Liquid crystal diffraction device with nanoscale patterns and method for fabricating same

Abstract

To provide liquid crystal diffractive devices with optimal nano-scale pattern and methods for manufacturing the liquid crystal diffractive devices.SOLUTION: The present disclosure relates to an optical device including virtual reality, augmented reality imaging and a visualization system. The optical device includes a liquid crystal layer having a first plurality of liquid crystal molecules arranged in a first pattern and a second plurality of liquid crystal molecules arranged in a second pattern. The first pattern and the second pattern are separated from each other by a distance of about 20 nm to about 100 nm along a longitudinal or a transverse axis of the liquid crystal layer. The first plurality of liquid crystal molecules and the second plurality of liquid crystal molecules are configured as a first grating structure and a second grating structure that can redirect light of visible or infrared wavelengths.SELECTED DRAWING: Figure 11A

Description

[Technical Field]

[0001] (Priority Claim) This application claims the benefit of priority to U.S. Application No. 15 / 795,067, filed October 26, 2017, and U.S. Provisional Patent Application No. 62 / 424,341, filed November 18, 2016, both of which are incorporated herein by reference in their entireties.

[0002] (Incorporated by reference) This application incorporates by reference the entirety of each of the following applications: U.S. Application No. 14 / 555,585, filed November 27, 2014; U.S. Application No. 14 / 690,401, filed April 18, 2015; U.S. Application No. 14 / 212,961, filed March 14, 2014; U.S. Application No. 14 / 331,218, filed July 14, 2014; and U.S. Application No. 15 / 072,290, filed March 16, 2016.

[0003] The present disclosure relates to optical devices, including virtual reality and augmented reality imaging and visualization systems. [Background technology]

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

[0005] Referring to Figure 1, an augmented reality scene 10 is depicted in which a user of the AR technology sees a real-world park-like setting 20 featuring people, trees, a building in the background, and a concrete platform 30. In addition to these items, the user of the AR technology also perceives that they are "seeing" "virtual content," such as a robotic figure 40 standing on the real-world platform 30 and a flying, cartoon-like avatar character 50 that appears to be an anthropomorphic bumblebee, although these elements 40, 50 do not exist in the real world. The human visual perception system is complex, making it difficult to produce AR technology that facilitates a comfortable, natural-feeling, and rich presentation of virtual image elements among other virtual or real-world image elements.

[0006] The systems and methods disclosed herein address various challenges associated with AR and VR technologies. Summary of the Invention [Means for solving the problem]

[0007] The systems, methods, and devices of the present disclosure each have several innovative aspects, no single one of which is responsible for the desirable attributes disclosed herein.

[0008] An innovative aspect of the present subject matter is embodied in an optical device comprising a liquid crystal layer having a first major surface, a second major surface, and a thickness, where the first and second major surfaces extend across a lateral direction and the thickness extends along a direction parallel to a surface normal to the first or second major surface. The liquid crystal layer comprises a plurality of sublayers dispersed across the thickness of the liquid crystal layer, each of the plurality of sublayers comprising a single layer of liquid crystal molecules, each having a longitudinal axis. Each sublayer comprises a first domain, in which the longitudinal axes of the plurality of liquid crystal molecules are arranged to form a first pattern, and a second domain, in which the longitudinal axes of the plurality of liquid crystal molecules are arranged to form a second pattern. The first domain is laterally separated from the second domain along the lateral direction by a domain gap having a distance D of about 10 nm to about 50 nm. The longitudinal axes of the liquid crystal molecules within the domain gap gradually transition from the first pattern to the second pattern.

[0009] In various embodiments of the device, the longitudinal axes of the molecules of the first domain of a sublayer can be twisted relative to the longitudinal axes of the molecules of the first domain of an adjacent sublayer. A second liquid crystal layer may be provided, and the liquid crystal molecules of the second liquid crystal layer may be configured to self-align in a first direction and a second direction within the first and second domains, respectively; 。The liquid crystal layer or the second liquid crystal layer can comprise a polymerizable liquid crystal material. Various embodiments of the device can further comprise a third liquid crystal layer over the second liquid crystal layer, where the plurality of liquid crystal molecules of the third liquid crystal can be aligned along a third direction. Various embodiments of the device can further comprise a fourth liquid crystal layer over the third liquid crystal layer, where the plurality of liquid crystals of the fourth liquid crystal layer can be configured to self-align in the third direction. In various embodiments, the second liquid crystal layer and / or the fourth liquid crystal layer can be disposed over a waveguide. The second liquid crystal layer and / or the fourth liquid crystal layer can comprise an incoupling optical element configured to incoupling an incident beam of light into the waveguide such that the incident beam of light propagates through the waveguide by total internal reflection. Various embodiments of the device can comprise a light modulation device configured to direct light into the waveguide via the incoupling optical element. The second liquid crystal layer and / or the fourth liquid crystal layer can comprise an outcoupling optical element configured to outcoupling the incident beam of light propagating through the waveguide by total internal reflection.

[0010] In various embodiments, the second liquid crystal layer and / or the fourth liquid crystal layer can comprise an orthogonal pupil expander configured to redirect light propagating through the waveguide by total internal reflection, and the redirected light continues to propagate through the waveguide by total internal reflection. In various embodiments of the device, the liquid crystal layer can comprise an internal coupling optical element configured to internally couple an incident beam of light into the waveguide so that the incident beam of light propagates through the waveguide by total internal reflection. In various embodiments of the device, the liquid crystal layer can comprise an external coupling optical element configured to externally couple a beam of light propagating through the waveguide by total internal reflection. The longitudinal axes of the plurality of liquid crystal molecules in the first domain can be aligned along a first direction, and the longitudinal axes of the plurality of liquid crystal molecules in the second domain can be aligned along a second direction. The longitudinal axes of the liquid crystal molecules in the domain gaps can gradually transition from the first direction to the second direction.

[0011] Another innovative aspect of the present subject matter includes a method for fabricating an optical device, the method including providing a polymerizable liquid crystal layer over a substrate, patterning the polymerizable liquid crystal layer, and depositing a liquid crystal layer onto the patterned polymerizable liquid crystal layer. Molecules of the deposited liquid crystal layer are self-aligned to the patterned polymerizable liquid crystal layer. Patterning the polymerizable liquid crystal layer includes imprinting the polymerizable liquid crystal layer with an imprint template having first domains comprising a first plurality of features and second domains comprising a second plurality of features, the first domains being separated from the second domains by feature-free regions, the feature-free regions having dimensions ranging from about 20 nm to about 100 nm. The dimensions can include at least one of length or width. The width of the first plurality of features can be between about 20 nm and about 100 nm. The width of the second plurality of features can be between about 20 nm and about 100 nm. The distance between the centers of two consecutive features of the first plurality of features can be about 20 nm or more and about 100 nm or less. The height of the first plurality of features can be about 10 nm or more and about 100 nm or less. The distance between the centers of two consecutive features of the second plurality of features can be about 20 nm or more and about 100 nm or less. The height of the second plurality of features can be about 10 nm or more and about 100 nm or less.

[0012] The first plurality of features of the first domain can be arranged to form a first pattern, and the second plurality of features of the second domain can be arranged to form a second pattern. The first pattern can be distinct from the second pattern. The first plurality of features can be oriented along a first direction, and the second plurality of features of the second domain can be arranged along a second direction. directionThe first direction can be distinctly different from the second direction. The first plurality of features can comprise at least one of linear grooves, curved grooves, linear facets, or curved facets. The second plurality of features can comprise at least one of linear grooves, curved grooves, linear facets, or curved facets. The imprint template can comprise a semiconductor material. In various embodiments, the imprint template can be fabricated using at least one of optical lithography, nanoimprint, or ion and electron beam lithography.

[0013] Another innovative aspect of the present subject matter is encompassed in a method for fabricating a liquid crystal device. The method includes depositing a layer of liquid crystal material on a substrate and imprinting the pattern onto the layer of liquid crystal material using an imprint template comprising a pattern, such that the molecules of the liquid crystal material self-align with the pattern. The pattern includes a first domain having a first plurality of features arranged to form a first pattern, and a second domain having a second plurality of features arranged to form a second pattern. The first domain is separated from the second domain by a feature-free region. At least one of the width or length of the feature-free region is between about 20 nm and about 100 nm.

[0014] In various embodiments, the method further includes depositing a layer of material having a refractive index lower than that of the liquid crystal material. The layer of low refractive index material can be configured as a planarization layer using a planarization template. The first plurality of features or the second plurality of features can include surface relief features. At least one of the length, width, or height of the first plurality of features or the second plurality of features can be about 10 nm to about 100 nm. The first domain or the second domain can include a PBPE structure. The liquid crystal device can include a metasurface and / or a metamaterial. The first domain or the second domain includes a grating array. In various embodiments, the first domain or the second domain can include a curved groove or an arc.

[0015] In various embodiments of the method, depositing the layer of liquid crystal material can include jet-depositing the layer of liquid crystal material. The method further includes depositing an additional layer of liquid crystal material over the layer of liquid crystal material. The additional layer of liquid crystal material can be self-aligned to the pattern in the layer of liquid crystal material. The pattern can be imprinted on the additional layer of liquid crystal material. The pattern imprinted on the additional layer of liquid crystal material can be different from the pattern imprinted on the layer of liquid crystal material. In various embodiments, the pattern imprinted on the layer of liquid crystal material can be configured to respond to a first wavelength, and the pattern imprinted on the additional layer of liquid crystal material can be configured to respond to a second wavelength.

[0016] Yet another innovative aspect of the present subject matter is encompassed in a method of manufacturing a liquid crystal device, the method including depositing a layer of polymerizable liquid crystal material on a substrate, imprinting a pattern onto the polymerizable liquid crystal material using an imprint template, and depositing a layer of liquid crystal material onto the patterned polymerizable liquid crystal material such that the molecules of the liquid crystal material are self-aligned to the pattern.

[0017] The imprint template comprises an imprint pattern including a first domain having a first plurality of features arranged to form a first pattern and a second domain having a second plurality of features arranged to form a second pattern, the first domains being separated from the second domains by inter-domain regions lacking features, and at least one of the width or length of the inter-domain regions being between about 20 nm and about 100 nm.

[0018] In various embodiments of the method, depositing the layer of polymerizable liquid crystal material can include jet-depositing the polymerizable liquid crystal material. The first or second plurality of features can comprise surface relief features. The first or second plurality of features can have a size of about 10 nm to about 100 nm. The first or second domains can comprise PBPE structures. The liquid crystal device can comprise a metasurface and / or metamaterial. The first or second domains can comprise a grating array. The first or second plurality of features can comprise curvilinear grooves or arcs. In various embodiments of the method, depositing the layer of liquid crystal material can include jet-depositing the layer of liquid crystal material.

[0019] The method may further include depositing an additional layer of liquid crystal material over the layer of liquid crystal material. The additional layer of liquid crystal material may be self-aligned to the pattern in the layer of liquid crystal material. The pattern may be imprinted on the additional layer of liquid crystal material. The pattern imprinted on the additional layer of liquid crystal material may be different from the pattern imprinted on the layer of liquid crystal material. The pattern imprinted on the layer of liquid crystal material may be configured to respond to a first wavelength, and the pattern imprinted on the additional layer of liquid crystal material may be configured to respond to a second wavelength.

[0020] Yet another innovative aspect of the present subject matter includes a method for fabricating a liquid crystal device. The method includes depositing a layer on a substrate, imprinting a pattern onto the layer using an imprint template having an imprint pattern, and depositing a layer of liquid crystal material onto the patterned layer such that molecules of the liquid crystal material self-align with the pattern. The imprint pattern includes a first domain having a first plurality of features arranged to form a first pattern and a second domain having a second plurality of features arranged to form a second pattern. The first domain is separated from the second domain by a domain gap region lacking features, and at least one of the width or length of the domain gap region is between about 20 nm and about 100 nm.

[0021] The layer can comprise a polymerizable liquid crystal material. In various embodiments of the method, depositing the layer includes jet-depositing the layer. The first or second plurality of features can include surface relief features. The first or second plurality of features can have a size of about 10 nm to about 100 nm. The first or second domain can include a PBPE structure or a metasurface. The first or second domain can include a grating array. The first or second plurality of features can include curvilinear grooves or arcs. In various embodiments, depositing the layer of liquid crystal material can include jet-depositing the layer of liquid crystal material.

[0022] Various embodiments of the method may further include depositing an additional layer of liquid crystal material over the layer of liquid crystal material. The additional layer of liquid crystal material may be self-aligned to the pattern in the layer of liquid crystal material. The pattern may be imprinted on the additional layer of liquid crystal material. The pattern imprinted on the additional layer of liquid crystal material may be different from the pattern imprinted on the layer of liquid crystal material. The pattern imprinted on the layer of liquid crystal material may be configured to affect a first wavelength, and the pattern imprinted on the additional layer of liquid crystal material may be configured to affect a second wavelength.

[0023] Another innovative aspect of the present subject matter includes a liquid crystal device comprising a substrate and a layer of liquid crystal material having a first surface adjacent to the substrate and a second surface opposite the first surface, wherein a first plurality of molecules of the layer of liquid crystal material on the second surface are arranged to form a first pattern, and a second plurality of molecules of the layer of liquid crystal material on the second surface are arranged to form a first pattern. of The plurality of molecules are arranged to form a second pattern. The first plurality of molecules are separated from the second plurality of molecules by gaps having a distance between about 20 nm and about 100 nm, and the molecules of the layer of liquid crystal material within the gaps are arranged to gradually transition from the first pattern to the second pattern. In various embodiments, the layer of liquid crystal material is configured as a polarization grating.

[0024] Another innovative aspect of the present subject matter includes a liquid crystal device comprising a substrate, a material having a first surface adjacent to the substrate and a second surface opposite the first surface, and a liquid crystal material on the second surface of the material. The material comprises a first pattern on the second surface and a second pattern on the second surface. The first pattern is separated from the second pattern by a gap having a distance of about 20 nm to about 100 nm. In various embodiments of the device, the material can comprise a polymerizable liquid crystal material.

[0025] Innovative aspects of the present subject matter are embodied in a method for fabricating a liquid crystal lens. The method includes providing an imprint layer over a substrate. The imprint layer includes at least a first zone having a first plurality of features oriented along a first direction and a second zone having a second plurality of features oriented along a second direction. The second direction can be rotated by an angle of about 1 degree to about 45 degrees relative to the first direction. The method further includes depositing a liquid crystal layer on the imprint layer, wherein molecules of the deposited liquid crystal layer are self-aligned to the first and second plurality of features. In various implementations, the imprint layer can include about 5 to 30 zones. The first and second zones can be separated by a gap of about 10 nm or less. For example, the first and second zones can be separated by a gap of about 5 nm or less, about 2 nm or less, and / or about 1 nm or less.

[0026] The first or second plurality of features can comprise nanofeatures, such as, for example, grooves. The length or width of the first and second plurality of features can be about 200 nm or less. For example, the length or width of the first and second plurality of features can be about 100 nm or less. The height or depth of the first and second plurality of features can be about 200 nm or less. For example, the height or depth of the first and second plurality of features can be about 100 nm or less.

[0027] The imprint layer can comprise a semiconductor material. The liquid crystal layer can comprise a polymerizable liquid crystal material. The method further includes polymerizing the polymerizable liquid crystal material after the molecules of the polymerizable liquid crystal material are self-aligned to the first and second plurality of features. Polymerizing the polymerizable liquid crystal material can include exposing the polymerizable liquid crystal material to ultraviolet light. The liquid crystal lens can comprise a diffractive lens. Depositing the liquid crystal layer on the imprint layer can include jet-depositing the liquid crystal.

[0028] The innovative aspects of the present subject matter are implemented in a liquid crystal lens. The liquid crystal lens comprises a patterned substrate comprising at least a first zone comprising a first plurality of features oriented along a first direction and a second zone comprising a second plurality of features oriented along a second direction. The first plurality of features and the second plurality of features have dimensions of about 100 nm or less. The lens comprises a liquid crystal layer over the patterned substrate, with molecules of the liquid crystal layer self-aligned to the first and second plurality of features. The dimensions can comprise the length, height, depth, or width of the features. The liquid crystal can comprise a polymerizable liquid crystal.

[0029] The patterned substrate can include a substrate having a patterned layer disposed thereon. The first and second zones can include concentric ring-shaped zones. The lens can include approximately 3 to 30 zones. For example, the lens can include at least five zones. The width of the zones can gradually decrease with distance from the center of the patterned substrate. In various implementations, the zones can have no gaps between them. In some implementations, the gap between the zones can be 5 nm or less. For example, the gap between the zones can be 1 nm or less. The lens can be configured as a diffractive lens. The lens can be configured to provide positive or negative refractive power.

[0030] Various embodiments of the liquid crystal device described herein can be included with a waveguide of a display system. The embodiments of the liquid crystal device described herein can be selectively configured to incouple at least one light stream from a multiplexed light stream into a waveguide and transmit one or more other light streams from the multiplexed light stream. Various embodiments of the liquid crystal device described herein can be included with an eyepiece of a head-mounted display.

