Efficient reflective liquid crystal polarization hologram for multiple wavelengths

Abstract

An apparatus (200) is provided. The apparatus (200) includes an optical film (215) including a plurality of optically anisotropic molecules (212) configured to form a plurality of helical structures (217) having a plurality of helical axes (218) and a pitch (Ph). The pitch (Ph) is a distance along the helical axis (218) over which the azimuth angle of the optically anisotropic molecules (212) varies by a predetermined value. The azimuth angle of the optically anisotropic molecule (212) over the pitch (Ph) of the helical structure (217) is configured to vary non-linearly with respect to the distance from the starting point of the pitch (Ph) to the local point at which the optically anisotropic molecule is located along the helical axis (218).

Description

Technical Field

[0001] The present disclosure relates generally to devices and, more particularly, to highly efficient reflective liquid crystal polarization holograms for multiple wavelengths. Background Art

[0002] Liquid crystal polarization holograms (LCPHs) combine the characteristics of liquid crystal devices with those of polarization holograms. Over the past few decades, liquid crystal displays (LCDs) have grown into a trillion-dollar industry and are the most successful example of LCD devices. The LCD industry has made huge investments in scaled manufacturing, from low-end Generation 2.5 (G2.5) production lines to high-end Generation 10.5+ (G10.5+) production lines to meet market demand for displays. However, the LCD industry has recently faced competition from organic light emitting diodes (OLEDs), electronic paper (e-paper), and other emerging display technologies, which has slowed the growth of the LCD industry and led to a large amount of early-stage overcapacity. This provides an opportunity to reuse idle LCD production capacity and existing supply chains to manufacture new LC optical devices featuring polarization holograms.

[0003] LCPH or LCPH elements have the following characteristics: such as small thickness (e.g., about 1 μm), light weight, compactness, large aperture, high efficiency, simple manufacturing, etc. Therefore, LCPH elements have gained increasing attention in optical devices and optical system applications (e.g., near-eye displays (NEDs), head-up displays (HUDs), head-mounted displays (HMDs), smartphones, laptops, televisions, or vehicles, etc.). For example, LCPH elements can be used to resolve vergence-accommodation conflicts, achieve thin and efficient eye tracking and depth sensing in space-constrained optical systems, develop optical combiners for imaging, correct chromatic aberration to improve the image resolution of refractive optical elements in compact optical systems, and improve the efficiency and reduce the size of optical systems. Summary of the Invention

[0004] According to one aspect of the present disclosure, a device is provided. The device includes an optical film comprising a plurality of optically anisotropic molecules, the optically anisotropic molecules being arranged to form a plurality of helical structures having a plurality of helical axes and a helical pitch. The helical pitch is a distance along the helical axis over which the azimuth angle of the optically anisotropic molecules varies by a predetermined value. At the helical pitch of the helical structure, the azimuth angle of the optically anisotropic molecules is arranged to vary nonlinearly with respect to the distance from the starting point of the helical pitch to the local point along the helical axis where the optically anisotropic molecules are located.

[0005] According to one aspect of the present disclosure, a method is provided. The method includes generating a plurality of polarized light beams. The plurality of polarized light beams includes at least three circularly polarized light beams, the at least three circularly polarized light beams including one or more left-handed circularly polarized light beams and one or more right-handed circularly polarized light beams, and the at least three circularly polarized light beams are configured to interfere with each other to generate a polarization interference pattern. The method also includes exposing a polarization-sensitive recording medium to the polarization interference pattern. The method also includes forming an optically anisotropic film on the polarization-sensitive recording medium that has been exposed to the polarization interference pattern. The optically anisotropic film includes a mixture of a host birefringent material and a chiral dopant.

[0006] Those skilled in the art will appreciate other aspects of the present disclosure based on the specification, claims and drawings of the present disclosure.The foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The following drawings are provided for illustrative purposes according to various disclosed embodiments and are not intended to limit the scope of the present disclosure. In the drawings:

[0008] Figure 1A A schematic diagram showing a conventional cholesteric liquid crystal (CLC) cell is shown;

[0009] Figure 1B A three-dimensional (3D) view of a conventional reflective polarization volume hologram (R-PVH) element is shown;

[0010] Figure 1C Simulation results showing the relationship between the reflection efficiency of a conventional broadband CLC device including three CLC layers and the wavelength of incident light are presented;

[0011] Figure 1D and Figure 1E schematically illustrates a diagram showing the relationship between the reflection efficiency of a conventional broadband CLC device comprising two CLC layers and the wavelength of incident light;

[0012] Figure 2A and Figure 2B shows a schematic diagram of a liquid crystal polarization hologram ("LCPH") element according to an embodiment of the present disclosure;

[0013] Figure 2C A schematic diagram of an LCPH element according to an embodiment of the present disclosure is shown;

[0014] Figure 2D presents simulation results according to various embodiments of the present disclosure showing a linear relationship between azimuth angle and out-of-plane axis distance for a single pitch of conventional reflective PVH ("R-PVH") elements, and Figure 2A Various nonlinear relationships between the azimuth angle and the out-of-plane axis distance for a single pitch of the LCPH element are shown;

[0015] Figure 2E presents simulation results showing the orientation angles of optically anisotropic molecules on a single helical pitch of a conventional R-PVH element for a range of out-of-plane axis distances, according to various embodiments of the present disclosure, and Figure 2A Azimuthal angles of optically anisotropic molecules on a single helical pitch of the LCPH element shown for a range of out-of-plane axis distances and a range of nonlinear term frequencies;

[0016] Figure 2F The embodiment according to the present disclosure is shown Figure 2A 3D exploded view of a portion of the LCPH element shown, illustrating the nonlinear azimuthal variation of the optically anisotropic molecules over a single helical pitch;

[0017] Figure 3A The embodiment according to the present disclosure is shown Figure 2C The simulation results of the relationship between the reflection efficiency of the LCPH element and the wavelength of the incident light are shown;

[0018] Figure 3B shows the results for conventional CLC elements and Figure 2C Simulation results showing the relationship between the reflection efficiency of the two LCPH elements and the angle of incidence (AOI) of the blue incident light and the green incident light;

[0019] Figure 3C The embodiment according to the present disclosure is shown Figure 2A and Figure 2BThe simulation results of the relationship between the reflection efficiency of the LCPH element and the wavelength of the incident light are shown;

[0020] Figure 3D Simulation results showing the relationship between the reflection efficiency of a conventional R-PVH element and the wavelength of incident light are presented;

[0021] Figure 4A The embodiment of the present disclosure shows the Figure 2C The simulation results of the relationship between the reflection efficiency of the LCPH element and the wavelength of the incident light are shown;

[0022] Figure 4B The embodiment according to the present disclosure is shown Figure 2C Simulation results showing the relationship between the reflection efficiency of the LCPH element and the AOI of blue incident light, green incident light, and red incident light;

[0023] Figure 4C The embodiment according to the present disclosure is shown Figure 2A and Figure 2B The simulation results of the relationship between the reflection efficiency of the LCPH element and the wavelength of the incident light are shown;

[0024] Figures 5A to 5E Schematic diagrams showing various LCPH devices according to various embodiments of the present disclosure;

[0025] Figure 6 Schematically illustrating a system including one or more LCPH devices according to an embodiment of the present disclosure;

[0026] Figure 7 Schematically illustrating a system including one or more LCPH devices according to an embodiment of the present disclosure;

[0027] Figure 8A Schematically illustrating a system including one or more LCPH devices according to an embodiment of the present disclosure;

[0028] Figure 8B Schematically illustrates the image light from the display element to the Figure 8A The optical path of the eyebox area of ​​the system is shown;

[0029] Figure 9 Schematically illustrating a system including one or more LCPH devices according to an embodiment of the present disclosure;

[0030] Figure 10A A schematic diagram of an artificial reality device according to an embodiment of the present disclosure is shown;

[0031] Figure 10BThe embodiment according to the present disclosure is shown Figure 10A A schematic cross-sectional view of an artificial reality device is shown;

[0032] Figures 11A to 11F Schematically illustrates a process for manufacturing an LCPH element according to an embodiment of the present disclosure;

[0033] Figure 12A and Figure 12B Schematically illustrates a process for manufacturing an LCPH element according to an embodiment of the present disclosure;

[0034] 13A to 13C schematically illustrates a process for manufacturing an LCPH element according to an embodiment of the present disclosure; and

[0035] Figure 14A and Figure 14B FIG. 1 is a flow chart illustrating a method for manufacturing an LCPH element according to various embodiments of the present disclosure. DETAILED DESCRIPTION

[0036] The embodiments consistent with the present disclosure will be described with reference to the accompanying drawings, which are examples for illustrative purposes only and are not intended to limit the scope of the present disclosure. Where possible, the same reference numerals will be used throughout the drawings to represent the same or similar parts, and detailed descriptions of these parts may be omitted.

[0037] In addition, in the present disclosure, the disclosed embodiments and the features of the disclosed embodiments may be combined. The described embodiments are some, but not all, embodiments of the present disclosure. Based on the disclosed embodiments, a person of ordinary skill in the art may derive other embodiments consistent with the present disclosure. For example, modifications, adaptations, replacements, additions, or other changes may be made based on the disclosed embodiments. Such changes to the disclosed embodiments are still within the scope of the present disclosure. Therefore, the present disclosure is not limited to the disclosed embodiments. Rather, the scope of the present disclosure is defined by the appended claims.

[0038] As used herein, the terms "coupling," "coupling," "connection," and the like may encompass optical coupling, mechanical coupling, electrical coupling, electromagnetic coupling, or any combination thereof. An "optical coupling" between two optical elements refers to a configuration in which the two optical elements are arranged in optical series and light output from one optical element can be received directly or indirectly by the other optical element. An optical series connection refers to the optical positioning of multiple optical elements in an optical path such that light output from one optical element can be transmitted, reflected, diffracted, converted, modified, or otherwise processed or manipulated by one or more of the other multiple optical elements. In some embodiments, the order in which the multiple optical elements are arranged may or may not affect the overall output of the multiple optical elements. The coupling may be direct coupling or indirect coupling (e.g., coupling through an intermediate element).

[0039] The phrase "at least one of A or B" may encompass all combinations of A and B, such as only A, only B, or A and B. Similarly, the phrase "at least one of A, B, or C" may encompass all combinations of A, B, and C, such as only A, only B, only C, A and B, A and C, B and C, or A and B and C. The phrase "A and / or B" may be interpreted in a manner similar to the phrase "at least one of A or B." For example, the phrase "A and / or B" may encompass all combinations of A and B, such as only A, only B, or A and B. Similarly, the phrase "A, B, and / or C" has a meaning similar to that of the phrase "at least one of A, B, or C." For example, the phrase "A, B, and / or C" may encompass all combinations of A, B, and C, such as only A, only B, only C, A and B, A and C, B and C, or A and B and C.

[0040] When a first element is described as being "attached," "provided," "formed," "bonded," "mounted," "fixed," "connected," "incorporated," "recorded," or "disposed" to, on, at, or at least partially in a second element, the first element can be "attached," "provided," "formed," "bonded," "mounted," "fixed," "connected," "incorporated," "recorded," or "disposed" to, on, at, or at least partially in a second element using any suitable mechanical or non-mechanical means (e.g., deposition, coating, etching, bonding, gluing, threading, press fit, snap fit, clamping, etc.). Additionally, the first element can be in direct contact with the second element, or there can be an intermediate element between the first and second elements. The first element can be disposed on any suitable side of the second element, such as the left side, right side, front side, back side, top side, or bottom side.

[0041] When a first element is shown or described as being disposed or arranged "on" a second element, the term "on" is used only to indicate an example relative orientation between the first element and the second element. The description can be based on the reference coordinate system shown in the figure, or can be based on the current view or example configuration shown in the figure. For example, when describing the view shown in the figure, the first element can be described as being disposed "on" the second element. It should be understood that the term "on" may not necessarily mean that the first element is located above the second element in the vertical, gravity direction. For example, when the assembly of the first element and the second element is rotated 180 degrees, the first element can be located "below" the second element (or the second element can be located "on" the first element). Therefore, it should be understood that when the drawings show that the first element is "on" the second element, this configuration is merely an illustrative example. The first element can be arranged or arranged in any suitable orientation relative to the second element (for example, above or above the second element, below or below the second element, to the left of the second element, to the right of the second element, behind the second element, in front of the second element, etc.).

[0042] When a first element is described as being disposed "on" a second element, the first element may be disposed directly or indirectly on the second element. Disposing the first element directly on the second element means that no additional elements are disposed between the first and second elements. Disposing the first element indirectly on the second element means that one or more additional elements are disposed between the first and second elements.

[0043] The terms "film", "layer", "coating" or "plate" may include rigid or flexible, self-supporting or free-standing films, layers, coatings or plates that may be disposed on a supporting substrate or between substrates. The terms "film", "layer", "coating" and "plate" may be interchangeable. The term "film plane" refers to a plane in a film, layer, coating or plate that is perpendicular to the thickness direction of the film, layer, coating or plate or the normal to the surface of the film, layer, coating or plate. The film plane may be a plane in the volume of the film, layer, coating or plate, or may be a surface plane of the film, layer, coating or plate. For example, the term "in-plane" in "in-plane orientation", "in-plane direction", "in-plane spacing", etc. refers to an orientation, direction or spacing that is in the film plane. The term "out-of-plane" as in, for example, "out-of-plane direction", "out-of-plane orientation" or "out-of-plane spacing", etc., refers to an orientation, direction or spacing that is not in the film plane (i.e., not parallel to the film plane). For example, the direction, orientation, or spacing can be along a line perpendicular to the plane of the film, or a line that forms an acute or obtuse angle relative to the plane of the film. For example, an "in-plane" direction or orientation can refer to a direction or orientation within the plane of the surface, and an "out-of-plane" direction or orientation can refer to a thickness direction or orientation that is not parallel (e.g., perpendicular) to the plane of the surface. In some embodiments, the "out-of-plane" direction or orientation can form an acute or right angle relative to the plane of the film.

[0044] The term "orthogonal" as used in "orthogonal polarizations" or the term "orthogonally" as used in "orthogonally polarized" means that the inner product of the two vectors representing the two polarizations is substantially zero. For example, two beams of light or two light beams with orthogonal polarization (or two orthogonally polarized light beams) can be two linearly polarized lights (or light beams) with two orthogonal polarization directions (e.g., the x-axis direction and the y-axis direction in a Cartesian coordinate system), or two circularly polarized lights with opposite handedness (e.g., left-handed circularly polarized light and right-handed circularly polarized light).

[0045] The wavelength ranges, spectra, or bands mentioned in the present disclosure are for illustrative purposes. The disclosed optical devices, systems, elements, assemblies, and methods can be applied to the visible band as well as other bands, for example, the ultraviolet (UV) band, the infrared (IR) band, or a combination thereof. The terms "substantially" or "primarily" used to modify the optical response action (e.g., transmission, reflection, diffraction, blocking, etc.) describing the light processing means that most (including all) of the light is transmitted, reflected, diffracted, or blocked, etc. The majority can be a predetermined percentage (greater than 50%) of the entire light, such as 100%, 95%, 90%, 85%, 80%, etc., which can be determined based on the specific application requirements.

[0046] Depending on the angular relationship between the propagation direction of the light beam and the surface normal of the optical element, the angle of the light beam relative to the surface normal (for example, the diffraction angle of a diffracted light beam, the reflection angle of reflected light, or the incident angle of an incident light beam) can be defined as a positive angle or a negative angle. For example, when the virtual line representing the propagation direction of the light beam deviates from the normal in a clockwise direction (or counterclockwise direction), the angle of the light beam relative to the normal can be defined as a positive angle, and when the virtual line representing the propagation direction of the light beam deviates from the normal in a counterclockwise direction (or clockwise direction), the angle of the light beam relative to the normal can be defined as a negative angle.

[0047] As used herein, the term "liquid crystal compound" or "mesogenic compound" may refer to a compound comprising one or more rod-shaped (rod-shaped, or plate-shaped / strip-shaped) or disc-shaped (disk-shaped) mesogenic groups. The term "mesogenic group" may refer to a group that has the ability to induce liquid crystal phase (or mesophase) behavior. In some embodiments, the compound comprising the mesogenic group may not exhibit a liquid crystal ("LC") phase by itself. Instead, these compounds may exhibit an LC phase when mixed with other compounds. In some embodiments, when the compound or a mixture comprising the compound is polymerized, these compounds may exhibit an LC phase. To simplify the discussion, the term "liquid crystal" used below refers to both mesogenic materials and LC materials. In some embodiments, the rod-shaped mesogenic group may include a mesogenic core comprising one or more aromatic or non-aromatic cyclic groups directly connected to each other or connected via a bonding group. In some embodiments, the rod-shaped mesogenic group may include an end group attached to the end of the mesogenic core. In some embodiments, the rod-shaped mesogenic group may include one or more side groups attached to the long side of the mesogenic core. These end and side groups may be selected, for example, from divalent carbyl or hydrocarbyl groups, polar groups (such as halogen, nitro, hydroxyl, etc.), or polymerizable groups.

[0048] As used herein, the term "reactive mesogen" (RM) may refer to a polymerizable mesogen compound or a liquid crystal compound. A polymerizable compound having one polymerizable group may also be referred to as a "single-reactive" compound. A compound having two polymerizable groups may be referred to as a "bi-reactive" compound, and a compound having more than two polymerizable groups may be referred to as a "multi-reactive" compound. A compound having no polymerizable groups may also be referred to as a "non-reactive" compound. For the purposes of discussion, the term "liquid crystal" may cover both polymerizable liquid crystals and non-polymerizable liquid crystals. As used herein, the term "director" may refer to the preferred orientation direction of the long molecular axis (e.g., in the case of a rod-shaped compound) or the short molecular axis (e.g., in the case of a disc-shaped compound) of the LC molecule. The term "optical axis" may refer to a direction in a crystal. Light propagating in the direction of the optical axis may not experience birefringence (or double refraction). The optical axis may be a direction rather than a single line.

[0049] Figure 1A FIG. 1 shows an xz cross-sectional view of a conventional CLC element 100. Figure 1A As shown, the CLC element 100 may include a CLC layer 105. LC molecules 112 adjacent to a surface 115 of the CLC layer 105 may have a uniform in-plane alignment pattern. For example, the plurality of LC molecules 112 may be positioned at Figure 1AThe LC molecules 112 are arranged uniformly in the x-axis direction shown. Within the volume of the CLC layer 105, the plurality of LC molecules 112 may be arranged to form a plurality of helical structures 117 having a plurality of helical axes 118, and a plurality of series of Bragg planes 114. The helical axes 118 may be perpendicular to the surface 115 and extend in the thickness direction of the CLC layer 105, and the Bragg planes 114 may be parallel to the surface 115 of the CLC layer 105. Figure 1A The Bragg plane 114 is shown to be in the xy plane, and the helical axis 118 extends in the z-axis direction, with the Bragg plane 114 being perpendicular to the helical axis 118 .

