Liquid crystal polarization hologram with enhanced angular brightness uniformity and system including same

Abstract

An apparatus is provided. The apparatus includes a light guide configured to guide a first light to propagate in the light guide. The device also includes an optical film coupled with the light guide, the optically anisotropic molecules in the optical film being configured with an in-plane orientation pattern having an in-plane pitch along a predetermined in-plane direction. Azimuth angles of the optically anisotropic molecules are configured to vary non-linearly in a predetermined in-plane direction within in-plane pitches of the in-plane orientation pattern. The optical film is configured to diffract the first light into a plurality of second light at a plurality of predetermined different diffraction efficiencies at a plurality of positions of the optical film.

Description

Technical Field

[0001] The present disclosure relates generally to devices and, more particularly, to liquid crystal polarization holograms with enhanced angular brightness uniformity and systems including the same. Background Art

[0002] Liquid crystal polarization holograms (LCPHs) combine the features of liquid crystal devices and 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 an LCD device. The LCD industry has made huge investments in scaled manufacturing, from low-end G2.5 production lines to high-end G10.5+ production lines, to meet market demand for displays. However, the LCD industry has recently faced competition from organic light-emitting diodes (OLEDs), e-paper, and other emerging display technologies, which has slowed the growth of the LCD industry and made a large amount of early-stage production capacity redundant. This provides an opportunity to reuse idle LCD production capacity and the existing supply chain to manufacture new liquid crystal (LC) optical devices that are characterized by their polarization holograms.

[0003] LCPH or LCPH elements have features such as small thickness (about 1 micrometer (μm)), light weight, compactness, large aperture, high efficiency, and simple manufacturing. Therefore, LCPH elements have gained increasing attention in optical devices and system applications, such as near-eye displays (NEDs), head-up displays (HUDs), head-mounted displays (HMDs), smartphones, laptop computers, televisions, or vehicles. For example, LCPH elements can be used to resolve focus-vergence conflicts, enable fine and efficient eye tracking and depth sensing in spatially constrained optical systems, develop optical combiners for image formation, correct chromatic aberration for improving 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 a first aspect of the present invention, a device is provided, comprising: a light guide configured to guide first light to propagate in the light guide; and an optical film coupled to the light guide, wherein a plurality of optically anisotropic molecules in the optical film are configured with an in-plane orientation pattern, the in-plane orientation pattern having an in-plane spacing along a predetermined in-plane direction, wherein, within the in-plane spacing of the in-plane orientation pattern, the azimuthal angles of the plurality of optically anisotropic molecules are configured to vary nonlinearly along the predetermined in-plane direction, and wherein the optical film is configured to diffract the first light into a plurality of second lights at a plurality of predetermined different diffraction efficiencies at a plurality of positions of the optical film.

[0005] In some embodiments, the optical film can include a polarizing volume hologram.

[0006] In some embodiments, the azimuthal angles of the plurality of optically anisotropic molecules are configured to vary nonlinearly and periodically along a predetermined in-plane direction of the in-plane orientation pattern; within the in-plane spacing of the in-plane orientation pattern, the azimuthal angles of the optically anisotropic molecules are configured to vary according to a nonlinear function of a parameter A, the in-plane spacing, and the position of the optically anisotropic molecules, and the parameter A is configured to have a plurality of different values ​​at a plurality of positions of the optical film.

[0007] In some embodiments, the plurality of second lights may be distributed along the pupil expansion direction of the device, the parameter A of the nonlinear function may be configured to decrease along the pupil expansion direction, and the plurality of predetermined different diffraction efficiencies may be configured to increase along the pupil expansion direction.

[0008] In some embodiments, the position of the optically anisotropic molecule can be correlated with the distance from the starting point of the in-plane spacing to the local point where the optically anisotropic molecule is located along a predetermined in-plane direction.

[0009] In some embodiments, the in-plane spacing may be defined as a distance along a predetermined in-plane direction where the azimuth angle of the optically anisotropic molecules changes by 180 degrees, and the azimuth angle of the optically anisotropic molecules located at the starting point of the in-plane spacing is zero degrees.

[0010] In some embodiments, within the in-plane spacing of the in-plane alignment pattern, the azimuthal angle of the optically anisotropic molecules may vary according to the following function: can be the azimuth angle of the optically anisotropic molecule, x can be the distance from the starting point of the in-plane spacing to the local point, Pin can be the in-plane spacing, can be a linear function of x, It can be a nonlinear function of x, and the parameter A can be a positive value less than or equal to 360°.

[0011] In some embodiments, the nonlinear function Can be And the function Can be

[0012] In some embodiments, the plurality of optically anisotropic molecules may form a plurality of helical structures within the volume of the optical film, and the azimuthal angles of the plurality of optically anisotropic molecules may be configured to vary nonlinearly along the helical axes of the helical structures.

[0013] In some embodiments, the azimuthal angle of the optically anisotropic molecules can vary as a nonlinear function of parameter A, the Bragg period PB of the optical film, and the position of the optically anisotropic molecules along the helical axis, and parameter A can be configured to have multiple different values ​​at multiple locations of the optical film.

[0014] In some embodiments, within the helical pitch of the helical structure, the azimuthal angle of the optically anisotropic molecule can be configured to vary nonlinearly with respect to the distance from the start of the helical pitch to the local point along the helical axis where the optically anisotropic molecule is located.

[0015] In some embodiments, the helical pitch may be a distance along the helical axis over which the azimuth angle of the optically anisotropic molecule changes by 360°, and the azimuth angle of the optically anisotropic molecule at the start of the helical pitch may be zero degrees.

[0016] In some embodiments, within the helical pitch of the helical structure, the azimuthal angle of the optically anisotropic molecule may vary according to the following function: in can be the azimuth angle of the optically anisotropic molecule, z can be the distance from the starting point of the helical pitch to the local point, PB can be the Bragg period, can be a linear function of z, It can be a nonlinear function of z, and the parameter A can be a positive value less than or equal to 360°.

[0017] In some embodiments, the nonlinear function Can be And the function Can be

[0018] In some embodiments, the optical film can be configured to diffract the first light out of the light guide as a plurality of second lights.

[0019] In some embodiments, the device may further include: a coupling element coupled to the light guide, wherein the optical film may be configured to diffract the first light into a plurality of second lights propagating toward the coupling element, and wherein the coupling element may be configured to couple the plurality of second lights out of the light guide as a plurality of third lights.

[0020] According to a second aspect of the present invention, there is provided a method comprising: 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; and exposing a polarization-sensitive recording medium to the polarization interference pattern to align a plurality of optically anisotropic molecules in the polarization-sensitive recording medium to form an in-plane orientation pattern.

[0021] 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.

[0022] In some embodiments, the polarization-sensitive recording medium may include a bulk photo-aligned 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-aligned material.

[0023] In some embodiments, within an in-plane pitch of the in-plane alignment pattern, azimuthal angles of the aligned plurality of optically anisotropic molecules may vary nonlinearly along a predetermined in-plane direction of the in-plane alignment pattern.

[0024] It will be appreciated that any feature described herein as suitable for incorporation into one or more aspects or embodiments of the present disclosure is intended to have generality in any and all aspects and embodiments of the present disclosure. Other aspects of the present disclosure will be apparent to those skilled in the art from the specification, claims, and drawings of the present disclosure. The foregoing general description and the following detailed description are merely exemplary and illustrative and are not intended to limit the claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] 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:

[0026] Figure 1A A three-dimensional (3D) view of a conventional reflective polarization volume hologram (R-PVH) element is shown;

[0027] Figure 1B The following simulation results are shown: Figure 1A The relationship between the diffraction efficiency of the conventional R-PVH element and the angle of incidence (“AOI”) of the incident light is shown in FIG.

[0028] Figure 1C Shown in Figure 1A and Figure 1B Diffracted light perceived at different viewing angles for the conventional R-PVH shown in FIG;

[0029] Figure 2A and Figure 2B shows a schematic diagram of a liquid crystal polarization hologram ("LCPH") element according to one or more embodiments of the present disclosure;

[0030] Figure 2C The following simulation results according to one or more embodiments of the present disclosure are shown: Figure 1A The traditional R-PVH components shown in Figure 2A The relationship between the azimuth angle of each optically anisotropic molecule and the in-plane axis distance at a single in-plane spacing for the LCPH element shown in FIG.

