible. Subsequently, a reactive mesogen mixture (e.g., comprising a liquid crystal monomer, solvent, photoinitiator, and surfactant) is coated to match the surface pattern formed by the two-beam exposure, as described above with respect to Figures 27A-27C.

[0357] Figures 29A-29B illustrate an exemplary method for constructing a matching layer for matching liquid crystal molecules within a broadband waveplate or broadband waveplate lens by fabricating a master waveplate or waveplate lens having a master matching pattern of LC molecules, and replicating the master matching pattern of LC molecules onto a target matching layer. Unlike the two-beam exposure method described above with respect to Figure 28, in which the interference of two orthogonal polarized beams is employed to directly construct the matching layer, in the illustrated embodiment, the master waveplate lens and a beam of one polarization are used to create a similar polarized hologram in the near field of view. Thus, once the master lens has a master matching pattern of LC molecules, it can be used as a template for fabricating multiple waveplates and waveplate lenses using a relatively simple one-beam exposure.

[0358] Figure 29A illustrates a master waveplate or waveplate lens 2904. The master waveplate or waveplate lens 2904 may be fabricated using a process described above with respect to Figures 27A-27C and 28, for example, which involves forming a matching layer using an optical interference pattern formed by a two-beam exposure process, then forming a reactive mesogen (RM) mixture layer (e.g., comprising liquid crystal monomers, solvents, photoinitiators, and surfactants) that self-matches with the matching layer, and then blanket UV curing of the RM mixture layer to polymerize the LC molecules in the RM mixture layer. Figure 29A further illustrates a working diagram 2900A of the master waveplate or waveplate lens 2904, which is designed to have a limited diffraction efficiency such that only a portion of the polarized incident light is diffracted while a portion is allowed to pass through unaffected. For example, in the illustrated embodiment, the master waveplate or waveplate lens 2904 is configured to diffract a portion of the incident light 2908 having a first polarization, e.g., RHCP (e.g., 30-70%, 40-60%, 45-55%, or any value within these ranges, e.g., about 50%) into diffracted light 2912 having a second polarization, e.g., LHCP, while allowing a portion of the incident light 2908 (e.g., 30-70%, 40-60%, 45-55%, or any value within these ranges, e.g., about 50%) to pass through the master lens 2904 without being diffracted as zero-order leaked light having the same first polarization, e.g., RHCP as the incident light beam 2908.

[0359] Figure 29B illustrates an exemplary fabricated configuration 2900B of a master lens 2904, fabricated and configured as described above with respect to Figure 29A, and an intermediate structure comprising a matching layer 1302-0 for matching LC molecules within a broadband waveplate or broadband waveplate lens. Referring to the fabricated configuration 2900B of Figure 29B, the illustrated intermediate structure includes an unpolymerized optical matching layer 1302-0 on a substrate 1312, as described above with respect to Figure 27A. The fabricated configuration 2900B includes a master lens 2904 positioned across the unpolymerized optical matching layer 1302-0. An incident light beam 2908 having a first polarization, e.g., RHCP, is directed towards the matching layer 1302-2. As described above with respect to Figure 29A, the master waveplate or waveplate lens is designed to diffract only a portion of the incident light, so that two light beams with opposite polarizations are incident on the matching layer 1302-0 as they pass through the master waveplate or waveplate lens 2904. In effect, the two light beams incident on the matching layer 1302-0 perform an effect similar to the two-beam exposure described above with respect to Figures 28A and 28B. In the illustrated embodiment, the light beams transmitted through the master waveplate or waveplate lens 2904 and incident on the matching layer 1302-0 are a diffracted light beam 2912 having a first polarization, e.g., RHCP, of the incident light beam 2908 and a second polarization, e.g., LHCP, opposite to that of the incident light beam 2908, and a leaked light beam 2916 having the same first polarization, e.g., RHCP, as the incident light beam 2908. Therefore, in a manner similar to that described above with respect to Figure 28, the diffracted light beam 2912 can converge or diverge and serve as a recording beam, while the leaked light beam 2916 can serve as a reference beam. The interference of the diffracted light beam 2912 and the leaked light beam 2915 produces a matching layer 1302-0 in a manner similar to that described above with respect to Figure 20. Subsequently, a reactive mesogen mixture (e.g., comprising a liquid crystal monomer, a solvent, a photoinitiator, and a surfactant) may be coated to match the surface pattern formed by the two-beam exposure, as described above with respect to Figures 27A-27C.Therefore, advantageously, once the master lens 2904 is fabricated using the relatively complex two-beam exposure method described above with respect to Figure 28, the subsequent configuration of the matching layer is carried out using a relatively simple one-beam exposure, as described above with respect to Figure 29B. Advantageously, under certain circumstances, the method illustrated with respect to Figure 29B can be carried out using a fully coherent light source, such as a laser, or a partially coherent light source, such as a UV lamp or light-emitting diode, with less precise optics, less vibration control, and looser matching compared to the two-beam exposure method described above with respect to Figures 28A-28B. (Processing of broadband waveplates and waveplate lenses using nanoimprint matching layers)