[0031] The details of one or more embodiments of the subject matter described herein are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages will become apparent from the description, drawings, and claims. It should be noted that the relative dimensions of the following figures may not be drawn to scale. (Item 1) 1. An optical device comprising a liquid crystal layer having a first major surface, a second major surface, and a thickness, wherein the first major surface and the second major surface extend transversely and the thickness extends along a direction parallel to a surface normal to the first major surface or the second major surface, the liquid crystal layer comprising a plurality of sub-layers dispersed across the thickness of the liquid crystal layer, each of the plurality of sub-layers comprising a single layer of liquid crystal molecules, each of the liquid crystal molecules having a longitudinal axis; Each sub-layer is a first domain in which longitudinal axes of a plurality of liquid crystal molecules are aligned to form a first pattern; a second domain in which the longitudinal axes of the liquid crystal molecules are aligned to form a second pattern; Equipped with the first domains are laterally separated from the second domains along the lateral direction by a domain gap having a distance D of about 10 nm to about 50 nm, and the longitudinal axes of the liquid crystal molecules within the domain gaps gradually transition from the first pattern to the second pattern. (Item 2) Item 10. The device of item 1, wherein the longitudinal axes of the molecules of the first domains of the sublayers can be twisted relative to the longitudinal axes of the molecules of the first domains of the adjacent sublayers. (Item 3) Item 14. The device of item 1, further comprising a second liquid crystal layer, wherein the liquid crystal molecules of the second liquid crystal layer are configured to self-align in the first direction and the second direction within the first domain and the second domain, respectively. (Item 4) Item 4. The device of item 3, wherein the liquid crystal layer or the second liquid crystal layer comprises a polymerizable liquid crystal material. (Item 5) Item 4. The device of item 3, further comprising a third liquid crystal layer over the second liquid crystal layer, wherein the liquid crystal molecules of the third liquid crystal are aligned along a third direction. (Item 6) Item 6. The device of item 5, further comprising a fourth liquid crystal layer over the third liquid crystal layer, wherein the plurality of liquid crystals of the fourth liquid crystal layer are configured to self-align in the third direction. (Item 7) 7. The device of claim 3 or 6, wherein the second liquid crystal layer and / or the fourth liquid crystal layer is disposed across a waveguide. (Item 8) 8. The device of claim 7, wherein the second liquid crystal layer and / or the fourth liquid crystal layer comprises an internal coupling optical element configured to internally couple an incident beam of light into the waveguide such that the incident beam of light propagates through the waveguide by total internal reflection. (Item 9) Item 9. The device of item 8, further comprising a light modulation device configured to direct light into the waveguide via the internal coupling optical element. (Item 10) Item 8. The device of item 7, wherein the second liquid crystal layer and / or the fourth liquid crystal layer comprises an outcoupling optical element configured to outcouple an incident beam of light propagating through the waveguide by total internal reflection. (Item 11) 8. The device of claim 7, wherein the second liquid crystal layer and / or the fourth liquid crystal layer comprises an orthogonal pupil expander configured to redirect light propagating through the waveguide by total internal reflection, and the redirected light continues to propagate through the waveguide by total internal reflection. (Item 12) Item 14. The device of item 1, wherein the liquid crystal layer comprises an internal coupling optical element configured to internally couple an incident beam of light into the waveguide such that the incident beam of light propagates through the waveguide by total internal reflection. (Item 13) Item 10. The device of item 1, wherein the liquid crystal layer comprises an outcoupling optical element configured to outcouple a beam of light propagating through the waveguide by total internal reflection. (Item 14) longitudinal axes of the liquid crystal molecules in the first domain are aligned along a first direction, and longitudinal axes of the liquid crystal molecules in the second domain are aligned along a second direction; Item 2. The device of item 1, wherein the longitudinal axes of the liquid crystal molecules within the domain gaps gradually transition from the first direction to the second direction. (Item 15) 1. A method for fabricating an optical device, the method comprising: providing a polymerizable liquid crystal layer over a substrate; patterning the polymerizable liquid crystal layer; depositing a liquid crystal layer onto the patterned polymerizable liquid crystal layer; Including, the molecules of the deposited liquid crystal layer are self-aligned with the patterned polymerizable liquid crystal layer; The method of claim 1, wherein patterning the polymerizable liquid crystal layer comprises imprinting the polymerizable liquid crystal layer with an imprint template having a first domain comprising a first plurality of features and a second domain comprising a second plurality of features, the first domain being separated from the second domain by a feature-free area, the feature-free area having a dimension between about 20 nm and about 100 nm. (Item 16) Item 16. The method of item 15, wherein the dimensions include at least one of length or width. (Item 17) Item 16. The method of item 15, wherein the width of the first plurality of features is about 20 nm or more and about 100 nm or less. (Item 18) Item 16. The method of item 15, wherein the width of the second plurality of features is about 20 nm or more and about 100 nm or less. (Item 19) Item 16. The method of item 15, wherein the distance between the centers of two consecutive features of the first plurality of features is about 20 nm or more and about 100 nm or less. (Item 20) Item 16. The method of item 15, wherein the height of the first plurality of features is about 10 nm or more and about 100 nm or less. (Item 21) Item 16. The method of item 15, wherein the distance between the centers of two consecutive features of the second plurality of features is about 20 nm or more and about 100 nm or less. (Item 22) Item 16. The method of item 15, wherein the height of the second plurality of features is about 10 nm or more and about 100 nm or less. (Item 23) Item 16. The method of item 15, wherein a first plurality of features of the first domain are arranged to form a first pattern and a second plurality of features of the second domain are arranged to form a second pattern. (Item 24) Item 24. The method according to item 23, wherein the first pattern is distinctly different from the second pattern. (Item 25) Item 16. The method of item 15, wherein the first plurality of features are oriented along a first direction and the second plurality of features of the second domain are oriented along a second direction. (Item 26) 26. The method according to claim 25, wherein the first direction is distinctly different from the second direction. (Item 27) Item 16. The method of item 15, wherein the first plurality of features includes at least one of linear grooves, curved grooves, linear facets, or curved facets. (Item 28) Item 16. The method of item 15, wherein the second plurality of features includes at least one of linear grooves, curved grooves, linear facets, or curved facets. (Item 29) Item 16. The method of item 15, wherein the imprint template comprises a semiconductor material. (Item 30) Item 16. The method of item 15, further comprising fabricating the imprint template using at least one of optical lithography, nanoimprint, or ion and electron beam lithography. (Item 31) 1. A method of manufacturing a liquid crystal device, the method comprising: depositing a layer of liquid crystal material on a substrate; using an imprint template comprising a pattern, imprinting the pattern onto the layer of liquid crystal material such that molecules of the liquid crystal material self-align with the pattern; Including, the pattern comprises a first domain having a first plurality of features arranged to form a first pattern and a second domain having a second plurality of features arranged to form a second pattern; the first domain is separated from the second domain by a region lacking features; The method, wherein at least one of the width or length of the feature-devoid region is from about 20 nm to about 100 nm. (Item 32) 32. The method of claim 31, further comprising depositing a layer of material having a refractive index lower than that of the liquid crystal material. (Item 33) Item 33. The method of item 32, wherein the layer of low refractive index material is configured as a planarization layer using a planarization template. (Item 34) Item 32. The method of item 31, wherein the first plurality of features or the second plurality of features comprises surface relief features. (Item 35) Item 32. The method of item 31, wherein at least one of the length, width, or height of the first plurality of features or the second plurality of features is about 10 nm to about 100 nm. (Item 36) Item 32. The method of item 31, wherein the first domain or the second domain comprises a PBPE structure. (Item 37) Item 32. The method of item 31, wherein the liquid crystal device comprises a metasurface. (Item 38) Item 32. The method of item 31, wherein the liquid crystal device comprises a metamaterial. (Item 39) Item 32. The method of item 31, wherein the first domain or the second domain comprises a lattice array. (Item 40) Item 32. The method of item 31, wherein the first domain or the second domain comprises a curved groove or an arc. (Item 41) 32. The method of claim 31, wherein depositing a layer of liquid crystal material comprises jet-depositing the layer of liquid crystal material. (Item 42) 32. The method of claim 31, further comprising depositing an additional layer of liquid crystal material over the layer of liquid crystal material. (Item 43) Item 43. The method of item 42, wherein the additional layer of liquid crystal material is self-aligned to the pattern of the layer of liquid crystal material. (Item 44) Item 43. The method of item 42, wherein a pattern is imprinted onto the additional layer of liquid crystal material. (Item 45) Item 45. The method of item 44, wherein the pattern imprinted on the additional layer of liquid crystal material is different from the pattern imprinted on the layer of liquid crystal material. (Item 46) Item 45. The method of item 44, wherein the pattern imprinted on the layer of liquid crystal material is configured to affect a first wavelength and the pattern imprinted on the additional layer of liquid crystal material is configured to affect a second wavelength. (Item 47) 1. A method of manufacturing a liquid crystal device, the method comprising: depositing a layer of polymerizable liquid crystal material on a substrate; imprinting a pattern onto said polymerizable liquid crystal material using an imprint template; depositing a layer of liquid crystal material onto the patterned polymerizable liquid crystal material such that the molecules of the liquid crystal material are self-aligned to the pattern; Including, the imprint template comprises an imprint pattern including a first domain having a first plurality of features arranged to form a first pattern and a second domain having a second plurality of features arranged to form a second pattern; the first domain is separated from the second domain by an interdomain region lacking features; The method, wherein at least one of the width or length of the domain gap region is from about 20 nm to about 100 nm. (Item 48) Item 48. The method of item 47, wherein depositing a layer of polymerizable liquid crystal material comprises jet-depositing the polymerizable liquid crystal material. (Item 49) Item 48. The method of item 47, wherein the first plurality of features or the second plurality of features comprises surface relief features. (Item 50) Item 48. The method according to Item 47, wherein the first plurality of features or the second plurality of features have a size of about 10 nm to about 100 nm. (Item 51) Item 48. The method of item 47, wherein the first domain or the second domain comprises a PBPE structure. (Item 52) Item 48. The method of item 47, wherein the liquid crystal device comprises a metasurface. (Item 53) Item 48. The method of item 47, wherein the liquid crystal device comprises a metamaterial. (Item 54) Item 48. The method of item 47, wherein the first domain or the second domain comprises a lattice array. (Item 55) Item 48. The method of item 47, wherein the first plurality of features or the second plurality of features comprises a curved groove or an arc. (Item 56) Item 48. The method of item 47, wherein depositing a layer of liquid crystal material comprises jet-depositing the layer of liquid crystal material. (Item 57) Item 48. The method of item 47, further comprising depositing an additional layer of liquid crystal material over the layer of liquid crystal material. (Item 58) Item 48. The method of item 47, wherein the additional layer of liquid crystal material is self-aligned to the pattern of the layer of liquid crystal material. (Item 59) Item 48. The method of item 47, wherein a pattern is imprinted onto the additional layer of liquid crystal material. (Item 60) Item 59. The method of item 59, wherein the pattern imprinted on the additional layer of liquid crystal material is different from the pattern imprinted on the layer of liquid crystal material. (Item 61) Item 59. The method of item 59, wherein the pattern imprinted on the layer of liquid crystal material is configured to affect a first wavelength and the pattern imprinted on the additional layer of liquid crystal material is configured to affect a second wavelength. (Item 62) 1. A method of manufacturing a liquid crystal device, the method comprising: depositing a layer on a substrate; imprinting a pattern onto the layer using an imprint template comprising an imprint pattern; depositing a layer of liquid crystal material over the patterned layer such that the molecules of the liquid crystal material are self-aligned to the pattern; Including, the imprint pattern comprises a first domain having a first plurality of features arranged to form a first pattern and a second domain having a second plurality of features arranged to form a second pattern; the first domain is separated from the second domain by an interdomain region lacking features; The method, wherein at least one of the width or length of the domain gap region is from about 20 nm to about 100 nm. (Item 63) Item 63. The method of item 62, wherein the layer comprises a polymerizable liquid crystal material. (Item 64) Item 63. The method of item 62, wherein depositing the layer comprises jet-depositing the layer. (Item 65) Item 63. The method of item 62, wherein the first plurality of features or the second plurality of features comprises surface relief features. (Item 66) Item 63. The method according to Item 62, wherein the first plurality of features or the second plurality of features have a size of about 10 nm to about 100 nm. (Item 67) Item 63. The method of item 62, wherein the first domain or the second domain comprises a PBPE structure or a metasurface. (Item 68) Item 63. The method of item 62, wherein the first domain or the second domain comprises a lattice array. (Item 69) Item 63. The method of item 62, wherein the first plurality of features or the second plurality of features comprises a curved groove or an arc. (Item 70) Item 63. The method of item 62, wherein depositing a layer of liquid crystal material comprises jet-depositing the layer of liquid crystal material. (Item 71) Item 63. The method of item 62, further comprising depositing an additional layer of liquid crystal material over the layer of liquid crystal material. (Item 72) Item 72. The method of item 71, wherein the additional layer of liquid crystal material is self-aligned to the pattern of the layer of liquid crystal material. (Item 73) Item 72. The method of item 71, wherein a pattern is imprinted onto the additional layer of liquid crystal material. (Item 74) Item 74. The method of item 73, wherein the pattern imprinted on the additional layer of liquid crystal material is different from the pattern imprinted on the layer of liquid crystal material. (Item 75) Item 74. The method of item 73, wherein the pattern imprinted on the layer of liquid crystal material is configured to affect a first wavelength and the pattern imprinted on the additional layer of liquid crystal material is configured to affect a second wavelength. (Item 76) A liquid crystal device, A substrate; a layer of liquid crystal material having a first surface adjacent to the substrate and a second surface opposite the first surface; Equipped with a first plurality of molecules of the layer of liquid crystal material on the second surface arranged to form a first pattern, a second first plurality of molecules of the layer of liquid crystal material on the second surface arranged to form a second pattern, the first plurality of molecules being separated from the second plurality of molecules by gaps having a distance of about 20 nm to about 100 nm, and the molecules of the layer of liquid crystal material within the gaps arranged to gradually transition from the first pattern to the second pattern. (Item 77) Item 77. A liquid crystal device according to item 76, wherein the layer of liquid crystal material is configured as a polarizing grating. (Item 78) 77. The liquid crystal device according to item 76, included together with a waveguide in a display system. (Item 79) Item 79. The liquid crystal device of item 78, configured to selectively in-couple at least one light stream from a multiplexed light stream into the waveguide and transmit one or more other light streams from the multiplexed light stream. (Item 80) 77. The liquid crystal device of item 76, included with an eyepiece of a head-mounted display. (Item 81) A liquid crystal device, A substrate; a material having a first surface adjacent to the substrate and a second surface opposite the first surface, the material comprising: a first pattern on the second surface; and a second pattern on the second surface; and wherein the first pattern is separated from the second pattern by a gap having a distance of about 20 nm to about 100 nm; a liquid crystal material on a second surface of the material; A liquid crystal device comprising: (Item 82) Item 82. The liquid crystal device of item 81, wherein the material comprises a polymerizable liquid crystal material. (Item 83) Item 31, Item 47, Item 62, or Item 81, the liquid crystal device included with an eyepiece of a head-mounted display. (Item 84) Item 84. A liquid crystal device as described in Item 83, configured to selectively internally couple at least one light stream from the multiplexed light stream into a waveguide of the eyepiece and transmit one or more other light streams from the multiplexed light stream. (Item 85) 16. The optical device of item 1 or 15, included with an eyepiece of a head-mounted display. (Item 86) Item 86. An optical device as described in Item 85, configured to selectively internally couple at least one light stream from the multiplexed light stream into a waveguide of the eyepiece and transmit one or more other light streams from the multiplexed light stream. (Item 87) 1. A method for fabricating a liquid crystal lens, the method comprising: providing an imprint layer over a substrate, the imprint layer comprising at least a first zone comprising a first plurality of features oriented along a first direction and a second zone comprising a second plurality of features oriented along a second direction; depositing a liquid crystal layer onto the imprint layer; wherein molecules of the deposited liquid crystal layer are self-aligned to the first plurality of features and the second plurality of features. (Item 88) Item 88. The method of item 87, wherein the first zone and second zone are separated by a gap of about 5 nm or less. (Item 89) Item 88. The method of item 87, wherein the first plurality of features or the second plurality of features comprises a groove. (Item 90) Item 88. The method according to item 87, wherein the second direction is rotated by an angle of about 1 degree to about 45 degrees relative to the first direction. (Item 91) Item 88. The method of item 87, wherein the imprint layer comprises a semiconductor material. (Item 92) Item 88. The method of item 87, wherein the liquid crystal layer comprises a polymerizable liquid crystal material. (Item 93) Item 92. The method of item 91, further comprising polymerizing the polymerizable liquid crystal material after the molecules of the polymerizable liquid crystal material are self-aligned with the first plurality of features and the second plurality of features. (Item 94) Item 93. The method of item 92, wherein polymerizing the polymerizable liquid crystal material comprises exposing the polymerizable liquid crystal material to ultraviolet light. (Item 95) 94. The method of any of items 87-93, wherein the lens comprises a diffractive lens. (Item 96) 94. The method of any of items 87-93, wherein depositing a liquid crystal layer onto the imprint layer comprises jet-depositing the liquid crystal. (Item 97) Item 88. The method of item 87, wherein the length or width of the first plurality of features and the second plurality of features is about 100 nm or less. (Item 98) Item 88. The method of item 87, wherein the height or depth of the first plurality of features and the second plurality of features is about 100 nm or less. (Item 99) A liquid crystal lens, a patterned substrate comprising at least a first zone comprising a first plurality of features oriented along a first direction and a second zone comprising a second plurality of features oriented along a second direction, wherein the first plurality of features and the second plurality of features have dimensions of about 100 nm or less; a liquid crystal layer over the patterned substrate; Equipped with The molecules of the liquid crystal layer are self-aligned to the first and second plurality of features. (Item 100) Item 100. The liquid crystal lens of item 99, wherein the patterned substrate comprises a substrate having a patterned layer disposed thereon. (Item 101) Item 101. The liquid crystal lens of item 99 or 100, wherein the at least first zone and second zone comprise concentric ring-shaped zones. (Item 102) Item 99 or 101, a liquid crystal lens comprising at least five zones. (Item 103) Item 103. The liquid crystal lens according to item 99 or 102, wherein the width of the zones gradually decreases with distance from the center of the patterned substrate. (Item 104) Item 99 or 103, wherein the zones have no gaps between them. (Item 105) Item 99 or 103, wherein the gap between the zones is 1 nm or less. (Item 106) Item 99 or 103, wherein the gap between the zones is 5 nm or less. (Item 107) Item 107. The liquid crystal lens of any of items 99-106, wherein the dimension comprises a length or width of the feature. (Item 108) Item 99-107. The liquid crystal lens of any of items 99-107, wherein the liquid crystal comprises a polymerized liquid crystal. (Item 109) Item 99-108. The liquid crystal lens of any of items 99-108, wherein the lens comprises a diffractive lens. (Item 110) 109. The liquid crystal lens of any of items 99-109, configured to provide optical power. [Brief explanation of the drawings]