[0031] Figure 2D The following simulation results according to one or more embodiments of the present disclosure are shown: Figure 1A The traditional R-PVH components shown in Figure 2A The LCPH element shown in Figure 1 shows the relationship between the azimuthal angle and the out-of-plane axis distance of the LC molecules within a single Bragg period.

[0032] Figure 2E The following simulation results according to one or more embodiments of the present disclosure are shown: The simulation results show that for the amplitude of the nonlinear term with different non-zero values Figure 2A The azimuthal angles of each optically anisotropic molecule for a range of in-plane axial distances at a single in-plane spacing for the LCPH element shown in FIG, and for a conventional R-PVH element when the amplitude is zero;

[0033] Figure 2F The present invention shows one or more embodiments of the present invention. Figure 2A Schematic diagram of a portion of the LCPH element shown in , illustrating the nonlinear azimuthal variation of each optically anisotropic molecule at a single in-plane spacing;

[0034] Figure 2G The following simulation results according to one or more embodiments of the present disclosure are shown: The simulation results show that when the amplitude of the nonlinear term is different non-zero values Figure 2A Azimuthal angles of each optically anisotropic molecule for a range of out-of-plane axis distances on a single helical pitch for the LCPH element shown, and for a conventional R-PVH element when the amplitude is zero;

[0035] Figure 2H The present invention shows one or more embodiments of the present invention. Figure 2A3D exploded view of a portion of the LCPH element shown in , showing the nonlinear azimuthal variation of each optically anisotropic molecule over a single helical pitch;

[0036] Figure 3A The following simulation results according to one or more embodiments of the present disclosure are shown: Figure 1A The conventional R-PVH components shown in Figure 2A The relationship between the diffraction efficiency and the angle of incidence (“AOI”) of the incident light for the LCPH element shown in FIG.

[0037] Figure 3B According to one or more embodiments of the present disclosure, Figure 2A Diffracted light perceived at different viewing angles of the LCPH element shown in FIG;

[0038] Figure 3C The following simulation results according to one or more embodiments of the present disclosure are shown: Figure 1A The conventional R-PVH components shown in Figure 2A The relationship between the diffraction efficiency and the wavelength of the incident light for the LCPH element shown in FIG.

[0039] Figure 4A and Figure 4B A schematic diagram illustrating an LCPH element according to one or more embodiments of the present disclosure is shown;

[0040] Figure 5A A schematic diagram illustrating a light guide display system according to one or more embodiments of the present disclosure is shown;

[0041] Figure 5B shows a schematic diagram illustrating diffraction of image light on the output side of a conventional light guide display system including an outcoupling grating with uniform diffraction efficiency;

[0042] Figure 5C Shown is a diagram illustrating one or more embodiments of the present disclosure. Figure 5A Schematic diagram of diffraction of an image light on the output side of the light guide display system shown in FIG;

[0043] Figure 5D Shown is a diagram illustrating one or more embodiments of the present disclosure. Figure 5A Schematic diagram of diffraction of multiple image lights at the output side of the light guide display system shown in ;

[0044] Figure 6A A schematic diagram illustrating an artificial reality device according to one or more embodiments of the present disclosure is shown;

[0045] Figure 6B The present invention shows one or more embodiments of the present invention. Figure 6A A schematic cross-sectional view of one half of the artificial reality device shown in ;

[0046] 7A to 7F Schematically illustrates a process for manufacturing an LCPH element according to one or more embodiments of the present disclosure;

[0047] Figure 8A and Figure 8B Schematically illustrates a process for manufacturing an LCPH element according to one or more embodiments of the present disclosure;

[0048] Figures 9A to 9C schematically illustrates a process for manufacturing an LCPH element according to one or more embodiments of the present disclosure; and

[0049] Figure 10A and Figure 10B is a flow chart illustrating a method of manufacturing an LCPH element according to one or more embodiments of the present disclosure. DETAILED DESCRIPTION

[0050] The embodiments of 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. Wherever possible, the same reference numerals will be used throughout the drawings to represent the same or similar parts, and their detailed description may be omitted.

[0051] In addition, in the present disclosure, the disclosed embodiments and features of the disclosed embodiments may be combined. The described embodiments are some embodiments of the present disclosure, but not all embodiments. Based on the disclosed embodiments, a person of ordinary skill in the art can deduce other embodiments according to the present disclosure. For example, modifications, adaptations, replacements, additions, or other variations may be made based on the disclosed embodiments. Such variations of 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.

[0052] As used herein, the terms "couple," "coupled," or "coupling," etc., may include optical coupling, mechanical coupling, electrical coupling, electromagnetic coupling, or any combination thereof. "Optical coupling" between two optical elements refers to a configuration in which the two optical elements are arranged in an optical sequence and light output from one optical element can be received directly or indirectly by the other optical element. An optical sequence 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 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. Coupling can be direct coupling or indirect coupling (e.g., coupling through an intermediate element).

[0053] The phrase "at least one of A or B" may include 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 include 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 include all combinations of A and B, such as only A, only B, or A and B. Likewise, the meaning of the phrase "at least one of A, B, or C" is similar to the meaning of the phrase "at least one of A, B, or C." For example, the phrase "A, B, and / or C" may include 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.

[0054] When a first element is described as being "attached," "provided," "formed," "attached," "mounted," "fixed," "connected," "incorporated," "recorded," or "disposed" to, on, at, or at least partially in, a second element, the first element may be "attached," "provided," "formed," "attached," "mounted," "fixed," "connected," "incorporated," "recorded," or "disposed" to, on, at, or at least partially in, the second element using any suitable mechanical or non-mechanical means (e.g., deposition, coating, etching, bonding, adhesive bonding, threaded coupling, press fit, snap fit, clamping, etc.). Furthermore, the first element may be in direct contact with the second element, or there may be an intermediate element between the first and second elements. The first element may be disposed on any suitable side of the second element, such as left, right, front, back, top, or bottom.

[0055] When a first element is shown or described as being set or arranged "on" a second element, the term "on..." is only used to indicate an exemplary 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 exemplary configuration shown in the figure. For example, when describing the view shown in the figure, the first element can be described as being set "on" the second element. It will be understood that the term "on..." does not necessarily mean that the first element is located above the second element in the vertical direction of gravity. For example, when the assembly of the first element and the second element is rotated 180 degrees, the first element can be "below" the second element (or the second element can be "on" the first element). Therefore, it should be understood that when the figure shows that the first element is "on" the second element, this configuration is only an illustrative example. The first element can be set or arranged in any suitable orientation relative to the second element (for example, on 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.).

[0056] 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. A first element disposed directly on a second element means that no additional elements are disposed between the first and second elements. A first element disposed indirectly on a second element means that one or more additional elements are disposed between the first and second elements.

[0057] The terms "film", "layer", "coating" or "plate" may include rigid or flexible, self-supporting or independent 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 or 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. The term "in-plane" as in, for example, "in-plane orientation", "in-plane direction", "in-plane spacing", etc., refers to an orientation, direction or spacing that is within 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 within the film plane (i.e., not parallel to the film plane). For example, the direction, orientation or spacing may be along a line perpendicular to the film plane, or a line that forms an acute angle or an obtuse angle relative to the film plane. 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 angle or a right angle relative to the plane of the film.

[0058] The term "orthogonal" as used in "orthogonal polarizations" or the term "orthogonal" as used in "orthogonally polarized" means that the inner product of two vectors representing the two polarizations is substantially zero. For example, two lights or light beams having orthogonal polarizations (or two orthogonally polarized light beams) can be two linearly polarized lights (or light beams) having 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 having opposite handedness (e.g., left-handed circularly polarized light and right-handed circularly polarized light).

[0059] The wavelength ranges, wavelength 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, such as 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, or 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.

[0060] The angle of a light beam relative to the surface normal of an optical element (e.g., the diffraction angle of a diffracted light beam, the reflection angle of reflected light, or the angle of incidence of an incident light beam) can be defined as positive or negative, depending on the angular relationship between the propagation direction of the light beam and the surface normal. For example, when the virtual line representing the propagation direction of the light beam deviates from the normal in a clockwise (or counterclockwise) direction, the angle of the light beam relative to the normal can be defined as a positive angle, while when the virtual line representing the propagation direction of the light beam deviates from the normal in a counterclockwise (or clockwise) direction, the angle of the light beam relative to the normal can be defined as a negative angle.