[0360] As described throughout this application, in various embodiments, LC molecules in the LC layer for broadband waveplates and waveplate lenses can be matched using a matching layer, for example, an optical matching layer which may be constructed using light. In other embodiments, LC molecules can be matched using patterned nanostructures. Hereinafter, a method for matching LC molecules using patterned nanostructures is described with respect to Figures 30A and 30B, and then an example of a patterned nanostructure suitable for serving as a waveplate lens is described with respect to Figure 30C.

[0361] Figures 30A and 30B illustrate cross-sectional views of intermediate structures 3000A and 3000B at different processing stages using a nanoimprint process according to several embodiments, respectively.

[0362] Referring to the intermediate structure 3000A in Figure 30A, the transparent substrate 1312 is provided in a manner similar to those described above with respect to various embodiments. A nanoimprint template (not shown) or nanoimprint mold having a predetermined topology pattern, configured to form a matched pattern of LC molecules in the subsequently formed LC layer 2704 (Figure 30B), for example, at least the lowest LC molecules in the LC layer 2704 closest to the substrate 1312, is brought into contact with a blanket base polymer layer (not shown). The template is then pressed into the blanket base polymer layer, which may contain a polymer that is thermoplastic at a temperature above the glass transition temperature of the blanket base polymer layer, for example, thereby transferring the pattern of the template into the softened blanket base polymer layer and forming an imprinted matched layer 3004. After cooling, the template is separated from the imprinted matched layer 3004, which has a matched pattern having a predetermined topology pattern, configured to form a matched pattern of LC molecules in the subsequently formed LC layer 2704 (Figure 30B). In another approach, the imprinted matching layer 3004, after being injected into the base polymer layer, is solidified by crosslinking under UV light.

[0363] The imprinted matching layer 3004 may include features of sub-wavelength dimensions. For example, the imprinted matching layer 3004 may include features having dimensions (e.g., length, width, and / or depth) of about a few nanometers, several hundred nanometers, and / or a few microns. In another embodiment, the imprinted matching layer 3004 may include features having a length greater than or equal to about 20 nm to less than or equal to about 100 nm. In yet another embodiment, the imprinted matching layer 3004 may include features having a width greater than or equal to about 20 nm to less than or equal to about 100 nm. In yet another embodiment, the imprinted matching layer 3004 may include features having a depth greater than or equal to about 10 nm to less than or equal to about 100 nm. In various embodiments, the length and / or width of the features may exceed the depth of the features. However, in some embodiments, the depth may be approximately equal to the length and / or width of the features. The features of each domain in the imprinted matching layer 3004 can be arranged to form a complex geometric pattern within each domain, where the direction and / or period between consecutive features vary along length scales of approximately a few nanometers, several hundred nanometers, and / or several microns.

[0364] An exemplary nanoimprinting process was described for forming a nanoimprinted matching layer 3004 as shown in Figure 30A, but embodiments are not limited thereto. In other embodiments, the imprinted matching layer 3004 may be fabricated using other patterning techniques, including lithography and etching. In addition, although the imprinted matching layer 3004 was described as being formed from a polymer material, embodiments are not limited thereto, and in various other embodiments, the imprinted matching layer 3004 may include a dielectric material, such as silicon or glass material.

[0365] Referring to the intermediate structure 3000B in Figure 30B, after the formation of the matching layer 3004, an unpolymerized LC layer 2704, for example, a layer of reactive mesogen, is deposited thereon according to the deposition process described above with respect to Figures 27A-27C. Although not bound by any theory, the imprinted matching layer 3004 acts as a matching layer, matching the LC molecules within the LC layer 2704 according to the pattern of the imprinted matching layer 3004. For example, the extension direction of LC molecules within a domain can generally be aligned parallel to the local extension direction of nanostructures within the imprinted matching layer 3004. Although not bound by any theory, the alignment of LC molecules to the pattern of the imprinted matching layer 3004 may be due to steric interactions with liquid crystal molecules and / or the anchoring energy imparted to the LC molecules deposited by the imprinted matching layer 3004.