[0050] In each helical structure 117, the plurality of LC molecules 112 may continuously rotate about the helical axis 118 along a predetermined rotation direction, and the azimuth angles of the plurality of LC molecules 112 may exhibit continuous periodic variation along the helical axis 118. The azimuth angle of the LC molecule 112 may be defined as the direction of the LC director relative to a predetermined in-plane direction within the Bragg plane 114 (e.g., Figure 1A The azimuth angle of the LC molecule 112 may have a value ranging from 0° to 360° (inclusive). The pitch P of the helical structure 117 is h may be defined as the distance along the helical axis 118 over which the azimuthal angles of the plurality of LC molecules 112 vary by 360°.

[0051] In the single pitch P of the helical structure 117 h In the embodiment, the plurality of LC molecules 112 may have a linear azimuth variation along the helical axis 118. For example, the azimuth angles of the LC molecules 112 may vary from a single helical pitch P to a linear azimuth variation. h The starting point (for example, the azimuth The distance from the starting point of the LC molecule 112 to the local point along the helical axis 118 is linearly proportional. For the purpose of discussion, the pitch P of a single helical structure 117 is h From the starting point (where the azimuth ) to a local point along the helical axis 118 where the LC molecule 112 is located can be referred to as the out-of-plane axis distance of the LC molecule 112. For example, in a single pitch P of the helical structure 117 h The azimuth angle of the LC molecule 112 is The distance z of the out-of-plane axis of the LC molecules 112 may be calculated according to a linear function changes linearly, where P B is the Bragg period (i.e. the pitch P h When the out-of-plane axis distances z of the LC molecules 112 are 0, 0.25*P B , 0.5*P B、0.75*P B 、P B 、1.25*P B 、1.5*P B 、1.75*P B and 2*P B When the azimuth angle of the LC molecule 112 is It can be 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315° and 360° respectively.

[0052] Figure 1B A 3D view of a conventional reflective PVH ("R-PVH") element 150 is shown. The R-PVH element 150 based on self-organized CLC may be referred to as a tilted or patterned CLC element. Figure 1B , the R-PVH element 150 can include an R-PVH layer 155. Within the volume of the R-PVH layer 155, a plurality of LC molecules 112 can be arranged to form a plurality of helical structures 167 having a plurality of helical axes 168, and a plurality of series of Bragg planes 164. The helical axes 168 can be tilted relative to a surface 165 of the R-PVH layer 155, and the Bragg planes 164 can form an angle (e.g., an acute angle) with the surface 165. Figure 1B The xyz coordinate system shown refers to the global coordinate system of the R-PVH element 150, and Figure 1B The x′-y′-z′ coordinate system shown refers to the local coordinate system of the helical structure 167 . Figure 1B The Bragg plane 164 is shown to be in the x'-y' plane, and the helical axis 168 extends in the z' direction. Figure 1A In the non-tilted CLC cell 100 shown, the x'-y'-z' coordinate system may coincide with the xyz coordinate system.

[0053] Similar to Figure 1A The non-tilted CLC element 100 shown in FIG. h The azimuth angle of the LC molecule 112 is Can be used with a single pitch P h The starting point (for example, where the azimuth ) to the local point where the LC molecule 112 is located along the helical axis 168. In addition, the plurality of LC molecules 112 in close proximity to the surface 165 may have an in-plane spacing of P inThe non-uniform in-plane orientation pattern of the LC molecules 112 can be formed by rotating the directors of the LC molecules 112 along a predetermined in-plane direction (or in-plane axis) 188 within the surface 165. Thus, the azimuthal angles of the LC molecules 112 proximate the surface 165 can vary in the predetermined in-plane direction 188. The azimuthal angles of the LC molecules 112 proximate the surface 165 of the R-PVH layer 155 can be defined as the azimuthal angle of the LC director relative to the predetermined in-plane direction 188 within the surface 165 (e.g., Figure 1B The angle of the x-axis direction shown in FIG. in may be defined as the distance along a predetermined in-plane direction 188 over which the azimuthal angles of the plurality of LC molecules 112 proximate the surface 165 change by 180°. For purposes of discussion, Figure 1B It is shown that the azimuth angles of the plurality of LC molecules 112 can be arranged in a predetermined in-plane direction 188 with a constant in-plane pitch P in Periodic changes.

[0054] The individual in-plane spacing P of the in-plane orientation pattern in On the other hand, the plurality of LC molecules 112 adjacent to the surface 165 may also have a linear azimuth variation along the predetermined in-plane direction 188. For example, the azimuth angles of the LC molecules 112 may vary from the in-plane pitch P to the in-plane pitch P. in The starting point (for example, where the azimuth ) to the local point where the LC molecules 112 are located along the predetermined in-plane direction 188. For the purpose of discussion, a single in-plane pitch P of the in-plane orientation pattern is linearly proportional to the distance from the local point where the LC molecules 112 are located along the predetermined in-plane direction 188. in From the starting point (where the azimuth ) to a local point where the LC molecule 112 is located along the predetermined in-plane direction 188 may be referred to as the in-plane axis distance of the LC molecule 112. For example, in a single pitch P of the helical structure 167 h The azimuth angle of the LC molecule 112 is According to the function where x is the in-plane axis distance of the LC molecules 112, P in is the in-plane spacing of the in-plane alignment pattern. When the in-plane axis distances x of the plurality of LC molecules 112 adjacent to the surface 165 are 0, 0.25*P respectively in , 0.5*P in 、0.75*P in and P in When the azimuth angles of these LC molecules 112 are It can be 0°, 45°, 90°, 135°, and 180° respectively.

[0055] In conventional technology, the reflection bandwidth of a conventional CLC layer may be limited by the birefringence (Δn) of the host birefringent material used in the conventional CLC layer. To broaden the reflection bandwidth of a CLC element, for example to substantially cover the entire visible spectrum, three CLC layers may be stacked to form a broadband CLC device. The three CLC layers can respectively reflect or deflect red, green, and blue light with high efficiency over a wide range of angles of incidence ("AOI") Figure 1C Simulation results showing the relationship between the reflection efficiency of a conventional broadband CLC device comprising three CLC layers and the wavelength of incident light are presented. Figure 1C As shown, the three CLC layers can reflect red ("R") light, green ("G") light, and blue ("B") light with relatively high efficiency (e.g., greater than 98%), respectively, and each CLC layer can include a host birefringent material with a birefringence of 0.16.

[0056] In some cases, when the host birefringent material has a large birefringence, e.g., a birefringence greater than 0.5, two CLC layers that reflect or deflect red ("R"), green ("G"), and blue ("B") light can be stacked to form a broadband CLC device. Figure 1D and Figure 1E Schematically illustrated is a diagram showing the relationship between the normalized reflection efficiency of a conventional broadband CLC device comprising two CLC layers and the wavelength of the incident light. Figure 1D As shown, the first CLC layer may exhibit a single reflection band including both the green wavelength range and the blue wavelength range, thereby reflecting both green ("G") light and blue ("B") light. Figure 1E As shown, the second CLC layer may exhibit a single reflection band including a red wavelength range, thereby reflecting red ("R") light. Figure 1D Also shown are the reflection spectra of the first CLC layer when the AOI is 0° and 20°, Figure 1E The reflectance spectra of the second CLC layer when the AOI is 0° and 20° are also shown. Figure 1D and Figure 1E As the AOI of incident light increases from 0° to 20°, the reflection band of each of the first and second CLC layers may blue-shift, and the reflection efficiency of each of the first and second CLC layers may decrease. Therefore, the reflection band of a conventional broadband CLC device may blue-shift, and the reflection efficiency may decrease.

[0057] In view of the limitations of conventional technologies, the present disclosure provides a reflective liquid crystal polarization hologram ("LCPH") element or device that is configured to efficiently deflect polychromatic light over a wide angle of incidence ("AOI") range. In the present disclosure, LCPH elements may include polarization volume hologram ("PVH") elements and cholesteric liquid crystal ("CLC") elements, among others. LCPH elements may be manufactured based on various methods, such as holographic interferometry, direct writing, inkjet printing, 3D printing, and various other forms of photolithography. Therefore, the "holograms" described herein are not limited to those produced by holographic interferometry or "holography."

[0058] Figure 2A A 3D view of an LCPH element 200 according to an embodiment of the present disclosure is shown. Figure 2B The embodiment according to the present disclosure is shown Figure 2A The xy cross-sectional view of the LCPH element 200 is shown. Figure 2A In the illustrated embodiment, the LCPH element 200 can be a reflective polarization volume hologram (R-PVH) element (also referred to as 200 for discussion purposes). The R-PVH element 200 can be configured to substantially reflect circularly polarized light having a predetermined handedness via reverse diffraction with high efficiency (e.g., 98% or greater) over a wide AOI range. The R-PVH element 200 can also substantially transmit circularly polarized light having a handedness opposite to the predetermined handedness with zero or negligible diffraction.

[0059] like Figure 2A As shown, the R-PVH element 200 may include an optically anisotropic film 215, which may be a thin layer of a birefringent material having intrinsic or induced (e.g., photoinduced) optical anisotropy, such as a liquid crystal, a liquid crystal polymer, or an amorphous polymer. In some embodiments, the birefringent material may include nematic LC, twist-bend LC, chiral nematic LC, smectic LC, ferroelectric LC, smectic LC, or any combination thereof. In some embodiments, the birefringent material may have induced chirality, such as by doping a chiral dopant. In some embodiments, the birefringent material may have intrinsic molecular chirality, such as by including chiral LC molecules or molecules having one or more chiral functional groups. The R-PVH element 200 may be an active element or a passive element.

[0060] The optically anisotropic film 215 may include a plurality of optically anisotropic molecules 212. The optical axis of the optically anisotropic film 215 may be configured with a 3D orientation pattern to provide a polarization-selective optical response. The orientation of the optical axis of the optically anisotropic film 215 may be determined by the local orientation of the elongated optically anisotropic molecules 212 or the elongated molecular units (e.g., small molecules or fragments of polymer molecules) included in the optically anisotropic molecules 212. For the purposes of this discussion, elongated optically anisotropic molecules (e.g., rod-shaped LC molecules, also referred to as 212 for the purposes of this discussion) are used as an example to describe the 3D orientation pattern of the optical axis of the optically anisotropic film 215. The optically anisotropic film 215 may also be referred to as an R-PVH layer 215.

[0061] refer to Figure 2A and Figure 2B The R-PVH element 200 can be configured to have a nonlinear azimuthal variation of the LC molecules 212 along a predetermined in-plane axis within the surface 205 of the R-PVH layer 215 and a helical axis 218 within the volume of the R-PVH layer 215, thereby generating one or more secondary (or minor) reflection bands in addition to a primary (or main) reflection band. The R-PVH element 200 can provide high reflection efficiency (e.g., greater than 98%) for the primary reflection band and the one or more secondary (or minor) reflection bands over a large AOI range (e.g., -25° to 25°, -30° to 30°, -35° to 35°, -45° to 45°, -50° to 50°, -60° to 60°, etc.).

[0062] like Figure 2A and Figure 2B As shown, the LC molecules 212 proximate the surface 205 (eg, in the xy plane) of the R-PVH layer 215 may be arranged to have an in-plane spacing (or horizontal spacing) of P. in The non-uniform in-plane orientation pattern of Figure 2B As shown, the directors of the plurality of LC molecules 212 proximate to the surface 205 may rotate periodically or aperiodically along at least one in-plane direction (or in-plane axis) 228 within the surface 205. Thus, the azimuthal angles of the plurality of LC molecules 212 proximate to the surface 205 may vary periodically or aperiodically along at least one in-plane direction 228. The azimuthal angles of the LC molecules 212 proximate to the surface 205 of the R-PVH layer 215 may be defined as the azimuthal angle of the LC director relative to a predetermined in-plane direction 228 within the surface 205 (e.g., Figure 2A The angle of the x-axis direction shown in FIG. in The interplanar pitch P may be defined as the distance along the predetermined in-plane direction 228 over which the azimuth angles of the plurality of LC molecules 212 proximate the surface 205 vary by 180°. inIt can be a constant in-plane spacing or a varying in-plane spacing. For the purpose of discussion, the in-plane spacing P of the non-uniform in-plane orientation pattern formed at the surface 205 is in It can also be referred to as the in-plane pitch P of the R-PVH element 200. in .

[0063] The predetermined in-plane direction 228 within the surface 205 can be an in-plane linear direction, an in-plane radial direction, an in-plane circumferential (e.g., azimuthal) direction, or a combination thereof. For example, in some embodiments, the R-PVH layer 215 can be coupled to an alignment structure (not shown) at the surface 205, and the alignment structure can at least partially align the LC molecules 212 proximate the surface 205 to have a non-uniform in-plane orientation pattern. The alignment structure can include a polyimide layer, a photo-alignment material (PAM) layer, a plurality of nanostructures or microstructures, an alignment network, or any combination thereof.

[0064] For discussion purposes, Figure 2A and Figure 2B A plurality of LC molecules 212 are shown in close proximity to the surface 205 with a constant in-plane spacing P. in In a predetermined in-plane direction 228 (e.g., Figure 2A and Figure 2B The LC molecules 212 in close proximity to the surface 205 may be arranged to have another suitable non-uniform in-plane alignment pattern, such as a lens pattern with varying in-plane spacing (e.g., a spherical lens pattern, a cylindrical lens pattern, an off-axis lens pattern, or a free-form lens pattern) or a lens array pattern.

[0065] In some embodiments, the individual in-plane pitch P of the in-plane orientation pattern is in , the plurality of LC molecules 212 proximate the surface 205 may be configured to have a nonlinear azimuthal variation along a predetermined in-plane direction 228. For the purposes of discussion, at a single in-plane pitch P in In some embodiments, the starting (or reference) point of the 180° change in the azimuth angle along the predetermined in-plane direction 228 may be defined as the point where the azimuth angle of the LC molecules 212 is 0°. inIn the embodiment of the present invention, the azimuth angle of the LC molecules 212 may be configured to vary nonlinearly with respect to a distance from a starting point (e.g., where the azimuth angle is 0°) to a local point where the LC molecules 212 are located along a predetermined in-plane direction 228. For the purposes of discussion, the distance from the starting point (e.g., where the azimuth angle is 0°) to a local point where the LC molecules 212 are located along the predetermined in-plane direction 228 may be referred to as an in-plane axis distance of the LC molecules 212.

[0066] In some embodiments, the individual in-plane pitch P of the in-plane orientation pattern is in The azimuth angle of the LC molecules 212 proximate the surface 205 can be expressed relative to the in-plane axis distance x (unit: micrometer (μm)) of the LC molecules 112 according to the nonlinear function varies nonlinearly, where is the azimuth angle of the LC molecule 212 (unit: degree), P in is the in-plane spacing (unit: μm) and can be a constant value (relative to x). It is a linear function of x, which means that this part of the azimuth is 180 / P in The rate (or slope) of the change with the distance x from the in-plane axis. is a nonlinear function of the in-plane axis distance x, where A is an amplitude parameter associated with the magnitude of the azimuthal variation introduced by the nonlinear function (for simplicity of discussion, this amplitude parameter may be referred to as "amplitude"). Parameter n is a frequency parameter associated with the frequency of the azimuthal variation introduced by the nonlinear function (for simplicity of discussion, this frequency parameter may also be referred to as "frequency"). Therefore, the nonlinear azimuthal variation with respect to the in-plane axis distance x is a combination of linear and nonlinear variations.

[0067] In some embodiments, the amplitude parameter A of the nonlinear function may be a constant value relative to the in-plane axis distance x. For example, the amplitude A may be configured as a positive value within a range greater than 0° and less than or equal to 360°. In some embodiments, the frequency n of the nonlinear function may be a constant value relative to the in-plane axis distance x. For example, the frequency n may be configured as a positive value within a range greater than 0 and less than or equal to 1. It can be any suitable nonlinear function, such as a quadratic function, a polynomial function, a rational function, an exponential function, a logarithmic function, a trigonometric function, or a combination thereof. For example, in some embodiments, the single in-plane spacing P of the R-PVH element 200 is in The azimuth angles of the LC molecules 212 proximate the surface 205 can be configured according to the function And changes, among which It is a nonlinear function .

[0068] Return Reference Figure 2A Within the volume of the R-PVH layer 215 , the plurality of LC molecules 212 may be arranged in a plurality of helical structures 217 and a plurality of series of Bragg planes 214 . Figure 2A The xyz coordinate system shown in refers to the global coordinate system of the R-PVH element 200, and Figure 2A The x'-y'-z' coordinate system shown in refers to the local coordinate system of the helical structure 217. For the purpose of discussion, Figure 2A The Bragg plane 214 is shown to be in the x′-y′ plane, the helical axis 218 is along the z′ axis, and the Bragg plane 214 is substantially perpendicular to the helical axis 218 .

[0069] The helical axis 218 of the helical structure 217 may be tilted relative to the surface 205 of the R-PVH layer 215 (or relative to the thickness direction of the R-PVH layer 215). The helical axis 218 may form an acute angle of less than 45° relative to the normal to the surface 205 or the thickness direction of the R-PVH layer 215 (e.g., the z-axis direction). In the helical structure 217, the directors of the plurality of LC molecules 212 may continuously rotate around the helical axis 218 in a predetermined rotation direction (e.g., clockwise or counterclockwise). Therefore, the helical structure 217 may exhibit handedness, such as right-handedness or left-handedness.

[0070] A plurality of LC molecules 212 having a first identical orientation (e.g., the same first tilt angle and the same first azimuth angle) can form a first series of tilted and parallel refractive index planes (i.e., a first series of Bragg planes) 214 periodically distributed within the volume of the R-PVH layer 215. Although not labeled, a plurality of LC molecules 212 having a second identical orientation (e.g., the same second tilt angle and the same second azimuth angle) different from the first identical orientation can form a second series of tilted and parallel refractive index planes (i.e., a second series of Bragg planes) 214 periodically distributed within the volume of the R-PVH layer 215. Different series of Bragg planes can be formed by LC molecules 212 having different orientations. In the same series of Bragg planes, each LC molecule 212 can have the same orientation and the same refractive index. Different series of Bragg planes can correspond to different refractive indices. When the number of Bragg planes (or the thickness of the R-PVH layer 215) increases to a sufficiently large value, Bragg diffraction can be established according to the principles of volume grating. The distance between adjacent Bragg planes 214 of the same series may be referred to as the Bragg period P B .exist Figure 2A In the illustrated embodiment, the Bragg plane 214 may form an acute angle with respect to the surface 205 of the R-PVH layer 215 .