[0061] As used herein, the term "liquid crystal compound" or "mesogenic compound" may refer to a compound that includes one or more rod-shaped (rod-shaped or plate-shaped / lath-shaped) or disc-shaped (disc-shaped) mesogenic groups. The term "mesogenic group" may refer to a group that has the ability to induce liquid crystal (or mesogenic) phase behavior. In some embodiments, a compound that includes a mesogenic group may not exhibit a liquid crystal ("LC") phase on its own. Instead, when mixed with other compounds, these compounds may exhibit an LC phase. In some embodiments, when the compound or a mixture containing the compound is polymerized, these compounds may exhibit a liquid crystal phase. For simplicity of discussion, the term "liquid crystal" will be used below for 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 linked or interconnected via linking groups. In some embodiments, the rod-shaped mesogenic group may include end groups attached to the ends of the mesogenic core. In some embodiments, the rod-shaped mesogenic group may include one or more side groups attached to the long sides of the mesogenic core. These terminal and side groups may be selected, for example, from: carbon or hydrocarbon groups; polar groups such as halogen, nitro, hydroxyl, etc.; or polymerizable groups.

[0062] As used herein, the term "reactive mesogen" ("RM") may refer to a polymerizable mesogen or liquid crystal compound. A polymerizable compound having one polymerizable group may be referred to as a "monoreactive" compound. A compound having two polymerizable groups may be referred to as a "direactive" compound, while a compound having more than two polymerizable groups may be referred to as a "multireactive" compound. A compound having no polymerizable groups may be referred to as a "non-reactive" compound. For the purposes of discussion, the term "liquid crystal" may include 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 discotic compound) of the LC molecules. 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 line.

[0063] The term "diffraction efficiency" as used herein is a quantitative measurement of the extent to which the energy of incident light is diffracted by a diffraction element. Diffraction efficiency can be defined as the ratio between the intensity (or optical power) of the diffracted light output from the diffraction element and the intensity (or optical power) of the incident light. The diffraction efficiency of a diffraction element can be calculated for a specific incident light or a specific polarization component in the incident light. The diffraction efficiency of a specific polarization component in the incident light can be the same as or different from the diffraction efficiency of the entire incident light. Diffraction can include forward diffraction and backward diffraction. For illustrative purposes, backward diffraction may be used as an example in the drawings and the following description. As an example, the term "diffraction efficiency" may be shown as reflection efficiency in some drawings.

[0064] Figure 1A A 3D view of a conventional reflective polarization volume hologram ("R-PVH") element 100 is shown. An R-PVH element 100 based on self-organized cholesteric liquid crystal (CLC) may be referred to as a tilted or patterned CLC element. Figure 1A , the R-PVH element 100 can include an R-PVH layer 155. Within the volume of the R-PVH layer 155, the 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 1A The xyz coordinate system shown in refers to the global coordinate system of the R-PVH element 100, and Figure 1A The x′-y′-z′ coordinate system shown in refers to the local coordinate system of the helical structure 167 . Figure 1A The Bragg plane 164 is shown to be in the x′-y′ plane, the helical axis 168 extends in the z′ axis direction, and the Bragg plane 164 is perpendicular to the helical axis 168 .

[0065] In each helical structure 167, the LC molecules 112 may continuously rotate about the helical axis 168 in a predetermined rotation direction, and the azimuth angle of the LC molecules 112 may exhibit a continuous periodic variation along the helical axis 168. The azimuth angle of the LC molecules 112 may be defined as the direction of the LC director relative to a predetermined in-plane direction within the Bragg plane 164 (e.g., Figure 1A The azimuth angle of the LC molecule 112 may have a value in the range of 0° to 360° (inclusive). The helical pitch P of the helical structure 167 may be h It is defined as the distance along the helical axis 168 over which the azimuthal angle of the LC molecules 112 changes by 360°.

[0066] The pitch P of a single helix in the helical structure 167 hThe azimuth angle of the LC molecule 112 is Can be with a single spiral pitch P h The starting point (for example, the azimuth ) to the local point along the helical axis 168 where the LC molecule 112 is located. For the purpose of discussion, the pitch P of a single helix of the helical structure 167 may be h The distance from the starting point to the local point where the LC molecule 112 is located along the helical axis 168 is called the out-of-plane axial pitch of the LC molecule 112. For example, the pitch P of a single helix of the helical structure 117 is h The azimuth angle of the LC molecule 112 is may vary linearly with respect to the out-of-plane axis distance z′ of the LC molecules 112 according to the following linear function: Among them, P B is the Bragg period (i.e. Figure 1A Medium spiral pitch P h When the out-of-plane axis distance z of the liquid crystal molecules 112 is 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 , 2*P B When the azimuth angle of the liquid crystal molecules 112 It can be 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°, and 360° respectively.

[0067] Furthermore, the LC molecules 112 located near the surface 165 may have an in-plane spacing of P in The non-uniform in-plane orientation pattern of the LC molecules 112 is formed in such a manner that the directors of the LC molecules 112 can rotate along a predetermined in-plane direction (or in-plane axis) 188 within the surface 165. Thus, the azimuthal angles of the LC molecules 112 located near the surface 165 can vary in the predetermined in-plane direction 188. The azimuthal angles of the LC molecules 112 located near the surface 165 of the R-PVH layer 155 can be defined as the angle of the LC director relative to the predetermined in-plane direction 188 within the surface 165 (e.g., Figure 1A The in-plane spacing P can be in is defined as the distance along the predetermined in-plane direction 188 over which the azimuthal angle of the LC molecules 112 located near the surface 165 changes by 180°. For discussion purposes, Figure 1A It shows that the azimuth angles of the LC molecules 112 can be constant with an in-plane pitch P in It changes periodically in a predetermined in-plane direction 188 .

[0068] The individual in-plane spacing P of the in-plane orientation pattern in On the other hand, the LC molecules 112 located near the surface 165 may also have a linear azimuth variation along the predetermined in-plane direction 188. For example, the azimuth of the LC molecules 112 may vary with the in-plane pitch P. in The starting point (for example, at this starting point, the azimuth ) to the local point where the LC molecules 112 are located along the predetermined in-plane direction 188. For discussion purposes, a single in-plane pitch P of the in-plane orientation pattern may be in The distance from the starting point to the local point where the liquid crystal molecule 112 is located along the predetermined in-plane direction 188 is called the in-plane axis distance of the liquid crystal molecule 112. For example, the pitch P of a single helix of the helical structure 167 is h The azimuth angle of the LC molecule 112 is Can vary according to the following functions: where x is the in-plane axial 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 LC molecules 112 near the surface 165 are 0, 0.25*P in , 0.5*P in 、0.75*P in and P in When φ is 0°, 45°, 90°, 135°, or 180°, the azimuth angles φ of the LC molecules 112 may be 0°, 45°, 90°, 135°, or 180°, respectively.

[0069] R-PVH element 100 may substantially reflect circularly polarized light having a predetermined handedness by back diffraction and substantially transmit circularly polarized light having a handedness opposite to the predetermined handedness with no or negligible diffraction. Figure 1B The following simulation results are shown: Figure 1A FIGURE 1 shows the relationship between the normalized diffraction efficiency of a conventional R-PVH element 100 and the angle of incidence ("AOI") of incident light. Since the conventional R-PVH element 100 reflects light by back diffraction, for discussion purposes, Figure 1B The normalized diffraction efficiency is shown as the normalized reflection efficiency. Curve 170 shows the relationship. Curve 170 can also be called a diffraction efficiency versus AOI curve. In the simulation, a single helical pitch P of the conventional R-PVH element 100 is h The azimuth angle of the LC molecule 112 is The out-of-plane axis distance z' of the LC molecules 112 varies linearly according to the following function: Among them, P B =0.1565 μm. In the conventional R-PVH element 100, the single in-plane pitch P inThe azimuth angle of the LC molecules 112 near the surface 165 is The in-plane axis distance x of the LC molecules 112 varies linearly according to the following function: Among them, P in =0.78μm.