[0032] [Figure 1] FIG. 1 illustrates a user's view of an augmented reality (AR) device. [Figure 2] FIG. 2 illustrates an example of a wearable display system. [Figure 3] FIG. 3 illustrates a conventional display system for simulating a three-dimensional image for a user. [Figure 4] FIG. 4 illustrates aspects of an approach for simulating a three-dimensional image using multiple depth planes. [Figure 5] 5A-5C illustrate the relationship between the radius of curvature and the radius of focus. [Figure 6] FIG. 6 illustrates an embodiment of a waveguide stack for outputting image information to a user. [Figure 7] FIG. 7 illustrates an example of an output beam output by a waveguide. [Figure 8] FIG. 8 illustrates an example of a stacked waveguide assembly where each depth plane contains an image formed using multiple different primary colors. [Figure 9A] FIG. 9A illustrates a cross-sectional side view of an example of a set of stacked waveguides, each including an internal coupling optical element. [Figure 9B] FIG. 9B illustrates a perspective view of the multiple stacked waveguide embodiment of FIG. 9A. [Figure 9C] FIG. 9C illustrates a top-down plan view of the multiple stacked waveguide embodiment of FIGS. 9A and 9B. [Figure 10A]Figure 10A illustrates a top view of an example liquid crystal layer comprising multiple domains of liquid crystal molecules. Figure 10B illustrates an enlarged top view of the liquid crystal layer depicted in Figure 10A, showing the orientation of the liquid crystal molecules within each domain. Figures 10C, 10D, 10E, and 10F illustrate side views of various embodiments of the liquid crystal layer depicted in Figure 10A. [Figure 10B] Figure 10A illustrates a top view of an example liquid crystal layer comprising multiple domains of liquid crystal molecules. Figure 10B illustrates an enlarged top view of the liquid crystal layer depicted in Figure 10A, showing the orientation of the liquid crystal molecules within each domain. Figures 10C, 10D, 10E, and 10F illustrate side views of various embodiments of the liquid crystal layer depicted in Figure 10A. [Figure 10C] Figure 10A illustrates a top view of an example liquid crystal layer comprising multiple domains of liquid crystal molecules. Figure 10B illustrates an enlarged top view of the liquid crystal layer depicted in Figure 10A, showing the orientation of the liquid crystal molecules within each domain. Figures 10C, 10D, 10E, and 10F illustrate side views of various embodiments of the liquid crystal layer depicted in Figure 10A. [Figure 10D] Figure 10A illustrates a top view of an example liquid crystal layer comprising multiple domains of liquid crystal molecules. Figure 10B illustrates an enlarged top view of the liquid crystal layer depicted in Figure 10A, showing the orientation of the liquid crystal molecules within each domain. Figures 10C, 10D, 10E, and 10F illustrate side views of various embodiments of the liquid crystal layer depicted in Figure 10A. [Figure 10E] Figure 10A illustrates a top view of an example liquid crystal layer comprising multiple domains of liquid crystal molecules. Figure 10B illustrates an enlarged top view of the liquid crystal layer depicted in Figure 10A, showing the orientation of the liquid crystal molecules within each domain. Figures 10C, 10D, 10E, and 10F illustrate side views of various embodiments of the liquid crystal layer depicted in Figure 10A. [Figure 10F] Figure 10A illustrates a top view of an example liquid crystal layer comprising multiple domains of liquid crystal molecules. Figure 10B illustrates an enlarged top view of the liquid crystal layer depicted in Figure 10A, showing the orientation of the liquid crystal molecules within each domain. Figures 10C, 10D, 10E, and 10F illustrate side views of various embodiments of the liquid crystal layer depicted in Figure 10A. [Figure 11A] FIG. 11A illustrates a top view of an imprint template including a plurality of surface features configured to produce the liquid crystal layer depicted in FIG. 10A. [Figure 11B] FIG. 11B illustrates a side view of the imprint template depicted in FIG. 11A. [Figure 12A] 12A-12D illustrate an embodiment of a method for fabricating a liquid crystal layer comprising multiple liquid crystal molecules arranged in different patterns, and FIG. 12E illustrates an embodiment of a stacked liquid crystal device comprising multiple liquid crystal layers. [Figure 12B] 12A-12D illustrate an embodiment of a method for fabricating a liquid crystal layer comprising multiple liquid crystal molecules arranged in different patterns, and FIG. 12E illustrates an embodiment of a stacked liquid crystal device comprising multiple liquid crystal layers. [Figure 12C] 12A-12D illustrate an embodiment of a method for fabricating a liquid crystal layer comprising multiple liquid crystal molecules arranged in different patterns, and FIG. 12E illustrates an embodiment of a stacked liquid crystal device comprising multiple liquid crystal layers. [Figure 12D] 12A-12D illustrate an embodiment of a method for fabricating a liquid crystal layer comprising multiple liquid crystal molecules arranged in different patterns, and FIG. 12E illustrates an embodiment of a stacked liquid crystal device comprising multiple liquid crystal layers. [Figure 12E] 12A-12D illustrate an embodiment of a method for fabricating a liquid crystal layer comprising multiple liquid crystal molecules arranged in different patterns, and FIG. 12E illustrates an embodiment of a stacked liquid crystal device comprising multiple liquid crystal layers. [Figure 13A] FIG. 13A illustrates a scanning electron microscope (SEM) image of an embodiment of an imprint template. [Figure 13B] FIG. 13B is an SEM image of a patterned PLC layer fabricated using the imprint template of FIG. 13A and the method discussed above with reference to FIGS. 12A-12C. [Figure 13C] FIG. 13C is a polarized light microscope image of the patterned PLC layer shown in FIG. 13B. [Figure 14] FIG. 14 illustrates an embodiment of an electrically controllable liquid crystal device. [Figure 15] 15A-15C illustrate examples of methods for fabricating various liquid crystal devices described herein. [Figure 16A] FIG. 16A illustrates a top view of an implementation of a diffractive lens with a liquid crystal material. [Figure 16B] Figure 16B illustrates a microscope image of the implementation of the lens between crossed polarizers. Figures 16B-1 and 16B-2 depict scanning electron microscope (SEM) images showing the pattern of the imprint layer that achieves the desired alignment of the longitudinal axes in various regions of the liquid crystal lens. [Figure 17] 17A-17C illustrate an embodiment of a method for manufacturing a liquid crystal lens. [Figure 18] Figure 18A illustrates a scanning electron microscope (SEM) image of an imprint layer used to fabricate a liquid crystal lens implementation, and Figure 18B illustrates a scanning electron microscope (SEM) image of a liquid crystal layer disposed over the imprint layer of Figure 18A. DETAILED DESCRIPTION OF THE INVENTION

[0033] Like reference numbers and designations in the various drawings indicate like elements.

[0034] Liquid crystals (LCs) comprise liquid crystal molecules with longitudinal axes that are arbitrarily oriented under certain conditions. However, under certain other conditions, the LC molecules can be aligned so that the longitudinal axes are oriented along an average direction (referred to herein as the director). Some liquid crystal molecules can be symmetric about their longitudinal axes. LCs are anisotropic materials that can have different optical properties for different wavelengths or polarizations of light depending on the direction of propagation of the light through the LC and the polarization of the light relative to the direction along which the LC molecules are generally oriented. For example, LC molecules will exhibit optical properties such that light polarized along the direction of the general orientation of the longitudinal axes of the LC molecules is polarized perpendicular to the general orientation of the longitudinal axes of the LC molecules. AlongLC materials exhibit birefringence, which means that their refractive index differs from that of polarized light. As a result of their birefringent nature, they are widely used in a variety of systems, including displays, optical communications, optical data storage, sensors, and the like. The refractive index of LC materials can be varied by varying the orientation of the longitudinal axes of the LC material's molecules. Thus, LC materials can be configured as phase gratings. LC grating structures can be used to selectively diffract light along different directions based on wavelength and / or polarization.

[0035] One method for fabricating LC grating structures includes mechanical methods such as abrasion processes, in which surface features are produced on a matching layer (e.g., a polymer) by abrading or scratching the surface of the matching layer using a mechanical object (e.g., a metal object, a cloth, the tip of an atomic force microscope, etc.). Molecules of the LC material deposited on the matching layer align with the surface features on the matching layer, forming a grating pattern. However, the abrasion process may mechanically damage the surface of the matching layer and / or introduce static electricity or impurities onto the surface of the matching layer, which may reduce the diffraction efficiency of the liquid crystal grating structure. Furthermore, it may be impractical to fabricate complex grating structures (e.g., LC gratings comprising patterns with different orientations of LC molecules) using abrasion methods. In addition, it may also be impractical to fabricate spatially varying nanoscale patterns of liquid crystal material that can be used to manipulate the phase, amplitude, and / or polarization of incident light. In contrast, various implementations described herein can be used to fabricate spatially varying nanoscale patterns of liquid crystal material that can be used to manipulate the phase, amplitude, and / or polarization of incident light. Some embodiments of the liquid crystal material with spatially varying nanoscale patterns can include liquid crystal metasurfaces. Other embodiments of the liquid crystal material with spatially varying nanoscale patterns can include liquid crystals comprising multiple adjacent domains, where the liquid crystal molecules within each domain can be arranged to form a nanoscale pattern.

[0036] In some embodiments, the LC grating structure may be utilized as a component of a display system. The display system may include a waveguide and an image injection device configured to direct a light beam into the waveguide. The LC grating structure may be used as one or more of an internal coupling optical element, an external coupling optical element, and an optical element to receive incident light propagating within the waveguide and redirect the incident light so that the redirected light continues to propagate through the waveguide by total internal reflection. Examples of the latter type of optical element include pupil expanders, such as an orthogonal pupil expander (OPE).

[0037] In some embodiments, the LC grating structure may be used to in-couple, out-couple, and / or redirect light propagating within the waveguide. The light may be light of a single wavelength or a single wavelength range. In some other embodiments, the light may be a light stream that is part of a multiplexed light stream including multiple light streams having different optical properties (e.g., each stream may have a different wavelength). For example, the waveguide may include an LC grating structure configured to selectively redirect a light beam formed from light having particular optical properties (e.g., a first wavelength) while being substantially transparent to one or more other light streams (e.g., having a wavelength different from the first wavelength). In some embodiments, the waveguide may include a second waveguide that is part of a stack of waveguides, the second waveguide including an in-coupling optical element configured to selectively redirect a second light stream while being transparent to one or more other light streams. In some embodiments, the in-coupling LC grating structure of the waveguide is configured to transmit at least one of the light streams to the in-coupling LC grating structure of the second waveguide.

[0038] Reference is now made to the figures, wherein like reference numerals refer to like parts throughout. It should be understood that the embodiments disclosed herein generally include an optical system, including a display system. In some embodiments, the display system is wearable, which may advantageously provide a more immersive VR or AR experience. For example, a display containing one or more waveguides (e.g., a stack of waveguides) may be configured to be worn and positioned over the eyes of a user, wearer, and / or viewer. In some embodiments, two stacks of waveguides, one for each viewer's eye, may be utilized to provide a different image to each eye. Exemplary Display Systems

[0039] FIG. 2 illustrates an example of a wearable display system 60. The display system 60 includes a display 70 and various mechanical and electronic modules and systems to support the functionality of the display 70. The display 70 may be coupled to a frame 80, which is wearable by a display system user or viewer 90 and configured to position the display 70 directly in front of the user's 90 eyes. The display 70 may, in some embodiments, be considered eyewear. In some embodiments, a speaker 100 is coupled to the frame 80 and configured to be positioned adjacent to the user's 90 ear canal (in some embodiments, another speaker, not shown, may be positioned adjacent the user's other ear canal to provide stereo / shapeable sound control). In some embodiments, the display system may also include one or more microphones 110 or other devices to detect sound. In some embodiments, the microphones may be configured to allow a user to provide input or commands to the system 60 (e.g., voice menu command selections, natural language queries, etc.) and / or enable audio communication with other persons (e.g., other users of similar display systems). The microphone may further be configured as an ambient sensor to collect audio data (e.g., sounds from the user and / or the environment). In some embodiments, the display system may also include an ambient sensor 120a, which may be separate from the frame 80 and attached to the body of the user 90 (e.g., on the head, torso, limbs, etc. of the user 90). The ambient sensor 120a, in some embodiments, may be configured to obtain data characterizing a physiological state of the user 90. For example, the sensor 120a may be an electrode.

[0040] 2, the display 70 is operably coupled by a communication link 130, such as wired or wireless connectivity, to a local data processing module 140, which may be mounted in a variety of configurations, such as fixedly attached to the frame 80, fixedly attached to a helmet or hat worn by the user, integrated into headphones, or otherwise removably attached to the user 90 (e.g., in a backpack-style configuration, in a belt-coupled configuration). Similarly, the sensor 120a may be operably coupled to the local processor and data module 140 by a communication link 120b, e.g., wired 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 utilized to aid in processing, caching, and storing data. The data includes a) data captured from sensors (e.g., which may be operatively coupled to frame 80 or otherwise attached to user 90), such as image capture devices (such as cameras), microphones, inertial measurement units, accelerometers, compasses, GPS units, wireless devices, gyroscopes, and / or other sensors disclosed herein, and / or b) data obtained and / or processed using remote processing module 150 and / or remote data repository 160 (including data related to virtual content), possibly for passing to display 70 after processing or readout. Local processing and data module 140 may be operatively coupled to remote processing module 150 and remote data repository 160 by communication links 170, 180, such as via wired or wireless communication links, such that these remote modules 150, 160 are operatively coupled to each other and available as resources to local processing and data module 140.In some embodiments, local processing and data module 140 may include one or more of an image capture 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 to frame 80 or may be a freestanding structure that communicates with local processing and data module 140 by a wired or wireless communication path.

[0041] 2 , in some embodiments, remote processing module 150 may comprise one or more processors configured to analyze and process data and / or image information. In some embodiments, remote data repository 160 may comprise a digital data storage facility, which may be available through the Internet or other networking configuration in a “cloud” resource configuration. In some embodiments, remote data repository 160 may include one or more remote servers that provide information, e.g., information for generating augmented reality content, to local processing and data module 140 and / or remote processing module 150. In some embodiments, all data is stored and all calculations are performed in the local processing and data module, allowing for fully autonomous use from the remote module.

[0042] The perception of an image as "three-dimensional" or "3-D" can be achieved by providing a slightly different presentation of the image to each eye of a viewer. FIG. 3 illustrates a conventional display system for simulating a three-dimensional image for a user. Two distinct images 190, 200 (one for each eye 210, 220) are output to the user. The images 190, 200 are spaced from the eyes 210, 220 by a distance 230 along an optical axis, or z-axis, parallel to the viewer's line of sight. The images 190, 200 are flat, and the eyes 210, 220 can focus on the images by assuming a single accommodative state. Such a 3-D display system relies on the human visual system to combine the images 190, 200 and provide the perception of depth and / or scale of the combined image.

[0043] However, it should be understood that the human visual system is complex and difficult to provide a realistic perception of depth. For example, many viewers of conventional “3-D” display systems find such systems uncomfortable or may not perceive any sense of depth at all. Without being limited by theory, it is believed that a viewer of an object may perceive the object as “three-dimensional” due to a combination of vergence and accommodation. Vergence movement of the two eyes relative to each other (i.e., rotation of the eyes such that the pupils move toward or away from each other, converging the lines of sight of the eyes, and fixating on an object) is closely linked to the focusing (or “accommodation”) of the eye lenses and pupils. Under normal conditions, a change in the focus of the eye's lens, or the eye's accommodation, to change focus from one object to another at a different distance will automatically produce a matching change in convergence-divergence to the same distance, under a relationship known as the "accommodation-vergence reflex" and pupil dilation and constriction. Similarly, a change in convergence-divergence will, under normal conditions, induce a matching change in accommodation in lens shape and pupil size. As described herein, many stereoscopic or "3-D" display systems display a scene using slightly different presentations (and therefore slightly different images) to each eye so that a three-dimensional perspective is perceived by the human visual system. However, such systems, among other things, simply provide different presentations of a scene, but are uncomfortable for many viewers because they work against the "accommodation-vergence reflex" when the eyes view all image information in a single accommodated state. Display systems that offer better alignment between accommodation and convergence-divergence movements may create a more realistic and comfortable simulation of three-dimensional images, contributing to increased wear duration and, ultimately, compliance with diagnostic and therapy protocols.

[0044] FIG. 4 illustrates aspects of an approach for simulating a three-dimensional image using multiple depth planes. With reference to FIG. 4 , objects at various distances from the eyes 210, 220 on the z-axis are accommodated by the eyes 210, 220 so that the objects are in focus. The eyes 210, 220 assume particular accommodated states, focusing objects at different distances along the z-axis. As a result, a particular accommodated state may be said to be associated with a particular one of the depth planes 240 having an associated focal length such that an object or portion of an object at a particular depth plane is in focus when the eye is in an accommodated state relative to that depth plane. In some embodiments, a three-dimensional image may be simulated by providing a different representation of an image for each eye 210, 220, and by providing a different representation of an image corresponding to each of the depth planes. While shown as separate for clarity of illustration, it should be understood that the fields of view of the eyes 210, 220 may overlap, for example, as the distance along the z-axis increases. Additionally, although shown as flat for ease of illustration, it should be understood that the contour of the depth plane may be curved in physical space so that all features within the depth plane are in focus with the eye in a particular accommodative state.

[0045] The distance between an object and the eye 210 or 220 can also change the amount of divergence of light from the object as viewed by that eye. Figures 5A-5C illustrate the relationship between distance and divergence of light rays. The distance between the object and the eye 210 is represented by decreasing distances R1, R2, and R3. As shown in Figures 5A-5C, light rays become more divergent as the distance to the object decreases. As the distance increases, the light rays become more collimated. In other words, the light field generated by a point (an object or part of an object) can be said to have a spherical wavefront curvature that is a function of the distance the point is from the user's eye. The curvature increases as the distance between the object and the eye 210 decreases. As a result, the divergence of light rays at different depth planes also differs, and the divergence increases as the distance between the depth plane and the viewer's eye 210 decreases. While only a single eye 210 is illustrated in Figures 5A-5C and other figures herein for clarity of illustration, it should be understood that the discussion regarding eye 210 may apply to both eyes 210 and 220 of a viewer.

[0046] Without being limited by theory, it is believed that the human eye is typically capable of interpreting a finite number of depth planes to provide depth perception. As a result, a highly realistic simulation of perceived depth can be achieved by providing the eye with different representations of images corresponding to each of these limited number of depth planes. The different representations may be focused separately by the viewer's eyes, thereby serving to provide depth cues to the user based on the ocular accommodation required to focus on different image features for a scene located on the different depth planes and / or based on the observation of different image features on the different depth planes that are out of focus.