[0366] Still referring to the intermediate structure 3000B in Figure 30B, the LC layer 2704 may be further processed according to different embodiments, including steps of polymerization, further aligning LC molecules on top of the bottommost LC molecules, and stacking multiple LC layers, as described above with respect to Figures 27A-27C.

[0367] Figure 30C shows a plan view of a nanoimprinted matching layer 3004 fabricated according to the method described above with respect to Figures 30A-30B. The imprinted matching layer 3004 serves as a matching layer and can form layers of LC molecules having various lateral arrangements as described herein, including, for example, the arrangements described above with respect to Figures 13A, 13C, 16A, 16B, 19A, 40, and 41, among other arrangements.

[0368] When the LC layer arising from the imprinted matching layer 3004 forms part of a waveplate lens, according to various embodiments, the imprinted matching layer 3004 comprises, for example, multiple zones in the xy plane such as concentric zones 3008-1, 3008-2, ..., 3008-n. The imprinted nanostructures within each zone of the imprinted matching layer 3004 are oriented along a specific orientation. The orientation of liquid crystal material molecules within adjacent zones may differ. For example, the extension direction or local orientation of LC molecules within various zones 3008-1, 3008-2, ..., 3008-n is such that the radius r from the center is different. n It can be continuously rotated radially according to a function that depends on the refractive force, where n can vary from about 1 to 3, for example, as described with respect to Figures 16A / 16B and 19.

[0369] The imprinted nanostructures and the resulting liquid crystal molecules may have different elongation directions within different zones 3008-1, 3008-2, ..., 3008-n. For example, the elongation directions of imprinted nanostructures within a continuous zone may be rotated clockwise by an angle of about 18 degrees relative to each other. However, embodiments are not limited in this way, and the relative rotation angles between continuous zones may be 1 degree, about 1 to 45 degrees, about 1 to 18 degrees, or about 18 to less than 45 degrees. (Integration of broadband adaptive lens assemblies with broadband waveplates and / or waveplate lenses)

[0370] According to the various embodiments described above, for example, a broadband adaptive lens assembly includes an integrated waveplate and a waveplate lens. Below, a method for integrating the waveplate and waveplate lens is described according to embodiments. Figures 31A-31C illustrate an exemplary method for fabricating a switchable broadband waveplate or a switchable broadband waveplate lens having liquid crystal using a gap-filling process. According to various embodiments, the method includes the steps of providing a lower stack including a first electrode layer on a first substrate and a first matching layer formed on the first electrode layer, and providing an upper stack including a second electrode layer on a second substrate and a second matching layer formed on the second electrode layer. The first and second stacks are then stacked in a single stack such that the first and second matching layers face each other, a spacer is formed between the lower and upper stacks, creating a gap between them, which is subsequently filled with liquid LC layer material.

[0371] Referring to Figure 31A, the method includes the steps of providing a substrate 1312 in a manner similar to that described above, for example, with respect to Figure 27A, and then forming a first electrode layer 1320, for example, a transparent electrode layer, on the substrate 1312 in a manner similar to that described above, for example, with respect to Figure 27A. Then, referring to Figure 31B, a first matching layer 1302-0 is formed on the substrate 1312, thereby forming a lower stack 3100A. The matching layer 1302-2 can be, for example, an optical matching layer similar to that described above with respect to Figures 27A-27C, 28, and 29, or an imprinted matching layer similar to that described above with respect to Figures 30A-30C.

[0372] Referring to Figure 31C, an upper stack 3100B comprising a second substrate 1312 is formed in a manner similar to that of forming the lower stack 3100A, and thereon a first electrode layer 1320, for example, a transparent electrode layer, and a second matching layer 1302-0 are formed in a manner similar to that described above with respect to the step of forming the lower stack 3100A, as described above with respect to Figure 31B.

[0373] In some embodiments, the first and second matching layers 1302-0, which may be optically matching layers or imprinted matching layers, may be configured differently, as described above with respect to various embodiments, such that the LC molecules directly adjacent to the first and second matching layers 1302-0 are matched in different ways, for example, so that the extension directions or orientation directions of the LC molecules intersect each other, for example, at about 90 degrees.