[0070] like Figure 1B As shown, the horizontal axis represents the angle of incidence ("AOI"), and the vertical axis represents the normalized diffraction efficiency. Figure 1B Curve 170 in FIG. 1 shows the relationship between the normalized diffraction efficiency (e.g., normalized reflection efficiency) of a conventional R-PVH element 100 and the AOI of the incident light. Different AOIs correspond to light entering the user's eye from different angles. Curve 170 shows that when the AOI is in the range of -10° to 10° (corresponding to an AOI range of 20°), the conventional R-PVH element 100 can provide a high diffraction efficiency of approximately 90%. As the AOI increases from 10° to approximately 25° (or from -10° to -25°), the reflection efficiency of the conventional R-PVH element 100 decreases monotonically from approximately 90% to approximately 73%. For an AOI range of 45° (from 22.5° to -22.5°), the reflection efficiency of the conventional R-PVH element 100 can vary between approximately 90% and approximately 80%. When light of the same intensity is incident on the R-PVH element 100 at different incident angles, diffracted light output from the conventional R-PVH element 100 may have different light intensities ranging from, for example, about 90% to about 80% of the incident light intensity.

[0071] Figure 1C Shown in Figure 1A and Figure 1B The diffracted light perceived at different AOIs (or viewing angles, or viewing directions) of the conventional R-PVH element 100 shown in FIG. Figure 1C As shown, the conventional R-PVH element 100 can reflect light 181, 183 and 185 with different incident angles into light 182, 184 and 186 with different diffraction angles, respectively, by back diffraction. The viewing angle (or field angle) can be defined as the same as the diffraction (or reflection) angle, or the viewing angle (or field angle) can be defined as the complementary angle of the diffraction (or reflection) angle. For the purpose of discussion, it is assumed that the incident angles of light 181, 183 and 185 are within the 45° AOI range (from 22.5° to -22.5°). According to Figure 1B, within an AOI of 45°, the reflection efficiency provided by the conventional R-PVH element 100 to the incident light 181, 183, and 185 varies between approximately 90% and approximately 80%. Therefore, when the light intensity of the incident light 181, 183, and 185 is the same, the light intensity of the diffracted light 182, 184, and 186 output from the conventional R-PVH element 100 may vary, for example, within a range of approximately 90% to approximately 80% of the input light intensity, due to the variation in reflection efficiency relative to the AOI. In other words, the brightness perceived in different field of view (FOV) directions of the R-PVH element 100 depends on the angle of the AOI.

[0072] Therefore, when the light intensity of the incident light 181, 183, and 185 is the same, the angular distribution of the brightness (or illuminance) on the output side of the R-PVH element 100 may be non-uniform within the field of view (FOV) of the R-PVH element 100 associated with a predetermined AOI range (e.g., a 45° range from 22.5° to -22.5°). In particular, when the AOI is greater than 10° (or -10°), a 10% decrease in reflective efficiency (from 90% to 80%) when the AOI changes from 10° to 22.5° (or from -10° to -22.5°) may result in a significant decrease in brightness. Angular brightness variation or angular illuminance variation may significantly degrade the optical performance of the R-PVH element 100.

[0073] For ease of description, when the luminance varies with respect to the AOI of the incident light, the uniformity level of the angular distribution of luminance is referred to as angular uniformity. The angular uniformity provided by the conventional R-PVH element 100 within a predetermined FOV (e.g., 45°) (corresponding to an AOI range of 45°) can be evaluated by a uniformity index U. The uniformity index U can be defined as: U = (I max -I min ) / I avg , where I max is the maximum intensity, I min is the minimum intensity, I avg is the average intensity within the FOV (or within the AOI). That is, the uniformity level of the angular distribution of brightness can be quantified by the ratio defined by dividing the difference between the maximum diffracted light intensity and the minimum diffracted light intensity by the average diffracted light intensity within a predetermined FOV.

[0074] When the intensity of the incident light at different AOIs is the same, the output intensity (or brightness) is proportional to the diffraction efficiency of the R-PVH element 100 at different AOIs. Therefore, the uniformity index U can be calculated as U = (R max -R min ) / R avg , where R maxis the maximum diffraction efficiency within a predetermined FOV (i.e., for a predetermined AOI range), R min It is the minimum diffraction efficiency within the predetermined FOV (or AOI range), R avg It is the average diffraction efficiency within a predetermined FOV (or AOI range). In other words, the angular uniformity within a predetermined FOV can be quantified by dividing the difference between the maximum diffraction efficiency and the minimum diffraction efficiency by the average diffraction efficiency within the predetermined FOV. A larger U value indicates greater non-uniformity in the output light intensity (or brightness), while a smaller U value indicates better uniformity in the output light intensity (or brightness).

[0075] refer to Figure 1B For the conventional R-PVH element 100, the calculated uniformity index U = 10.8% within the field of view (FOV) of 22.5° to -22.5° indicates that the angular distribution of luminance on the output side of the R-PVH element 100 is highly non-uniform. If the thickness of the conventional R-PVH element 100 is further reduced, the uniformity index U of the conventional R-PVH element 100 may further increase, meaning that the angular distribution of luminance becomes even more non-uniform. In conventional technology, the non-uniformity of the angular distribution of luminance within a predetermined FOV may result in a poor visual experience for the user. The non-uniformity of the angular distribution of luminance within the predetermined FOV of conventional R-PVH elements 100 is typically uncontrolled.

[0076] In view of the limitations of conventional technologies, the present disclosure provides a liquid crystal polarization hologram ("LCPH") element configured with nonlinear azimuthal angle variation. The disclosed LCPH element can be configured to provide enhanced uniformity of angular distribution of brightness (or illumination) within a predetermined FOV of the LCPH element. In other words, the disclosed LCPH element can be configured to provide enhanced angular brightness (or illumination) uniformity within a predetermined FOV. The LCPH element may include a polarization volume hologram ("PVH") element and a cholesteric liquid crystal ("CLC") element, among others. The LCPH element 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 "hologram" described herein is not limited to being produced by holographic interferometry or "holography."

[0077] 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 2Ais an xy cross-sectional view of an LCPH element 200 shown in . The LCPH element 200 may be a reflective polarization volume hologram ("R-PVH") element or a transmissive polarization volume hologram ("T-PVH") element. The LCPH element 200 may be configured to substantially diffract circularly polarized light having a predetermined handedness and substantially transmit circularly polarized light having a handedness opposite to the predetermined handedness with no diffraction or negligible diffraction. The LCPH element 200 may be configured to provide enhanced angular brightness (or illumination) uniformity within a FOV on an output side of the LCPH element 200.

[0078] like Figure 2A As shown, the LCPH 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., light-induced) 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, twisted-bend LC, chiral nematic LC, smectic LC, ferroelectric 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 LCPH element 200 may be an active element or a passive element.

[0079] The optically anisotropic film 215 may include 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 extended optically anisotropic molecules 212 or extended molecular units (e.g., small molecules or fragments of polymer molecules) included in the optically anisotropic molecules 212. For the purpose of discussion, the 3D orientation pattern of the optical axis of the optically anisotropic film 215 is described using extended optically anisotropic molecules (e.g., rod-shaped LC molecules, also referred to as 212 for the purpose of discussion) as an example. For the purpose of discussion, Figure 2A In the embodiment shown in FIG, an R-PVH element is used as an example of the LCPH element 200 (also referred to as the R-PVH element 200 for discussion purposes). When the R-PVH element is used as an example of the LCPH element 200, the optically anisotropic film 215 included in the LCPH element 200 may also be referred to as the R-PVH layer 215.

[0080] In the present disclosure, 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. Figure 2A and Figure 2B As shown, the LC molecules 212 located near the surface 205 of the R-PVH layer 215 (eg, in the xy plane) can be configured 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 LC molecules 212 located near the surface 205 may rotate periodically or aperiodically along at least one in-plane direction (or in-plane axis) 228 within the surface 205. Therefore, the azimuthal angles of the LC molecules 212 located near the surface 205 may vary periodically or aperiodically along at least one in-plane direction 228. The azimuthal angles of the LC molecules 212 located near 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. and azimuth The orientations of the LC directors at the azimuth angles may be equal, for example, the orientations of the LC directors at the azimuth angles of 0° and 180° may be equal, the orientations of the LC directors at the azimuth angles of 45° and 225° may be equal, the orientations of the LC directors at the azimuth angles of 90° and 270° may be equal, and the orientations of the LC directors at the azimuth angles of 135° and 315° may be equal.

[0081] The in-plane spacing P can be in The in-plane pitch P is defined as the distance along the predetermined in-plane direction 228 over which the azimuth angle of the LC molecules 212 located near the surface 205 changes by 180°. in It can be a constant in-plane spacing or a varying in-plane spacing. For discussion purposes, the in-plane spacing P of the non-uniform in-plane orientation pattern of the LC molecules 212 located near the surface 205 can also be referred to as in The in-plane spacing P of the R-PVH element 200 or the R-PVH layer 215 is referred to as in .