[0071] When the directors of the plurality of LC molecules 212 continuously rotate about the helical axis 218 in a predetermined rotation direction, the azimuthal angles of the plurality of LC molecules 212 within the volume of the R-PVH layer 215 may exhibit a continuous periodic variation along the helical axis 218. The azimuthal angles of the LC molecules 212 within the volume of the R-PVH layer 215 may be defined as the direction of the LC director relative to a predetermined in-plane direction within the Bragg plane 214 (e.g., Figure 2A The pitch P of the helical structure 217 is h It can be defined as the distance along the helical axis 218 over which the orientation of the LC director rotates 360° or the azimuth angle of the LC molecule 212 changes 360°. Assuming the helical pitch P h is constant across the entire R-PVH layer 215. The Bragg period P B Can be smaller than the pitch P h For discussion purposes, Figure 2A shows the Bragg period P B is the pitch P h In some embodiments, although not shown, the Bragg period P B Can be smaller or larger than the pitch P h half.

[0072] In some embodiments, a single pitch P of the helical structure 217 h , the plurality of LC molecules 212 within the volume of the R-PVH layer 215 may be configured to have a nonlinear azimuthal variation along the helical axis 218. For discussion purposes, a local point at the helical axis 218 where the azimuthal angle of the LC molecules 212 is 0° may be defined as the starting point for the 360° variation in azimuthal angle along the helical axis 218. h In FIG. 2 , the azimuth angle of the LC molecules 212 can be configured to vary nonlinearly with respect to the distance from the starting point (e.g., where the azimuth angle is 0°) to the local point where the LC molecules 212 are located along the helical axis 218. For the purpose of discussion, the pitch P of a single helical structure 217 is h In the embodiment, the distance from the starting point (eg, where the azimuth angle is 0°) to the local point where the LC molecule 212 is located along the helical axis 218 may be referred to as the out-of-plane axis distance of the LC molecule 212 .

[0073] In some embodiments, a single pitch P of the helical structure 217 h The azimuth angle of the LC molecules 212 can be calculated according to the function changes, among which is the azimuthal angle of the LC molecules 212, z' is the out-of-plane axis distance of the LC molecules 112, PB is the Bragg period. is a linear function of z', the term is a nonlinear function of z', A is an amplitude parameter of the nonlinear function, and n is a frequency parameter of the nonlinear function. In some embodiments, the amplitude A of the nonlinear function can be configured as a positive value within a range greater than 0° and less than or equal to 360°, and the frequency n of the nonlinear function can be configured as a positive value within a range greater than 0 and less than or equal to 1. Nonlinear function It can be any suitable nonlinear function, such as a quadratic function, a polynomial function, a rational function, an exponential function, a logarithmic function, a trigonometric function, or a combination thereof.

[0074] Figure 2C 2 shows an xz cross-sectional view of an LCPH element 250 according to an embodiment of the present disclosure. Figure 2C In the illustrated embodiment, the LCPH element 250 may be a non-tilted CLC element (also referred to as 250 for discussion purposes) configured to substantially reflect circularly polarized light having a predetermined handedness and substantially transmit circularly polarized light having a handedness opposite to the predetermined handedness. The CLC element 250 may include Figure 2A The R-PVH layer 215 is shown similar to an optically anisotropic film (referred to as a CLC layer) 265. A plurality of LC molecules 212 disposed proximate to a surface 255 (eg, in the xy plane) of the CLC layer 265 may be configured to have a uniform in-plane alignment pattern.

[0075] Within the volume of the CLC layer 265, the plurality of LC molecules 212 may be arranged in a plurality of helical structures 267 and a plurality of series of Bragg planes 264. The helical axes 268 of the helical structures 267 may extend in the thickness direction of the CLC layer 265 and may be substantially perpendicular to the surface 255 of the CLC layer 365. The Bragg planes 264 formed within the volume of the CLC layer 265 may be parallel to the surface 255 of the CLC layer 365. Figure 2C The Bragg plane 264 is shown to lie in the xy plane, with the helical axis 268 extending in the z-axis direction. The azimuthal angle of the LC molecules 212 within the volume of the CLC layer 265 can be defined as the LC director relative to a predetermined in-plane direction within the Bragg plane 264 (e.g., Figure 2C The angle of the x-axis in the direction of the thread. Assume that the thread pitch P h is constant across the CLC layer 265. In the CLC element 250, the coordinate system of the CLC element 250 may coincide with the coordinate system of the spiral structure 267.

[0076] Similar to Figure 2A The R-PVH element 200 shown in FIG. Figure 2CIn the CLC element 250 shown, a single pitch P of the helical structure 267 h In the embodiment, the LC molecules 212 can be configured to have a nonlinear azimuthal variation along the helical axis 268. For example, the azimuthal angle of the LC molecules 212 can be determined according to the function changes, among which is the azimuth angle of the LC molecule 212, z is the out-of-plane axis distance of the LC molecule 112, P B is the Bragg period. The description of the nonlinear azimuthal angle variation of the LC molecules 212 along the helical axis 268 can be referred to in conjunction with Figure 2A The nonlinear azimuthal angle variation of the LC molecules 212 along the helical axis 268 of the CLC element 250 can generate one or more sub-reflection bands in addition to the main reflection band. The CLC element 250 can provide high reflection efficiency (e.g., greater than 98%) over a large AOI range for the main reflection band and the one or more sub-reflection bands.

[0077] Figures 2D to 2F A single pitch P of the helical structure 218 in the R-PVH element 200 is shown according to various embodiments of the present disclosure. h The CLC element 250 can also be configured to have a single pitch P of the helical structure 268. h There is a similar nonlinear azimuthal variation of the LC molecules 212 on the surface.

[0078] Figure 2D Simulation results showing the individual pitches P of the helical structure 218 formed in the R-PVH element 200 according to various embodiments of the present disclosure are presented. h The azimuth angle of the upper LC molecule 212 The distance z′ from the out-of-plane axis of the LC molecules 212 (e.g. Figure 2A As shown in Figure 2, various nonlinear relationships between Figure 2D As shown, the horizontal axis represents the out-of-plane axis distance z' (unit: μm) of the LC molecules 212, and the vertical axis represents the azimuth angle of the LC molecules 212. (Unit: degrees). In these simulations, the pitch P of the helical structure 217 is h The azimuth angle of the LC molecule 212 is According to the function changes, among which is a linear function of the out-of-plane axis distance z', It is a nonlinear function For example, A=18°, P B =0.2μm.

[0079] Figure 2DThe curve 221 in FIG. 2 shows the azimuth angle of the LC molecules 212 when n=1. and the nonlinear relationship between the out-of-plane axis distance z' of the LC molecules 212. Curve 222 shows the azimuth angle of the LC molecules 212 when n=0.75. and the nonlinear relationship between the out-of-plane axis distance z' of the LC molecules 212. Curve 223 shows the azimuth angle of the LC molecules 212 when n=0.5. and the out-of-plane axis distance z' of the LC molecules 212. Line 224 shows the linear term This linear term or line 224 is also shown in Figure 1B The single pitch P of the helical structure 117 formed in the conventional R-PVH element 150 is shown. h The azimuth angle of the upper LC molecule 112 The linear relationship between the distance z' from the axis of the LC molecule 112. The straight line 224 has a 180° / P B The constant slope of , indicating that the single pitch P of the helical structure 117 formed in the conventional R-PVH element 150 h The azimuth angle of the LC molecules The linear increase with the increase of the out-of-plane axis distance z' of the LC molecules 112. Each of the curves 221 to 223 is shown as a wavy line that oscillates around the straight line 224, indicating that the single pitch P of the helical structure 218 h The azimuth angle of the LC molecule 212 is The nonlinearity increases with the increase of the out-of-plane axis distance z' of the LC molecules 212. The oscillation around the line 224 can vary with the frequency n of the nonlinear term. The nonlinear azimuthal angle variation is the result of the combination of the linear term and the nonlinear term, as shown by the function shown.

[0080] Figure 2E The following table shows the single pitch P of the R-PVH element 200 according to various embodiments of the present disclosure. h For a series of out-of-plane axis distances (z'=0.25*P B , 0.5*P B , 0.75*P B , 1.25*P B , 1.5*P B , 1.75*P B and 2*P B ) and a series of frequencies (n = 1, 0.75 and 0.5) of the simulated azimuthal angle δ of the LC molecule 212. As shown in Table 1, the single pitch P of the helical structure 218 h The azimuth angle of the LC molecule 212 is It increases nonlinearly with the increase of the out-of-plane axis distance z′ of the LC molecules 212 . Figure 2E The last column of the table shown (labeled "Linear") also shows the Figure 1B The single pitch P of the helical structure 118 formed in the conventional R-PVH element 150 is shown. h For a series of axis distances (z'=0.25*P B , 0.5*P B , 0.75*P B , P B , 1.25*P B , 1.5*P B , 1.75*P B , 2*P B ) The calculated azimuthal angle δ of the LC molecules 112.

[0081] Figure 2F Shown Figure 2A A 3D exploded view of a portion of the R-PVH element 200 is shown, showing that when n=1, the LC molecules 212 are in a single pitch P of the helical structure 217. h For the purpose of discussion, Figure 2F The single pitch P of the helical structure 217 is shown h 2. The LC molecules 212 are organized into nine consecutive sub-layers (or Bragg planes) 271-279 that are equally spaced from each other along the helical axis 218. In the same sub-layer, the LC directors (indicated by the dashed lines) can be oriented in the same direction, while in different sub-layers, the LC directors (indicated by the dashed lines) can be oriented in different directions. h The starting point of the 360° change in azimuth along the spiral axis 218 can be at At sub-layer 271 with an angle of 0°. Figure 2F The corresponding azimuth angles of the LC molecules 212 are shown when the axis distances z' of the sub-layers 272-279 are 0.05 μm, 0.1 μm, 0.15 μm, 0.2 μm, 0.25 μm, 0.3 μm, 0.35 μm and 0.4 μm, respectively. They are 63°, 90°, 117°, 180°, 243°, 270°, 297° and 360° respectively.

[0082] The nonlinear azimuthal variation of the LC molecules 212 in the R-PVH element 200 or the CLC element 250 can generate one or more secondary (or minor) reflection bands in addition to the primary reflection band. In some embodiments, the nonlinear azimuthal variation of the LC molecules 212 in the R-PVH element 200 or the CLC element 250 can generate at least two series of Bragg planes having different Bragg periods within the volume of the PVH element 200 or the CLC element 250, such as a first series of Bragg planes (e.g., 214) having a first Bragg period, a second series of Bragg planes (e.g., 215) having a second Bragg period, and a third series of Bragg planes (e.g., 216) having a second Bragg period. Figure 2A In some embodiments, due to the nonlinear azimuthal variation of the LC molecules 212 in the R-PVH element 200, the LC molecules 212 within the R-PVH element 200 may have an in-plane alignment pattern within the film plane of the R-PVH element 200. The in-plane alignment pattern within the film plane of the R-PVH element 200 may have at least one in-plane pitch that is different from the in-plane pitch P of the in-plane alignment pattern formed at the surface 205 of the R-PVH element 200. in .

[0083] Figure 3A Various embodiments according to the present disclosure are shown Figure 2C The simulation results of the relationship between the reflection efficiency of the CLC element 250 and the wavelength of the incident light are shown in FIG. In these simulations, the single pitch P of the spiral structure 267 in the CLC element 250 is h The azimuth angle of the LC molecule 212 is According to the function Change, where A = 18°, P B =0.2 μm, and the birefringent material in the CLC element 250 has a birefringence of 0.35.

[0084] like Figure 3A As shown in FIG. 3 , the horizontal axis represents the incident light wavelength (or incident wavelength) (unit: μm), and the vertical axis represents the normalized reflection efficiency. Curve 301 shows the relationship between the normalized reflection efficiency and the incident wavelength when n=1. Curve 302 shows the relationship between the normalized reflection efficiency and the incident wavelength when n=0.75. Curve 303 shows the relationship between the normalized reflection efficiency and the incident wavelength when n=0.5. Curves 301, 302, and 303 show the relationship between the normalized reflection efficiency and the incident wavelength when the LC molecules 212 are arranged in a single helical pitch P. h When the optical element 250 has a nonlinear azimuth variation, the CLC element 250 presents a sub-reflection band in addition to the main reflection band.

[0085] The main reflection band and the secondary reflection band can be separated from each other. The main reflection band can have a relatively wide bandwidth, and the secondary reflection band can have a relatively narrow bandwidth. Both the main reflection band and the secondary reflection band can have a relatively high reflection efficiency, for example, greater than 95%. For the purpose of discussion, Figure 3A It is shown that the main reflection band is the red wavelength range, while the sub-reflection band is the blue wavelength range. Therefore, the CLC element 250 can reflect both red light and blue light with relatively high reflection efficiency. Figure 3A It is also shown that when the frequency n decreases from 1 to 0.5, the separation distance between the main reflection band and the sub-reflection band can decrease. In other words, when the frequency n gradually decreases, the sub-reflection band can gradually approach the main reflection band.

[0086] refer to Figure 1C and Figure 3A , Figure 3A The main reflection band of the CLC element 250 is shown as Figure 1C The reflection band of the illustrated CLC layer (reflecting red light) can have substantially the same bandwidth (e.g., about 100 nanometers (nm)) and a relatively high reflection efficiency (e.g., greater than 98%). That is, although the nonlinear azimuthal angle variation of the LC molecules 212 along the helical axis 268 introduces a secondary reflection band, the bandwidth and reflection efficiency of the primary reflection band can be substantially maintained.

[0087] refer to Figure 1D and Figure 3A , to provide a reflection band including two different wavelength ranges, Figure 1D The conventional CLC layer shown may use a birefringent material having a relatively high birefringence (e.g., 0.5 for a wavelength range including blue and green), while the disclosed CLC layer 265 may use a birefringent material having a low birefringence (e.g., 0.35 for a wavelength range including blue and red). Figure 1D Compared to the conventional CLC layer configured with a linear azimuthal angle variation as shown, the disclosed CLC element 250 can be manufactured based on a wide range of birefringent materials because materials with high birefringence are limited while materials with low birefringence are more widely available, and the stability and response time of the disclosed CLC element 250 can be improved.

[0088] In this disclosure, including Figure 2C The illustrated CLC element 250 of a single CLC layer 265 can provide high reflection efficiency for both the primary and secondary reflection bands over a wide angle of incidence ("AOI") range. Figure 3B The embodiment according to the present disclosure is shown Figure 2CThe simulation results of the relationship between the reflection efficiency of the CLC element 250 and the AOI of red light and blue light are shown. Figure 3B As shown, the horizontal axis represents the angle of incidence ("AOI") and the vertical axis represents the normalized reflection efficiency. In these simulations, the single pitch P of the helical structure 267 in the CLC element 250 is h The azimuth angle of the LC molecule 212 is According to the function Change, where A = 18°, n = 0.75, P B =0.2 μm, and the birefringent material in the CLC element 250 has a birefringence of 0.35.

[0089] like Figure 3B As shown, curve 321 shows the relationship between the normalized reflective efficiency of the CLC element 250 and the AOI of blue incident light, and curve 323 shows the relationship between the normalized reflective efficiency of the CLC element 250 and the AOI of red incident light. Curves 321 and 323 show that as the AOI increases from 0° to 30°, the CLC element 250 provides a relatively high reflective efficiency (e.g., greater than 98%) for both blue incident light and red incident light. In other words, as the AOI increases from 0° to 30°, the CLC element 250 can substantially maintain a high reflective efficiency (e.g., greater than 98%) for both blue incident light and red incident light throughout the entire AOI range (e.g., 30°).

[0090] Figure 3B Also shown is Figure 1D Simulation results of the relationship between the reflectance efficiency of a conventional CLC layer configured with a linear azimuthal angle variation and the AOI for blue and green light are shown. Curve 326 shows the relationship between the normalized reflectance efficiency of the conventional CLC layer and the AOI for blue incident light, and curve 324 shows the relationship between the normalized reflectance efficiency of the conventional CLC layer and the AOI for green incident light. Figure 3B Curve 326 is shown to substantially overlap curve 323. Curve 326 shows that as AOI increases from 0° to 30°, Figure 1D The conventional CLC layer shown provides a relatively high reflection efficiency (e.g., greater than 98%) for blue incident light. Curve 324 shows that for green incident light, when the AOI is in the range of 0° to 10°, Figure 1D The conventional CLC layer shown provides a fairly high (e.g., greater than 98%) reflection efficiency. However, when the AOI increases from 10° to 30°, the reflection efficiency decreases significantly. That is, for blue incident light and green incident light, Figure 1D The conventional CLC layer shown in FIG may not be able to maintain high reflection efficiency (eg, greater than 98%) throughout the entire AOI range (eg, 30°).

[0091] Figure 3C The embodiment according to the present disclosure is shown Figure 2A and Figure 2B The simulation results of the relationship between the reflection efficiency (or diffraction efficiency) of the R-PVH element 200 and the wavelength of the incident light (or incident wavelength) are shown. In these simulations, the azimuth angle of the LC molecules 212 is Can be configured to be in a single pitch P h According to the function Variation. Nonlinear function The amplitude A and Bragg period P B is assumed to be a constant value, for example A = 18°, and P B =0.2 μm. The value of frequency n can be configured so that the R-PVH element 200 can provide a sub-reflection band in addition to the main reflection band. By configuring the nonlinear azimuth angle variation of the LC molecules 212, the R-PVH element 200 can provide high reflection efficiency in a large AOI range in both the main and sub-reflection bands.

[0092] In contrast, Figure 3D Conventional R-PVH components (e.g. Figure 1B The simulation results of the relationship between the reflection efficiency (or diffraction efficiency) of the R-PVH element 150 shown in FIG. Figure 3C and Figure 3D , the vertical axis represents the incident wavelength (unit: μm) and the horizontal axis represents the diffraction angle (unit: degree). A color bar 330 or 340 (from blue (0) to red (1)) is shown to represent the normalized reflection efficiency. On the color bar 330 or 340, blue represents a lower normalized reflection efficiency (between 0 and 0.3) and red represents a higher normalized reflection efficiency (between 0.8 and 1). In the middle of the color bar is green / yellow, representing a medium normalized reflection efficiency between 0.3 and 0.8. As the color gradually changes from blue to red, the normalized reflection efficiency gradually increases from 0 to 1.