[0374] Still referring to Figure 31C, the upper and lower stacks 3100B, 3100A are subsequently stacked in a single stack such that the first and second matching layers 1302-0 face each other, with a gap 1302 formed between them. The gap 1302 may be formed by a spacer 1350 formed between the lower and upper stacks 3100A, 3100B.

[0375] The spacer 1350 may be formed from a suitable material, such as silica beads, having a diameter for producing a gap, the distance of which defines the target thickness of the LC material subsequently inserted. In some implementations, the spacer 1350 in the form of silica beads can be dispersed across one or both surfaces of the upper and lower stacks 3100B, 3100A using a drying process. In other implementations, the spacer 1350 in the form of silica beads can be mixed with an adhesive and applied to the edges of one or both surfaces of the upper and lower stacks 3100B, 3100A. The upper and lower stacks 3100B, 3100A are then pressed against each other until a final gap distance corresponding to the resulting thickness of the LC layer is obtained. The gap distance can be monitored using interference fringes of a Fabry-Perot interferometer.

[0376] After forming the gap 1302, the LC material is inserted into the gap 1302. The inserted LC material can be a reactive mesogen mixture containing, for example, a liquid crystal monomer, a solvent, a photoinitiator, and a surfactant, as described above. The LC material may be inserted into the ...

Claims

1. An optical element, wherein the optical element is A substrate extending along a horizontal direction, wherein the substrate has a normal vector directed perpendicular to the horizontal direction, The first vertically aligned layer, The second horizontal matching layer, A liquid crystal layer comprising liquid crystal molecules, wherein the liquid crystal molecules are aligned with a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, the first vertically aligned layer such that the liquid crystal molecules are oriented more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer such that the liquid crystal molecules are oriented more horizontally than in the case without the second horizontally aligned layer. Equipped with, The angle depends on the relative strength of the first vertically matched layer and the second horizontally matched layer. The first vertically aligned layer and the second horizontally aligned layer are optical elements arranged to cover the substrate.

2. An optical element, wherein the optical element is A substrate extending along a horizontal direction, wherein the substrate has a normal vector directed perpendicular to the horizontal direction, The first vertically aligned layer, The second horizontal matching layer, A liquid crystal layer comprising liquid crystal molecules, wherein the liquid crystal molecules are aligned with a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, the first vertically aligned layer such that the liquid crystal molecules are oriented more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer such that the liquid crystal molecules are oriented more horizontally than in the case without the second horizontally aligned layer. Equipped with, The optical element comprising a second horizontally aligned layer having a first region and a second region, wherein the first region is configured such that the liquid crystal molecules are more horizontal than those in the second region.

3. An optical element, wherein the optical element is A substrate extending along a horizontal direction, wherein the substrate has a normal vector directed perpendicular to the horizontal direction, The first vertically aligned layer, The second horizontal matching layer, A liquid crystal layer comprising liquid crystal molecules, wherein the liquid crystal molecules are aligned with a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, the first vertically aligned layer such that the liquid crystal molecules are oriented more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer such that the liquid crystal molecules are oriented more horizontally than in the case without the second horizontally aligned layer. Equipped with, The optical element comprises a region configured such that the oblique angle is not made more horizontal, wherein the second horizontal matching layer is configured to prevent the angle from becoming more horizontal.

4. An optical element, wherein the optical element is A substrate extending along a horizontal direction, wherein the substrate has a normal vector directed perpendicular to the horizontal direction, The first vertically aligned layer, The second horizontal matching layer, A liquid crystal layer comprising liquid crystal molecules, wherein the liquid crystal molecules are aligned with a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, the first vertically aligned layer such that the liquid crystal molecules are oriented more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer such that the liquid crystal molecules are oriented more horizontally than in the case without the second horizontally aligned layer. Equipped with, An optical element comprising a second horizontal matching layer, the second horizontal matching layer having at least one region configured to prevent the angle from becoming more horizontal, which is located between two regions of the second horizontal matching layer configured to make the angle more horizontal.