[0047] FIG. 6 illustrates an example of a waveguide stack for outputting image information to a user. Display system 250 includes a stack of waveguides or stacked waveguide assembly 260 that can be utilized to provide a three-dimensional perception to the eye / brain using multiple waveguides 270, 280, 290, 300, 310. In some embodiments, display system 250 is system 60 of FIG. 2 , and FIG. 6 diagrammatically illustrates some portions of system 60 in greater detail. For example, waveguide assembly 260 may be part of display 70 of FIG. 2 . It should be understood that display system 250 may, in some embodiments, be considered a light field display.

[0048] Continuing with reference to FIG. 6 , the waveguide assembly 260 may also include multiple features 320, 330, 340, 350 between the waveguides. In some embodiments, the features 320, 330, 340, 350 may be one or more lenses. The waveguides 270, 280, 290, 300, 310 and / or multiple lenses 320, 330, 340, 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 particular depth plane and configured to output image information corresponding to that depth plane. The image injection devices 360, 370, 380, 390, 400 may act as light sources for the waveguides and may be utilized to inject image information into the waveguides 270, 280, 290, 300, 310, each configured to disperse incident light across each individual waveguide for output toward the eye 210, as described herein. Light exits output surfaces 410, 420, 430, 440, 450 of the image injection devices 360, 370, 380, 390, 400 and is injected into corresponding input surfaces 460, 470, 480, 490, 500 of the waveguides 270, 280, 290, 300, 310. In some embodiments, each input surface 460, 470, 480, 490, 500 may be an edge of the corresponding waveguide or may be a portion of a major 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 launched into each waveguide, outputting a total field of cloned collimated beams directed toward the eye 210 at a particular angle (and divergence) corresponding to the depth plane associated with the particular waveguide. In some embodiments, a single one of the image launch devices 360, 370, 380, 390, 400 may be associated with and launch light into multiple (e.g., three) waveguides 270, 280, 290, 300, 310.

[0049] In some embodiments, each of the image input devices 360, 370, 380, 390, 400 is a discrete display that generates image information for input into a corresponding waveguide 270, 280, 290, 300, 310. In some other embodiments, the image input devices 360, 370, 380, 390, 400 are the output of a single multiplexed display that may, for example, send image information via one or more optical conduits (such as fiber optic cables) to each of the image input devices 360, 370, 380, 390, 400. It should be understood that the image information provided by the image input devices 360, 370, 380, 390, 400 may include light of different wavelengths or colors (e.g., different primary colors, as discussed herein).

[0050] In some embodiments, light injected into the waveguides 270, 280, 290, 300, 310 is provided by a light projector system 520, which includes a light module 530, which may include a light emitter such as a light emitting diode (LED). Light from the light module 530 may be directed and modified by a light modulator 540, e.g., a spatial light modulator, via a beam splitter 550. The light modulator 540 may be configured to vary the perceived intensity of the light injected into the waveguides 270, 280, 290, 300, 310. Examples of spatial light modulators include liquid crystal displays (LCDs), including liquid crystal on silicon (LCOS) displays.

[0051] 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 scan, spiral scan, Lissajous pattern, 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 injection devices 360, 370, 380, 390, 400 may diagrammatically represent a single scanning fiber or a bundle of scanning fibers configured to inject light into one or more waveguides 270, 280, 290, 300, 310. In some other embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may diagrammatically represent multiple scanning fibers or multiple bundles of scanning fibers, each configured to inject light into an associated one of the 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 of the waveguides 270, 280, 290, 300, 310. It should be understood that one or more intervening optical structures may be provided between the scanning fiber(s) and one or more of the waveguides 270, 280, 290, 300, 310, for example, to redirect light exiting the scanning fiber into one or more of the waveguides 270, 280, 290, 300, 310.

[0052] Controller 560 controls the operation of one or more of stacked waveguide assemblies 260, including the operation of image input devices 360, 370, 380, 390, 400, light source 530, and light module 540. In some embodiments, controller 560 is part of local data processing module 140. Controller 560 includes programming (e.g., instructions in a non-transitory medium) that coordinates the timing and provision of image information to 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 a wired or wireless communication channel. Controller 560 may, in some embodiments, be part of processing module 140 or 150 (FIG. 2).

[0053] Continuing with reference to FIG. 6 , the waveguides 270, 280, 290, 300, and 310 may be configured to propagate light within each individual waveguide by total internal reflection (TIR). Each of the waveguides 270, 280, 290, 300, and 310 may be planar or have another shape (e.g., curved) with major top and bottom surfaces and edges extending between the major top and bottom surfaces. In the illustrated configuration, the waveguides 270, 280, 290, 300, and 310 may each include outcoupling optical elements 570, 580, 590, 600, and 610 configured to extract light from the waveguides by redirecting the light, causing it to propagate within each individual waveguide, and outputting image information from the waveguides to the eye 210. The extracted light may also be referred to as outcoupled light, and the optical element that outcouples light may also be referred to as a light extraction optical element. The extracted beam of light may be output by the waveguide at a location where light propagating within the waveguide strikes the light extraction optical element. The outcoupling optical element 570, 580, 590, 600, 610 may be a grating, for example, including diffractive optical features as discussed further herein. While shown disposed on the bottom major surface of the waveguides 270, 280, 290, 300, 310 for ease of explanation and clarity of drawing, in some embodiments, the outcoupling optical element 570, 580, 590, 600, 610 may be disposed on the top and / or bottom major surfaces and / or directly within the volume of the waveguides 270, 280, 290, 300, 310, as discussed further herein. In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 may be formed within a layer of material attached to a transparent substrate and forming 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 outcoupling optical elements 570, 580, 590, 600, 610 may be formed on and / or within the material components.

[0054] Continuing with reference to FIG. 6 , as discussed herein, each waveguide 270, 280, 290, 300, 310 is configured to output light and form an image corresponding to a particular 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 an optical infinity focal plane. The next upper waveguide 280 may be configured to send collimated light that passes through a first lens 350 (e.g., a negative lens) before reaching the eye 210. The first lens 350 may be configured to generate a slight convex wavefront curvature so that the eye / brain interprets light emerging from the next upper waveguide 280 as emerging 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 produce another, increasing amount of wavefront curvature such that the eye / brain interprets the light emerging from the third waveguide 290 as originating from a second focal plane that is closer inward from optical infinity towards the person than was the light from the next upper waveguide 280.

[0055] The other waveguide layers 300, 310 and lenses 330, 320 are similarly configured, with the highest waveguide 310 in the stack sending its output through all of the lenses between it and the eye for a collective focal power representing the focal plane closest to the person. To compensate for the stack of lenses 320, 330, 340, 350 when viewing / interpreting light originating from the world 510 on the other side of the stacked waveguide assembly 260, a compensating lens layer 620 may be placed on top of the stack to compensate for the collective power of the lower lens stacks 320, 330, 340, 350. Such a configuration provides as many perceived focal planes as there are available waveguide / lens pairs. Both the waveguide outcoupling optical elements and the focusing sides of the lenses may be static (i.e., not dynamic or electro-active). In some alternative embodiments, one or both may be dynamic using electro-active features.

[0056] In some embodiments, two or more of the waveguides 270, 280, 290, 300, 310 may have the same associated depth plane. For example, multiple waveguides 270, 280, 290, 300, 310 may be configured to output images set at the same depth plane, or multiple subsets of waveguides 270, 280, 290, 300, 310 may be configured to output images set at the same depth planes, with one set per depth plane. This may provide the advantage of forming tiled images to provide an extended field of view at those depth planes.

[0057] Continuing with reference to FIG. 6 , the outcoupling optical elements 570, 580, 590, 600, 610 may be configured to redirect light from its respective waveguide and output the light with an appropriate amount of divergence or collimation for a particular depth plane associated with that waveguide. As a result, waveguides with different associated depth planes may have different configurations of outcoupling optical elements 570, 580, 590, 600, 610, which 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, 610 may be volume or surface features, which may be configured to output light at specific angles. For example, the light-extraction optical elements 570, 580, 590, 600, 610 may be volume holograms, surface holograms, and / or diffraction gratings. In some embodiments, features 320, 330, 340, 350 may not be lenses. Rather, they may simply be spacers (e.g., cladding layers and / or structures for forming air gaps).

[0058] In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 are diffractive features that form a diffraction pattern or "diffractive optical element" (also referred to herein as "DOE"). Preferably, the DOE has a sufficiently low diffraction efficiency so that only a portion of the light in the beam is deflected toward the eye 210 at each intersection of the DOE, while the remainder continues traveling through the waveguide via TIR. The light carrying the image information is thus split into several related output beams that exit the waveguide at multiple locations, resulting in a very uniform pattern of output emission toward the eye 210 for this particular collimated beam bouncing within the waveguide.

[0059] 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 comprise a diffractive pattern in a 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).

[0060] In some embodiments, a camera assembly 630 (e.g., a digital camera, including a visible light and infrared light camera) may be provided to capture images of the eye 210 and / or tissue surrounding the eye 210, for example, to detect user input and / or monitor the user's physiological state. As used herein, a camera may be any image capture device. In some embodiments, the camera assembly 630 may include an image capture device and a light source that projects light (e.g., infrared light) onto the eye, which may then be reflected by the eye and detected by the image capture device. In some embodiments, the camera assembly 630 may be mounted on the frame 80 ( FIG. 2 ) and may be in electrical communication with processing modules 140 and / or 150, which may process image information from the camera assembly 630 as discussed herein and make various determinations, for example, regarding the user's physiological state. It should be understood that information regarding the user's physiological state may be used to determine the user's behavior or emotional state. Examples of such information include the user's movements and / or the user's facial expressions. The user's behavior or emotional state may then be triangulated with the collected environmental and / or virtual content data to determine relationships between the behavior or emotional state, the physiological state, and the environmental or virtual content data. In some embodiments, one camera assembly 630 may be utilized per eye to monitor each eye separately.

[0061] 7, an example of an output beam output by a waveguide is shown. While one waveguide is illustrated, it should be understood that other waveguides in waveguide assembly 260 (FIG. 6) may function similarly, and that waveguide assembly 260 includes multiple waveguides. Light 640 is launched into waveguide 270 at input surface 460 of waveguide 270 and propagates within waveguide 270 by TIR. At the point where light 640 impinges on DOE 570, a portion of the light exits the waveguide as output beam 650. Output beam 650 is illustrated as being approximately parallel, but may be redirected to propagate to eye 210 at an angle (e.g., divergent output beam formation), as discussed herein, and depending on the depth plane associated with waveguide 270. It should be understood that a nearly collimated exit beam may refer to a waveguide with outcoupling optics that outcouples light to form an image that appears to be set at a depth plane at a long distance (e.g., optical infinity) from the eye 210. Other waveguides or other sets of outcoupling optics may output a more divergent exit beam pattern, which would require the eye 210 to accommodate 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.

[0062] In some embodiments, a full-color image may be formed at each depth plane by overlaying an image in each of the primary colors, for example, three or more primary colors. FIG. 8 illustrates an example of a stacked waveguide assembly, with each depth plane including an image formed using multiple different primary colors. The illustrated embodiment shows depth planes 240a-240f, but more or fewer depths are also contemplated. Each depth plane may have three or more primary color images associated with it, including a first image in a first color G, a second image in a second color R, and a third image in a third color B. Different depth planes are indicated in the diagram by different numbers for diopters (dpt) following the letters G, R, and B. By way of example only, the number following each of these letters indicates the diopter (1 / m), i.e., the inverse distance of the depth plane from the viewer, and each box in the diagram represents an individual primary color image. In some embodiments, the exact locations of the depth planes for different primary colors may be varied to account for differences in the eye's focusing of light of different wavelengths. 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 an arrangement may increase visual acuity and user comfort and / or reduce chromatic aberrations.

[0063] In some embodiments, light for each primary color may be output by a single dedicated waveguide, such that each depth plane may have multiple waveguides associated with it. In such embodiments, each box in the diagram containing the letter G, R, or B may be understood to represent an individual waveguide, and three waveguides may be provided per depth plane, resulting in three primary color images per depth plane. While the waveguides associated with each depth plane are shown adjacent to each other in this drawing for ease of illustration, it should be understood that in a physical device, the waveguides may all be arranged in a stack with one waveguide per level. In some other embodiments, multiple primary colors may be output by the same waveguide, such that, for example, only a single waveguide may be provided per depth plane.

[0064] 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 may replace one or more of the red, green, or blue colors. In some embodiments, features 320, 330, 340, and 350 may block or otherwise obstruct light from the surrounding environment to the viewer's eyes. Selectively transparent The optical filter may be an active or passive optical filter configured to:

[0065] It should be understood that references throughout this disclosure to a given color of light are understood to encompass light of one or more wavelengths within the range of wavelengths of light that are perceived by a viewer as that given color. For example, red light may include one or more wavelengths of light that are within the range of about 620-780 nm, green light may include one or more wavelengths of light that are within the range of about 492-577 nm, and blue light may include one or more wavelengths of light that are within the range of about 435-493 nm.

[0066] In some embodiments, light source 530 (FIG. 6) may be configured to emit light at one or more wavelengths outside the range of a viewer's visual perception, e.g., infrared and / or ultraviolet wavelengths. Additionally, the waveguide incoupling, outcoupling, and other light redirecting structures of display 250 may be configured to direct and emit this light from the display toward the user's eye 210, e.g., for imaging and / or user stimulation applications.

[0067] Referring now to FIG. 9A , in some embodiments, light impinging on a waveguide may need to be redirected to incoupling the light into the waveguide. An incoupling optical element may be used to redirect and incoupling the light into its corresponding waveguide. FIG. 9A illustrates a cross-sectional side view of an example of a plurality or set 660 of stacked waveguides, each including an incoupling optical element. The waveguides may each be configured to output light of one or more different wavelengths or one or more different wavelength ranges. While stack 660 may correspond to stack 260 ( FIG. 6 ), and the illustrated waveguides of stack 660 may correspond to a portion of multiple waveguides 270, 280, 290, 300, 310, it should be understood that light from one or more of image injection devices 360, 370, 380, 390, 400 is injected into the waveguide from a location requiring the light to be redirected for incoupling.

[0068] The illustrated set 660 of stacked waveguides includes waveguides 670, 680, and 690. Each waveguide includes an associated internal coupling optical element (which may also be referred to as the light input area on the waveguide), for example, internal coupling optical element 700 is disposed on a major surface (e.g., the top major surface) of waveguide 670, internal coupling optical element 710 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and internal coupling optical element 720 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some embodiments, one or more of internal coupling optical elements 700, 710, 720 may be disposed on the bottom major surface of an individual waveguide 670, 680, 690 (particularly, one or more internal coupling optical elements are reflective polarizing optical elements). As shown, the internal coupling optical elements 700, 710, 720 may be disposed on the upper major surface of the respective waveguide 670, 680, 690 (or on top of the next lower waveguide), and in particular, the internal coupling optical elements are transmissive turning optical elements. In some embodiments, the internal coupling optical elements 700, 710, 720 may be disposed within the body of the respective waveguide 670, 680, 690. In some embodiments, as discussed herein, the internal coupling optical elements 700, 710, 720 are wavelength selective, such that they selectively redirect one or more wavelengths of light while transmitting other wavelengths of light. While illustrated on one side or corner of the respective waveguide 670, 680, 690, it should be understood that the internal coupling optical elements 700, 710, 720 may be disposed within other areas of the respective waveguide 670, 680, 690 in some embodiments.

[0069] As shown, the in-coupling optical elements 700, 710, 720 may be laterally offset from one another. In some embodiments, each in-coupling optical element may be offset to receive light without that light passing through another in-coupling optical element. For example, each in-coupling optical element 700, 710, 720 may be configured to receive light from different image input devices 360, 370, 380, 390, and 400, as shown in FIG. 6 , and may be separated (e.g., laterally spaced) from the other in-coupling optical elements 700, 710, 720 so as to receive substantially no light from others of the in-coupling optical elements 700, 710, 720.

[0070] Each waveguide also includes an associated optically dispersive element, for example, optically dispersive element 730 is disposed on a major surface (e.g., the top major surface) of waveguide 670, optically dispersive element 740 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and optically dispersive element 750 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some other embodiments, optically dispersive elements 730, 740, 750 may be disposed on the bottom major surfaces of the associated waveguides 670, 680, 690, respectively. In some other embodiments, the optically dispersive elements 730, 740, 750 may be disposed on both the top and bottom major surfaces of the associated waveguides 670, 680, 690, respectively, or the optically dispersive elements 730, 740, 750 may be disposed on different ones of the top and bottom major surfaces in different associated waveguides 670, 680, 690, respectively.

[0071] Waveguides 670, 680, 690 may be spaced apart and separated, for example, by gas, 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 immediately adjacent waveguides 670, 680, 690). Preferably, the refractive index of the material forming layers 760a, 760b is 0.05 or more or 0.10 or less than the refractive index of the material forming waveguides 670, 680, 690. Advantageously, the lower refractive index layers 760a, 760b may function as cladding layers to promote TIR of light through the waveguides 670, 680, 690 (e.g., TIR between the top and bottom major surfaces of each waveguide). In some embodiments, the layers 760a, 760b are formed from air. Although not shown, it should be understood that the top and bottom of the illustrated set of waveguides 660 may include immediate cladding layers.

[0072] Preferably, for ease of manufacturing and other considerations, the materials forming waveguides 670, 680, 690 are similar or the same, and the materials forming layers 760a, 760b are similar or the same. In some embodiments, the materials forming waveguides 670, 680, 690 may differ between one or more waveguides, and / or the materials forming layers 760a, 760b may differ while still maintaining the various refractive index relationships discussed above.

[0073] 9A, light rays 770, 780, 790 enter the set of waveguides 660. It should be understood that light rays 770, 780, 790 may be injected into the waveguides 670, 680, 690 by one or more image injection devices 360, 370, 380, 390, 400 (FIG. 6).

[0074] In some embodiments, the light rays 770, 780, 790 have different properties, such as different wavelengths or different wavelength ranges, which may correspond to different colors. Each of the internal coupling optical elements 700, 710, 720 deflects the incident light so that the light propagates through a respective one of the waveguides 670, 680, 690 by TIR.