[0093] refer to Figure 3C , Figure 2A and Figure 2BThe R-PVH element 200 shown exhibits a sub-reflection band 332 in addition to a main reflection band 331, thereby providing a relatively high reflection efficiency for both the main reflection band 331 and the sub-reflection band 332 within a large AOI range. The main reflection band 331 and the sub-reflection band 332 can be separated from each other. The main reflection band 331 can have a relatively wide bandwidth, and the sub-reflection band 332 can have a relatively narrow bandwidth. Both the main reflection band 331 and the sub-reflection band 332 can have a relatively high reflection efficiency (or diffraction efficiency) (e.g., greater than 95%). For the purpose of discussion, Figure 3C It is shown that the main reflection band 331 includes the red wavelength range and the secondary reflection band 332 includes the blue wavelength range. Therefore, the R-PVH element 200 can reflect red light and blue light with a relatively high reflection efficiency (or diffraction efficiency) (for example, greater than 98%) via reverse diffraction. Figure 3D , conventional R-PVH components (e.g., Figure 1B The illustrated R-PVH element 150 can provide a single reflective band 341 that includes the red wavelength range, thereby reflecting red light with a relatively high reflection efficiency (eg, greater than 98%).

[0094] In some embodiments, Figure 2A and Figure 2B The R-PVH element 200 shown or Figure 2C The LC molecules 212 in the CLC element 250 are shown to be arranged in a single helical pitch P h The nonlinear azimuthal angle variation within the R-PVH element 200 or CLC element 250 can be configured such that, in addition to the primary reflection band, the R-PVH element 200 or CLC element 250 can also present two additional secondary (or minor) reflection bands. The R-PVH element 200 or CLC element 250 can provide high reflection efficiency for the primary reflection band and the two secondary reflection bands over a large AOI range.

[0095] Figure 4A FIG. 1 shows an embodiment according to the present disclosure showing that for various incident angles, Figure 2C The simulation results of the relationship between the reflection efficiency of the CLC element 250 and the wavelength of the incident light are shown in FIG. Figure 4A As shown, the horizontal axis represents the incident light wavelength (or incident wavelength) (unit: μm), and the vertical axis represents the normalized reflection efficiency. In these simulations, the azimuth angle of the LC molecule 212 is Can be configured to be in a single pitch P h According to the function Variation. Nonlinear function The amplitude A and Bragg period P B is assumed to be a constant value, for example A = 18°, and P B=0.2 μm. The value of the frequency n can be configured so that the CLC element 250 can provide a main reflection band and two additional sub-reflection bands with high reflection efficiency within a large AOI range.

[0096] Curve 401 shows the relationship between normalized reflection efficiency and incident wavelength when AOI = 0°. Curve 402 shows the relationship between normalized reflection efficiency and incident wavelength when AOI = 20°. Curve 403 shows the relationship between normalized reflection efficiency and incident wavelength when AOI = 25°. Curves 401, 402, and 403 each show that the CLC element 250 exhibits a main reflection band and two sub-reflection bands. The main reflection band and the two sub-reflection bands may be separated from each other, and the two sub-reflection bands may be located on either side of the main reflection band. The main reflection band may have a relatively wide bandwidth, and the sub-reflection bands may have a relatively narrow bandwidth.

[0097] For discussion purposes, Figure 4A The main reflection band is shown to include the green wavelength range, and the two sub-reflection bands include the blue wavelength range and the red wavelength range, respectively. Therefore, the CLC element 250 including a single CLC layer 265 can be used as a broadband CLC device covering the visible wavelength range. In some embodiments, although not shown, the main reflection band can be configured to include a suitable wavelength range other than the green wavelength range, and the two sub-reflection bands can be configured to include a suitable wavelength range other than the blue wavelength range and the red wavelength range.

[0098] Figure 4B The embodiment according to the present disclosure is shown Figure 4A The simulation results of the relationship between the reflection efficiency of the CLC element 250 and the AOI of the blue incident light, the green incident light and the red incident light are shown. Figure 4B As shown, the horizontal axis represents the angle of incidence ("AOI") and the vertical axis represents the normalized reflection efficiency. Curve 421 shows the relationship between the normalized reflection efficiency and the AOI for red incident light. Curve 422 shows the relationship between the normalized reflection efficiency and the AOI for green incident light. Curve 423 shows the relationship between the normalized reflection efficiency and the AOI for blue incident light.

[0099] Curves 421, 422, and 423 show that the CLC element 250 provides relatively high reflection efficiency (e.g., greater than 98%) for red incident light, green incident light, and blue incident light within an AOI range of approximately 25°. Curves 421, 422, and 423 also show that as the AOI further increases from 25° to 30°, the reflection efficiency of the CLC element 250 for blue incident light decreases to approximately 90%, while the high reflection efficiency of the CLC element 250 for red incident light and green incident light is substantially maintained (e.g., greater than 98%). In summary, the CLC element 250 including a single CLC layer 265 can be used as a broadband CLC device that provides relatively high reflection efficiency (e.g., greater than 98%) for the visible wavelength range within a large AOI range of 25°.

[0100] Figure 4C The embodiment according to the present disclosure is shown Figure 2A and Figure 2B The simulation results of the relationship between the reflection efficiency (or diffraction efficiency) of the R-PVH element 200 and the wavelength of the incident light (or incident wavelength) are shown. In these simulations, the azimuth angle of the LC molecules 212 is Can be configured to be in a single pitch P h According to the function The amplitude A and Bragg period P of the nonlinear function B is assumed to be a constant value, for example A = 18° and P B =0.2 μm. The value of frequency n can be configured so that the R-PVH element 200 can provide a main (primary) reflection band and two additional secondary (or secondary) reflection bands. By configuring the nonlinear azimuthal angle variation of the LC molecules 212, the R-PVH element 200 can provide high reflection efficiency in both the main reflection band and the two secondary reflection bands over a large AOI range.

[0101] exist Figure 4C , the vertical axis represents the incident wavelength (unit: μm) and the horizontal axis represents the diffraction angle (unit: degree). A color bar 430 (from blue (0) to red (1)) is shown to represent the normalized reflection efficiency. On the color bar 430, blue represents a lower normalized reflection efficiency (between 0 and 0.3) and red represents a higher normalized reflection efficiency (between 0.8 and 1). In the middle of the color bar is green / yellow, representing a medium normalized reflection efficiency between 0.3 and 0.8. As the color gradually changes from blue to red, the normalized reflection efficiency gradually increases from 0 to 1.

[0102] refer to Figure 4C , Figure 2A and Figure 2BThe R-PVH element 200 shown can be configured to have a main reflection band 431 and two sub-reflection bands 432 and 433 located on either side of the main reflection band 431. The main reflection band 431 and the two sub-reflection bands 432 and 433 can be separated from each other. The main reflection band 431 can have a relatively wide bandwidth, and the sub-reflection band 432 or 433 can have a relatively narrow bandwidth. The R-PVH element 200 can provide a relatively high reflection efficiency (e.g., greater than 95%) for the main reflection band 431 and each of the two sub-reflection bands 432 and 433 within a large AOI range.

[0103] For discussion purposes, Figure 4C The main reflection band 431 is shown to include a green wavelength range, and the two secondary reflection bands 432 and 433 include a red wavelength range and a blue wavelength range, respectively. Thus, the R-PVH element 200 including a single R-PVH layer 215 can be used as a broadband R-PVH device covering the visible wavelength range with a relatively high reflection efficiency (e.g., greater than 95%) over a large AOI range. In some embodiments, although not shown, the main reflection band 431 can be configured to include a suitable wavelength range other than the green wavelength range, and the two secondary reflection bands 432 and 433 can be configured to include a suitable wavelength range other than the red wavelength range and the blue wavelength range.

[0104] Figures 5A to 5E Schematic diagrams of various broadband LCPH devices according to various embodiments of the present disclosure are shown. A broadband LCPH device may include one or more disclosed LCPH elements configured with a nonlinearly varying azimuthal distribution to provide a relatively high reflection efficiency over a large AOI range. For discussion purposes, Figures 5A to 5E The broadband LCPH device shown is configured for the visible wavelength range, which is used as an example to illustrate and explain the principles of configuring a broadband LCPH device based on one or more disclosed LCPH elements. These principles can be applied to configure broadband LCPH devices for other multiple wavelength ranges.

[0105] Figure 5A FIG. 5 shows an xz cross-sectional view of a broadband LCPH device 500 according to an embodiment of the present disclosure. Figure 5A As shown, the LCPH device 500 may be a broadband CLC device (also referred to as 500 for discussion purposes) including a stack of a first CLC layer 501 and a second CLC layer 503. In some embodiments, the first CLC layer 501 may be a disclosed CLC layer (e.g., Figure 3A and Figure 3BThe embodiment shown is configured with a CLC layer 265 having a nonlinear azimuthal angle variation (e.g., n=0.75 or 0.5). For example, the first CLC layer 501 can be configured to have two operating wavelength ranges (or reflection bands) associated with the red wavelength range and the blue wavelength range, respectively. In some embodiments, the second CLC layer 503 can be a conventional CLC layer having an operating wavelength range (or reflection band) associated with the green wavelength range.

[0106] The input light 511 of the CLC device 500 can be polychromatic light, including a red component 511R, a green component 511G, and a blue component 511B. For the purposes of discussion, the CLC device 500 can be a left-handed CLC device, and the input light 511 can be left-handed circularly polarized polychromatic light that is substantially perpendicularly incident on the CLC device 500. The CLC device 500 can reflect the polychromatic input light 511 into polychromatic output light 513 with a relatively high reflection efficiency (e.g., greater than 98%) over a large AOI range. For example, the first CLC layer 501 can reflect the red component (or red input light) 511R and the blue component (or blue input light) 511B as the red component (or red output light) 513R and the blue component (or blue output light) 513B of the polychromatic output light 513, respectively, while the second CLC layer 503 can reflect the green component (or green input light) 511G as the green component (or green output light) 513G of the polychromatic output light 513.

[0107] In some embodiments, although not shown, the second CLC layer 503 may also be an embodiment of a disclosed CLC layer having a nonlinear azimuthal variation. For example, the first CLC layer 501 may be configured to have a primary operating wavelength range (or reflection band) associated with the red wavelength range, and a secondary operating wavelength range associated with the blue wavelength range, wherein the blue reflection band may have a narrower bandwidth than the red reflection band. The second CLC layer 503 may be configured to have a primary operating wavelength range associated with the green wavelength range, and a secondary operating wavelength range associated with the blue wavelength range, wherein the blue reflection band may have a narrower bandwidth than the green reflection band. The blue reflection bands provided by the first and second CLC layers 501, 503 may be configured to slightly overlap, thereby further widening the overall blue reflection band of the CLC device 500 (i.e., the combination of the two blue reflection bands provided by the first and second CLC layers 501, 503). The nonlinear azimuthal variation in the first and second CLC layers 501, 503 may differ.

[0108] Figure 5B FIG. 5 shows an xz cross-sectional view of a broadband LCPH device 520 according to an embodiment of the present disclosure. Figure 5BAs shown, the LCPH device 520 may be a broadband CLC device (also referred to as 520 for discussion purposes) including a single CLC layer 521. The CLC layer 521 may be a disclosed CLC layer (e.g., Figure 4A and Figure 4B The embodiment shown is configured with a nonlinear azimuthal CLC layer 265. For example, the CLC layer 521 can be configured to have three operating wavelength ranges (or reflection bands) associated with the red wavelength range, the green wavelength range, and the blue wavelength range, respectively.

[0109] Input light 531 to the CLC device 520 can be polychromatic light, including a red portion 531R, a green portion 531G, and a blue portion 531B. For the purposes of this discussion, the CLC device 520 can be a left-handed CLC device, and the input light 531 can be left-handed circularly polarized polychromatic light that is substantially perpendicularly incident on the CLC device 520. The CLC device 520 can reflect the polychromatic input light 531 into polychromatic output light 533 with a relatively high reflection efficiency (e.g., greater than 98%) over a large AOI range. For example, the CLC layer 521 can reflect the red portion (or red input light) 531R, the green portion (or green input light) 531G, and the blue portion (or blue input light) 531B into a red portion (or red output light) 533R, a green portion (or green output light) 533G, and a blue portion (or blue output light) 533B of the polychromatic output light 533, respectively.

[0110] Figure 5C 1 shows an xz cross-sectional view of a broadband LCPH device 540 according to an embodiment of the present disclosure. Figure 5C As shown, the LCPH device 540 can be a broadband R-PVH device (also referred to as 540 for discussion purposes) that includes a stack of a first R-PVH layer 541 and a second R-PVH layer 543. In some embodiments, the first R-PVH layer 541 can be a disclosed R-PVH layer (e.g., Figure 3C 1 and 2. The embodiment of the R-PVH layer 215 is shown as being configured with a nonlinear azimuthal variation. For example, the first R-PVH layer 541 can be configured to have two operating wavelength ranges associated with a red wavelength range and a blue wavelength range, respectively. In some embodiments, the second R-PVH layer 543 can be a conventional R-PVH layer having an operating wavelength range associated with a green wavelength range.

[0111] The input light 551 of the R-PVH device 540 can be polychromatic light, including a red portion 551R, a green portion 551G, and a blue portion 551B. For the purposes of this discussion, the R-PVH device 540 can be a left-handed R-PVH device configured to substantially diffract left-handed circularly polarized light and substantially transmit right-handed circularly polarized light with zero or negligible diffraction. The input light 551 can be left-handed circularly polarized polychromatic light that is substantially perpendicularly incident on the R-PVH device 540. The R-PVH device 540 can substantially back-diffract the polychromatic input light 551 into polychromatic output light 553 with a relatively high diffraction efficiency (e.g., greater than 98%) over a large AOI. For example, the first R-PVH layer 541 can diffract the red part (or red input light) 551R and the blue part (or blue input light) 551B into the red part (or red output light) 553R and the blue part (or blue output light) 553B of the multi-color output light 553, respectively, while the second R-PVH layer 543 can diffract the green part (or green input light) 551G into the green part (or green output light) 553G of the multi-color output light 553.

[0112] In some embodiments, although not shown, the second R-PVH layer 543 may also be an embodiment of the disclosed R-PVH layer having a nonlinear azimuthal variation. For example, the first R-PVH layer 541 may be configured to have a primary operating wavelength range associated with the red wavelength range and a secondary operating wavelength range associated with the blue wavelength range, wherein the blue reflection band may have a narrower bandwidth than the red reflection band. The second R-PVH layer 543 may be configured to have a primary operating wavelength range associated with the green wavelength range and a secondary operating wavelength range associated with the blue wavelength range, wherein the blue reflection band may have a narrower bandwidth than the green reflection band. The blue reflection bands provided by the first R-PVH layer 541 and the second R-PVH layer 543 may be configured to slightly overlap each other, so that the overall blue reflection band of the R-PVH device 540 (i.e., the combination of the two blue reflection bands provided by the first R-PVH layer 541 and the second R-PVH layer 543) may be further widened.

[0113] Figure 5D 1 shows an xz cross-sectional view of a broadband LCPH device 560 according to an embodiment of the present disclosure. Figure 5D As shown, the LCPH device 560 can be a broadband R-PVH device (also referred to as 560 for discussion purposes) that includes a single R-PVH layer 561. The R-PVH layer 561 can be a disclosed R-PVH layer (e.g., Figure 4CThe embodiment shown is configured with a nonlinear azimuthal variation of the R-PVH layer 215. For example, the R-PVH layer 561 can be configured to have three operating wavelength ranges associated with the red wavelength range, the green wavelength range, and the blue wavelength range, respectively.

[0114] The input light 571 of the R-PVH device 560 can be polychromatic light, including a red portion 571R, a green portion 571G, and a blue portion 571B. For the purposes of this discussion, the R-PVH device 560 can be a left-handed R-PVH device, and the input light 571 can be left-handed circularly polarized polychromatic light that is substantially perpendicularly incident on the R-PVH device 560. The R-PVH device 560 can diffract the polychromatic input light 571 into polychromatic output light 573 with a relatively high diffraction efficiency (e.g., greater than 98%) over a large AOI range. For example, the R-PVH layer 561 can diffract the red portion (or red input light) 571R, the green portion (or green input light) 571G, and the blue portion (or blue input light) 571B into a red portion (or red output light) 573R, a green portion (or green output light) 573G, and a blue portion (or blue output light) 573B of the polychromatic output light 573, respectively.

[0115] For discussion purposes, Figure 5C R-PVH equipment 540 and Figure 5D The R-PVH devices 560 in FIG. 5 are shown as functioning as R-PVH gratings that back-diffract red incident light, green incident light, and blue incident light at different diffraction angles (or reflect red incident light, green incident light, and blue incident light at different reflection angles). For example, Figure 5C and Figure 5D The diffraction angles for red, green, and blue light are shown to gradually decrease. In some embodiments, although not shown, the nonlinear azimuthal variation of the LC molecules in the disclosed R-PVH device can be configured such that the disclosed R-PVH device can be configured to back-diffract red, green, and blue light at the same diffraction angle (or reflect red, green, and blue incident light at the same reflection angle), thereby functioning as an apochromatic R-PVH device.

[0116] Figure 5E 1 shows an xz cross-sectional view of a broadband LCPH device 580 according to an embodiment of the present disclosure. Figure 5E As shown, the LCPH device 580 can be a broadband R-PVH device (also referred to as 580 for discussion purposes) including a single R-PVH layer 581. The R-PVH layer 581 can be an embodiment of the disclosed R-PVH layer. For example, the R-PVH layer 581 can be configured to have three operating wavelength ranges associated with a red wavelength range, a green wavelength range, and a blue wavelength range, respectively. Figure 5E In the illustrated embodiment, the R-PVH device 580 can be an apochromatic R-PVH lens configured to back-diffract light of three wavelength ranges at a common diffraction angle and focus the light of the three wavelength ranges to a common focus F.

[0117] The input light 591 of the R-PVH device 580 can be polychromatic light, including a red portion 591R, a green portion 591G, and a blue portion 591B. For the purposes of discussion, the R-PVH device 580 can be a left-handed R-PVH device, and the input light 591 can be left-handed circularly polarized polychromatic light that is substantially perpendicularly incident on the R-PVH device 580. The R-PVH device 580 can substantially back-diffract the red portion (or red input light) 591R, the green portion (or green input light) 591G, and the blue portion (or blue input light) 591B of the input light 591 into red light 593R, green light 593G, and blue light 593B having a common diffraction angle. The red light 593R, the green light 593G, and the blue light 593B can be focused to a common focal point F. In other words, the R-PVH device 580 can focus the polychromatic input light 591 to the common focal point F. On the output side of the R-PVH device 580 , the red light 593R, the green light 593G, and the blue light 593B may form a multi-color output light 593 focused to a common focal point F.