[0082] 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 located near 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.

[0083] For the purpose of discussion, Figure 2A and Figure 2B The LC molecules 212 located near the surface 205 are shown to be spaced apart with a constant in-plane spacing P. in Along a predetermined in-plane direction 228 (e.g., Figure 2A and Figure 2B The LC molecules 212 located near the surface 205 may be arranged with another suitable non-uniform in-plane alignment pattern, such as a lens pattern (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.

[0084] In some embodiments, the individual in-plane pitch P of the in-plane orientation pattern is in 2. The LC molecules 212 located near the surface 205 can be configured to have a nonlinear azimuthal variation along a predetermined in-plane direction 228. For discussion purposes, the LC molecules 212 located near the surface 205 can be configured to have a nonlinear azimuthal variation along a predetermined in-plane direction 228. in In the embodiment, the starting point (or reference point) of the 180° change in the azimuth angle along the predetermined in-plane direction 228 is defined as the point where the azimuth angle of the LC molecules 212 is 0°. In some embodiments, the single in-plane pitch P of the in-plane alignment pattern is in In the embodiment of the present invention, the azimuth angle of the LC molecules 212 may be configured to vary nonlinearly with respect to the distance from a starting point (e.g., a position at which 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 purpose of discussion, the distance from the starting point (e.g., a position at which the azimuth angle is 0°) to a local point where the liquid crystal molecules 212 are located along the predetermined in-plane direction 228 may be referred to as the in-plane axis distance of the liquid crystal molecules 212.

[0085] In some embodiments, the individual in-plane pitch P of the in-plane orientation pattern is in The azimuth angle of the liquid crystal molecules 212 located near the surface 205 may vary according to the following function: in is the azimuth angle of the liquid crystal molecules 212 (unit: degree), x is the in-plane axis distance of the liquid crystal molecules 212 (unit: μm), P in is the in-plane spacing (unit: μm), which can be a constant value (with respect to x). is a linear function of x, meaning that this portion of the azimuth angle varies with the in-plane axis distance x at 180° / P in The rate (or slope) of change. is a nonlinear function of the in-plane wheelbase x, where A is an amplitude parameter associated with the magnitude of the azimuthal variation introduced by this nonlinear function (to simplify the discussion, this may be referred to as "amplitude"). Therefore, the nonlinear azimuthal variation with respect to the in-plane wheelbase x is a combination of linear and nonlinear variations. Here, the term "amplitude parameter" or "amplitude" is used merely for convenience in distinguishing parameter A from other parameters.

[0086] In some embodiments, the amplitude A of the nonlinear function can be a constant value with respect to the in-plane axis distance x. For example, the amplitude A can be configured as a constant positive value greater than 0° and less than or equal to 360°. The amplitude A can be selected according to the specific application needs. 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 spacing P in a single plane of the LCPH element 200 is in The azimuthal angles of the LC molecules 212 located near the surface 205 can be configured to vary nonlinearly with respect to the in-plane axis distance x according to the following function: in, It is a nonlinear function .

[0087] Return Reference Figure 2A When the LCPH element 200 is an R-PVH element, within the volume of the R-PVH layer 215 , the LC molecules 212 may be arranged into 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 LCPH element 200, and Figure 2A The x'-y'-z' coordinate system shown refers to the local coordinate system of the helical structure 217. For discussion purposes, Figure 2A It is shown that the Bragg plane 214 lies 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 .

[0088] In some embodiments, the helical axis 218 of the helical structure 217 can 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 can 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). In the helical structure 217, the directors of the LC molecules 212 can continuously rotate around the helical axis 218 in a predetermined rotation direction (e.g., clockwise or counterclockwise). Therefore, the helical structure 217 can exhibit handedness, such as right-handedness or left-handedness.

[0089] 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, which are periodically distributed within the volume of the R-PVH layer 215. Although not labeled, 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, which are periodically distributed within the volume of the R-PVH layer 215. LC molecules 212 having different orientations can form different series of Bragg planes. Within the same series of Bragg planes, the LC molecules 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 sufficient 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 .

[0090] Since the directors of the LC molecules 212 continuously rotate about the helical axis 218 in a predetermined rotational direction, the azimuthal angles of the 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 angle of the LC director relative to a predetermined in-plane direction within the Bragg plane 214 (e.g., Figure 2A The helical pitch P of the helical structure 217 can be h It is 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 hIt is constant across the entire R-PVH layer 215 .

[0091] In some embodiments, the LCPH element 200 can be configured such that the azimuth angles of the LC molecules 212 within the volume of the R-PVH layer 215 vary linearly along the helical axis 218. In some embodiments, the LCPH element 200 can be configured such that the azimuth angles of the LC molecules 212 within the volume of the R-PVH layer 215 vary nonlinearly along the helical axis 218. For example, within a single helical pitch P of the helical structure 217, the azimuth angles of the LC molecules 212 within the volume of the R-PVH layer 215 vary linearly along the helical axis 218. h , the LC molecules 212 within the volume of the R-PVH layer 215 can be configured to have a nonlinear azimuthal angle variation along the helical axis 218. For discussion purposes, a local point on the helical axis 218 where the azimuthal angle of the LC molecules 212 is 0° can be defined as the starting point of the 360° variation of the azimuthal angle along the helical axis 218. h In the embodiment, 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., the position 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 helix in the helical structure 217 can be referred to as h In FIG. 2 , 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 is referred to as the out-of-plane axis pitch of the LC molecule 212 .

[0092] In some embodiments, the pitch P of a single helix of the helical structure 217 is h The azimuth angle of the LC molecules 212 may vary according to the following function: in is the azimuthal angle of the LC molecules 212 positioned along the helical axis 218, z′ is the out-of-plane axial distance of the LC molecules 112, and P B is the Bragg period. is a linear function of the out-of-plane axis distance z', the term is a nonlinear function of the out-of-plane axis distance z', and A is the amplitude parameter of the nonlinear function, which is related to the amplitude of the azimuthal angle variation introduced by the nonlinear function. Therefore, the nonlinear azimuthal angle variation with respect to the out-of-plane axis distance z' is a combination of linear variation and nonlinear variation.

[0093] In some embodiments, the amplitude parameter A of the nonlinear function can be a constant value with respect to the out-of-plane axis distance z'. For example, the amplitude A can be configured as a constant positive value greater than 0° and less than or equal to 360°. The amplitude A can be selected according to the specific application needs. 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 pitch P of a single spiral of the spiral structure 217 is h The azimuthal angles of the LC molecules 212 positioned along the helical axis 218 can be configured to vary nonlinearly with respect to the out-of-plane axis distance z′ according to the following function: in It is a nonlinear function In some embodiments, the following two items may be the same or different: an amplitude parameter A of the nonlinear function associated with the nonlinear azimuthal variation along the helical axis 218; an amplitude parameter A of the nonlinear function associated with the nonlinear azimuthal variation along the in-plane direction 228. In some embodiments, when the azimuthal angles of molecules located at or near the surface 205 have a nonlinear variation along the in-plane direction 228, the azimuthal angles of molecules positioned along the helical axis 218 may have a linear variation or may have a nonlinear variation. Note that although in the nonlinear function, the same symbol "A" is used to represent the amplitude parameter when describing the nonlinear azimuthal variation in the in-plane direction and the helical axis direction, the specific values ​​of the amplitude parameter A may be the same or different for the nonlinear azimuthal variation in the in-plane direction and the helical axis direction.

[0094] Figure 2C The following simulation results are shown: Figure 1A The conventional R-PVH element 100 shown in FIG. Figure 2A The LCPH element 200 shown in FIG (using an R-PVH element as an example) shows the relationship between the azimuth angle of the LC molecules and the in-plane axis distance at a single in-plane spacing. Figure 2C As shown, the horizontal axis represents the in-plane axis distance x of the LC molecules (unit: μm), and the vertical axis represents the azimuth angle of the LC molecules. (Unit: degree). Line 232 shows the Figure 1A In the conventional R-PVH element 100 shown in FIG, the single in-plane pitch P in The linear relationship between the azimuth angle of the LC molecules 112 and the in-plane axis distance is shown in FIG. Figure 2A In the LCPH element 200 shown in FIG, the single in-plane spacing P in The nonlinear relationship between the azimuth angle of the LC molecules 212 and the in-plane axis distance is shown in FIG. in The azimuth angle of the LC molecules 212 near the surface 205 is Varies according to the following function: in is a linear function of the in-plane wheelbase x, It is a nonlinear function For example, A=18°, P in =0.78μm.