[0075] For example, in-coupling optical element 700 may be configured to selectively deflect light ray 770 having a first wavelength or range of wavelengths. Similarly, transmitted light ray 780 impinges on and is deflected by in-coupling optical element 710, which is configured to deflect light of a second wavelength or range of wavelengths. Similarly, light ray 790 is deflected by in-coupling optical element 720, which is configured to selectively deflect light of a third wavelength or range of wavelengths.

[0076] 9A , the deflected light rays 770, 780, 790 are deflected to propagate through the corresponding waveguides 670, 680, 690. That is, the in-coupling optical element 700, 710, 720 of each waveguide deflects the light into its corresponding waveguide 670, 680, 690, in-coupling the light into the corresponding waveguide. The light rays 770, 780, 790 are deflected at an angle that causes the light to propagate through the respective waveguides 670, 680, 690 by TIR. The light rays 770, 780, 790 propagate through the respective waveguides 670, 680, 690 by TIR until they impinge on the waveguide's corresponding optical dispersive element 730, 740, 750.

[0077] 9B, a perspective view of the multiple stacked waveguide embodiment of FIG. 9A is illustrated. As previously described, in-coupled light rays 770, 780, 790 are deflected by in-coupling optical elements 700, 710, 720, respectively, and then propagate by TIR within waveguides 670, 680, 690, respectively. Light rays 770, 780, 790 then impinge on optically dispersive elements 730, 740, 750, respectively. Optically dispersive elements 730, 740, 750 deflect light rays 770, 780, 790 to propagate toward out-coupling optical elements 800, 810, 820, respectively.

[0078] In some embodiments, the optically dispersive elements 730, 740, 750 are orthogonal pupil expanders (OPEs). In some embodiments, the OPEs may both deflect or disperse light into the out-coupling optical elements 800, 810, 820 and also increase the beam or spot size of this light as it propagates into the out-coupling optical elements. In some embodiments, for example, if the beam size is already the desired size, the optically dispersive elements 730, 740, 750 may be omitted and the in-coupling optical elements 700, 710, 720 may be configured to deflect light directly into the out-coupling optical elements 800, 810, 820. For example, referring to FIG. 9A , the optically dispersive elements 730, 740, 750 may be replaced with the out-coupling optical elements 800, 810, 820, respectively, in some embodiments. In some embodiments, the outcoupling optical element 800, 810, 820 is an exit pupil (EP) or exit pupil expander (EPE) that directs light to the viewer's eye 210 (FIG. 7). The OPE may be configured to increase the size of the eyebox in at least one axis, and the EPE may increase the size of the eyebox in an axis that intersects, e.g., is perpendicular to, the axis of the OPE. It is configured to It should be understood that this is also acceptable.

[0079] 9A and 9B, in some embodiments, a waveguide set 660 includes, for each primary color, waveguides 670, 680, 690, in-coupling optical elements 700, 710, 720, optically dispersive elements (e.g., OPEs) 730, 740, 750, and out-coupling optical elements (e.g., EPs) 800, 810, 820. The waveguides 670, 680, 690 may be stacked with an air gap / cladding layer between each one. The in-coupling optical elements 700, 710, 720 redirect or deflect incident light into their respective waveguides (with different in-coupling optical elements receiving light of different wavelengths). The light then propagates at an angle that will result in TIR within the individual waveguides 670, 680, 690. In the example shown, light ray 770 (e.g., blue light) is polarized by the first in-coupling optical element 700 in the manner described above, then continues bouncing down the waveguide, interacting with an optically dispersive element (e.g., OPE) 730 and then an out-coupling optical element (e.g., EP) 800. Light rays 780 and 790 (e.g., green and red light, respectively) pass through waveguide 670, with light ray 780 impinging on and being deflected by in-coupling optical element 710. Light ray 780 will then, via TIR, bounce down waveguide 680, travel to its optically dispersive element (e.g., OPE) 740 and then to the out-coupling optical element (e.g., EP) 810. Finally, light ray 790 (e.g., red light) passes through waveguide 690 and impinges on in-coupling optical element 720 of waveguide 690. The light in-coupling optical element 720 deflects the light ray 790 so that it propagates by TIR to the light dispersive element (e.g., OPE) 750 and then by TIR to the out-coupling optical element (e.g., EP) 820. The out-coupling optical element 820 then finally out-couples the light ray 790 to a viewer, who also receives the out-coupled light from the other waveguides 670, 680.

[0080] FIG. 9C illustrates a top-down plan view of an example of the multiple stacked waveguides of FIGS. 9A and 9B. As shown, waveguides 670, 680, 690 may be vertically aligned, along with each waveguide's associated optically dispersive elements 730, 740, 750 and associated out-coupling optical elements 800, 810, 820. However, as discussed herein, the in-coupling optical elements 700, 710, 720 are not vertically aligned. Rather, the in-coupling optical elements are preferably non-overlapping (e.g., laterally spaced apart, as seen in the top-down view). As discussed further herein, this non-overlapping spatial arrangement facilitates the injection of light from different sources into different waveguides on a one-to-one basis, thereby allowing a specific light source to be uniquely coupled to a specific waveguide. In some embodiments, arrays including non-overlapping, spatially separated in-coupling optical elements may be referred to as shifted-pupil systems, and the in-coupling optical elements in these arrays may correspond to sub-pupils. (liquid crystal grid)

[0081] Liquid crystals are partially ordered materials whose molecules are often shaped like rods or plates that can be aligned along a certain direction. The direction and pattern along which the liquid crystal molecules are oriented can be manipulated through the use of template patterns that interact with the molecules (e.g., through steric and / or tethering energy interactions). In addition, the liquid crystal material may comprise a chiral dopant and / or a reactive mesogen (RM). The chiral dopant can induce rotation of the liquid crystal molecules across the thickness of the liquid crystal material, and the reactive mesogen can allow the orientation and position of the liquid crystal molecules to be fixed through polymerization. The rotation can be in increments corresponding to the twist angle (Φ) as shown in Figure 10C.

[0082] As described herein, the in-coupling optical elements 700, 710, 720, light dispersive elements (e.g., OPEs) 730, 740, 750, and out-coupling optical elements (e.g., EPs) 800, 810, 820 discussed above with reference to Figures 9A and 9B can include liquid crystal grating structures for steering light into and / or out of the waveguides 670, 680, 690. The liquid crystal grating structures preferably diffract or redirect light at large angles relative to the normal to the grating, for example, to facilitate in-coupling of light into the waveguide so that the light propagates through the waveguide by TIR. In addition, it may be preferable if the liquid crystal grating structure has high diffraction efficiency over a wide range of incident angles. Some types of liquid crystal gratings, i.e., polarization gratings, can exhibit high diffraction efficiency over a wide range of incident angles at large diffraction angles, which can guide light into the waveguide by TIR. However, conventional alignment methods, including optical alignment and micro-polishing techniques, have challenges in scaling for mass manufacturing and fundamental limitations in spatial patterns of LC materials. LC alignment using imprint templates with subwavelength features (e.g., nanoscale patterns) can enable mass manufacturing and / or provide the flexibility to create arbitrary spatial patterns.

[0083] Various embodiments of conventional diffraction gratings can achieve high diffraction efficiency only over a small wavelength range. Therefore, they may not be capable of broadband operation. Metasurfaces with subwavelength features have been found to be capable of shaping optical wavefronts by altering the phase, amplitude, and / or polarization of incident light. LC materials aligned using an imprint template with nanoscale features, from which LC molecules form the metasurface, may be used to obtain liquid crystal metasurfaces, which may have optical properties different from those of the liquid crystal bulk material. For example, liquid crystal metasurfaces are broadband and capable of diffracting incident light within a wide range of wavelengths incident at a wide range of angles of incidence with high efficiency. For example, LC metasurfaces may be capable of diffracting incident light of red, green, and blue wavelengths along a desired direction with nearly identical diffraction efficiency. Examples of LC metasurfaces include liquid crystal metamaterials and / or liquid crystal-based Pancharatnam Berry Phase Optical Elements (PBPEs).

[0084] Alignment of liquid crystal molecules using nanoimprinting techniques as discussed herein can be used to fabricate liquid crystal materials with multiple distinct alignment patterns that involve progressive transitions (e.g., successive transitions) of liquid crystal molecular directors between adjacent alignment patterns. In various embodiments, the grating period can refer to the distance between the centers of two consecutive liquid crystal molecules in a grating structure that has its longitudinal axes aligned along the same direction. In some embodiments of liquid crystal materials with multiple adjacent alignment patterns, the grating period can refer to the distance between the centers of consecutive liquid crystal molecules in each alignment pattern.

[0085] Advantageously, the various liquid crystal grating structures discussed herein are preferably configured to provide high diffraction efficiency over a wide range of incident angles (e.g., at least about ±20 degrees around the surface normal, at least about ±30 degrees around the surface normal, at least about ±45 degrees around the surface normal, etc.). For example, the liquid crystal grating structures can be configured to provide a diffraction efficiency of at least about 10% (e.g., at least 20%, 30%, 40%, 50%, 60%, or 75%) for light incident at an angle of about ±50 degrees relative to the surface normal for wavelengths of about 400 nm to about 700 nm. Thus, the liquid crystal grating structures described herein can advantageously have low sensitivity to the incident angle of light. In some embodiments, the liquid crystal grating structures discussed herein are configured to be narrow-band. For example, the liquid crystal grating structures discussed herein can be configured to diffract wavelengths within the visible spectrum of about 400 nm to about 450 nm, about 450 nm to about 500 nm, about 500 nm to about 550 nm, about 550 nm to about 600 nm, about 600 nm to about 650 nm, or about 650 nm to about 700 nm. In some other embodiments, the liquid crystal grating structures discussed herein can be configured to be broadband. For example, the liquid crystal grating structures discussed herein can be configured to diffract wavelengths within the visible spectrum of about 400 nm to about 700 nm. As another example, the liquid crystal grating structures discussed herein can be configured to diffract wavelengths within the ultraviolet spectrum of about 250 nm-400 nm. As yet another example, the liquid crystal grating structures discussed herein can be configured to diffract wavelengths within the infrared spectral range, such as, for example, from about 700 nm to 1 micron, from about 1 micron to 3 microns, from about 1.5 microns to 5 microns, from about 3 microns to 10 microns, or any combination of these ranges or any subrange or combination of subranges within these ranges. As another example, the grating structure can be configured to diffract incident light having a wavelength within the range of about 300 nm to about 10 microns.Preferably, when a liquid crystal grating structure as discussed herein is employed in a display application, the grating structure is configured to diffract visible light (e.g., in the red, green, and / or blue spectral ranges). In various embodiments, the liquid crystal grating structure can diffract visible light (e.g., in the red, green, and / or blue spectral ranges) such that the light propagates from the grating structure at wide diffraction angles, e.g., angles suitable for TIR within a waveguide on which the grating structure may be formed. The liquid crystal grating structures discussed herein can have grating periods in the range of about 100 nm to about 100 μm, depending on the wavelength range over which the grating structure is configured to operate. For example, the periodicity of the grating structure may be about 10 nm to about 50 nm, about 20 nm to about 60 nm, about 30 nm to about 70 nm, about 40 nm to about 80 nm, about 50 nm to about 90 nm, about 60 nm to about 100 nm, about 100 nm to about 200 nm, about 200 nm to about 350 nm, about 330 nm to about 410 nm, about 370 nm to about 480 nm, about 450 nm to about 510 nm, about 500 nm to about 570 nm, about 550 nm to about 70 0 nm, about 650 nm to about 1 μm, about 980 nm to about 3 μm, about 1.3 μm to about 3.2 μm, about 2.3 μm to about 5 μm, about 5 μm to about 10 μm, about 5 μm to about 20 μm, about 15 μm to about 45 μm, about 25 μm to about 60 μm, about 35 μm to about 75 μm, about 45 μm to about 100 μm, or any combination of these ranges or any sub-range or combination of sub-ranges within these ranges.

[0086] The grating structure may be fabricated using a variety of methods, including, but not limited to, aligning liquid crystal molecules in a layer of polymerizable liquid crystal material using a patterned alignment layer that may be underneath the liquid crystal material. The alignment layer may be patterned using imprinting techniques or by using optical methods.

[0087] As discussed above, in some embodiments, liquid crystal grating structures may form light redirecting elements for various waveguides of waveguide stack 260 (FIG. 6) or 660 (FIGS. 9A-9C). For example, such liquid crystal grating structures may advantageously 、The liquid crystal grating structures may be applied to form in-coupling optical elements 700, 710, 720, light dispersive elements 730, 740, 750, and / or out-coupling optical elements 800, 810, 820 (FIGS. 9A-9C). In addition to AR display systems, the liquid crystal grating structures may be applied to other applications in which diffractive optical elements are utilized. For example, the liquid crystal grating structures may be used to steer light in other optical systems, including VR display systems, flat panel computer monitors or televisions, illuminated signs, imaging systems, etc.

[0088] FIG. 10A illustrates a top-down perspective view of an example liquid crystal layer 1000 including multiple adjacent domains (e.g., domains 1001a, 1001b, 1001c, 1001d, 1001e, and 1001f). The longitudinal axes of the liquid crystal molecules in each domain may generally be aligned along the same direction. The longitudinal axes of the liquid crystal molecules in adjacent domains need not be aligned along the same direction. For example, the longitudinal axes of the liquid crystal molecules in domains 1001b and 1001d adjacent to domain 1001a are aligned along a different direction than the direction along which the longitudinal axes of the liquid crystal molecules in domain 1001a are aligned. In the embodiment illustrated in FIG. 10A, only nine domains are shown, but other embodiments may have fewer or more than nine domains. Furthermore, although only three different orientations of the longitudinal axes of the liquid crystal molecules are shown in FIG. 10A, other embodiments may include domains with more or fewer different orientations. Additionally, in various embodiments of the liquid crystal layer, different domains can have different shapes and / or sizes. In various embodiments, different domains can have different shapes (e.g., square, rectangular, hexagonal, octagonal, oval, circular, etc.). In various embodiments, different domains can have irregular shapes.

[0089] 10B illustrates an enlarged top view of the liquid crystal layer 1000 illustrated in FIG. 10A. This top view in FIG. 10B shows the liquid crystal molecules in the top portion of the liquid crystal layer 1000, which may be referred to herein as the top sublayer. The liquid crystal molecules directly below the top or topmost liquid crystal molecules (e.g., directly below the top or topmost sublayer) may have a different orientation, as shown in FIG. 10C. FIGS. 10C-10F illustrate the orientation of the liquid crystal molecules along axis X-X' of the liquid crystal layer 1000. Ta 10C-10F, the liquid crystal layer 1000 has two major surfaces 1002a and 1002b. The two major surfaces 1002a and 1002b are intersected by a surface normal 1003. The two major surfaces 1002a and 1002b extend in the xy plane, and the surface normal 1003 extends parallel to the z-axis. As shown in the enlarged top view of FIG. 10B, the longitudinal axes of the uppermost liquid crystal molecules in the first domain 1001a are generally aligned parallel to the y-axis. The longitudinal axes of the liquid crystal molecules in the second domain 1001b are generally aligned at an angle (e.g., about 30 to 60 degrees) to the y-axis. The longitudinal axes of the liquid crystal molecules in the third domain 1001c are generally aligned perpendicular to the y- and z-axes.

[0090] Liquid crystal layer 1000 may be considered to have multiple sublayers, such as sublayers 1010a, 1010b, 1010c, and 1010d. Each sublayer (e.g., 1010a, 1010b, 1010c, or 1010d) may be defined by multiple liquid crystal molecules aligned in a common plane, and thus each sublayer may be only a single liquid crystal molecule thick. The sublayers form a consolidated layer of liquid crystal material having a thickness T, which may be equal to the total thickness of all the sublayers. While three-quarters sublayers are illustrated, it should be understood that liquid crystal layer 1000 may include more or fewer sublayers.

[0091] In various embodiments, the liquid crystal layer 1000 can comprise a chiral nematic liquid crystal material. For example, the plurality of liquid crystal material sublayers may comprise cholesteric liquid crystal materials. In embodiments of the liquid crystal layer 1000 comprising chiral materials, the liquid crystal molecules may have a twist angle φ defined by the angular rotation between the longitudinal axes of the liquid crystal molecules (e.g., 1005a) of a sublayer (e.g., 1010a) of the liquid crystal layer 1000 and the longitudinal axes of the underlying liquid crystal molecules (e.g., 1005b) of an adjacent sublayer (e.g., 1010b), as shown in FIG. 10C. The liquid crystal material may also be polymerizable. As discussed herein, the liquid crystal material may comprise a reactive mesogen (RM), such as, for example, a liquid crystalline diacrylate. Also, as discussed herein, the liquid crystal layer 1000 may include a chiral dopant. Examples of chiral dopants include cholesteryl benzoate, cholesteryl nonanoate, cholesteryl chloride, and cholesteryl oleyl carbonate.

[0092] However, the liquid crystal need not be a chiral liquid crystal material. As shown in Figures 10D-10F, the longitudinal axes of the molecules in sublayer 1010a are not twisted relative to the molecules in underlying sublayers 1010b or 1010c. The longitudinal axes of the liquid crystal molecules can be aligned along either the x-, y-, or z-axis. For example, as shown in Figure 10D, the longitudinal axes of the liquid crystal molecules are aligned parallel to the y-axis. As another example, as shown in Figure 10E, the longitudinal axes of the liquid crystal molecules are aligned parallel to the x-axis. As yet another example, as shown in Figure 10F, the longitudinal axes of the liquid crystal molecules are aligned parallel to the z-axis. The side views shown in Figures 10C-10F may equally correspond to Figures 10A or 10B.