[0118] The LCPH elements or devices disclosed herein have the following characteristics: high efficiency over a large AOI range, high apochromatic efficiency, low thickness, light weight, compactness, no aperture limitation, simple manufacturing, etc. The LCPH elements or devices disclosed herein can be implemented in various systems for augmented reality (AR), virtual reality (VR), and / or mixed reality (MR) applications, such as near-eye displays (NEDs), head-up displays (HUDs), head-mounted displays (HMDs), smartphones, laptops, televisions, vehicles, etc. For example, in some embodiments, the disclosed LCPH elements or devices can be implemented in displays and optical modules to realize pupil-steered AR, VR, and / or MR display systems, such as holographic near-eye displays, retinal projection eyewear, and wedge-shaped waveguide displays. Pupil-steering AR, VR and / or MR display systems have the following characteristics: compactness, large field of view (FOV), high system efficiency and small eyebox. The disclosed LCPH element or device can be implemented in a pupil-steering AR, VR and / or MR display system to expand the eyebox spatially and / or temporally. In some embodiments, the disclosed LCPH element or device can be implemented in an AR, VR and / or MR sensing module to detect objects over a wide angle range, thereby realizing other functions. In some embodiments, the disclosed LCPH element or device can be implemented in an AR, VR and / or MR sensing module to expand the FOV (or detection range) of a sensor in a spatially constrained optical system, increase the detection resolution or accuracy of the sensor, and / or reduce signal processing time. The disclosed LCPH element or device can also be used in a light detection and ranging (Lidar) system in an autonomous vehicle.

[0119] Figure 6 Schematically illustrates an xz cross-sectional view of a system 600 according to an embodiment of the present disclosure. The system 600 may also be referred to as a light guide display system or assembly. Figure 6As shown, system 600 may include a light source assembly 605, a light guide 610 coupled to an incoupling element (or input coupler) 635 and an outcoupling element (or output coupler) 645, and a controller 640. Light source assembly 605 may include a display element (e.g., a display panel) 620 and a collimating lens 625. Light guide 610 coupled to incoupling element 635 and outcoupling element 645 may also be referred to as a light guide image combiner.

[0120] The display panel 620 may output image light 629 representing a virtual image (having a predetermined image size associated with the linear size of the display panel 620) to the collimating lens 625. The image light 629 may be a divergent image light including a beam of light. The image light 629 may be polychromatic light or monochromatic light. For the purposes of discussion, Figure 6 A single ray of image light 629 is shown. Collimating lens 625 can transmit image light 629 as image light 630 having a predetermined input FOV (e.g., α) toward the input side of light guide 610. Collimating lens 625 can transform or convert a linear distribution of pixels in a virtual image formed by image light 629 into an angular distribution of pixels in image light 630 having a predetermined input FOV. Each ray in image light 630 can represent a FOV direction of the input FOV. For discussion purposes, Figure 6 A single ray of image light 630 (eg, a central ray) is shown perpendicularly incident on the incoupling element 635 and may represent a single FOV direction of the input FOV (eg, a 0° FOV direction).

[0121] The in-coupling element 635 can couple the image light 630 into the light guide 610 as in-coupled image light 631, which can propagate within the light guide 610 toward the out-coupling element 645 via total internal reflection (TIR). The out-coupling element 645 can couple the in-coupled image light 631 out of the light guide 610 as a plurality of output image lights 632 at different positions along the longitudinal direction (e.g., the x-axis direction) of the light guide 610, each of which can have an output FOV (e.g., as shown by the angle α) that can be substantially the same as the input FOV. For discussion purposes, Figure 6 Three output image lights 632 are shown, and a single ray (e.g., a center ray) is shown for each output image light 632. At least one of the incoupling element 635 or the outcoupling element 645 may include a grating that couples the image light into or out of the light guide 610 via diffraction, and the grating may include an LCPH element or device disclosed herein, such as Figure 5C The LCPH device 540 shown in or Figure 5D LCPH device 560 shown in .

[0122] Each output image light 632 may include the same image content as the virtual image displayed on the display panel 620. Thus, the light guide 610 coupled with the incoupling element 635 and the outcoupling element 645 may replicate the image light 630 at the output side of the light guide 610 to expand the effective pupil of the system 600. For discussion purposes, Figure 6 Shown along Figure 6 In some embodiments, the system 600 may also provide, for example, one-dimensional pupil expansion along the x-axis. Figure 6 , and a 2D pupil expansion in both the x-axis direction and the y-axis direction. For example, in some embodiments, although not shown, the system 600 may further include a redirecting element (or diffraction element) coupled to the light guide 610 and configured to redirect the in-coupled image light 631 to the out-coupling element 645. The redirecting element may be configured to expand the input image light 630 in a first direction (e.g., the y-axis direction), and the out-coupling element 645 may be configured to expand the input image light 630 in a different second direction (e.g., the x-axis direction). In some embodiments, the redirecting element may include a grating that redirects the in-coupled image light 631 to the out-coupling element 645 via diffraction, and the grating may include an LCPH element or device disclosed herein, such as Figure 5C The LCPH device 540 shown in or Figure 5D LCPH device 560 shown in .

[0123] Multiple image lights 632 can propagate through multiple exit pupils 657 located in an eyebox region 659 of system 600. Exit pupil 657 can correspond to the spatial region in which an eye pupil 658 of a user's eye 660 can be located in the eyebox region 659 of system 600 to perceive a virtual image. The size of a single exit pupil 657 can be larger than and comparable to the size of an eye pupil 658. Multiple exit pupils 657 can be sufficiently spaced apart such that when one of the multiple exit pupils 657 substantially coincides with the location of eye pupil 658, the remaining one or more exit pupils 657 can be located outside the location of eye pupil 658 (e.g., outside eye 660). Light guide 610 and outcoupling element 645 can also transmit light 642 from the real-world environment (referred to as real-world light 642), combine real-world light 642 with output image light 632, and deliver the combined light to eye 660. As a result, eye 660 can observe a virtual scene optically integrated with the real-world scene.

[0124] Figure 7 Schematically illustrates an xz cross-sectional view of a system 700 according to an embodiment of the present disclosure. Figure 7As shown, system 700 may include a display element 705, an image combiner 750 including a reflective lens 720 and a beam steering device 725, an eye tracking device 735, and a controller 640. Controller 640 may be electrically coupled to and control various devices in system 700, including but not limited to display element 705, eye tracking device 735, and beam steering device 725. Beam steering device 725 may be disposed on the side of reflective lens 752 facing the user. Display element 705 may be configured to generate image light 722 representing a virtual image. In some embodiments, display element 705 may include a projector (e.g., a retinal projection display) configured to output image light 722. In some embodiments, display element 705 may be an off-axis display element configured to provide off-axis projection relative to reflective lens 720. For example, image light 722 may be an off-axis beam relative to reflective lens 720.

[0125] The image combiner 750 can be configured to reflect and focus the image light 722 to propagate through one or more exit pupils 657 within the eyebox region 659 of the system 700. The reflective lens 720 can include one or more disclosed LCPH elements or devices, such as Figure 5E LCPH device 580 is shown. Reflective lens 720 can function as an off-axis reflective lens configured to reflect and focus off-axis image light 722 to one or more points within the eyebox area 659 of system 700. For example, reflective lens 720 can reflect and focus off-axis image light 722 into image light 724 that propagates toward beam steering device 725. Beam steering device 725 can steer image light 724 to one or more exit pupils 657 within the eyebox area 659.

[0126] The eye tracking device 735 can be configured to provide eye tracking information related to the pupils 658 of the eyes of the users of the system 700. Any suitable eye tracking device 735 can be used. The eye tracking device 735 can include, for example, one or more light sources to illuminate one or both eyes of the user, and one or more cameras to capture images of one or both eyes. The eye tracking device 735 can be configured to track the position, movement, and / or viewing direction of the pupils 658 of the eyes. In some embodiments, the eye tracking device 735 can measure eye position and / or eye movement in up to six degrees of freedom (i.e., 3D position, roll, pitch, and yaw) for each eye. In some embodiments, the eye tracking device 735 can measure pupil size. The eye tracking device 735 can provide a signal (or feedback) including the position and / or movement of the pupils 658 of the eyes to the controller 640.

[0127] For discussion purposes, Figure 7 Two operational states of beam steering device 725 are shown. For example, at a first moment, eye tracking device 735 may detect that user's eye pupil 658 is located at position P1 within eyebox area 659. Based on the eye tracking information, controller 640 may control beam steering device 725 to redirect image light 724 to propagate through an exit pupil corresponding to position P1 within eyebox area 659. At a second moment, eye tracking device 735 may detect that user's eye pupil 658 has moved in the x-axis direction from previous position P1 to a new position P2 within eyebox area 659. Based on new eye tracking information associated with new position P2, controller 640 may control beam steering device 725 to redirect image light 724 to propagate through an exit pupil corresponding to position P2 within eyebox area 659.

[0128] For discussion purposes, Figure 7 The beam steering device 725 is shown to provide 1D pupil steering, e.g. Figure 7 In some embodiments, although not shown, the beam steering device 725 can provide 2D pupil steering, for example, by steering the exit pupil 657 in two different directions (e.g., Figure 7 In some embodiments, although not shown, the reflective lens 720 may provide adjustable optical power, and the beam steering device 725 and the reflective lens 720 may together provide 3D pupil steering, such as steering the exit pupil 657 in three different directions (e.g., Figure 7 The device is turned in the x-axis direction, y-axis direction and z-axis direction as shown.

[0129] When configured for AR or MR applications, the image combiner 750 can also combine the image light 722 received from the display element 705 with the light beam 710 from the real-world environment (referred to as real-world light beam 710) and direct the light beams 710 and 722 toward the eyebox area 659. In some embodiments, the system 700 can include a compensator 780 coupled to (e.g., overlaid with) the image combiner 750. The image combiner 750 can be disposed between the compensator 780 and the eyebox area 659. The real-world light beam 710 can be incident on the compensator 780 before being incident on the image combiner 750. In some embodiments, the controller 640 can be configured to control the compensator 780 and the image combiner 750 to provide opposite steering and lensing effects to the real-world light beam 710. For example, the optical powers provided by the compensator 780 and the image combiner 750 can have opposite signs and substantially the same absolute values, and the steering provided by the compensator 780 and the image combiner 750 can have opposite directions. Thus, the compensator 780 can compensate for the distortion of the real-world beam 710 caused by the image combiner 750 so that the image of the real-world object viewed through the system 700 can be substantially unchanged. In some embodiments, the compensator 780 can include one or more disclosed LCPH elements or devices, such as Figure 5E LCPH device 580 is shown. In some embodiments, when system 700 is configured for VR applications, compensator 780 can be omitted.

[0130] Figure 8A Schematically illustrates a zx cross-sectional view of a system 800 according to an embodiment of the present disclosure. The system 800 may include a light source assembly (e.g., a display element) 850 configured to output image light 821 (e.g., divergent image light) representing a virtual image. In some embodiments, the display element 850 may be a multicolor display (e.g., a red, green, and blue ("RGB") display) that includes a broadband multicolor light source (e.g., a 300 nm bandwidth light source covering the visible wavelength range). In some embodiments, the display element 850 may be a multicolor display (e.g., an RGB display) that may include a stack of multiple monochrome displays that may each include a corresponding narrowband monochromatic light source. In some embodiments, the image light 821 emitted from the display element 850 may be circularly polarized light.

[0131] The system 800 may further include a path-folding lens assembly (e.g., a pancake lens assembly) 801 configured to fold the optical path of the image light 821 and convert light rays emitted from each light output unit of the display element 850 (forming divergent image light 821) into a bundle of parallel light rays that substantially covers one or more exit pupils 657 in the eyebox area 659 of the system 800. Due to the path folding, the lens assembly 801 can increase the FOV of the system 800 without increasing the physical distance between the display element 850 and the eyebox area 659 and without compromising image quality.

[0132] In some embodiments, the pancake lens assembly 801 can include a first optical element (e.g., a first optical lens) 805 and a second optical element (e.g., a second optical lens) 810. In some embodiments, the pancake lens assembly 801 can be configured as a monolithic pancake lens assembly without any air gaps between the optical elements included in the pancake lens assembly. In some embodiments, one or more surfaces of the first optical element 805 and the second optical element 810 can be shaped (e.g., curved) to compensate for field curvature. In some embodiments, one or more surfaces of the first optical element 805 and / or the second optical element 810 can be shaped into a spheroconcave shape (e.g., a portion of a sphere), a spheroconvex shape, a rotationally symmetric aspheric shape, a freeform shape, or some other shape that can mitigate field curvature. In some embodiments, the shape of one or more surfaces of the first optical element 805 and / or the second optical element 810 can be designed to additionally compensate for other forms of optical aberrations. In some embodiments, the first optical element 805 and the second optical element 810 can be coupled together by an adhesive 815.

[0133] The first optical element 805 can include a first surface 805-1 facing the display element 850 and an opposing second surface 805-2 facing the eye 660. The pancake lens assembly 801 can include a circular polarizer 802 and a reflector 806 arranged in an optical series, each of which can be a separate layer, film, or coating disposed at (e.g., bonded to or formed on) the first optical element 805. The circular polarizer 802 or the reflector 806 can be disposed at (e.g., bonded to or formed on) the first surface 805-1 or the second surface 805-2 of the first optical element 805. For purposes of discussion, Figure 8A The circular polarizer 802 is shown disposed at (eg, bonded to or formed on) a first surface 805 - 1 facing the display element 850 , and the reflector 806 is shown disposed at (eg, bonded to or formed on) a second surface 805 - 2 facing the second optical element 810 .

[0134] The circular polarizer 802 can be configured to substantially transmit image light 821 emitted from the display element 850. In some embodiments, the reflector 806 can be a polarization non-selective partial reflector that is partially reflective to reflect a portion of the received light. In some embodiments, the reflector 806 can be configured to transmit approximately 50% and reflect approximately 50% of the received light and can be referred to as a "50 / 50 reflector." In some embodiments, the handedness of the reflected light can be reversed, while the handedness of the transmitted light can remain unchanged.

[0135] The second optical element 810 can have a first surface 810-1 facing the first optical element 805 and an opposing second surface 810-2 facing the eye 660. The pancake lens assembly 801 can also include a reflective polarizer 808, which can be a separate layer, film, or coating disposed at (e.g., bonded to or formed on) the second optical element 810. The reflective polarizer 808 can be disposed at (e.g., bonded to or formed on) the first surface 810-1 or the second surface 810-2 of the second optical element 810 and can receive light output from the reflector 806. For purposes of discussion, Figure 8A The reflective polarizer 808 is shown disposed at (e.g., bonded to or formed on) a first surface 810-1 of a second optical element 810. The reflective polarizer 808 can be configured to primarily reflect circularly polarized light having a first handedness and primarily transmit circularly polarized light having a second handedness orthogonal to the first handedness. The reflective polarizer 808 can include an LCPH element as disclosed herein, for example Figure 5A The LCPH device 500 shown or Figure 5B LCPH device 520 is shown.

[0136] Figure 8A The pancake lens assembly 801 is shown for illustration purposes only. In some embodiments, one or more of the first surface 805-1 and the second surface 805-2 of the first optical element 805 and the first surface 810-1 and the second surface 810-2 of the second optical element 810 can be one or more curved surfaces or one or more flat surfaces. In some embodiments, the pancake lens assembly 801 can also include Figure 8A Additional optical elements not shown in the figure may include one or more linear polarizers, one or more wave plates, one or more circular polarizers, etc.

[0137] Figure 8B The embodiment according to the present disclosure is shown in Figure 8ASchematic cross-sectional view of the optical path 860 of light propagating in the pancake lens assembly 801 shown. In the light propagation path 860, the polarization change of the light is shown. Therefore, in order to simplify the illustration, the first optical element 805 and the second optical element 810, which are assumed to be lenses that do not affect the polarization of the light, are omitted. Figure 8B , the letter “R” appended to a reference numeral (eg, “827R”) represents right-handed circularly polarized light, and the letter “L” appended to a reference numeral (eg, “825L”) represents left-handed circularly polarized light.

[0138] For the purpose of discussion, Figure 8B As shown, image light 821 emitted from display element 850 can be left-handed circularly polarized light. Circular polarizer 802 can be configured to transmit left-handed circularly polarized light and block right-handed circularly polarized light via absorption. Reflective polarizer 808 can be a left-handed reflective polarizer that is configured to reflect left-handed circularly polarized light and transmit right-handed circularly polarized light. For the purposes of this discussion, circular polarizer 802, mirror 806, and reflective polarizer 808 are shown in FIG. Figure 8B In some embodiments, one or more of circular polarizer 802, mirror 806, and reflective polarizer 808 can have curved surfaces.

[0139] like Figure 8B As shown, display element 850 can generate left-handed circularly polarized image light 821L covering a predetermined spectrum (e.g., a portion of the visible spectrum range or substantially the entire visible spectrum range). Left-handed circularly polarized image light 821L can be transmitted by circular polarizer 802 as left-handed circularly polarized image light 825. Reflector 806 can reflect a first portion of left-handed circularly polarized image light 825 back to circular polarizer 802 as right-handed circularly polarized image light 827, and transmit a second portion of left-handed circularly polarized image light 825 as left-handed circularly polarized image light 828 toward reflective polarizer 808. Circular polarizer 802 can block right-handed circularly polarized image light 827 from being incident on display element 850. Reflective polarizer 808 can reflect left-handed circularly polarized image light 828 back to reflector 806 as left-handed circularly polarized image light 829. Mirror 806 may reflect left-handed circularly polarized image light 829 as right-handed circularly polarized image light 831 , which may be transmitted through reflective polarizer 808 as right-handed circularly polarized image light 833 toward eyebox region 659 .

[0140] Figure 9An xz cross-sectional view of a system 900 according to an embodiment of the present disclosure is schematically illustrated. The system 900 may include a display element 850 (the display element is an example of a light source) configured to output image light 921 representing a virtual image and a path folding lens assembly 901 (also referred to as lens assembly 901) configured to fold the path of the image light 921 from the display element 850 to the eyebox area 659. The lens assembly 901 may be disposed between the display element 850 and the eyebox area 659. The lens assembly 901 may convert light emitted from each light output unit of the display element 850 (forming divergent image light) into a beam of parallel light that substantially covers one or more exit pupils 657 in the eyebox area 659 of the system 900. For purposes of discussion, Figure 9 A single ray of image light 921 is shown emitted from a light output unit (eg, pixel) at the top half of display element 850 .

[0141] The lens assembly 901 may include a first circular polarizer 903, a first polarization-selective reflector 905 (e.g., a first LCPH element configured with a first optical power (i.e., serving as a first LCPH lens)), a polarization-non-selective partial reflector 907 (also referred to as partial reflector 907), a second polarization-selective reflector 915 (e.g., a second LCPH element configured with a second optical power (i.e., serving as a second LCPH lens)), and a second circular polarizer 913, arranged in optical series. For purposes of discussion, the first polarization-selective reflector 905 and the second polarization-selective reflector 915 are referred to as the first LCPH element 905 and the second LCPH element 915, respectively. Figure 9 In the illustrated embodiment, at least one of the first LCPH element 905 or the second LCPH element 915 may include a disclosed LCPH element or device, such as Figure 5E LCPH device 580 is shown.