[0095] Curve 231 shows the nonlinear function The straight line 232 shows the linear function Figure 1A The azimuth angle in the conventional R-PVH element 100 shown in FIG is set according to this function. The straight line 232 has a 180° / P in The constant slope of represents the single helical pitch P of the helical structure 117 formed in the conventional R-PVH element 100. h The azimuth angle of the LC molecule 112 is The linear increase with the increase of the in-plane axis distance x of the LC molecules 112. Curve 231 is shown as a wavy line oscillating around a straight line 232, which represents the single in-plane pitch P of the LCPH element 200. in The azimuth angle of the LC molecule 212 is The nonlinear azimuthal angle increases nonlinearly with increasing in-plane axis distance x of the LC molecules 212. The amplitude of the oscillation about the line 232 can be controlled by selecting the amplitude A of the nonlinear term. The nonlinear azimuthal angle variation is a combination of the linear and nonlinear terms, such as the overall nonlinear function shown.

[0096] Figure 2D The following simulation results are shown: Figure 1A The conventional R-PVH element 100 shown in FIG. Figure 2A The LCPH element 200 shown in FIG. 1 has a single Bragg period P B The relationship between the azimuth angle and the out-of-plane axis distance within the range (the distance in which the azimuth angle changes by 180°). Figure 2D As shown, the horizontal axis represents the out-of-plane axis distance z' of the LC molecules (unit: μm), and the vertical axis represents the azimuth angle of the LC molecules. (Unit: degrees). Line 242 shows the Figure 1A The conventional R-PVH element 100 shown in FIG. 1 has a single Bragg period P B The linear relationship between the azimuth angle of the LC molecules 112 and the out-of-plane axis distance is shown in curve 241. Figure 2A The LCPH element 200 shown in FIG. 1 has a single Bragg period P B The nonlinear relationship between the azimuthal angle and the out-of-plane axis distance of the LC molecules 212 is shown in FIG. 2 . In this simulation, the single helical pitch P of the LCPH element 200 is h (Azimuth The azimuth angle of the LC molecule 212 is Can vary according to the following functions: in is a linear function of the out-of-plane wheelbase z', It is a nonlinear function For example, A=18°, P B =0.1565μm.

[0097] Figure 2D The curve 241 in FIG. 240 shows the nonlinear function The straight line 242 shows the linear function Figure 1A The azimuth angle in the conventional R-PVH element 100 shown in FIG is set according to this function. The straight line 242 has a 180° / P B The constant slope indicates that a single Bragg period P of the conventional R-PVH element 100 B 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. Curve 241 is shown as a wavy line oscillating around a straight line 242, representing the single Bragg period P of the disclosed LCPH element 200. B The azimuth angle of the LC molecules 212 The nonlinear azimuthal angle increases with the increase of the out-of-plane axis distance z' of the LC molecules 212. The amplitude of the oscillation about the line 242 can be controlled by selecting the amplitude A 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.

[0098] Figure 2E A table is shown which shows the amplitude A for different non-zero values. Figure 2A The LCPH element 200 shown in FIG, and the ... Figure 1A The conventional R-PVH element 100 shown in FIG. 1 shows a conventional R-PVH element 100 for different in-plane wheelbases x (where x = 0.25*P in , 0.5*P in 、0.75*P in 、P in 、1.25*P in 、1.5*P in 、1.75*P in and 2*P in ), the simulated azimuthal angle of the LC molecules For the LCPH element 200, the amplitude A of the nonlinear term is selected to be A=9°, 18° and 36°. As shown in Table 1, the single in-plane spacing P of the LCPH element 200 isin As the in-plane axis distance x of the LC molecules 212 increases, the azimuth angle of the LC molecules 212 Increase nonlinearly. Figure 2E The last column of Table 1 (labeled "A = 0 (linear)") also shows Figure 1A The single in-plane pitch P of the conventional R-PVH element 100 shown in FIG. in For a series of in-plane wheelbases x (x = 0.25*P in , 0.5*P in 、0.75*P in and P in ) calculated azimuth angle of the LC molecule 112

[0099] Figure 2F The embodiment according to the present invention is shown Figure 2A The xy cross-sectional view of a portion of the LCPH element 200 shown in FIG. 1 shows that when the amplitude of the nonlinear function is selected to be A=18°, the spacing P in a single plane is h The nonlinear azimuthal angle of the LC molecules 212 located near the surface 205 varies. For example, in a single in-plane pitch P of the LCPH element 200 h In the embodiment, the five LC molecules 212-1 to 212-5 are equidistantly spaced from each other along the predetermined in-plane direction 228. h The starting point of the 180° change can be in azimuth The LC molecule 212-1 is at 0°. Figure 2F It is shown that when the in-plane axis distances x of the LC molecules 212-2 to 212-5 are 0.25*P in , 0.5*P in 、0.75*P in and P in When the corresponding azimuth angles of the LC molecules 212-2 to 212-5 are They are 63°, 90°, 117° and 180° respectively.

[0100] Figure 2G The following simulation results are shown: The simulation results show that when the amplitude of the nonlinear term is different non-zero values Figure 2A The LCPH element 200 shown in FIG, and the LCPH element 200 for the case where the amplitude is zero Figure 1A Table 2 shows the azimuth angles of each optically anisotropic molecule for a range of out-of-plane axial distances at a single helical pitch for the conventional R-PVH element 100 shown in FIG. h On the surface, the wheelbase z' changes at different planes (z'=0.25*P B , 0.5*PB 、0.75*P B 、P B 、1.25*P B 、1.5*P B 、1.75*P B and 2*P B ), the simulated azimuth angle of the LC molecule 212 The amplitude A of the nonlinear term is selected to be A=9°, 18°, and 36°. As shown in Table 2, the single spiral pitch P of the LCPH element 200 is h For any selected amplitude, as the out-of-plane axis distance z' of the LC molecules 212 increases, the azimuthal angle of the LC molecules 212 Increase nonlinearly. Figure 2G The last column of Table 2 (labeled "A = 0 (linear)") shown in FIG. Figure 1A The single helical pitch P of the conventional R-PVH element 100 shown in FIG. h On the different out-of-plane wheelbase z' (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 ) calculated at the azimuth angle of the LC molecule 112

[0101] Figure 2H The embodiment according to the present disclosure is shown Figure 2A The 3D exploded view of a portion of the LCPH element 200 shown in FIG. 1 shows that when the amplitude of the nonlinear term is A=18°, the single spiral pitch P h The nonlinear azimuthal angle of the upper LC molecules 212 changes. For illustration purposes, Figure 2G Nine consecutive sublayers (or Bragg planes) 271 to 279 are shown. For better illustration, the sublayers are separated. In each sublayer, the LC directors (indicated by dashed lines) of the plurality of LC molecules 212 may be oriented in the same direction. In different sublayers, the LC directors may be oriented in different directions. In a single helical pitch P of the helical structure 217, the helical pitch P is 1 / 2 of the helical structure 217. h The starting point of the 360° change in the azimuth angle (which is related to the direction of the LC director) along the helical axis 218 may be located at the azimuth angle At sub-layer 271 with an angle of 0°. Figure 2G It is shown that when the out-of-plane axial distance z' of the sub-layers 272 to 279 is 0.25*P B , 0.5*PB 、0.75*P B 、P B 、1.25*P B 、1.5*P B 、1.75*P B and 2*P B When the LC molecule 212 has a corresponding azimuth angle They are 63°, 90°, 117°, 180°, 243°, 270°, 297° and 360° respectively.