[0093] 10A and 10B, it may be desirable to introduce a small domain gap "d" between adjacent domains with different alignment patterns. The presence of small gaps between adjacent domains with different alignment patterns can advantageously reduce the occurrence of disclinations or other surface defects along the domain boundaries during fabrication of liquid crystal layer 1000. Reduced disclinations or other surface defects along the domain boundaries of liquid crystal layer 1000 can reduce undesired light scattering and other undesirable optical effects. The domain gap "d" may refer to the shortest distance between the nearest edges of an adjacent pair of domains. For example, in the illustrated embodiment, the domain gap between domain 1001e and domain 1001b is d1, the domain distance between domain 1001e and domain 1001d is d2, and the domain distance between domain 1001e and domain 1001f is d3. The domain gap "d" between adjacent domains with different alignment patterns can be configured to achieve a progressive transition of the longitudinal axes of the liquid crystal molecules between adjacent domains with different alignment patterns and to have reduced occurrence of disclinations or other surface defects along the domain boundaries. For example, the domain gap "d" between adjacent domains with different alignment patterns can be configured to achieve a continuous transition of the longitudinal axes of the liquid crystal molecules between adjacent domains with different alignment patterns. The domain gap between adjacent domains with different alignment patterns configured to achieve a continuous transition of the liquid crystal molecules can be less than 200 nm. For example, the domain gap between adjacent domains with different alignment patterns can be about 1 nm to about 20 nm, about 5 nm to about 30 nm, about 10 nm to about 50 nm, about 25 nm to about 75 nm, about 45 nm to about 100 nm, about 60 nm to about 120 nm, about 80 nm to about 150 nm, 100 nm to about 200 nm, or any combination of these ranges or any subrange or combination of subranges within these ranges.As discussed above, the domain gaps are configured such that while the longitudinal axes of the liquid crystal molecules within each domain are aligned according to the alignment pattern within each pattern, the longitudinal axes of the liquid crystal molecules within the gaps between adjacent domains are oriented to provide a gradient or gradual transition, such as a substantially smooth or continuous transition, of the longitudinal axes of the liquid crystal molecules between adjacent domains.

[0094] The liquid crystal layer 1000 can be fabricated using an alignment layer with surface relief features. The surface relief features of the alignment layer can induce alignment of molecules of a liquid crystal material deposited on the alignment layer. Under certain conditions, the anchoring energy (W) provided by the surface relief structures of the alignment layer can be expressed as follows: [ka] where K is the deformation constant of the liquid crystal material, D is the depth of the surface relief features of the alignment layer, and Λ is the width or pitch of the surface relief features (the distance between two consecutive surface relief features). Without any loss of generality, the anchoring energy (W) discussed above can provide a measure of the energy required to change the longitudinal axes of the LC molecules from their initial orientation to a desired orientation in the plane of the liquid crystal surface. From the above equation, it can be seen that as the width or pitch (Λ) of the surface relief structures is reduced (for patterns of the same aspect ratio, i.e., depth / period [ka] Note that, assuming constant, a higher anchoring energy is provided by the surface relief features.

[0095] Thus, alignment layers comprising surface relief features can be used to fabricate liquid crystal devices in which liquid crystal molecules are aligned to the pattern formed by the surface relief features. The surface relief features of the alignment layer can comprise a variety of groove geometries that can vary in width, pitch, and / or orientation along length scales on the order of a few nanometers, hundreds of nanometers, and / or microns. Because the anchoring energy discussed above is inversely proportional to the cube of the width or pitch of the surface relief features, large variations in anchoring energy can be obtained across the surface of the liquid crystal by introducing small variations in the width or pitch of the surface relief features. For example, consider an embodiment of an alignment layer comprising a first domain comprising a first set of surface relief features arranged to form a first pattern, separated by an area that does not include surface relief features from a second domain comprising a second set of surface relief features arranged to form the first pattern. Such an embodiment of the alignment layer can be used to fabricate a liquid crystal device with a first domain in which the longitudinal axes of the liquid crystal molecules are aligned along the direction of a first set of surface relief features and a second domain in which the longitudinal axes of the liquid crystal molecules are aligned along the direction of a second set of surface relief features. The longitudinal axes of the liquid crystal molecules in the region of the liquid crystal device between the first and second domains can gradually transition from the direction of the first set of surface relief features to the direction of the second set of surface relief features. The domain gap can be selected so that the transition between the orientation of the longitudinal axes of the liquid crystal molecules in the first domain and the orientation of the longitudinal axes of the liquid crystal molecules in the second domain is generally smooth, rather than abrupt or discontinuous. For example, the domain gap corresponding to the region of the alignment layer that does not include surface relief features can be selected so that the transition between the orientation of the longitudinal axes of the liquid crystal molecules in the first domain and the orientation of the longitudinal axes of the liquid crystal molecules in the second domain is continuous.

[0096] In some embodiments of methods for fabricating liquid crystal devices in which liquid crystal molecules are aligned to various groove geometries whose width, period, and / or direction can vary along length scales on the order of nanometers, hundreds of nanometers, and / or microns, the alignment layer can comprise a polymerizable liquid crystal (PLC), also known as a reactive mesogen (RM). The alignment layer can be fabricated by contacting a layer of PLC material with an imprint template comprising various grooves whose width, period, and direction can vary along length scales on the order of nanometers, hundreds of nanometers, and / or microns. The longitudinal axes of the molecules in the PLC layer can be allowed to self-align with the grooves of the imprint template. For example, the longitudinal axes of the molecules in the PLC layer can self-align with the grooves of the imprint template in response to the application of heat, irradiation with UV light, and / or after a sufficient period of time. Once the longitudinal axes of the molecules in the PLC layer are self-aligned with the imprint template grooves, the PLC layer is polymerized, for example, by irradiation with heat and / or UV illumination. The polymerization advantageously fixes the longitudinal axes of the molecules of the PLC layer so that the orientation of the molecules of the PLC layer is maintained after the PLC layer is separated from the imprint template.

[0097] Using an imprint template to fabricate alignment layers comprising surface relief features with dimensions (e.g., length, width, and / or depth) on the order of a few nanometers, hundreds of nanometers, and / or microns, and / or surface relief features arranged to form complex geometric patterns in which the direction and / or periodicity between successive features varies along length scales on the order of a few nanometers, hundreds of nanometers, and / or microns, may be advantageous over other liquid crystal fabrication methods, such as polishing or photoalignment methods. For example, as discussed above, it may not be practical to produce surface relief features with dimensions (e.g., length, width, and / or depth) on the order of a few nanometers, hundreds of nanometers, using some micropolishing methods, which are low-resolution methods. In addition, it may not be possible to fabricate alignment layers with the throughput required to achieve mass production using some polishing methods. While photoalignment methods can be used to fabricate alignment layers with uniform and non-uniform alignment of liquid crystal molecules, in some instances, it may not be practical to produce alignment layers with complex spatial patterns using photoalignment methods. As with polishing methods, it is difficult to achieve the throughput required to achieve high-volume fabrication of complex spatial LC patterns using some optical alignment methods.

[0098] FIG. 11A illustrates a plan view of an embodiment of an imprint template 1100 comprising multiple features that can be used to fabricate a liquid crystal layer 1000, such as the layer 1000 shown in FIG. 10A. FIG. 11B illustrates a cross-sectional view of the imprint template 1100 along axis B-B′. The imprint template 1100 comprises multiple domains (e.g., 1101a, 1101b, and 1101c). Each of the multiple domains includes multiple surface relief features. The surface relief features can include linear or curved elongated grooves and / or protrusions, prisms, arcs, raised bumps, or recesses. The surface relief features within each of the multiple domains can be arranged to form simple or complex geometric patterns. The arrangement of the surface relief features can be configured to manipulate the amplitude, phase, and / or polarization of incident light to achieve a desired optical effect.

[0099] In various embodiments, each domain can include subwavelength features. In such embodiments, the size of the surface relief features or the spacing between adjacent surface relief features can have a short length scale, on the order of a few nanometers, hundreds of nanometers, or even a few microns. For example, the width "λ" of each surface relief feature within each of the plurality of domains can be about 20 nm to about 100 nm, about 30 nm to about 90 nm, about 40 nm to about 80 nm, about 50 nm to about 75 nm, about 60 nm to about 70 nm, or any combination of ranges or any subranges or combinations of subranges within these ranges. As another example, the spacing "Λ" between consecutive features within each of the plurality of domains can be about 20 nm to about 100 nm, about 30 nm to about 90 nm, about 40 nm to about 80 nm, about 50 nm to about 75 nm, about 60 nm to about 70 nm, or any combination of ranges or any subranges or combinations of subranges within these ranges. Without any loss of generality, the spacing "Λ" between consecutive features may correspond to the pitch. As yet another example, the depth (or height) "D" of the features within each of the plurality of domains can be from about 10 nm to about 100 nm, from about 20 nm to about 90 nm, from about 30 nm to about 80 nm, from about 40 nm to about 75 nm, from about 50 nm to about 70 nm, or any combination of these ranges or any subrange or combination of subranges within these ranges.

[0100] In various embodiments, the domain spacing "d" between adjacent domains can be about 10 nm to about 100 nm, about 20 nm to about 90 nm, about 30 nm to about 80 nm, about 40 nm to about 75 nm, about 50 nm to about 70 nm, or any combination of these ranges or any subrange or combination of subranges within these ranges. In various embodiments, the multiple domains comprising surface relief features can be arranged in a square grid across the surface of the imprint template 1100 such that the domain spacing "d" between each pair of adjacent domains is uniform. In other embodiments, the multiple domains comprising surface relief features can be arranged irregularly across the surface of the imprint template 1100 such that the domain spacing "d" between different pairs of adjacent domains is not uniform. As discussed above, the domain spacing introduced between adjacent domains can help reduce disclinations or other surface defects that may occur along domain boundaries during the fabrication of liquid crystals. (Exemplary Methods of Manufacturing Liquid Crystal Devices)

[0101] 12A-12D illustrate examples of methods for fabricating various liquid crystal devices described herein. Referring to FIG. 12A, a polymer liquid crystal (PLC) layer 1203 is disposed over a substrate 1201. The substrate 1201 is preferably optically transparent. Examples of suitable materials for the substrate 1201 include glass, quartz, sapphire, indium tin oxide (ITO), or polymeric materials, including polycarbonate, polyacetate, and acrylic. In some embodiments, the substrate 1201 can be transparent to light in at least one of visible or infrared wavelengths. The substrate can include a pair of major surfaces and a surrounding edge. The major surface can be the largest-area surface of the substrate or can be one of a pair of similarly sized opposing surfaces having a larger area than the other surface. The liquid crystal device can be configured to reflect, refract, diffract, or otherwise redirect light incident on or against the major surface of the substrate.

[0102] In some embodiments, the PLC layer 1203 is configured as an alignment layer that causes the liquid crystal molecules to adopt a specific orientation or pattern, for example, due to steric interactions with the liquid crystal molecules and / or anchoring energy imparted to the liquid crystal molecules by a subsequently deposited optical alignment layer. The PLC layer 1203 can include a polymerizable liquid crystal material (reactive mesogen). In some embodiments, the PLC layer 1203 can include an azo-containing polymer. The PLC layer 1203 can be disposed on one of the major surfaces of the substrate by, for example, a spin-coating process or jet deposition. The PLC layer 1203 can have a thickness of approximately 10 nm to 10 microns.

[0103] PLC layer 1203 is imprinted with a plurality of surface relief features by contacting the exposed surface of the PLC layer with imprint template 1205, as depicted in Figures 12A and 12B. Imprint template 1205 can include features that are the inverse of the features to be imprinted on the exposed surface of the PLC layer. In various embodiments, imprint template 1205 can include features with sub-wavelength dimensions. haveFor example, the imprint template 1205 may include features having dimensions (e.g., length, width, and / or depth) on the order of a few nanometers, hundreds of nanometers, and / or microns. For example, the imprint template 1205 may include features having lengths of about 20 nm to about 100 nm. As another example, the imprint template 1205 may include features having widths of about 20 nm to about 100 nm. As yet another example, the imprint template 1205 may include features having depths of about 10 nm to about 100 nm. In various embodiments, the length and / or width of the feature may exceed the depth of the feature. However, in some embodiments, the depth may be approximately equal to the length and / or width of the feature. The features of each domain of the imprint template 1205 may be arranged to form complex geometric patterns within each domain, with the direction and / or periodicity between successive features varying along length scales on the order of a few nanometers, hundreds of nanometers, and / or microns. In various embodiments, the imprint template 1205 can include a plurality of spaced apart domains. Each domain can include a plurality of features having sub-wavelength dimensions. Each domain can be separated from neighboring domains by a domain spacing. The domain spacing can have a value between about 10 nm and about 100 nm, between about 20 nm and about 90 nm, between about 30 nm and about 80 nm, between about 40 nm and about 75 nm, between about 50 nm and about 70 nm, or any combination of these ranges or any subrange or combination of subranges within these ranges. In various implementations, the domain spacing can be 10 nm or less and / or 100 nm or more. For example, the domain spacing can be 5 nm or less, 2 nm or less, 1 nm or less, or a value between 0 nm and 10 nm. The imprint template 1205 can have similar characteristics to the imprint template 1100 discussed above with reference to FIGS. 11A and 11B.For example, the multiple domains of the imprint template 1205 may be arranged in a square grid across the surface of the imprint template 1205 such that the domain spacing between neighboring domains is uniform. As another example, the imprint template. 1205 The multiple domains may be arranged as concentric circular or elliptical regions, hi other embodiments, the multiple domains may be arranged irregularly across the surface of the imprint template 1205 such that the domain spacing between neighboring domains is not uniform.

[0104] The imprint template 1205 with sub-wavelength features can be designed and fabricated using nanopatterning techniques, including optical lithography, nanoimprint, and ion and electron beam lithography. In various embodiments, the imprint template can comprise a semiconductor material, such as silicon or a glass material.

[0105] When the PLC layer 1203 comes into direct contact with the features of the imprint template 1205, the longitudinal axes of the liquid crystal molecules in the PLC layer 1203 are aligned with the features of the imprint template. In this manner, the exposed surface of the PLC layer is imprinted with a pattern that corresponds to or is complementary to the pattern of the imprint template. After the exposed surface of the PLC layer 1203 is patterned by the imprint template 1205, the PLC layer 1203 is polymerized. Polymerization of the PLC layer 1203 can be achieved by various methods, including, but not limited to, exposure to ultraviolet (UV) radiation as shown in FIG. 12B, application of heat, the passage of time, etc. Polymerization of the PLC layer 1203 can advantageously fix the orientation of the longitudinal axes of the liquid crystal molecules in the PLC layer 1203 even after the PLC layer 1203 is separated from the imprint template, as shown in FIG. 12C.

[0106] After polymerization of the patterned PLC layer 1203, a layer of liquid crystal material 1207 is disposed over the polymerized, patterned PLC layer 1203. The liquid crystal layer can be deposited over the PLC layer 1203 by spin coating, slot coating, bar coating, or jet deposition. The layer of liquid crystal material 1207 can have a thickness of approximately 10 nm to 10 microns. The layer of liquid crystal material 1207 can include doped or undoped liquid crystal material. In various embodiments, the layer of liquid crystal material 1207 can be a polymerizable liquid crystal material, a polymer-stabilized liquid crystal material, or a non-polymerizable liquid crystal material.

[0107] The longitudinal axes of the molecules in the layer of liquid crystal material 1207 self-align to the pattern imprinted on the PLC layer 1203. Thus, the PLC layer 1203 serves as an alignment layer for the layer of liquid crystal material 1207. In some embodiments, the alignment of the longitudinal axes of the molecules in the layer of liquid crystal material 1207 can be accelerated by the application of heat and / or the passage of sufficient time. Using the PLC layer 1203 as an alignment layer for the layer of liquid crystal material 1207 can have several advantages. The first advantage is that the PLC layer 1203 can provide a stronger alignment state for the layer of liquid crystal material 1207 compared to an alignment layer that does not include a polymerizable liquid crystal material. The second advantage is that a homogeneous interface can be achieved when the material of the PLC layer 1203 has similar optical properties to the material of the layer of liquid crystal material 1207. This can advantageously reduce refraction / diffraction from the boundary between the PLC layer 1203 and the layer of liquid crystal material 1207.

[0108] As shown in Figure 12E, additional PLC layers 1209 and 1213, which serve as alignment layers for additional liquid crystal layers 1211 and 1215, may be successively deposited over the aligned layer of liquid crystal material 1207 by repeating the process of Figures 12A-12D. For example, a second PLC layer 1209 is disposed over the layer of liquid crystal material 1207, and subsequently patterned and polymerized using an imprint template. A second layer of liquid crystal material 1211 is disposed over the patterned and polymerized PLC layer 1209 and allowed to self-assemble such that the molecules of the second layer of liquid crystal material 1211 are aligned to the pattern imprinted on the second PLC layer 1209. 3A PLC layer 1213 of liquid crystal material is disposed over the layer 1209, then patterned using an imprint template and polymerized. A third layer 1215 of liquid crystal material is disposed over the patterned and polymerized PLC layer 1213, and the molecules of the third layer 1215 of liquid crystal material are allowed to self-assemble so that they align with the pattern imprinted on the third PLC layer 1213. This sequence may be repeated for additional liquid crystal layers. Preferably, the additional PLC layers 1209 and 1213 may comprise a polymerizable liquid crystal material (reactive mesogen). Preferably, the liquid crystal materials 1207, 1211, and 1215 may comprise a polymerizable liquid crystal material (reactive mesogen). The pattern imprinted on PLC layers 1209 and / or 1213 may be different from the pattern imprinted on PLC layer 1203. However, in some embodiments, the pattern imprinted on PLC layers 1209 and / or 1213 can be the same as the pattern imprinted on PLC layer 1203. In various embodiments, an isolation layer, such as a thin oxide film (with a thickness ranging from a few nm to hundreds of nm), may be deposited over the layer of liquid crystal material (e.g., layer 1207 or layer 1211) before providing the additional PLC layer to reduce the effect of the pattern on the liquid crystal layer (e.g., layer 1207 or layer 1211) directly below. In some embodiments, a planarization template can be used to planarize the exposed surface of the layer of liquid crystal material (e.g., layer 1207, layer 1211, or layer 1215) before providing the additional PLC layer.

[0109] 13A illustrates a scanning electron microscope (SEM) image of an embodiment of an imprint template. The imprint template comprises three domains 1301, 1303, and 1305 separated from one another by domain gaps. The domain gap between the first domain 1301 and the second domain 1303 is d1, and the domain gap between the second domain 1303 and the first domain 1301 is d2. 1303The domain gap between the first domain 1301 and the third domain 1305 is d2. Each of the three domains 1301, 1303, and 1305 comprises a plurality of features. Each dimension (e.g., length, width, or depth) of the plurality of features is less than 100 nm. The domain gaps d1 and d2 are equal to or less than 100 nm. Figure 13B is an SEM image of a patterned PLC layer fabricated using the imprint template of Figure 13A and the method discussed above with reference to Figures 12A-12C. Figure 13C is a polarized light microscope image of the patterned PLC layer shown in Figure 13B. Figure 13C depicts a gray-scale pattern showing the LC orientation relative to the polarizer / analyzer of the polarized light microscope. Note from Figure 13C that the polarized light microscope image exhibits a uniform pattern indicating LC alignment substantially free of alignment defects (i.e., disclinations).