5. An optical element, wherein the optical element is A substrate extending along a horizontal direction, wherein the substrate has a normal vector directed perpendicular to the horizontal direction, The first vertically aligned layer, The second horizontal matching layer, A liquid crystal layer comprising liquid crystal molecules, wherein the liquid crystal molecules are aligned with a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, the first vertically aligned layer such that the liquid crystal molecules are oriented more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer such that the liquid crystal molecules are oriented more horizontally than in the case without the second horizontally aligned layer. Equipped with, The first vertically aligned layer has a first region and a second region, wherein the first region is configured such that the liquid crystal molecules are more perpendicular to the second region. An optical element wherein the first region and the second region of the first vertically aligned layer have different thicknesses such that the liquid crystal molecules closer to the first region are more perpendicular than the liquid crystal molecules closer to the second region.

6. An optical element, wherein the optical element is A substrate extending along a horizontal direction, wherein the substrate has a normal vector directed perpendicular to the horizontal direction, The first vertically aligned layer, The second horizontal matching layer, A liquid crystal layer comprising liquid crystal molecules, wherein the liquid crystal molecules are aligned with a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, the first vertically aligned layer such that the liquid crystal molecules are oriented more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer such that the liquid crystal molecules are oriented more horizontally than in the case without the second horizontally aligned layer. Equipped with, The optical element comprises a region in which the first vertical matching layer is configured to prevent the oblique angle from becoming more vertical.

7. An optical element, wherein the optical element is A substrate extending along a horizontal direction, wherein the substrate has a normal vector directed perpendicular to the horizontal direction, The first vertically aligned layer, The second horizontal matching layer, A liquid crystal layer comprising liquid crystal molecules, wherein the liquid crystal molecules are aligned with a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, the first vertically aligned layer such that the liquid crystal molecules are oriented more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer such that the liquid crystal molecules are oriented more horizontally than in the case without the second horizontally aligned layer. Equipped with, An optical element wherein the first vertical matching layer comprises at least one region configured to prevent the angle from becoming more vertical, located between two regions of the first vertical matching layer configured to make the angle more vertical.

8. An optical element, wherein the optical element is A substrate extending along a horizontal direction, wherein the substrate has a normal vector directed perpendicular to the horizontal direction, The first vertically aligned layer, The second horizontal matching layer, A liquid crystal layer comprising liquid crystal molecules, wherein the liquid crystal molecules are aligned with a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, the first vertically aligned layer such that the liquid crystal molecules are oriented more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer such that the liquid crystal molecules are oriented more horizontally than in the case without the second horizontally aligned layer. Equipped with, The optical element comprises a waveplate, The first vertically aligned layer and the second horizontally aligned layer are optical elements arranged to cover the substrate.

9. An optical element, wherein the optical element is A substrate extending along a horizontal direction, wherein the substrate has a normal vector directed perpendicular to the horizontal direction, The first vertically aligned layer, The second horizontal matching layer, A liquid crystal layer comprising liquid crystal molecules, wherein the liquid crystal molecules are aligned with a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, the first vertically aligned layer such that the liquid crystal molecules are oriented more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer such that the liquid crystal molecules are oriented more horizontally than in the case without the second horizontally aligned layer. Equipped with, The optical element comprises a switchable waveplate, The first vertically aligned layer and the second horizontally aligned layer are optical elements arranged to cover the substrate.

10. An optical element, wherein the optical element is A substrate extending along a horizontal direction, wherein the substrate has a normal vector directed perpendicular to the horizontal direction, The first vertically aligned layer, The second horizontal matching layer, A liquid crystal layer comprising liquid crystal molecules, wherein the liquid crystal molecules are aligned with a first vertically aligned layer and a second horizontally aligned layer such that the liquid crystal molecules are oriented at a certain oblique angle with respect to the vertical and horizontal directions, the first vertically aligned layer such that the liquid crystal molecules are oriented more vertically than in the case without the first vertically aligned layer, and the second horizontally aligned layer such that the liquid crystal molecules are oriented more horizontally than in the case without the second horizontally aligned layer. Equipped with, The optical element comprises a waveplate lens, The first vertically aligned layer and the second horizontally aligned layer are optical elements arranged to cover the substrate.

11. The optical element according to claim 2, wherein the first region and the second region of the second horizontally aligned layer have features, and the features in the first region have a larger size than the features in the second region such that the liquid crystal molecules closer to the first region are more horizontal than the liquid crystal molecules closer to the second region.

12. The optical element according to claim 2 or 11, wherein the first region and the second region of the second horizontally matched layer are characterized, and the characteristic in the first region has a greater height than the characteristic in the second region such that the liquid crystal molecules closer to the first region are more horizontal than the liquid crystal molecules closer to the second region.