[0142] The partial reflector 907 can be configured to partially transmit the input light while maintaining the polarization and propagation direction, and partially reflect the input light while changing the polarization, regardless of the polarization of the input light. In other words, the partial reflector 907 can partially transmit the input light and partially reflect the input light regardless of the polarization of the input light. For the purposes of this discussion, the partial reflector 907 is also referred to as a reflector. In some embodiments, the reflector 907 can be configured to transmit approximately 50% of the input light and reflect approximately 50% of the input light (referred to as a 50 / 50 reflector).

[0143] Figure 9The optical path or propagation path of image light 921 from display element 850 through lens assembly 901 to eyebox region 659 is shown. In the following figures, the letter "R" appended to a reference numeral (e.g., "1124R") indicates right-handed circularly polarized ("RHCP") light, and the letter "L" appended to a reference numeral (e.g., "1123L") indicates left-handed circularly polarized ("LHCP") light.

[0144] exist Figure 9 In the illustrated embodiment, the first LCPH element 905 and the second LCPH element 915 can have the same optical power and different polarization selectivity (e.g., can reflect orthogonal polarizations). For example, the first LCPH element 905 can function as a right-handed LCPH lens that reflects and focuses right-handed circularly polarized light via diffraction and transmits left-handed circularly polarized light with negligible or zero diffraction. The second LCPH element 915 can function as a left-handed LCPH lens that reflects and focuses left-handed circularly polarized light via diffraction and transmits right-handed circularly polarized light with negligible or zero diffraction. The distance between the first LCPH element 905 and the reflector 907 (e.g., L1) can be equal to the distance between the second LCPH element 915 and the reflector 907 (e.g., L1). In some embodiments, the first LCPH element 905 and the second LCPH element 915 can have different optical powers, and the distance between the first LCPH element 905 and the reflector 907 can be different from the distance between the second LCPH element 915 and the reflector 907. For the purpose of discussion, Figure 9 In the illustrated embodiment, image light 921 may be left-handed circularly polarized light.

[0145] like Figure 9As shown, first circular polarizer 903 can transmit image light 921 as image light 922L. First LCPH element 905 can substantially transmit image light 922L as image light 923L toward reflector 907. Reflector 907 can transmit a first portion of image light 923L as image light 925L toward second LCPH element 915, and reflect a second portion of image light 923L back to first LCPH element 905 as image light 924R. Second LCPH element 915 can substantially reflect and focus image light 925L via diffraction as image light 927L toward reflector 907. Reflector 907 can transmit a first portion of image light 927L toward first LCPH element 905 as left-handed circularly polarized image light (not shown), and reflect a second portion of image light 927L back to second LCPH element 915 as image light 929R. Second LCPH element 915 can substantially transmit image light 929R while maintaining polarization and propagation direction. The second circular polarizer 913 may transmit the image light 929R as image light 931R toward the eyebox area 659 .

[0146] When the image light 923L is perpendicularly incident on the reflector 907, the image light 924R may propagate in a direction opposite to the propagation direction of the image light 923L. That is, the image light 924R and the image light 923L may substantially coincide with each other and have opposite propagation directions. To better illustrate the optical paths of the image light 924R and the image light 923L, Figure 9 A small gap is shown between image light 924R and image light 923L. The first LCPH element 905 can reflect and converge image light 924R via diffraction as image light 926R toward the reflector 907. The reflector 907 can transmit a first portion of the image light 926R toward the second LCPH element 915 as image light 928R, and reflect a second portion of the image light 926R back to the first LCPH element 905 as left-handed circularly polarized image light (not shown). The second LCPH element 915 can substantially transmit image light 928R while maintaining the propagation direction and polarization. The second circular polarizer 913 can transmit image light 928R as image light 930R toward the eyebox area 659. Figure 9 , since the first LCPH element 905 and the second LCPH element 915 have the same optical focal length and the same axial distance (e.g., L1) from the reflector 907 along the optical axis 920 of the system 900, the image light 930R and the image light 931R can basically coincide or overlap with each other, thereby forming a single image with high image quality within the eyebox area 659.

[0147] Figure 10AA schematic diagram of an artificial reality device 1000 according to an embodiment of the present disclosure is shown. In some embodiments, the artificial reality device 1000 can generate VR, AR and / or MR content for a user, such as images, video, audio, or a combination thereof. In some embodiments, the artificial reality device 1000 can be smart glasses. In one embodiment, the artificial reality device 1000 can be a near-eye display ("NED"). In some embodiments, the artificial reality device 1000 can be in the form of glasses, goggles, a helmet, a head-mounted display, or some other type of eye-mounted device. In some embodiments, the artificial reality device 1000 can be configured to be worn on the user's head (e.g., by having eyepieces or glasses, such as Figure 10A ), or included as part of a helmet worn by the user. In some embodiments, the artificial reality device 1000 may be configured to be placed near one or both of the user's eyes, in a fixed position in front of one or both of the eyes, rather than being mounted on the user's head. In some embodiments, the artificial reality device 1000 may be in the form of glasses that provide vision correction to the user's vision. In some embodiments, the artificial reality device 1000 may be in the form of sunglasses that protect the user's eyes from the effects of strong sunlight. In some embodiments, the artificial reality device 1000 may be in the form of safety glasses that protect the user's eyes. In some embodiments, the artificial reality device 1000 may be in the form of a night vision device or infrared goggles that enhance the user's vision at night.

[0148] For discussion purposes, Figure 10A The artificial reality device 1000 is shown to include a frame 1005 configured to be mounted to a user's head and a left-eye display system 1010L and a right-eye display system 1010R mounted to the frame 1005. Figure 10B According to an embodiment of the present disclosure Figure 10A A cross-sectional view of one half of the artificial reality device 1000 is shown. For discussion purposes, Figure 10B A cross-sectional view associated with left-eye display system 1010L is shown. Frame 1005 is merely an example structure upon which various components of artificial reality device 1000 may be mounted. Other suitable types of fixtures may be used in place of or in conjunction with frame 1005.

[0149] In some embodiments, the left-eye display system 1010L and the right-eye display system 1010R may each include suitable image display components configured to generate image light representing a virtual image. In some embodiments, the left-eye display system 1010L and the right-eye display system 1010R may each include suitable optical components configured to guide the image light toward the eyebox area 659. For example, in some embodiments, the left-eye display system 1010L and the right-eye display system 1010R may each include a light guide display system, such as Figure 6 In some embodiments, the left-eye display system 1010L and the right-eye display system 1010R may each include Figure 7 The system 700 shown, Figure 8A or Figure 9 Display element 850 is shown.

[0150] In some embodiments, the artificial reality device 1000 may further include an observation optical system 1024 disposed between the left-eye display system 1010L or the right-eye display system 1010R and the eyebox area 659. The observation optical system 1024 may be configured to guide image light (representing a computer-generated virtual image) output from the left-eye display system 1010L or the right-eye display system 1010R to propagate through one or more exit pupils 657 within the eyebox area 659. For example, the observation optical system 1024 may include Figure 8A The path shown is folded lens assembly 801 or Figure 9 Each of the illustrated path-folding lens assembly 901, path-folding lens assembly 801, and path-folding lens assembly 901 can include an LCPH configured with the aforementioned nonlinear azimuthal angle variation. In some embodiments, the observation optical system 1024 can also be configured to perform appropriate optical adjustments to the image light output from the left-eye display system 1010L or the right-eye display system 1010R, such as correcting aberrations of the image light, adjusting the position of the focus of the image light within the eyebox region 659, and the like.

[0151] In some embodiments, as Figure 10B As shown, the artificial reality device 1000 may further include an object tracking system 1050 (e.g., an eye tracking system and / or a face tracking system). The object tracking system 1050 may include an IR light source 1051 configured to illuminate the eye 660 and / or the face, a light deflection element 1052 configured to deflect the IR light reflected by the eye 660, and an optical sensor 1055 configured to receive the IR light deflected by the deflection element 1052 and generate a tracking signal. The controller (e.g., Figure 6 A controller similar to the controller 640 shown) may be included in the artificial reality device 1000.

[0152] The present disclosure also provides a process for fabricating an LCPH element or device having nonlinear azimuthal angle variation. Figures 11A to 11F A process for fabricating an LCPH element with nonlinear azimuthal angle variation according to an embodiment of the present disclosure is schematically illustrated. Figures 11A to 11F The manufacturing process shown can include holographic recording of the alignment pattern in the photo-alignment film and alignment of molecules of anisotropic material (e.g., LC material) through the photo-alignment film. Holographic recording of the alignment pattern in the photo-alignment film can also be referred to as surface recording. This alignment process can be referred to as surface-mediated photo-alignment. For the purposes of discussion, the substrate and the various layers, films, or structures formed thereon are shown as having flat surfaces. In some embodiments, the substrate and the various layers, films, or structures can have curved surfaces.

[0153] like Figure 11A As shown, a recording medium layer 1110 can be formed on a surface (e.g., top surface) of the substrate 1105 by dispensing (e.g., coating, printing, or depositing) a polarization-sensitive material on the surface. The recording medium layer 1110 may include a polarization-sensitive material, which is an optically recordable polarization-sensitive material (e.g., a photoaligned material) configured to have photoinduced optical anisotropy when exposed to polarized light. The molecules (or fragments) and / or photoproducts of the polarization-sensitive material may be configured to produce orientational order under polarized light irradiation. In some embodiments, the polarization-sensitive material may be dissolved in a solvent to form a solution. The solution may be dispensed on the substrate 1105 using any suitable solution coating process (e.g., spin coating, slit coating, doctor blade coating, spray coating, or jet (inkjet) coating or printing). The solvent may be removed from the coated solution using a suitable process (e.g., drying or heating), thereby leaving the polarization-sensitive material on the substrate 1105 to form the recording medium layer 1110.

[0154] After forming the recording medium layer 1110 on the substrate 1105, as shown in FIG. Figure 11B As shown, the recording medium layer 1110 may be exposed to a polarization interference pattern (eg, Figure 11C 1120 shown). The recording beams 1121 to 1124 may be coherent circularly polarized beams, including at least one left-handed circularly polarized recording beam and at least one right-handed circularly polarized recording beam. For the purpose of discussion, Figure 11B Four recording beams 1121 to 1124 (e.g., two right-handed circularly polarized beams 1121 and 1122 and two left-handed circularly polarized beams 1123 and 1124) are shown for generating a polarization interference pattern. In some embodiments, although not shown, three recording beams or five recording beams, etc., can be used to generate a polarization interference pattern.

[0155] The wavelengths of the recording light beams 1121 to 1124 may be within the absorption band of the recording medium layer 1110 (e.g., an ultraviolet ("UV") beam, a violet beam, a blue beam, or a green beam). In some embodiments, the recording light beams 1121 to 1124 may be laser beams, such as a UV laser beam, a violet laser beam, a blue laser beam, or a green laser beam. In some embodiments, the superposition of the recording light beams 1121 to 1124 may generate a superposition wave having a spatially uniform intensity and a spatially varying linear polarization direction. For example, the linear polarization direction of the superposition wave may spatially vary within a spatial region where the recording light beams 1121 to 1124 interfere with each other. In other words, the superposition wave may have a linear polarization whose polarization direction spatially varies within the spatial region where the recording light beams 1121 to 1124 interfere with each other.

[0156] The superposition of the recording beams 1121 to 1124 can produce a Figure 2C Polarization interference pattern 1120 is shown. Polarization interference pattern 1120 can also be referred to as a pattern of spatially varying orientation (or polarization direction) of the linear polarization of the superimposed waves, or a pattern of varying linear polarization of the superimposed waves. Figure 11C As shown, the orientation (or polarization direction) of the linear polarization can be arranged at a pitch P within the surface of the recording medium layer 1110. O The polarization interference pattern 1120 may vary periodically or aperiodically along at least one in-plane direction 1128. In some embodiments, the pitch P of the polarization interference pattern 1120 may vary periodically or aperiodically. O may be referred to as the distance along the in-plane direction 1128 over which the orientation (or polarization direction) of the linear polarization rotates 180°. For purposes of discussion, Figure 11C It is shown that in the polarization interference pattern 1120, the orientations (or polarization directions) of the linear polarizations are arranged at a constant pitch P. O It changes periodically along the in-plane direction 1128 .

[0157] In some embodiments, the angles between the recording beams 1121 to 1124 can be configured so that at a single pitch P of the polarization interference pattern 1120, O The orientation (or polarization direction) of the linear polarization can be configured to rotate along the in-plane direction 1128 in a predetermined nonlinear manner. For example, at a single pitch P of the polarization interference pattern 1120 O In the embodiment of the present invention, the angle of the orientation (or polarization direction) of the linear polarization relative to the in-plane direction 1128 can be configured to vary in a predetermined nonlinear manner (or according to a predetermined nonlinear function) along the in-plane direction 1128. For the purpose of discussion, the polarization interference pattern 1120 can be referred to as a nonlinear polarization interference pattern 1120.

[0158] In some embodiments, the nonlinear polarization interference pattern 1120 may be generated by superposition of a first linear polarization interference pattern generated based on the right-handed circularly polarized recording beam 1121 and the left-handed circularly polarized recording beam 1123 and a second linear polarization interference pattern generated based on the right-handed circularly polarized recording beam 1122 and the left-handed circularly polarized recording beam 1124. For example, referring to Figure 11B , the right-handed circularly polarized recording beam 1121 and the left-handed circularly polarized recording beam 1123 can interfere with each other to generate a first linear polarization interference pattern having a first pitch P1 in the in-plane direction 1128. At a single first pitch P1 of the first linear polarization interference pattern, the angle of the orientation (or polarization direction) of the linear polarization relative to the in-plane direction 1128 can be configured to change along the in-plane direction 1128 in a first predetermined linear manner (or according to a first predetermined linear function). In addition, the right-handed circularly polarized recording beam 1122 and the left-handed circularly polarized recording beam 1124 can interfere with each other to generate a second linear polarization interference pattern having a second pitch P2 in the in-plane direction 1128. At a single second pitch P2 of the second linear polarization interference pattern, the angle of the orientation (or polarization direction) of the linear polarization relative to the in-plane direction 1128 can be configured to change along the in-plane direction 1128 in a second predetermined linear manner (or according to a second predetermined linear function).

[0159] In some embodiments, the first angle formed between the right-handed circularly polarized recording beam 1121 and the left-handed circularly polarized recording beam 1123 can be configured to be different from the second angle formed between the right-handed circularly polarized recording beam 1122 and the left-handed circularly polarized recording beam 1124. Therefore, the first pitch P1 of the first linear polarization interference pattern can be configured to be different from the second pitch P2 of the second linear polarization interference pattern, and the first predetermined linear mode can be configured to be different from the first predetermined linear mode. The superposition of the first linear polarization interference pattern and the second linear polarization interference pattern can produce Figure 11C The nonlinear polarization interference pattern 1120 is shown.

[0160] refer to Figure 11B and Figure 11C, the recording medium layer 1110 can be optically patterned when exposed to a polarized interference pattern 1120 generated based on recording beams 1121 to 1124 during a polarized interference exposure process. The orientation pattern of the optical axis of the recording medium layer 1110 can be defined by the polarized interference pattern 1120. In some embodiments, the recording medium layer 1110 can include elongated anisotropic photosensitive units (e.g., fragments of small molecules or polymer molecules). After sufficient exposure to the polarized interference pattern 1120, the local alignment direction of the anisotropic photosensitive units can be induced in the recording medium layer 1110 by the polarized interference pattern 1120, thereby generating an alignment pattern (or in-plane modulation) of the optical axis of the recording medium layer 1110 due to the photo-alignment of the anisotropic photosensitive units. After the recording medium layer 1110 is optically patterned under the polarized interference pattern 1120, the recording medium layer 1110 can be referred to as a patterned recording medium layer having an alignment pattern.

[0161] like Figure 11D As shown, after forming the patterned recording medium layer 1110, a first optically anisotropic film 1115a can be formed on the patterned recording medium layer 1110 by dispensing a birefringent medium onto the patterned recording medium layer 1110. For example, the birefringent medium can be dissolved in a solvent to form a solution. A suitable amount of the solution can be dispensed (e.g., by coating, printing, or spraying) onto the patterned recording medium layer 1110 to form the first optically anisotropic film 1115a. In some embodiments, the solution containing the birefringent medium can be dispensed onto the patterned recording medium layer 1110 using a suitable process (e.g., spin coating, slit coating, doctor blade coating, spray coating, 3D printing, or inkjet coating or printing).

[0162] The birefringent medium may include a host birefringent material having an intrinsic birefringence (e.g., a non-polymerizable LC or a polymerizable LC (e.g., a reactive mesogen ("RM"))) and a chiral dopant. The chiral dopant may distort the LC molecules in the host birefringent material to form a helical twisted structure (also referred to as a helical structure). In some embodiments, the birefringent medium may further include or be mixed with other components, such as a solvent, an initiator (e.g., a photoinitiator or a thermal initiator), or a surfactant. The chirality of the birefringent medium may be introduced by doping the chiral dopant into the host birefringent material.

[0163] The patterned recording medium layer 1110 can be configured to provide surface alignment to the LC molecules in the first optically anisotropic film 1115a, thereby at least partially aligning the LC molecules proximate to the patterned recording medium layer 1110 with a predetermined non-uniform in-plane alignment pattern. For example, the LC molecules proximate to the patterned recording medium layer 1110 can be at least partially aligned along the local alignment direction of the anisotropic photosensitive elements in the patterned recording medium layer 1110, forming a predetermined non-uniform in-plane alignment pattern. Thus, the alignment pattern recorded in the patterned recording medium layer 1110 (or the in-plane alignment pattern of the optical axis of the recording medium layer 1110) can be transferred to the LC molecules proximate to the patterned recording medium layer 1110. Consequently, the LC molecules proximate to the patterned recording medium layer 1110 can exhibit a nonlinear azimuthal angle variation along the in-plane direction 1128. The patterned recording medium layer 1110 can function as a photo-alignment material (PAM) layer for the LC molecules proximate to the patterned recording medium layer 1110. This alignment process can be referred to as surface-mediated photoalignment.