[0110] The methods described herein can be used to fabricate electrically controllable liquid crystal devices that include a liquid crystal layer with subwavelength features. Figure 14 illustrates an embodiment of an electrically controllable liquid crystal device in which a liquid crystal layer 1407, whose molecules are aligned to a patterned alignment layer 1403, is sandwiched between two electrode layers 1420 and 1425. In some embodiments, alignment layer 1403 can comprise a patterned polymerizable liquid crystal layer. In some embodiments, alignment layer 1403 can include a patterned polymer layer, which directly aligns the LC material with the nanoscale surface structures. The two electrode layers 1420 and 1425 can comprise a material (e.g., indium tin oxide (ITO)) that is transparent to light in the visible spectral range (e.g., about 400 nm to about 700 nm). In various embodiments, the two electrode layers 1420 and 1425 can each comprise a substrate 1401 a and 1401 b coated with a layer of ITO 1404 a and 1404 b, respectively. In various embodiments, an electrically controllable liquid crystal device can be fabricated by constructing a liquid crystal cell structure that comprises the two electrode layers and a patterned alignment layer 1403. A liquid crystal material that forms layer 1407 can be injected into the cell structure to fabricate an electrically controllable liquid crystal device. The alignment layer 1403 can be about 20 nm to about 10 mm thick. The liquid crystal layer 1407 can have a thickness of approximately 100 nm to 10 microns. The matching layer 1403 can be patterned using an imprint template comprising a plurality of subwavelength features similar to the template 1100 and / or template 1205 discussed above. For example, the imprint template used to pattern the matching layer 1403 can include a plurality of spaced apart domains. Each domain can include a plurality of features having dimensions (e.g., length, width, and / or depth) on the order of a few nanometers, hundreds of nanometers, or even a few microns. As discussed above, the matching layer 1403 can be polymerized after patterning to fix the longitudinal axes of the molecules in the matching layer 1403.The molecules of the liquid crystal layer 1407 can be allowed to self-assemble into the pattern to be imprinted on the layer 1403. After self-assembly, the molecules of the liquid crystal layer 1407 form distinct domains corresponding to the distinct domains of the imprint template, with the longitudinal axes of the liquid crystal molecules in each domain aligned along the direction of the individual features in the corresponding domain. The longitudinal axes of the liquid crystal molecules in the gaps between adjacent domains can gradually transition from the orientation of the longitudinal axes of the molecules in one domain to the orientation of the longitudinal axes of the molecules in the adjacent domain without any abrupt discontinuity. For example, the longitudinal axes of the liquid crystal molecules in the gaps between adjacent domains can gradually transition from the orientation of the longitudinal axes of the molecules in one domain to the orientation of the longitudinal axes of the molecules in the adjacent domain in a substantially continuous manner. In various embodiments, the liquid crystal layer 1407 can comprise a complex, spatially varying nanoscale pattern.

[0111] The orientation of the longitudinal axes of the liquid crystal molecules in one or more domains can be varied by applying a voltage across the electrode layers 1420 and 1425. Under certain conditions, for example, the LC molecules align along the direction of the electric field across the electrode layers 1420 and 1425. Thus, by applying a voltage across the electrode layers 1420 and 1425, the lattice structure in the liquid crystal layer 1407 can be switched on or off.

[0112] 15A-15C illustrate an example of a method for fabricating various liquid crystal devices described herein. The method includes providing an imprint layer 1505 over a substrate 1501. Various physical and / or chemical properties of the imprint layer 1505 and the substrate 1501 can be similar to the imprint template 1205 and the substrate 1201, respectively, discussed above. For example, the substrate 1501 is often optically transparent. Examples of suitable materials for the substrate 1501 include glass, quartz, sapphire, indium tin oxide (ITO), or polymeric materials, including polycarbonate, polyacetate, and acrylic. In some implementations, the substrate 1501 can be transparent to light in at least one of visible or infrared wavelengths. The substrate can include a pair of major surfaces and a surrounding edge. The major surfaces can be the largest-area surface of the substrate or can be one of a pair of similarly sized opposing surfaces, each having a larger area than the other surface (e.g., the edge). The liquid crystal device can be configured to reflect, refract, diffract, or otherwise redirect light incident on or against a major surface of the substrate.

[0113] An imprint layer 1505 can be disposed across a major surface of the substrate 1501. As discussed above, the imprint layer 1505 can include features having sub-wavelength dimensions. For example, the imprint layer 1505 can include features having dimensions (e.g., length, width, and / or depth) on the order of a few nanometers, hundreds of nanometers, and / or a few microns. As another example, the imprint layer 1505 can include features having lengths of about 20 nm or more and about 100 nm or less. As yet another example, the imprint layer 1505 can include features having widths of about 20 nm or more and about 100 nm or less. As yet another example, the imprint layer 1505 can include features having depths of about 10 nm or more and about 100 nm or less. In various embodiments, the length and / or width of the feature can exceed the depth of the feature. However, in some embodiments, the depth can be approximately equal to the length and / or width of the feature. However, features having dimensions outside these ranges are also contemplated.

[0114] The features of each domain of the imprint layer 1505 can be arranged to form complex geometric patterns within each domain, with the direction and / or periodicity between successive features varying along length scales on the order of nanometers, hundreds of nanometers, and / or microns. In various embodiments, the imprint layer 1505 can include multiple spaced-apart domains. Each domain can include multiple features having subwavelength dimensions. Each domain can be separated from neighboring domains by a domain spacing. The domain spacing can have a value between about 10 nm and about 100 nm, between about 20 nm and about 90 nm, between about 30 nm and about 80 nm, between about 40 nm and about 75 nm, between about 50 nm and about 70 nm, or any combination of these ranges or any subrange or combination of subranges within these ranges. In various implementations, the domain spacing can be 10 nm or less and / or 100 nm or more. For example, the domain spacing can be 5 nm or less, 2 nm or less, 1 nm or less, or a value between 0 nm and 10 nm. In some implementations, the multiple domains of the imprint template 1505 may be arranged in a square grid across the surface of the imprint template 1505 such that the domain spacing between neighboring domains is uniform. In some implementations, the multiple domains of the imprint template 1505 may be arranged as concentric circular or elliptical regions. The multiple domains may be arranged irregularly across the surface of the imprint template 1505 such that the domain spacing between neighboring domains is not uniform. The imprint layer 1505 may be formed using the imprint template 1100 and / or the imprint layer 1505 as discussed above. Templates It may have similar properties to 1205.

[0115] The imprint layer 1505 with sub-wavelength features can be designed and fabricated using nanopatterning techniques, including optical lithography, nanoimprint, and ion and electron beam lithography. In various embodiments, the imprint layer 1505 can comprise a semiconductor material, such as photoresist, silicon, or a glass material.

[0116] A polymerizable liquid crystal (PLC) layer 1503 is disposed over the imprint layer 1505. The PLC layer 1503 can be disposed over the imprint layer 1505 by a spin-coating process or jet deposition. The PLC layer 1503 can have a thickness of approximately 10 nm to 10 microns. The PLC layer 1503 can include a polymerizable liquid crystal material (e.g., a reactive mesogen) and / or an azo-containing polymer. The imprint layer 1505 acts as an alignment layer, aligning the liquid crystal molecules of the PLC layer 1503 to the pattern of the imprint layer 1505. When the PLC layer 1503 contacts the features of the imprint layer 1505, the longitudinal axes of the liquid crystal molecules of the PLC layer 1503 may be aligned to the features of the imprint layer 1505. In this manner, the surface of the PLC layer 1503 is imprinted with a pattern corresponding to the pattern of the imprint layer 1503. The alignment of the liquid crystal molecules of PLC layer 1503 with the pattern of imprint layer 1505 may be due to steric interactions with the liquid crystal molecules and / or anchoring energy imparted by imprint layer 1505 onto the deposited liquid crystal molecules. PLC layer 1503 can be polymerized after being deposited on imprint layer 1505. Polymerization of PLC layer 1503 can be achieved by various methods, including, but not limited to, exposure to ultraviolet (UV) radiation, application of heat, the passage of time, or a combination thereof. Polymerization of PLC layer 1503 can advantageously fix the orientation of the longitudinal axes of the liquid crystal molecules in PLC layer 1503.

[0117] After polymerization of the patterned PLC layer 1503, another layer 1520 of liquid crystal material is disposed over the polymerized, patterned PLC layer 1503. The layer of liquid crystal material 1520 can be deposited over the PLC layer 1503 by spin coating, slot coating, bar coating, blade coating, jet deposition, or possibly other methods. The layer of liquid crystal material 1520 can have a thickness of approximately 10 nm to 10 microns. The layer of liquid crystal material 1520 can include doped or undoped liquid crystal material. In various embodiments, the layer of liquid crystal material 1520 can be a polymerizable liquid crystal material, a polymer-stabilized liquid crystal material, or a non-polymerizable liquid crystal material.

[0118] The longitudinal axes of the molecules in the layer of liquid crystal material 1520 self-align to the pattern imprinted on the PLC layer 1503. In various implementations, only the molecules of the sublayer of the layer of liquid crystal material 1520 in contact with the imprint layer 1505 may be aligned to the longitudinal axes of the pattern in the imprint layer 1505. Other sublayers of the layer of liquid crystal material 1520 may have different orientations, as discussed above with reference to FIG. 10C . Thus, the PLC layer 1503 serves as an alignment layer for the layer of liquid crystal material 1520. In some embodiments, the alignment of the longitudinal axes of the molecules in the layer of liquid crystal material 1520 may be promoted by the application of heat and / or the passage of a sufficient amount of time.

[0119] As discussed above, using PLC layer 1503 as a matching layer for layer of liquid crystal material 1520 can have several advantages. The first advantage is that PLC layer 1503 can provide a stronger matching state for layer of liquid crystal material 1520 compared to a matching layer that does not comprise a polymerizable liquid crystal material. The second advantage is that a homogeneous interface can be achieved when the material of PLC layer 1503 has similar optical properties to the material of layer of liquid crystal material 1520. This can advantageously reduce refraction / diffraction from the boundary between PLC layer 1503 and layer of liquid crystal material 1520.

[0120] The methods discussed herein may be used to fabricate liquid crystal metamaterials or liquid crystal metasurfaces. Various embodiments of liquid crystal layers comprising differently spaced domains, the domains comprising multiple subwavelength scale patterns, may be formed on a substrate, which may be adjacent to a transmissive waveguide or the waveguide itself may be the substrate. In such embodiments, the liquid crystal layer with the subwavelength scale pattern may be configured, for example, to diffract light incident at an angle of about ±30 degrees relative to the normal to the waveguide, such that the diffracted light can be coupled into a guided mode of the waveguide disposed adjacent to the liquid crystal layer. In some embodiments, the waveguide may be disposed directly adjacent to the liquid crystal layer without any intervening layer. In some other embodiments, an intervening layer may be disposed between the waveguide and the liquid crystal layer adjacent to the waveguide. In some such embodiments, the liquid crystal layer with the subwavelength scale pattern may also be configured to outcouple light propagating through the waveguide. Liquid crystal layers with subwavelength scale patterns may be configured to be narrowband so that they are wavelength selective or broadband so that they can efficiently diffract light over a wide range of wavelengths (e.g., wavelengths within the red / green / blue spectral ranges of the visible spectrum). The methods discussed herein can also be used to fabricate other liquid crystal devices. For example, the methods discussed herein can be used to fabricate diffractive liquid crystal lens implementations, as discussed below. (diffractive liquid crystal lens)

[0121] FIG. 16A illustrates a top view of an implementation of a diffractive lens 1600 comprising a liquid crystal material. Lens 1600 comprises multiple zones, such as zones 1605 and 1610, in the xy plane. The number of zones can range from 2 to approximately 50. For example, the number of zones can be 3 or more, 5 or more, 8 or more, 10 or more, 15 or more, 18 or more, 22 or more, 50 or less, 42 or less, 30 or less, 20 or less, or any number within a range / subrange defined by these values. The molecules of the liquid crystal material within each of the multiple zones of lens 1600 are oriented along a particular orientation or range about the center thereof. The molecules of the liquid crystal material within adjacent zones can be different. For example, in lens 1600, the longitudinal axes of the liquid crystal molecules within zone 1605 can be aligned parallel to the y-axis, while the longitudinal axes of the liquid crystal molecules within zone 1610 can be rotated clockwise by an angle of approximately 18 degrees relative to the y-axis. In the lens 1600 depicted in FIG. 16A , the longitudinal axes of the molecules in each successive zone can be rotated clockwise by an angle of approximately 18 degrees relative to the longitudinal axes of the liquid crystal molecules in the preceding zone. In other lens implementations, the angle between the longitudinal axes of the liquid crystal molecules in a zone and the longitudinal axes of the liquid crystal molecules in the preceding zone can be other than 18 degrees. For example, the angle between the longitudinal axes of the liquid crystal molecules in a zone and the longitudinal axes of the liquid crystal molecules in the preceding zone can be approximately 45 degrees or less. For example, the angle between the longitudinal axes of the liquid crystal molecules in a zone and the longitudinal axes of the liquid crystal molecules in the preceding zone can be approximately 1 degree or more, approximately 2 degrees or more, approximately 5 degrees or more, approximately 10 degrees or less, approximately 17 degrees or less, approximately 20 degrees or less, approximately 25 degrees or less, approximately 30 degrees or less, approximately 35 degrees or less, approximately 40 degrees or less, and / or approximately 45 degrees or less, or any angle within any range defined by any of these values.

[0122] In the implementation of lens 1600 depicted in FIG. 16A , the angle between the longitudinal axes of the liquid crystal molecules and the direction of the y-axis gradually increases by a fixed amount (e.g., 18 degrees) so that the liquid crystal molecules in the tenth zone 1655 have the same orientation as the liquid crystal molecules in the first zone 1605. However, the angular difference in the orientation of the longitudinal axes of the liquid crystal molecules in adjacent zones need not be fixed or constant. Instead, the angular difference in the orientation of the longitudinal axes of the liquid crystal molecules between adjacent zones can vary across the lens. For example, the angular difference in the orientation of the longitudinal axes of the liquid crystal molecules between two adjacent zones can be 35 degrees, while the angular difference in the orientation of the longitudinal axes of the liquid crystal molecules between two other adjacent zones can be 10 degrees. Thus, in various implementations of liquid crystal lenses, the angular difference in the orientation of the longitudinal axes of the liquid crystal molecules between successive zones can be variable, non-constant, and / or random.

[0123] The multiple zones can be ring-shaped or annular. The multiple zones can be concentric. For example, in FIG. 16A , the first zone 1605 is configured as a central zone surrounded by the other multiple zones. The multiple zones can be concentric rings or annular, as depicted in FIG. 16A . However, in other implementations, the multiple zones can be elliptical or possibly have other shapes. The multiple zones need not be closed curves. Instead, some of the multiple zones can be open curves (e.g., arcs). In various implementations, the widths of the multiple zones can decrease with increasing distance from the first (or central) zone. Thus, the width of the first (or central) zone can be maximum, and the width of each successive zone can decrease successively. The widths of the multiple zones can decrease linearly or nonlinearly with increasing distance from the central zone and / or the center of the lens. The widths of the multiple zones can, in some cases, be governed by a mathematical equation.

[0124] In various implementations, the regions and features contained therein are configured to have shapes, sizes, orientations, etc., such that the multiple zones form an optical element, such as a lens, having a refractive power. This power may be positive or negative. The refractive power may also be positive or negative depending on the polarization of the incident light. For example, the refractive power may be positive for right-handed circularly polarized light and negative for left-handed circularly polarized light, and vice versa. The optical element, e.g., a lens, may be a diffractive optical element, such as a diffractive lens.

[0125] Each of the multiple zones can be considered a domain, as discussed above. The multiple zones can be spaced apart from one another by a gap (corresponding to the domain gap) of about 1 nm to about 200 nm. However, in various implementations, the multiple zones can be arranged such that they are spaced apart by gaps of less than 5.0 nm or less than 1.0 nm. For example, in some implementations, there are no gaps between the multiple zones. In other words, the gap between adjacent zones can be zero. The domain gap can vary depending on the angular difference in the orientation of the longitudinal axes of the liquid crystal molecules in adjacent zones. Thus, depending on the difference in the orientation of the longitudinal axes of the liquid crystal molecules between adjacent zones, the gap can be from zero to about 200 nm.

[0126] FIG. 16B illustrates a microscope image of lens 1600 between crossed polarizers positioned on either side of lens 1600. The crossed polarizers can be linear polarizers positioned so that their polarization axes are mutually orthogonal. The crossed polarizers will exhibit different regions that rotate the polarization of light by different amounts, resulting in different intensities depending on how much the light's polarization matches the polarizer orientation. The more the polarization of the light matches the polarizer, the brighter the light will be, and vice versa. To obtain a microscope image of lens 1600, circularly polarized light transmitted through one of the two crossed polarizers is incident on lens 1600. The output of lens 1600 is transmitted through the other of the two crossed polarizers and observed through a microscope. The orientation of the longitudinal axes of the liquid crystal molecules in the dark regions (e.g., region 1660) of the image depicted in FIG. 16B is parallel or perpendicular to the optical axis of the polarizer. The orientation of the longitudinal axes of the liquid crystal molecules in the light regions (e.g., region 1662) of the image depicted in Figure 16B is approximately ±45 degrees with respect to the optical axis of the polarizer. The variation between the lighter and darker regions is associated with variations in polarization orientation caused by different orientations of the liquid crystal molecules and the optical axis of birefringence within a particular region.