[0102] By arranging the azimuth angles of the LC molecules 212 to be Figure 2A The LCPH element 200 shown in FIG has a nonlinear change, which is related to Figure 1A The diffraction efficiency versus AOI curve of the LCPH element 200 may be changed compared to the diffraction efficiency versus AOI curve of the conventional R-PVH element 100 shown in FIG. Figure 3A The following simulation results are shown: Figure 1A The traditional R-PVH components shown in Figure 2A The relationship between the diffraction efficiency and the angle of incidence ("AOI") of the incident light for the LCPH element shown in FIG. Figure 3A In FIG, the horizontal axis represents AOI and the vertical axis represents normalized diffraction efficiency (eg, normalized reflection efficiency). Curve 170 (also in FIG. Figure 1B ) shows Figure 1A The relationship between the diffraction efficiency and AOI of the conventional R-PVH element 100 is shown in FIG. 3 , where curve 305 shows Figure 2A The relationship between the diffraction efficiency and AOI of the LCPH element 200 is shown in FIG. In this simulation, the single spiral pitch P of the LCPH element 200 is h The azimuth angle of the LC molecules 212 positioned along the helical axis 218 is varies nonlinearly with respect to the out-of-plane axis distance z' according to the following function: Where A=18°, P B =0.1565 μm. The single in-plane pitch P of the LCPH element 200 in The azimuth angle of the LC molecules 212 near the surface 205 is varies nonlinearly with respect to the in-plane axis distance x according to the following function: Where A=18°, P in =0.78μm.

[0103] Curve 305 shows that the LCPH element 200 of the present disclosure provides a high diffraction efficiency of approximately 90% when the AOI is in the range of approximately -10° to approximately 10° (i.e., within an AOI range of 20°). Curve 305 also shows that as the AOI increases from 10° to 22.5° (or from -10° to -22.5°), the diffraction efficiency of the LCPH element 200 does not decrease as in curve 170, but instead slightly increases from approximately 90% to approximately 93% (at 20°) and then drops back to approximately 90% (at 22.5°). Overall, the LCPH element 200 provides a diffraction efficiency of 90% or higher throughout the entire AOI range of 45° (from -22.5° to 22.5°). Figure 3A The curve 305 shown in FIG. 3 is for a specific amplitude A. The amplitude A can be adjusted to different values ​​to produce a curve similar to the curve 305, which can provide a high diffraction efficiency of 90% or higher across the entire AOI range. When the amplitude A is 0°, the curve 305 can be transformed into the curve 170 for the conventional R-PVH element 100, in which the azimuth angle is linearly distributed.

[0104] Furthermore, the diffraction efficiency distribution within the AOI range shown by curve 305 is more uniform than the diffraction efficiency distribution shown by curve 170. As described above, according to curve 170, for the conventional R-PVH element 100, the uniformity index U is calculated to be 10.8% over the FOV from 22.5° to -22.5°. For the LCPH element 200 of the present disclosure, the uniformity index U is calculated to be approximately 3.6% over the FOV from 22.5° to -22.5°, which is much smaller than the 10.8% of the conventional R-PVH element 100. As described above, a smaller uniformity index U means greater angular uniformity. Therefore, the LCPH element 200 can provide enhanced angular uniformity of the brightness of diffracted light throughout the entire FOV.

[0105] Figure 3B It is shown that the diffracted light perceived at different viewing angles of the LCPH element 200 has substantially the same light intensity, which indicates that the angular uniformity of the output side of the LCPH element 200 is enhanced within a predetermined FOV. Figure 3B As shown in FIG. 1 , the LCPH element 200 can reflect light 321, 323, and 325 with different incident angles into light 322, 324, and 326 with different diffraction angles, respectively, through back diffraction. Assuming that the light 321, 323, and 325 have the same light intensity, by configuring the azimuth angle in the LCPH element 200 to have a nonlinear change, the curve of diffraction efficiency versus AOI can be as follows: Figure 3A The distribution is shown by the curve 305 shown. Therefore, Figure 1CCompared to the conventional R-PVH element 100 shown, the angular distribution of the light intensity (or brightness) of the diffracted lights 322, 324, and 326 output from the LCPH element 200 can become more uniform.

[0106] like Figure 1C As shown, the output lights 182, 184, and 186 corresponding to different viewing angles have different intensities (indicated by lines of different thicknesses). In contrast, the output lights 322, 324, and 326 corresponding to different viewing angles (or different FOV directions) have uniform intensities. Therefore, the LCPH element 200 can provide enhanced angular uniformity within a predetermined FOV (e.g., from 22.5° to -22.5°) on the output side. As a result, the eye 160 located on the output side of the LCPH element 200 can perceive a substantially uniform angular distribution of brightness or illumination within the predetermined FOV (e.g., from 22.5° to -22.5°). In other words, when the eye 160 receives diffracted light from different FOV directions, the angular distribution of brightness or illumination of the diffracted light output from the LCPH element 200 configured with a nonlinearly varying azimuth angle as described above can become more uniform.

[0107] Figure 3C The following simulation results are shown: Figure 1A The conventional R-PVH element 100 shown in FIG. Figure 2A The relationship between the diffraction efficiency and the wavelength of the incident light for the LCPH element 200 shown in FIG. Figure 1A The other two curves 350 and 355 show the relationship of the conventional R-PVH element 100 shown in FIG. Figure 2A , the relationship between the LCPH element 200 shown in FIG. 2 and FIG. 3 when the amplitude A of the nonlinear function is selected to be two different non-zero values.

[0108] In this simulation, for the LCPH element 200, at a single helical pitch P h The azimuth angle of the LC molecules 212 positioned along the helical axis 218 is According to the nonlinear function The out-of-plane axis distance z' varies non-linearly. in The azimuth angle of the LC molecules 212 near the surface 205 is varies nonlinearly with respect to the in-plane axis distance x according to the following nonlinear function: Among them, P B =0.1565μm, P in =0.78 μm. For the conventional R-PVH element 100, the azimuthal angle of the LC molecules 112 positioned along the helical axis 168 is According to the linear function varies linearly with respect to the out-of-plane axis distance z', and within a single in-plane spacing P in The azimuth angle of the LC molecules 112 near the surface 165 is Varies linearly with respect to the in-plane axis distance x according to the following linear function: Among them, P B =0.1565μm, P in = 0.78 μm. Note that when A = 0°, the linear function is a special case of the nonlinear function. Assume that the AOI of the incident light is the same for the LCPH element 200 and the conventional R-PVH element 100.

[0109] like Figure 3C As shown, the horizontal axis represents the wavelength (unit: μm) of the incident light (or the incident wavelength), and the vertical axis represents the normalized diffraction efficiency (e.g., the normalized diffraction efficiency of the first diffraction order). Curve 350 shows the relationship between the normalized diffraction efficiency and the wavelength for the LCPH element 200 when the amplitude A = 36°. Curve 355 shows the relationship between the diffraction efficiency and the wavelength for the LCPH element 200 when the amplitude A = 18°. Curve 370 shows the relationship between the diffraction efficiency and the wavelength for the conventional R-PVH element 100 (i.e., when the amplitude A = 0° in the nonlinear function).

[0110] Curve 350 shows that when the amplitude A = 36°, the diffraction efficiency of the LCPH element 200 is approximately 65%, and curve 355 shows that when the amplitude A = 18°, the diffraction efficiency of the LCPH element 200 is approximately 90%. Curve 370 shows that when the amplitude A = 0°, the diffraction efficiency of the conventional R-PVH element 100 is close to 98%. Curves 350, 355, and 370 show that each of the LCPH element 200 and the conventional R-PVH element 100 has a diffraction band associated with the green wavelength range (approximately 495 nm to approximately 570 nm). Curves 350 and 355 show that the diffraction efficiency of the LCPH element 200 increases as the amplitude A of the nonlinear function decreases. For example, when the amplitude A decreases from 36° to 18°, the diffraction efficiency of the LCPH element 200 increases from approximately 65% ​​to approximately 90%. As the amplitude A further decreases, the diffraction efficiency of the LCPH element 200 can further increase. In a conventional R-PVH element 100 with a linear azimuthal variation in the bulk and at the surface 165 (which can be viewed as a special case of a nonlinear variation with an amplitude A of 0°), the diffraction efficiency approaches 98%, as shown by curve 370 .

[0111] in other words, Figure 3C It is shown that by selecting different amplitudes A to configure different nonlinear azimuth changes in the LCPH element 200, the LCPH element 200 can be configured within a predetermined wavelength range (e.g., Figure 3CDifferent diffraction efficiencies can be provided within the visible wavelength range shown in FIG. In some embodiments, by configuring the azimuth angles at different portions (or at different spatial locations) according to different nonlinear functions (each of these nonlinear functions uses a different amplitude A), variations in diffraction efficiency can be introduced in different portions of LCPH element 200. By doing so, the diffracted light output from different portions of LCPH element 200 can have different light intensities. In other words, a specific light intensity variation can be configured for the output side of LCPH element 200.