[0164] like Figure 11E As shown, after forming a first optical anisotropic film 1115a on the patterned recording medium layer 1110, a second optical anisotropic film 1115b can be formed on the first optical anisotropic film 1115a. The first optical anisotropic film 1115a and the second optical anisotropic film 1115b can be manufactured based on similar birefringent media, which include a host birefringent material and a chiral dopant. Figure 11D and Figure 11E The chiral dopant included in the optically anisotropic film 1115a or 1115b may have a helical twisting power (HTP) (unit: μm -1 ), the helical twisting force is the ability of the chiral dopant to twist the host birefringent material. The HTP of the chiral dopant can exhibit handedness, such as right-handed or left-handed. The pitch P of the helical twisted structure formed in the optically anisotropic film 1115a or 1115b is h The pitch P of the helical twisted structure formed in the optically anisotropic film 1115a or 1115b may be determined in part by the HTP of the chiral dopant and the weight concentration (or mole fraction) of the chiral dopant in the host birefringent material. h It is inversely proportional to the HTP of the chiral dopant and inversely proportional to the weight concentration (or mole fraction) of the chiral dopant in the host material. When the weight concentration of the chiral dopant is constant, the larger the HTP of the chiral dopant, the larger the pitch P of the helical twisted structure. hWhen the HTP of the chiral dopant is constant, the greater the weight concentration (or mole fraction) of the chiral dopant in the host birefringent material, the shorter the pitch P of the helical twisted structure. h Can be shorter.

[0165] In some embodiments, the chiral dopants included in the first optically anisotropic film 1115a and the second optically anisotropic film 1115b may be configured to have at least one difference in HTP or weight concentration, so that the helical twisted structures formed in the first optically anisotropic film 1115a and the second optically anisotropic film 1115b may have different pitches P. h In some embodiments, when the first optically anisotropic film 1115a and the second optically anisotropic film 1115b are manufactured to have the same predetermined thickness, due to the pitch P h Due to the difference in thickness, the first optically anisotropic film 1115a and the second optically anisotropic film 1115b may exhibit different amounts of azimuthal angle changes of LC molecules at the same predetermined thickness.

[0166] For example, reference Figure 2E and Figure 11E The first optically anisotropic film 1115a and the second optically anisotropic film 1115b can be manufactured to have the same predetermined thickness (0.05 μm). The azimuth angle of the LC molecules in the first optically anisotropic film 1115a can vary from 0° to 63° along the helical axis from the bottom surface of the first optically anisotropic film 1115a to the interface between the first and second optically anisotropic films 1115a and 1115b. The azimuth angle of the LC molecules in the first optically anisotropic film 1115a can vary from 63° to 90° along the helical axis from the interface between the first and second optically anisotropic films 1115a and 1115b to the top surface of the second optically anisotropic film 1115b.

[0167] For discussion purposes, Figure 11E Only two optically anisotropic films 1115a and 1115b are shown, and additional optically anisotropic films can be formed continuously on the second optically anisotropic film 1115b. For example, the azimuth angle of the LC molecules in the third optically anisotropic film can be configured to vary from 90° to 117° along the helical axis, and the azimuth angle of the LC molecules in the fourth optically anisotropic film can be configured to vary from 117° to 180° along the helical axis, and so on. Multiple optically anisotropic films can form an optically anisotropic layer, and nonlinear azimuth angle variation of the LC molecules can be established within the volume of the optically anisotropic layer.

[0168] In some embodiments, as Figure 11FAs shown, the first optically anisotropic film 1115a and the second optically anisotropic film 1115b can be exposed to polymerization irradiation 1144 to form a polymerized optically anisotropic layer 1129 to stabilize the nonlinear azimuthal angle variation. In some embodiments, the exposure of the first optically anisotropic film 1115a and the second optically anisotropic film 1115b to the polymerization irradiation 1144 can be performed in air, in an inert atmosphere formed by, for example, nitrogen, argon, carbon dioxide, etc., or in a vacuum. The polymerization irradiation 1144 can have a wavelength range within the absorption band of the photoinitiator, thereby activating the photoinitiator to produce a polymerization initiating species. In some embodiments, the polymerization irradiation 1144 can be ultraviolet ("UV") irradiation. For example, as Figure 11F As shown, the first optically anisotropic film 1115a and the second optically anisotropic film 1115b can be exposed to a UV beam (also referred to as 1144 for discussion purposes). Upon sufficient exposure to the UV beam 1144, the birefringent material (e.g., RM monomer) in the first and second optically anisotropic films 1115a, 1115b can polymerize or crosslink to stabilize the orientation of the LC molecules, thereby stabilizing the nonlinear azimuthal angle variation. In some embodiments, although not shown, the first optically anisotropic film 1115a can be exposed to polymerizing radiation 1144 to first form a first polymerized optically anisotropic film. Then, the second optically anisotropic film 1115b can be formed on the first polymerized optically anisotropic film and exposed to polymerizing radiation 1144 to form a second polymerized optically anisotropic film.

[0169] Figure 11F Also shown are xz views of an LCPH element 1100 including a polymeric optically anisotropic layer 1129. The LCPH element 1100 may be an R-PVH element and the polymeric optically anisotropic layer 1129 may be an R-PVH layer, such as a Figure 2AThe R-PVH layer 200 is shown. In some embodiments, the substrate 1105 and / or the alignment structure 1110 can be used to manufacture, store, or transport the manufactured LCPH element 1100. In some embodiments, the substrate 1105 and / or the alignment structure 1110 can be detached or removed from the manufactured LCPH element 1100 after the LCPH element 1100 is manufactured or transported to another location or device. That is, the substrate 1105 and / or the alignment structure 1110 can be used during manufacturing, transportation, and / or storage to support the LCPH element 1100 disposed thereon, and when the manufacturing of the LCPH element 1100 is completed, or when the LCPH element 1100 is to be implemented in an optical device, the substrate 1105 and / or the alignment structure 1110 can be separated or removed from the LCPH element 1100. In some embodiments, the substrate 1105 and / or the alignment structure 1110 may not be separated from the LCPH element 1100.

[0170] Figure 12A and Figure 12B A process for fabricating an LCPH element with nonlinear azimuthal angle variation according to an embodiment of the present disclosure is schematically illustrated. Figure 12A and Figure 12B The fabrication process shown may include holographic recording and volume-mediated photoalignment (also called volume recording). Figure 12A and Figure 12B The manufacturing process shown may include Figures 11A to 11F The steps are similar to those shown in the following example. Figure 12A and Figure 12B The LCPH components manufactured by the process shown may include Figures 11A to 11F The LCPH element is similar to the LCPH element manufactured by the process shown in FIG. The description of similar steps and similar elements, structures or functions can refer to the above combined Figures 11A to 11F Although the substrate and layers are shown as having flat surfaces, in some embodiments, the substrate and layers formed thereon may have curved surfaces.

[0171] Similar to Figure 11A and Figure 11B The embodiment shown, Figure 12A and Figure 12BThe illustrated process may include dispensing (e.g., coating, depositing, etc.) a recording medium onto a surface (e.g., top surface) of substrate 1105 to form a recording medium layer 1210. The recording medium may be a polarization-sensitive recording medium. The recording medium may include an optically recordable polarization-sensitive material (e.g., a photoaligned material) configured to exhibit photoinduced optical anisotropy when exposed to polarized light. Under polarized light illumination, molecules (or fragments) and / or photoproducts of the optically recordable polarization-sensitive material may produce an anisotropic angular distribution in the film plane of the layer of the recording medium. In some embodiments, the recording medium may include or be mixed with other components, such as a solvent in which the optically recordable polarization-sensitive material may be dissolved to form a solution, and a photosensitizer. The solution may be dispensed onto substrate 1105 using a suitable process (e.g., spin coating, slot coating, doctor blading, spray coating, or inkjet (inkjet) coating or printing). The solvent may be removed from the applied solution using a suitable method (e.g., drying or heating), thereby leaving the recording medium on substrate 1105.

[0172] After the recording medium layer 1210 is formed on the substrate 1105, Figure 12B As shown, recording medium layer 1210 can be exposed to a polarization interference pattern generated based on four recording light beams 1121 to 1124. In some embodiments, although not shown, three recording light beams, five recording light beams, etc., can be used to generate the polarization interference pattern. After being exposed to the polarization interference pattern, recording medium layer 1210 can be optically patterned. The orientation pattern of the optical axis of recording medium layer 1210 in the exposed area can be defined by the polarization interference pattern.

[0173] exist Figure 12A and Figure 12B In the illustrated embodiment, the recording medium may include a photosensitive polymer. The molecules of the photosensitive polymer may include one or more polarization-sensitive photoreactive groups embedded in the main polymer chain or the side polymer chain. During the polarization interference exposure process of the recording medium layer 1210, the photoalignment of the polarization-sensitive photoreactive groups may occur within the volume of the recording medium layer 1210 (or in the volume, inside the volume). That is, the 3D polarization field or 3D polarization change generated by the interface of the recording light beams 1121 to 1124 can be directly recorded within the volume of the recording medium layer 1210 (or in the volume, inside the volume). Figure 12A and Figure 12B In the embodiment shown, the 3D orientation pattern of the optical axis can be directly recorded in the recording medium layer 1210 via bulk-mediated photoalignment in the exposed areas. The step of providing an additional optically anisotropic layer on the patterned recording medium layer 1210 can be omitted. The patterned recording medium layer 1210 can be used as the LCPH element 1200.

[0174] Figure 12B The alignment process shown can be referred to as bulk-mediated photoalignment. Figure 12B The recording medium layer 1210 shown in the volume-mediated photoalignment can be compared to the recording medium layer 1210 used for Figures 11A to 11F The surface-mediated photoaligned recording medium layer 1110 is shown to be relatively thicker. Figure 12B The recording medium included in the bulk-mediated photoaligned recording medium layer 1210 may also be referred to as a bulk recording medium or a bulk PAM.

[0175] In some embodiments, the photosensitive polymer included in the recording medium layer 1210 may include an amorphous polymer, an LC polymer, and the like. The molecules of the photosensitive polymer may include one or more polarization-sensitive photoreactive groups embedded in the main polymer chain or the side polymer chain. In some embodiments, the polarization-sensitive photoreactive group may include an azobenzene group, a cinnamate group, a coumarin group, and the like. In some embodiments, the photosensitive polymer may be an amorphous polymer that may initially be optically isotropic before undergoing a polarization interference exposure process and may exhibit induced (e.g., photoinduced) optical anisotropy after undergoing a polarization interference exposure process. In some embodiments, the photosensitive polymer may be an LC polymer in which birefringence and in-plane orientation patterns may be recorded due to the influence of photoinduced optical anisotropy. In some embodiments, the photosensitive polymer may be an LC polymer having polarization-sensitive cinnamate groups embedded in side polymer chains. In some embodiments, when the recording medium layer 1210 includes an LC polymer, the patterned recording medium layer 1210 may be heat-treated (e.g., annealed) within a temperature range corresponding to the liquid crystal state of the LC polymer to enhance the photoinduced optical anisotropy (e.g., photoinduced optical anisotropy) of the LC polymer. Figure 12B not shown).

[0176] 13A to 13C A process for fabricating an LCPH element with nonlinear azimuthal angle variation according to an embodiment of the present disclosure is schematically illustrated. 13A to 13C The fabrication process shown may include holographic recording and surface-mediated photoalignment. 13A to 13C The manufacturing process shown may include Figures 11A to 11F The steps are similar to those shown in the following example. 13A to 13C The LCPH components manufactured by the process shown may include Figures 11A to 11F The LCPH element is similar to the LCPH element manufactured by the process shown in FIG. The description of similar steps and similar elements, structures or functions can refer to the above combined Figures 11A to 11F Although the substrate and layers are shown as having flat surfaces, in some embodiments, the substrate and layers formed thereon may have curved surfaces.

[0177] Similar to Figure 11A and Figure 11B The embodiment shown, Figure 13A The process shown may include dispensing (e.g., coating, depositing, etc.) a recording medium onto a surface (e.g., top surface) of a substrate 1105 to form a recording medium layer 1110. The recording medium layer 1110 may be exposed to a nonlinear polarization interference pattern generated based on a plurality of recording beams 1321 to 1323. The recording beams 1321 to 1323 may be similar to Figure 11B The recording beams 1121 to 1124 are shown. For example, the recording beams 1321 to 1323 can be coherent circularly polarized beams, including at least one left-handed circularly polarized recording beam and at least one right-handed circularly polarized recording beam. For the purpose of discussion, Figure 13A Three recording beams 1321 to 1323 (e.g., two right-handed circularly polarized beams 1321 and 1322 and one left-handed circularly polarized beam 1323) are shown for generating a nonlinear polarization interference pattern. In some embodiments, although not shown, four recording beams, five recording beams, etc., can be used to generate a nonlinear polarization interference pattern.

[0178] In some embodiments, the nonlinear polarization interference pattern generated based on the recording beams 1321 to 1323 can be generated by superposition of a first linear polarization interference pattern generated based on the right-handed circularly polarized recording beam 1321 and the left-handed circularly polarized recording beam 1323 and a second linear polarization interference pattern generated based on the right-handed circularly polarized recording beam 1322 and the left-handed circularly polarized recording beam 1323. For example, referring to Figure 11B , the right-handed circularly polarized recording beam 1321 and the left-handed circularly polarized recording beam 1323 can interfere with each other to generate a first linear polarization interference pattern having a first pitch P1 in the in-plane direction 1128. At a single first pitch P1 of the first linear polarization interference pattern, the angle of the orientation (or polarization direction) of the linear polarization relative to the in-plane direction 1128 can be configured to vary along the in-plane direction 1128 in a first predetermined linear manner (or according to a first predetermined linear function). In addition, the right-handed circularly polarized recording beam 1322 and the left-handed circularly polarized recording beam 1323 can interfere with each other to generate a second linear polarization interference pattern having a second pitch P2 in the in-plane direction 1128. At a single second pitch P2 of the second linear polarization interference pattern, the angle of the orientation (or polarization direction) of the linear polarization relative to the in-plane direction 1128 can be configured to vary along the in-plane direction 1128 in a second predetermined linear manner (or according to a second predetermined linear function).

[0179] In some embodiments, the first angle formed between right-handed circularly polarized recording beam 1321 and left-handed circularly polarized recording beam 1323 can be configured to be different from the second angle formed between right-handed circularly polarized recording beam 1322 and left-handed circularly polarized recording beam 1323. Therefore, the first pitch P1 of the first linear polarization interference pattern can be configured to be different from the second pitch P2 of the second linear polarization interference pattern, and the first predetermined linear mode can be configured to be different from the first predetermined linear mode. The superposition of the first linear polarization interference pattern and the second linear polarization interference pattern can generate a nonlinear polarization interference pattern.

[0180] Similar to Figure 11D The process shown, Figure 13B The illustrated process may include forming an optically anisotropic layer 1315 on the patterned recording medium layer 1110 by dispensing a birefringent medium onto the patterned recording medium layer 1110. The birefringent medium forming the optically anisotropic layer 1315 may be similar to Figure 11D The birefringent medium forming the optically anisotropic film 1115a is shown. For example, the birefringent medium can include a host birefringent material having an intrinsic birefringence (e.g., a non-polymerizable LC or a polymerizable LC (e.g., RM)) and a photoresponsive chiral dopant 1302. The patterned recording medium layer 1110 can be configured to provide surface alignment to the LC molecules in the optically anisotropic layer 1315. As a result, the LC molecules in close proximity to the patterned recording medium layer 1110 can exhibit a nonlinear azimuthal angle variation along the in-plane direction 1128.

[0181] The photoresponsive chiral dopant 1302 can distort LC molecules in the host birefringent material to form a helically twisted structure. Due to the photoisomerization of the photoresponsive chiral dopant 1302, the photoresponsive chiral dopant 1302 can have a photoresponsive HTP that can change when exposed to light of a suitable wavelength range. As the degree of photoisomerization of the photoresponsive chiral dopant 1302 changes, the HTP of the photoresponsive chiral dopant 1302 can change (e.g., increase, decrease, or reverse handedness). In some embodiments, the photoisomerization of the photoresponsive chiral dopant 1302 can be reversible. Light irradiation used to change the HTP of the photoresponsive chiral dopant 1302 (or to which the photoresponsive chiral dopant 1302 is sensitive) can be referred to as stimulus irradiation.

[0182] Stimulating irradiation may activate only the stimuli-responsive chiral dopant 1302 to change the HTP, while not activating the photoinitiator (if contained in the birefringent medium) to produce a polymerization-initiating species. The wavelength (or wavelength range) of the stimulating irradiation may be within (or correspond to) the UV wavelength range, the visible light wavelength range, the infrared wavelength range, or a combination thereof, depending on the different types of photoresponsive chiral dopants. In some embodiments, the photoresponsive chiral dopant 1302 may undergo different degrees of photoisomerization in response to stimulating irradiation having different light intensities. In some embodiments, the photoresponsive chiral dopant 1302 may include azobenzene, a diarylethene overcrowded alkene, a spirooxazine, a fulgide, an α,β-unsaturated ketone, a naphthopyran, or a combination thereof.

[0183] like Figure 13B As shown, the optically anisotropic layer 1315 can be exposed to an intensity interference pattern generated based on two recording beams 1351 and 1352. The recording beams 1351 and 1352 can be coherent polarized beams with the same polarization. For example, the recording beams 1351 and 1352 can be two linearly polarized beams with the same linear polarization direction, or two circularly polarized beams with the same handedness. The recording beams 1351 and 1352 can have a wavelength range to which the photoresponsive chiral dopant 1302 is sensitive. In some embodiments, the interference of the recording beams 1351 and 1352 can generate an intensity interference pattern having a spatially constant polarization and a spatially varying intensity within the spatial region where the recording beams 1351 and 1352 interfere with each other. In other words, the intensity interference pattern can exhibit a 3D intensity variation within the spatial region where the recording beams 1351 and 1352 interfere with each other. This intensity interference pattern having a 3D intensity variation can serve as a stimulating illumination for the photoresponsive chiral dopant 1302.

[0184] During exposure to the intensity interference pattern of the optically anisotropic layer 1315, the photoresponsive chiral dopant 1302 distributed within the volume of the optically anisotropic layer 1315 may undergo varying degrees of photoisomerization in response to the intensity interference pattern having a 3D intensity variation, thereby inducing a variation in the 3D helical twisting force of the photoresponsive chiral dopant 1302 within the volume of the optically anisotropic layer 1315. When the weight concentration of the photoresponsive chiral dopant 1302 is assumed to be constant across the optically anisotropic layer 1315, the variation in the 3D helical twisting force of the photoresponsive chiral dopant 1302 may induce a variation in the 3D pitch of the helical twisted structure within the volume of the optically anisotropic layer 1315. In some embodiments, by configuring two recording beams 1351 and 1352, a variation in the 3D pitch of the helical twisted structure within the volume of the optically anisotropic layer 1315 may be configured, which may induce a predetermined nonlinear azimuthal variation in the LC molecules along the helical axis of the helical twisted structure.