[0127] Alignment of the longitudinal axes of the liquid crystal molecules in the zones can be achieved by using an imprint layer, as discussed above. Figure 16B-1 depicts a scanning electron microscope (SEM) image showing a pattern of imprint layer 1670 that achieves the desired alignment of the longitudinal axes of the liquid crystal molecules in region 1664, which comprises zones 1605 and 1610. The SEM image in Figure 16B-2 shows a pattern of imprint layer 1670 that achieves the desired alignment of the longitudinal axes of the liquid crystal molecules in region 1666. Region 1672 of imprint layer 1670 includes features (e.g., grooves) parallel to the y-axis. As a result, the longitudinal axes of the liquid crystal molecules overlapping region 1672 of imprint layer 1670 are aligned parallel to the y-axis, forming zone 1605. Region 1674 of imprint layer 1670 includes features (e.g., grooves) that are rotated clockwise by an angle (e.g., about 18 degrees) relative to the y-axis. Thus, the longitudinal axes of the liquid crystal molecules overlapping region 1674 of imprint layer 1670 are rotated clockwise by an angle (e.g., about 18 degrees) relative to the y-axis, forming zone 1610. Regions 1680, 1682, 1684, 1686, and 1688 of imprint layer 1670 exhibit different arrangements of features (e.g., grooves). The longitudinal axes of the liquid crystal molecules overlapping regions 1680, 1682, 1684, 1686, and 1688 of imprint layer 1670 will be aligned parallel to the grooves in the individual regions 1680, 1682, 1684, 1686, and 1688.

[0128] The features in the various regions 1672, 1674, 1680, 1682, 1684, 1686, and 1688 of the imprint layer 1670 can be sub-wavelength in size. For example, the length, height, width, and / or depth of the features in the various regions 1672, 1674, 1680, 1682, 1684, 1686, and 1688 of the imprint layer 1670 can be on the order of a few nanometers, hundreds of nanometers, or a few microns. As another example, the length, height, width, and / or depth of features in the various regions 1672, 1674, 1680, 1682, 1684, 1686, and 1688 of imprint layer 1670 can be about 20 nm to about 100 nm, about 30 nm to about 90 nm, about 40 nm to about 80 nm, about 50 nm to about 75 nm, about 60 nm to about 70 nm, or any combination of these ranges or any subrange or combination of subranges within these ranges. In various implementations, the length, height, width, and / or depth of features in the various regions 1672, 1674, 1680, 1682, 1684, 1686, and 1688 of imprint layer 1670 can be about 20 nm or less or about 100 nm or more. For example, the length, height, width, and / or depth of features in various regions 1672, 1674, 1680, 1682, 1684, 1686, and 1688 of imprint layer 1670 can be 1 nm or more, 5 nm or more, 10 nm or more, 15 nm or more, 100 nm or less, 125 nm or less, 150 nm or less, 200 nm or less, 250 nm or less, 1 micron or less, or values ​​within any range / subrange defined by these values.

[0129] 17A-17C illustrate an example of a method for fabricating a lens 1600. The method includes providing an imprint layer 1670 over a substrate 1701. Various physical and / or chemical properties of the imprint layer 1670 and the substrate 1701 can be similar to the liquid crystal layer 1203 and the substrate 1201, respectively, discussed above. For example, in various cases, the substrate 1701 is optically transmissive and / or transparent. Examples of suitable materials for the substrate 1701 include glass, quartz, sapphire, indium tin oxide (ITO), or polymeric materials, including polycarbonate, polyacetate, and acrylic. In some embodiments, the substrate 1701 can be transmissive to light in at least one of visible or infrared wavelengths. The substrate can include a pair of major surfaces and a surrounding edge. The major surfaces can be the largest-area surface of the substrate or can be one of a pair of similarly sized opposing surfaces, each having a larger area than the other surface (e.g., the edge). The liquid crystal device can be configured to reflect, refract, diffract, or otherwise redirect light incident on or against a major surface of the substrate.

[0130] The imprint layer 1670 can be disposed across a major surface of the substrate 1701. As discussed above, the imprint layer 1670 includes a plurality of zones comprising features (e.g., grooves). The features can have sub-wavelength dimensions. For example, the imprint layer 1670 can include features having dimensions (e.g., length, width, and / or depth) on the order of a few nanometers, hundreds of nanometers, and / or a few microns. As another example, the imprint layer 1670 can include features having lengths of about 20 nm or more and about 100 nm or less. As yet another example, the imprint layer 1670 can include features having widths of about 20 nm or more and about 100 nm or less. As yet another example, the imprint layer 1670 can include features having depths of about 10 nm or more and about 100 nm or less. In various embodiments, the length and / or width of the feature can exceed the depth of the feature. However, in some embodiments, the depth can be approximately equal to the length and / or width of the feature. Other dimensions outside these ranges are also possible.

[0131] In various implementations, the features in each of the multiple zones are oriented along the same direction. The direction along which the features in one of the multiple zones are oriented may be rotated by an angle relative to the direction along which the features in a zone adjacent to the one of the multiple zones are oriented. hmm The zones can be spaced apart from one another by gaps having a value of about 1 nm to about 100 nm, about 20 nm to about 90 nm, about 30 nm to about 80 nm, about 40 nm to about 75 nm, about 50 nm to about 70 nm, or any combination of these ranges or any subrange or combination of subranges within these ranges. In some implementations, the zones can be spaced apart from one another by gaps less than about 5 nm or 1 nm. In some implementations, the zones can be spaced apart from one another by no gap (or 0 nm gap). The zones can be ring-shaped and can be arranged concentrically. The width of the zones can vary depending on the imprint layer. 1670can decrease as the distance from the center increases.

[0132] Imprinted layer with subwavelength features 1670 can be fabricated using nanopatterning techniques, including optical lithography, nanoimprinting, and ion and electron beam lithography. In various embodiments, the imprint layer 1670 may comprise a semiconductor material such as photoresist, silicon, or glass material.

[0133] A liquid crystal (LC) layer 1703 is an imprint layer 1670 The liquid crystal layer 1703 can be a polymerizable liquid crystal layer. The LC layer 1703 can be formed by a spin coating process, a slot die coating process, a bar coating process, a blade die coating process, or jet deposition to form an imprint layer. 1670 The LC layer 1703 can have a thickness of about 10 nm to 10 microns. 1703 The imprint layer may comprise a polymerizable liquid crystal material (e.g., a reactive mesogen) and / or an azo-containing polymer. 1670 The liquid crystal molecules of the LC layer 1703 are imprinted onto the 1670 The LC layer 1703 acts as a matching layer to match the pattern of the imprint layer. 1670 When in contact with the features of the imprint layer, the longitudinal axes of the liquid crystal molecules of the LC layer 1703 are aligned with the 1670 In this way, the surface of the LC layer 1703 can be made to match the characteristics of the imprint layer. 1670 The LC layer 1703 is imprinted with a pattern corresponding to the pattern of the imprint layer. 1670After being deposited thereon, the LC layer 1703 can be polymerized. Polymerization of the LC layer 1703 can be achieved by a variety of methods, including, but not limited to, exposure to ultraviolet (UV) radiation 1710 as illustrated diagrammatically in Figure 17C, application of heat, the passage of time, or a combination thereof. Polymerization of the LC layer 1703 can advantageously fix the orientation of the longitudinal axes of the liquid crystal molecules of the PLC layer 1703.

[0134] 18A illustrates a scanning electron microscope (SEM) image of an imprint layer 1670 provided on a substrate comprising silicon (Si). As depicted in FIG. 18A, the imprint layer 1670 comprises a first zone having a first plurality of features oriented along a first direction and a second zone having a second plurality of features oriented along a second direction different from the first direction. The first and second zones are separated by a gap of less than 1 nm (e.g., no gap).

[0135] 18B illustrates a scanning electron microscope (SEM) image of liquid crystal layer 1703 disposed over imprint layer 1670. The longitudinal axes of the liquid crystal molecules in the portion of liquid crystal layer 1703 overlapping with the first zone are aligned along a first direction, and the longitudinal axes of the liquid crystal molecules in the portion of liquid crystal layer 1703 overlapping with the second zone are aligned along a second direction.

[0136] It is contemplated that various embodiments may be implemented in or associated with a variety of applications, such as imaging systems and devices, display systems and devices, spatial light modulators, liquid crystal-based devices, polarizers, wave guide plates, etc. The structures, devices, and methods described herein may find use in displays, such as wearable displays (e.g., head-mounted displays), that may be used for augmented and / or virtual reality, among others. More generally, the described embodiments may be implemented within any device, apparatus, or system that may be configured to display images, whether in motion (such as video) or stationary (such as still images), and whether text, graphics, or photographs. However, the described embodiments may be used in a variety of devices, including, but not limited to, mobile phones, multimedia internet-enabled cellular phones, mobile television receivers, wireless devices, smartphones, Bluetooth® devices, personal digital assistants (PDAs), wireless email receivers, handheld or portable computers, netbooks, notebooks, smart books, tablets, printers, copiers, scanners, fax devices, Global Positioning System (GPS) receivers / navigators, cameras, digital media players (such as MP3 players), camcorders, game consoles, wristwatches, clocks, calculators, television monitors, flat panel displays, electronic readout devices, and the like. It is contemplated that the electronic device may be contained within or associated with a variety of electronic devices, such as computers (e.g., electronic readers), computer monitors, automotive displays (including odometer and speedometer displays, etc.), cockpit controls and / or displays, camera view displays (such as rear camera displays in vehicles), electrophotography, electronic billboards or signs, projectors, architectural structures, microwave ovens, refrigerators, stereo systems, cassette recorders or players, DVD players, CD players, VCRs, radios, portable memory chips, washing machines, dryers, washer-dryers, parking meters, head-mounted displays, and various imaging systems.Accordingly, the present teachings are not limited to only the embodiments depicted in the figures, but instead are intended to have wide applicability that will be readily apparent to those skilled in the art.

[0137] Various modifications of the embodiments described in this disclosure will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments without departing from the spirit or scope of the disclosure. Various changes may be made to the invention described, and equivalents may be substituted, without departing from the true spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation, material, composition of matter, process, process acts or steps, to the objective, spirit or scope of the present invention. All such modifications are intended to be within the scope of the claims associated with this disclosure.

[0138] The word "exemplary" is used exclusively herein to mean "serving as an example, instance, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. In addition, those skilled in the art will readily understand that the terms "upper" and "lower," "above" and "below," etc. are sometimes used for ease of describing the figures, indicate relative positions corresponding to the orientation of the figure on a suitably oriented page, and may not reflect the orientation of structures described herein as those structures are implemented.

[0139] Certain features described herein in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, while features may be described above as operative in a combination and may even initially be claimed as such, one or more features from the claimed combination may, in some cases, be deviated from the combination, and the claimed combination may be directed to a subcombination or a variation of the subcombination.

[0140] Similarly, while operations are depicted in the figures in a particular order, it should be recognized that such operations need not be performed in the particular order shown, or in sequential order, or that all of the depicted operations need not be performed, to achieve desirable results. Furthermore, the figures may diagrammatically depict one or more exemplary processes in the form of a flowchart. However, other operations not depicted may be incorporated within the diagrammatically depicted exemplary process. For example, one or more additional operations may be performed before, after, simultaneously with, or between any of the depicted operations. In some situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system components in the above-described embodiments should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems may generally be integrated together in a single software product or packaged into multiple software products. Additionally, other embodiments are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results.

[0141] The present invention includes methods that may be carried out using the present device. The method may include the act of providing such a suitable device. Such provision may be performed by a user. In other words, the act of "providing" requires the user to obtain, access, approach, locate, configure, activate, power on, or otherwise act to provide the requisite device in the present method. Methods described herein may be carried out in any order of the recited events, and in the recited order of events, that is logically possible.

[0142] Exemplary aspects of the invention, along with details regarding material selection and manufacturing, have been described above. As for other details of the invention, these may be understood in conjunction with the above-referenced patents and publications and may generally be understood or understood by those skilled in the art. The same may be true with respect to method-based aspects of the invention in terms of additional acts as generally or theoretically employed.

[0143] Additionally, while the present invention has been described with reference to several embodiments that optionally incorporate various features, the present invention is not limited to what has been described or indicated as being considered with respect to each variation of the invention. Various modifications may be made to the invention as described, and equivalents may be substituted (whether described herein or not included for purposes of brevity) without departing from the true spirit and scope of the invention. Additionally, when a range of values ​​is provided, it is understood that all intervening values ​​between the upper and lower limits of that range, and any other stated or intervening value within that stated range, are encompassed within the invention.

[0144] It is also contemplated that any optional features of the inventive variations described herein may be described and claimed independently or in combination with any one or more of the features described herein. Reference to a singular item includes the possibility that there are plural of the same items. More specifically, as used herein and in the claims associated therewith, the singular forms "a," "an," "said," and "the" include plural referents unless specifically stated otherwise. In other words, the use of articles in the above description and in the claims associated with this disclosure allows for "at least one" of the subject item. Furthermore, it should be noted that such claims may be drafted to exclude any optional element. Accordingly, this statement is intended to serve as a predicate for the use of such exclusive terminology, such as "only," "only," and the like, or the use of "negative" limitations, in connection with the recitation of claim elements.

[0145] Without using such exclusive language, the term "comprising" in the claims associated with this disclosure shall permit the inclusion of any additional elements, regardless of whether a given number of elements are recited in such claims or whether the addition of features can be considered as changing the nature of the elements recited in such claims. Except as specifically defined herein, all technical and scientific terms used herein shall be given the broadest possible commonly understood meaning while maintaining the validity of the claims.

[0146] The scope of the present invention is not intended to be limited to the examples provided and / or this specification, but rather is intended to be limited only by the scope of the claims associated with this disclosure.

Claims

1. 1. An optical device, comprising: a liquid crystal layer having a first major surface, a second major surface, and a thickness; an alignment layer for said liquid crystal layer; the first major surface and the second major surface extend transversely, the thickness extends along a direction parallel to a surface normal of the first major surface or the second major surface, the liquid crystal layer comprising a plurality of sub-layers dispersed across the thickness of the liquid crystal layer, each of the plurality of sub-layers being formed by a single layer of liquid crystal molecules, each of the liquid crystal molecules having a longitudinal axis; Each sub-layer is a first domain in which longitudinal axes of a plurality of liquid crystal molecules are aligned to form a first pattern; a second domain in which the longitudinal axes of the plurality of liquid crystal molecules are aligned to form a second pattern; a third domain in which the longitudinal axes of the liquid crystal molecules are aligned to form a third pattern; Equipped with the first domains are laterally separated from the second domains by first domain gaps having a distance D1 of 10 nm to 50 nm, and the longitudinal axes of the liquid crystal molecules within the domain gaps gradually transition from the first pattern to the second pattern; the first domains are laterally separated from the third domains by second domain gaps having a distance D2 of 10 nm to 50 nm, and the longitudinal axes of the liquid crystal molecules within the domain gaps gradually transition from the first pattern to the third pattern; D1 is different from D2 in that The matching layer comprises: a first matching layer domain comprising a first plurality of spaced apart surface relief features and corresponding to the first domain; a second matching layer domain corresponding to the second domain, the second matching layer domain comprising a second plurality of spaced apart surface relief features arranged differently from the first plurality of spaced apart surface relief features; a third matching layer domain corresponding to the third domain, the third matching layer domain comprising a third plurality of spaced apart surface relief features arranged differently from the first plurality of spaced apart surface relief features; and a gap between the first matching layer domain and the second matching layer domain and a gap between the first matching layer domain and the third matching layer domain lacking surface relief features.

2. 2. The device of claim 1, wherein the longitudinal axes of the molecules of the first domains of a sublayer of the plurality of sublayers are twisted relative to the longitudinal axes of the molecules of the first domains of a sublayer adjacent to the sublayer.

3. 10. The device of claim 1, further comprising a second liquid crystal layer spanning the liquid crystal layer, wherein the liquid crystal molecules of the second liquid crystal layer are configured to self-align in a first direction, a second direction, and a third direction within a first domain, a second domain, and a third domain, respectively.

4. The device of claim 3 , wherein the liquid crystal layer or the second liquid crystal layer comprises a polymerizable liquid crystal material.

5. The device of claim 3 , wherein at least one of the liquid crystal layer or the second liquid crystal layer is disposed across a waveguide.

6. 6. The device of claim 5, wherein the second liquid crystal layer comprises an internal coupling optical element configured to internally couple an incident beam of light into the waveguide such that the incident beam of light propagates through the waveguide by total internal reflection.

7. The device of claim 6 , further comprising a light modulation device configured to direct light into the waveguide through the incoupling optical element.

8. 6. The device of claim 5, wherein at least one of the liquid crystal layer or the second liquid crystal layer comprises an outcoupling optical element configured to outcouple an incident beam of light propagating through the waveguide by total internal reflection.

9. 6. The device of claim 5, wherein at least one of the liquid crystal layer or the second liquid crystal layer comprises an orthogonal pupil expander configured to redirect light propagating through the waveguide by total internal reflection, the redirected light continuing to propagate through the waveguide by total internal reflection.

10. 10. The device of claim 1, wherein the liquid crystal layer comprises an internal coupling optical element configured to internally couple an incident beam of light into the waveguide such that the incident beam of light propagates through the waveguide by total internal reflection.

11. The device of claim 1 , wherein the liquid crystal layer comprises an outcoupling optical element configured to outcouple a beam of light propagating through a waveguide by total internal reflection.

12. The device of claim 1 , wherein the first pattern is different from at least one of the second pattern or the third pattern.

13. The device of claim 1 , wherein the first pattern, the second pattern, and the third pattern are different from one another.

14. 2. The device of claim 1, wherein longitudinal axes of the liquid crystal molecules in the first domain are aligned along a first direction, longitudinal axes of the liquid crystal molecules in the second domain are aligned along a second direction, and longitudinal axes of the liquid crystal molecules in the third domain are aligned along a third direction.

15. The device of claim 14 , wherein the first direction is different from at least one of the second direction or the third direction.

16. The device of claim 14 , wherein the first direction, the second direction, and the third direction are different from one another.

17. 15. The device of claim 14, wherein the longitudinal axes of the liquid crystal molecules within the first domain gap gradually transition from the first direction to the second direction, and the longitudinal axes of the liquid crystal molecules within the second domain gap gradually transition from the second direction to the third direction.

18. 2. The device of claim 1, wherein the first domain is laterally spaced from the second domain along a first lateral direction, and the first domain is laterally spaced from the third domain along a second lateral direction different from the first lateral direction.

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