13. The optical element according to any one of claims 2, 11 to 12, wherein the first region and the second region of the second horizontally aligned layer are characterized, and the characteristic within the first region is wider than the characteristic within the second region such that the liquid crystal molecules closer to the first region are more horizontal than the liquid crystal molecules closer to the second region.

14. The optical element according to any one of claims 2, 11 to 13, wherein the first region and the second region of the second horizontally aligned layer are characterized, and the characteristics in the first region have a higher pitch than the characteristics in the second region such that the liquid crystal molecules closer to the first region are more horizontal than the liquid crystal molecules closer to the second region.

15. The optical element according to any one of claims 2, 11 to 14, wherein the first region and the second region of the second horizontally matched layer are characterized, and the features in the first region have a higher duty cycle than the features in the second region such that the liquid crystal molecules closer to the first region are more horizontal than the liquid crystal molecules closer to the second region.

16. The optical element according to any one of claims 2, 11 to 15, wherein the first region and the second region of the second horizontally aligned layer are characterized, and the characteristic in the first region has a different profile from the characteristic in the second region so that the liquid crystal molecules more proximal to the first region are more horizontal than the liquid crystal molecules more proximal to the second region.

17. The optical element according to any one of claims 2, 11 to 16, wherein the first region and the second region of the second horizontally aligned layer are characterized, and the features in the first region have a different aspect ratio from the features in the second region so that the liquid crystal molecules more proximal to the first region are more horizontal than the liquid crystal molecules more proximal to the second region.

18. The optical element according to any one of claims 1 to 4, 6 to 17, wherein the first vertically aligned layer has a first region and a second region, the first region is configured such that the liquid crystal molecules are more perpendicular to the second region.

19. The optical element according to any one of claims 1 to 18, wherein the first vertically aligned layer is configured such that liquid crystal molecules proximal to the first vertically aligned layer are oriented along the vertical direction rather than the horizontal direction.

20. The optical element according to any one of claims 1 to 19, wherein the second horizontally aligned layer is configured such that liquid crystal molecules proximal to the second horizontally aligned layer are oriented along the horizontal direction rather than the vertical direction.

21. The optical element according to any one of claims 1 to 20, wherein the second horizontal matching layer comprises a patterned layer.

22. The optical element according to claim 21, wherein the patterned layer comprises an imprint layer.

23. The optical element according to claim 22, wherein the imprint layer comprises a nanoimprint layer.

24. The optical element according to any one of claims 2 to 7, 11 to 23, except as made by reference of any one of claims 1, 8 to 10, wherein the first vertically aligned layer and the second horizontally aligned layer are arranged to cover the substrate.

25. The optical element according to any one of claims 1 to 24, wherein the first vertically aligned layer is disposed between the second horizontally aligned layer and the substrate.

26. The optical element according to any one of claims 1 to 25, wherein the second horizontally aligned layer is disposed between the first vertically aligned layer and the liquid crystal layer.

27. The aforementioned optical element is The third vertically aligned layer, The fourth horizontal matching layer and Furthermore, The optical element according to any one of claims 1 to 26, wherein the first vertically aligned layer is configured such that the liquid crystal layer is oriented more vertically than when the third vertically aligned layer is absent, and the fourth horizontally aligned layer is configured such that the liquid crystal molecules are more horizontal than when the fourth horizontally aligned layer is absent.

28. The liquid crystal layer is positioned between the first vertically aligned layer and the third vertically aligned layer. The optical element according to claim 27.

29. The optical element according to claim 27 or 28, wherein the liquid crystal layer is disposed between the second horizontally aligned layer and the fourth horizontally aligned layer.

30. The optical element according to any one of claims 1 to 29, wherein the angle of inclination is 0° to 90° with respect to the horizontal direction.

31. The optical element according to any one of claims 1 to 29, wherein the angle of obliqueness with respect to most of the liquid crystal molecules in the liquid crystal layer is 5° to 85° with respect to the horizontal direction.

32. The optical element according to any one of claims 1 to 31, wherein the oblique angle with respect to most of the liquid crystal molecules in the liquid crystal layer is 5° to 45° with respect to the horizontal direction.

33. The optical element according to any one of claims 1 to 32, further comprising forming an electrode configured to apply an electrical signal to the liquid crystal layer.

Images