[0185] In some embodiments, as Figure 13C As shown, after the intensity interference pattern is exposed, the optically anisotropic layer 1315 can be exposed to polymerizing radiation 1144 to form a polymerized optically anisotropic layer 1329 to stabilize the nonlinear azimuthal angle variation. Figure 13B and Figure 13C , the polymerization radiation 1144 may be different from the stimulation radiation generated by the recording light beams 1351 and 1352. The stimulation radiation may only activate the photoresponsive chiral dopant 1302 to change its HTP, and may not activate the photoinitiator to produce a polymerization-initiating substance. That is, the photoinitiator may not respond to the stimulation radiation, and the stimulation radiation may not cause polymerization of the RM material in the optically anisotropic layer 1315. The polymerization radiation 1144 may only activate the photoinitiator to produce a polymerization-initiating substance, and may not activate the photoresponsive chiral dopant 1302 to change its HTP. That is, the photoresponsive chiral dopant 1302 may not respond to the polymerization radiation, and the polymerization radiation may not change the HTP of the photoresponsive chiral dopant 1302.

[0186] Figure 14A and Figure 14B Flowcharts illustrating various methods for fabricating an LCPH element with nonlinear azimuthal angle variation according to various embodiments of the present disclosure. Figure 14A FIG1 is a flow chart showing a method 1400 for manufacturing an LCPH element with nonlinear azimuthal angle variation according to an embodiment of the present disclosure. Figure 14AAs shown, method 1400 may include generating at least three circularly polarized light beams, wherein the at least three circularly polarized light beams include one or more left-handed circularly polarized light beams and one or more right-handed circularly polarized light beams, and the at least three circularly polarized light beams are configured to interfere with each other to generate a polarization interference pattern (step 1410). Method 1400 may also include exposing a polarization-sensitive recording medium to the polarization interference pattern, wherein, in a pitch of a helical structure in the polarization-sensitive recording medium that has been exposed to the polarization interference pattern, an azimuthal angle of an optically anisotropic molecule varies nonlinearly with respect to a distance from a starting point of the pitch to a local point along the helical axis where the optically anisotropic molecule is located (step 1415).

[0187] In some embodiments, the at least three circularly polarized light beams may include a first light beam, a second light beam, and a third light beam, and a first angle formed between the first light beam and the second light beam is different from a second angle formed between the second light beam and the third light beam. In some embodiments, the polarization-sensitive recording medium may include a bulk photo-alignment material, and exposing the polarization-sensitive recording medium to the polarization interference pattern may cause the polarization interference pattern to be recorded in the bulk photo-alignment material.

[0188] Figure 14B 14 is a flow chart illustrating a method 1430 for fabricating an LCPH element with nonlinear azimuthal angle variation according to an embodiment of the present disclosure. Method 1430 may include generating a plurality of polarized light beams, wherein the plurality of polarized light beams includes at least three circularly polarized light beams, the at least three circularly polarized light beams including one or more left-handed circularly polarized light beams and one or more right-handed circularly polarized light beams, and the at least three circularly polarized light beams are configured to interfere with each other to generate a polarization interference pattern (step 1435). Method 1430 may also include exposing a polarization-sensitive recording medium to the polarization interference pattern (step 1440). Method 1430 may also include forming an optically anisotropic film on the polarization-sensitive recording medium that has been exposed to the polarization interference pattern, wherein the optically anisotropic film includes a mixture of a host birefringent material and a chiral dopant (step 1445).

[0189] In some embodiments, the polarization-sensitive recording medium may include a surface photoalignment material. In some embodiments, the optically anisotropic film may be a first optically anisotropic film, the mixture may be a first mixture of a host birefringent material and a first chiral dopant, and the first chiral dopant may have a first helical twisting force and a first weight concentration in the first mixture. Method 1430 may also include forming a second optically anisotropic film on the first optically anisotropic film. The second optically anisotropic film may include a second mixture of a host birefringent material and a second chiral dopant, and the second chiral dopant may have a second helical twisting force and a second weight concentration in the second mixture. The first chiral dopant and the second chiral dopant may be configured to have at least one difference between the first helical twisting force and the second helical twisting force, or between the first weight concentration and the second weight concentration. In some embodiments, method 1430 may also include exposing the first and second optically anisotropic films to polymerizing radiation.

[0190] In some embodiments, the chiral dopant may include a photoresponsive chiral dopant, the plurality of polarized light beams may be a first plurality of polarized light beams, and method 1430 may further include generating a second plurality of polarized light beams, wherein the second plurality of polarized light beams includes two polarized light beams configured to interfere with each other to produce an intensity interference pattern within the spatial region where the optically anisotropic film is disposed. Method 1430 may further include exposing the optically anisotropic film to the intensity interference pattern. In some embodiments, the method may further include exposing the optically anisotropic film to polymerizing radiation.

[0191] In some embodiments, the present disclosure provides a method. The method includes directing a plurality of polarized light beams toward a polarization-sensitive recording medium. The plurality of polarized light beams include at least three circularly polarized light beams, the at least three circularly polarized light beams including one or more left-handed circularly polarized light beams and one or more right-handed circularly polarized light beams, and the at least three circularly polarized light beams are configured to interfere with each other to produce a polarization interference pattern. The method also includes exposing the polarization-sensitive recording medium to the polarization interference pattern. In some embodiments, the at least three circularly polarized coherent light beams include a first light beam, a second light beam, and a third light beam, and a first angle formed between the first light beam and the second light beam is different from a second angle formed between the second light beam and the third light beam. In some embodiments, the polarization-sensitive recording medium includes a bulk photo-aligned material, and exposing the polarization-sensitive recording medium to the polarization interference pattern causes the polarization interference pattern to be recorded in the bulk photo-aligned material.

[0192] In some embodiments, the polarization-sensitive recording medium includes a surface photoalignment material, and after exposing the polarization-sensitive recording medium to the polarization interference pattern, the method further includes forming an optically anisotropic film based on a mixture of a host birefringent material and a chiral dopant on the polarization-sensitive recording medium. In some embodiments, the optically anisotropic film based on a mixture of the host birefringent material and the chiral dopant is a first optically anisotropic film based on a first mixture of the host birefringent material and a first chiral dopant, the first chiral dopant having a first helical twisting power and a first weight concentration in the first mixture. The method further includes forming a second optically anisotropic film based on a second mixture of the host birefringent material and a second chiral dopant, the second chiral dopant having a second helical twisting power and a second weight concentration in the second mixture, on the first optically anisotropic film. The first chiral dopant and the second chiral dopant are configured to have at least one difference between the first helical twisting power and the second helical twisting power or between the first weight concentration and the second weight concentration. In some embodiments, the method further includes exposing the first optically anisotropic film and the second optically anisotropic film to polymerizing radiation.

[0193] In some embodiments, the chiral dopant comprises a photoresponsive chiral dopant, the plurality of polarized light beams comprises a first plurality of polarized light beams, and the method further comprises: directing a second plurality of polarized light beams toward the optically anisotropic film, the second plurality of polarized light beams comprising two polarized light beams, the two polarized light beams being configured to interfere with each other to produce an intensity interference pattern within a spatial region where the optically anisotropic film is disposed; and exposing the optically anisotropic film to the intensity interference pattern. In some embodiments, the method further comprises exposing the optically anisotropic film to polymerizing radiation.

[0194] In some embodiments, the present disclosure provides a device comprising an optical film comprising a plurality of optically anisotropic molecules, the optically anisotropic molecules being configured to form a plurality of helical structures having a plurality of helical axes and a helical pitch. The helical pitch is a distance along the helical axis over which an azimuth angle of the optically anisotropic molecules varies by a predetermined value. At the helical pitch of the helical structure, the azimuth angle of the optically anisotropic molecules is configured to vary nonlinearly with respect to a distance from a starting point of the helical pitch to a local point along the helical axis where the optically anisotropic molecules are located.

[0195] In some embodiments, on the pitch of the helical structure, the azimuth angle of the optically anisotropic molecules located at the starting point of the pitch is zero degrees, and the predetermined value associated with the pitch is 180 degrees. In some embodiments, the optical film is configured to provide a main reflection band and at least one sub-reflection band spaced apart from the main reflection band. In some embodiments, the main reflection band and the at least one sub-reflection band include a red wavelength range and a blue wavelength range. In some embodiments, the optical film is a first optical film, and the device further includes a second optical film, the second optical film being configured to provide a reflection band including a green wavelength range. In some embodiments, the at least one sub-reflection band includes two sub-reflection bands located on different sides of the main reflection band. In some embodiments, the main reflection band includes a green wavelength range, and the two sub-reflection bands include a red wavelength range and a blue wavelength range. In some embodiments, for polarized light with a wavelength range within the main reflection band or the at least one sub-reflection band, the optical film is configured to reflect the polarized light when the polarized light has a first chirality, and to transmit the polarized light when the polarized light has a second chirality opposite to the first chirality.

[0196] In some embodiments, the optical film is configured to: reflect first polarized light at a first reflection angle, the first polarized light having a first wavelength range within the main reflection band and a predetermined chirality; and reflect second polarized light at a second reflection angle different from the first reflection angle, the second polarized light having a second wavelength range within the at least one secondary reflection band and the predetermined chirality.

[0197] In some embodiments, the optical film is configured to: reflect first polarized light at a first reflection angle, the first polarized light having a first wavelength range within the main reflection band and a predetermined chirality; and reflect second polarized light at a second reflection angle that is the same as the first reflection angle, the second polarized light having a second wavelength range within the at least one secondary reflection band and the predetermined chirality.

[0198] In some embodiments, the azimuth angle of the optically anisotropic molecule at the pitch of the helical structure is according to the function change. is the azimuth angle of the optically anisotropic molecule, z is the distance from the starting point of the pitch to the local point where the optically anisotropic molecule is located along the helical axis, P B is the Bragg cycle, is a linear function of z, is a nonlinear function of z, A is an amplitude parameter of the nonlinear function and is a positive value less than or equal to 360°, and n is a frequency parameter of the nonlinear function and is a positive value less than or equal to 1.

[0199] In some embodiments, the nonlinear function for And the function for

[0200] In some embodiments, the optical film includes a cholesteric liquid crystal ("CLC") layer, and the optically anisotropic molecules proximate a surface of the optical film are arranged in a uniform in-plane alignment pattern.

[0201] In some embodiments, the optical film includes a reflective polarizer volume hologram ("PVH") layer, and the optically anisotropic molecules proximate the surface of the optical film are arranged in a non-uniform in-plane orientation pattern having an in-plane spacing along a predetermined in-plane direction, the in-plane spacing being defined as the distance along the predetermined in-plane direction over which the azimuthal angles of the optically anisotropic molecules proximate the surface of the optical film vary by 180°.

[0202] In some embodiments, at the in-plane spacing of the non-uniform in-plane orientation pattern, the azimuth angle of the optically anisotropic molecules adjacent to the surface of the optical film is configured to vary nonlinearly with respect to a distance from a starting point of the in-plane spacing to a local point at which the optically anisotropic molecules are located along the predetermined in-plane direction, and at the in-plane spacing of the non-uniform in-plane orientation pattern, the azimuth angle of the optically anisotropic molecules located at the starting point of the in-plane spacing is zero degrees.

[0203] Any of the steps, operations, or processes described herein can be performed or implemented using one or more hardware and / or software modules, either alone or in combination with other devices. In one embodiment, the software modules are implemented using a computer program product comprising a computer-readable medium containing computer program code that can be executed by a computer processor to perform any or all of the steps, operations, or processes described. In some embodiments, the hardware modules can include hardware components, such as devices, systems, optical elements, controllers, electronic circuits, logic gates, and the like.

[0204] Furthermore, when an embodiment shown in a drawing shows a single element, it should be understood that that embodiment, or another embodiment not shown in the drawing but within the scope of the present disclosure, may include multiple such elements. Similarly, when an embodiment shown in a drawing shows multiple such elements, it should be understood that that embodiment, or another embodiment not shown in the drawing but within the scope of the present disclosure, may include only one such element. The number of elements shown in the drawings is for illustrative purposes only and should not be construed as limiting the scope of the embodiments. Furthermore, unless otherwise specified, the multiple embodiments shown in the drawings are not mutually exclusive and may be combined in any suitable manner. For example, an element shown in one drawing / embodiment but not in another drawing / embodiment may still be included in another drawing / embodiment. In any optical device disclosed herein that includes one or more optical layers, films, plates, or elements, the number of layers, films, plates, or elements shown in the drawings is for illustrative purposes only. In other embodiments not shown in the drawings but still within the scope of the present disclosure, the same or different layers, films, plates, or elements shown in the same or different drawings / embodiments may be combined or repeated in various ways to form a stack.

[0205] Various embodiments have been described to illustrate exemplary implementations. Based on the disclosed embodiments, a person of ordinary skill in the art may make various other changes, modifications, rearrangements, and substitutions without departing from the scope of the present disclosure. Therefore, although the present disclosure has been described in detail with reference to the above embodiments, the present disclosure is not limited to the above embodiments. The present disclosure may be embodied in other equivalent forms without departing from the scope of the present disclosure. The scope of the present disclosure is defined in the appended claims.

Claims

1. A device, comprising: An optical film comprising a plurality of optically anisotropic molecules arranged to form a plurality of helical structures having a plurality of helical axes and pitches, wherein the pitch is the distance along the helical axis over which the azimuthal angle of the optically anisotropic molecule changes by a predetermined value, and Here, on the pitch of the helical structure, the azimuth angle of the optically anisotropic molecule is configured to change nonlinearly with respect to a distance from a starting point of the pitch to a local point along the helical axis where the optically anisotropic molecule is located.

2. The device according to claim 1, wherein On the pitch of the helical structure, the azimuth angle of the optically anisotropic molecule located at the starting point of the pitch is zero degrees, and the predetermined value associated with the pitch is 180 degrees.

3. The device according to claim 1, wherein The optical film is configured to provide a primary reflection band and at least one secondary reflection band spaced apart from the primary reflection band.

4. The device according to claim 3, wherein The main reflection band and the at least one sub-reflection band include a red wavelength range and a blue wavelength range.

5. The device according to claim 4, wherein The optical film is a first optical film, and the apparatus further includes a second optical film configured to provide a reflection band including a green wavelength range.

6. The apparatus according to claim 3, wherein The at least one sub-reflection band includes two sub-reflection bands located on different sides of the main reflection band.

7. The apparatus according to claim 6, wherein The main reflection band includes a green wavelength range, and the two sub-reflection bands include a red wavelength range and a blue wavelength range.

8. The apparatus according to claim 3, wherein For polarized light with a wavelength range within the main reflection band or the at least one sub-reflection band, the optical film is configured to reflect the polarized light when the polarized light has a first chirality, and to transmit the polarized light when the polarized light has a second chirality opposite to the first chirality.

9. The apparatus according to claim 3, wherein The optical film is configured to: reflecting first polarized light at a first reflection angle, the first polarized light having a first wavelength range within the main reflection band and a predetermined handedness, and A second polarized light is reflected at a second reflection angle different from the first reflection angle, the second polarized light having a second wavelength range within the at least one sub-reflection wavelength band and the predetermined handedness.

10. The apparatus according to claim 3, wherein The optical film is configured to: reflecting first polarized light at a first reflection angle, the first polarized light having a first wavelength range within the main reflection band and a predetermined handedness, and A second polarized light is reflected at a second reflection angle that is the same as the first reflection angle, the second polarized light having a second wavelength range within the at least one sub-reflection wavelength band and the predetermined handedness.

11. The device according to claim 1, in, On the pitch of the helical structure, the azimuth angle of the optically anisotropic molecule is determined according to the function change, in, is the azimuth angle of the optically anisotropic molecule, z is the distance from the starting point of the helical pitch to the local point where the optically anisotropic molecule is located along the helical axis, P B is the Bragg cycle, is a linear function of z, is a nonlinear function of z, A is an amplitude parameter of the nonlinear function and is a positive value less than or equal to 360°, and n is a frequency parameter of the nonlinear function and is a positive value less than or equal to 1.

12. The apparatus according to claim 11, wherein The nonlinear function for And the function for 13. The apparatus according to claim 1, wherein The optical film includes a cholesteric liquid crystal ("CLC") layer, and A plurality of optically anisotropic molecules adjacent to a surface of the optical film are arranged in a uniform in-plane alignment pattern.

14. The apparatus according to claim 1, wherein The optical film includes a reflective polarizing volume hologram ("PVH") layer, and A plurality of optically anisotropic molecules adjacent to the surface of the optical film are arranged in a non-uniform in-plane orientation pattern having an in-plane spacing along a predetermined in-plane direction, wherein the in-plane spacing is defined as the following distance along the predetermined in-plane direction: at this distance, the azimuth angle of the optically anisotropic molecules adjacent to the surface of the optical film changes by 180°.

15. The apparatus according to claim 14, wherein In the in-plane spacing of the non-uniform in-plane alignment pattern, the azimuth angle of the optically anisotropic molecules immediately adjacent to the surface of the optical film is configured to change nonlinearly with respect to the distance from the starting point of the in-plane spacing to the local point where the optically anisotropic molecules are located along the predetermined in-plane direction, and In the in-plane spacing of the non-uniform in-plane alignment pattern, the azimuth angle of the optically anisotropic molecules located at the starting point of the in-plane spacing is zero degree.

16. A method comprising: generating a plurality of polarized light beams, wherein the plurality of polarized light beams include at least three circularly polarized light beams, the at least three circularly polarized light beams include one or more left-handed circularly polarized light beams and one or more right-handed circularly polarized light beams, and the at least three circularly polarized light beams are configured to interfere with each other to generate a polarization interference pattern; exposing a polarization-sensitive recording medium to the polarization interference pattern; and An optically anisotropic film is formed on the polarization-sensitive recording medium that has been exposed to the polarization interference pattern, wherein the optically anisotropic film includes a mixture of a host birefringent material and a chiral dopant.

17. The method according to claim 16, wherein The optically anisotropic film is a first optically anisotropic film, the mixture is a first mixture of the host birefringent material and a first chiral dopant, the first chiral dopant having a first helical twisting power and a first weight concentration in the first mixture, and the method further comprises: forming a second optically anisotropic film on the first optically anisotropic film, wherein the second optically anisotropic film comprises a second mixture of the host birefringent material and a second chiral dopant, the second chiral dopant having a second helical twisting power and a second weight concentration in the second mixture, The first chiral dopant and the second chiral dopant are configured to have at least one difference in the first helical twisting force and the second helical twisting force or in the first weight concentration and the second weight concentration.

18. The method of claim 17, further comprising exposing the first optically anisotropic film and the second optically anisotropic film to polymerizing radiation.

19. The method according to claim 16, wherein The chiral dopant comprises a photoresponsive chiral dopant, and the plurality of polarized light beams is a first plurality of polarized light beams, the method further comprising: generating a second plurality of polarized light beams, the second plurality of polarized light beams comprising two polarized light beams configured to interfere with each other to generate an intensity interference pattern in a spatial region where the optically anisotropic film is disposed; and The optically anisotropic film is exposed to the intensity interference pattern.

20. The method of claim 19, further comprising exposing the optically anisotropic film to polymerizing radiation.

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