[0112] For example, when the amplitude A of the nonlinear term is configured to vary in various portions of the LCPH element 200, the LCPH element 200 can provide different diffraction efficiencies to light incident on the various portions with the same AOI. Therefore, the diffracted light output from the various portions of the LCPH element 200 can have the same diffraction angle and different light intensities. In addition, in each portion of the LCPH element 200 configured with a specific amplitude A for the nonlinear term, the diffracted light output from the portion can have a uniform local brightness (or local intensity) angular distribution within the entire FOV. When the amplitude A of the nonlinear term is configured to be constant on the LCPH element 200, the LCPH element 200 can provide the same diffraction efficiency to light incident on the various portions with the same AOI, and the diffracted light output from the various portions of the LCPH element 200 can have the same diffraction angle and the same light intensity.

[0113] Figure 4A and Figure 4B FIG. 4 shows an xz cross-sectional view of an LCPH element 400 according to an embodiment of the present disclosure. The LCPH element 400 may include Figure 2A The LCPH element 200 shown in FIG. 1 includes similar or identical elements. For the description of the same or similar elements or features, reference can be made to the corresponding description above, including the description in conjunction with FIG. Figure 2A The LCPH element 400 may be an R-PVH element or a T-PVH element. An R-PVH element is used as an example of the LCPH element 400. The LCPH element 400 may be configured to substantially back-diffract (e.g., reflect) circularly polarized light having a predetermined handedness and substantially transmit circularly polarized light having a handedness opposite to the predetermined handedness without diffraction or with negligible diffraction.

[0114] For the purpose of discussion, Figure 4A In the embodiment shown in FIG, an R-PVH element serving as an example of an LCPH element 400 is also referred to as 400. Figure 2A, the R-PVH element 400 may include an R-PVH layer 415. LC molecules 212 (not shown) located near a surface 405 of the R-PVH element 400 or the R-PVH layer 415 may be configured to have a nonlinear azimuthal variation along at least one in-plane direction (or in-plane axis) 428 within the surface 405. In some embodiments, the LC molecules 212 (not shown) may also be configured to have a nonlinear azimuthal variation along the helical axis of a helical twisted structure (also referred to as a helical structure) formed within the volume of the R-PVH layer 415. In some embodiments, the LC molecules 212 (not shown) may also be configured to have a linear azimuthal variation along the helical axis of the helical twisted structure (formed within the volume of the R-PVH layer 415).

[0115] exist Figure 4A In the illustrated embodiment, the R-PVH element 400 can be configured to have a predetermined variation in the amplitude A of the nonlinear term (referred to as the amplitude variation of the nonlinear term) along one or more in-plane dimensions (e.g., along the x-axis and / or y-axis within the film plane of the R-PVH element 400). That is, the amplitude A can have different values ​​for the nonlinear azimuthal distribution for different portions along the x-axis and / or y-axis of the R-PVH element 400. In some embodiments, the film plane of the R-PVH element 400 can be parallel to the surface 405 of the R-PVH element 400 and can be perpendicular to the thickness direction of the R-PVH element 400 (e.g., the z-axis). That is, the R-PVH element 400 can be configured to have one or more predetermined 1D or 2D amplitude variations of the nonlinear term within the film plane of the R-PVH element 400.

[0116] Because the diffraction efficiency of the LCPH element 400 varies with the amplitude A of the nonlinear term, the LCPH element 400 can be configured to provide a predetermined diffraction efficiency variation along one or more in-plane dimensions within the film plane of the LCPH element 400. Therefore, when the LCPH element 400 back-diffracts a plurality of lights 401 incident thereon having the same AOI and the same input light intensity, the diffracted lights 402 a to 402 d output from the LCPH element 400 can have a predetermined light intensity variation along one or more in-plane dimensions within the film plane of the LCPH element 400. In some embodiments, the diffracted lights 402 a to 402 d can correspond to a plurality of first-order diffracted lights having the same diffraction angle.

[0117] For example, when the amplitude A of the nonlinear term varies in one direction within the film plane of the LCPH element 400, the LCPH element 400 can provide a 1D diffraction efficiency variation, and the diffracted lights 402a to 402d can have a 1D light intensity variation at the output side of the LCPH element 400. When the amplitude A of the nonlinear term varies in two directions within the film plane of the LCPH element 400, the LCPH element 400 can provide a 2D diffraction efficiency variation, and the diffracted lights 402a to 402d can have a 2D light intensity variation at the output side of the LCPH element 400.

[0118] For the purposes of discussion, in LCPH element 400, it is assumed that the amplitude A of the nonlinear term has a 1D variation along the x-axis, that is, the amplitude A decreases monotonically in the +x-axis direction. The monotonous manner can be a linear gradient, a nonlinear gradient, a step gradient, or a suitable combination thereof. Therefore, the diffraction efficiency provided by LCPH element 400 to the plurality of incident light beams 401 can increase in the +x-axis direction. Assuming that the plurality of incident light beams 401 have the same light intensity and the same AOI, the light intensity of the diffracted light beams 402a to 402d can increase in the +x-axis direction.

[0119] like Figure 4B As shown, when portions M1 and M2 of the LCPH element 400 are configured with different amplitudes A, the LCPH element 400 can provide different diffraction efficiencies for light incident on the different portions M1 and M2. Here, multiple light beams 411, 412, and 413 are incident on portion M1 of the LCPH element 400 at different incident angles and the same light intensity. Portion M1 can be configured with a nonlinear azimuthal angle variation by employing amplitude A1. The LCPH element 400 can diffract (e.g., reflect) the light beams 411, 412, and 413 backward with substantially the same diffraction efficiency R1. Consequently, the diffracted light beams 421, 422, and 423 output from portion M1 of the LCPH element 400 can provide a substantially uniform angular brightness distribution within a predetermined FOV corresponding to the AOI of the incident light beams 411, 412, and 413. The eye 160, located at the output side P1 of the LCPH element 400, can perceive a substantially uniform angular brightness or illumination within the predetermined FOV.

[0120] Another plurality of lights 431, 432, and 433 may be incident on another portion M2 of the LCPH element 400 with different AOIs and the same light intensity (assuming that the light intensity is the same as the light intensity of the lights 411, 412, and 413). The portion M2 may be configured with a nonlinear azimuthal angle variation by employing a different amplitude A2. Thus, the diffraction efficiency provided by the portion M2 may be different from the diffraction efficiency provided by the portion M1. The portion M2 may provide substantially the same diffraction efficiency for the lights 431, 432, and 433. Thus, the diffracted lights 441, 442, and 443 output from the portion M2 of the LCPH element 400 may provide a substantially uniform angular distribution of brightness within a predetermined FOV corresponding to the AOI of the incident lights 431, 432, and 433. The eye 160 located at the output side P2 of the LCPH element 400 may perceive a substantially uniform angular brightness or illumination within the predetermined FOV. For purposes of discussion, Figure 4B , the amplitude A1 at the portion M1 is configured to be greater than the amplitude A2 at the portion M2, and therefore, the brightness perceived at the position P1 is lower than the brightness perceived at the position P2.

[0121] Compared with traditional LCPH elements, the LCPH elements disclosed herein can provide enhanced angular illumination uniformity, configurable 1D or 2D light intensity variation over a large AOI range, small thickness, light weight, compactness, no aperture restrictions, simple manufacturing, etc. The LCPH elements disclosed herein can be implemented in many technical fields. For example, the LCPH elements 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 (NED), head-up displays (HUD), head-mounted displays (HMD), smartphones, laptops, televisions, vehicles, etc.

[0122] Artificial reality systems, such as head-mounted display (“HMD”) or head-up display (“HUD”) systems, typically include a near-eye display (“NED”) system in the form of a headset or a pair of glasses, and can be configured to present content to a user through, for example, an electronic or optical display located within approximately 10 mm to 20 mm in front of the user's eyes. NED systems can display virtual objects or combine images of real objects with virtual objects, such as in VR, AR, or MR applications. For example, in an AR system or MR system, a user can view images of virtual objects (e.g., computer-generated images (“CGI”)) and images of the surrounding environment by looking through, for example, transparent display glasses or lenses. One example of an AR system may include an expanded pupil light guide (or waveguide) display system, in which image light representing the CGI can be coupled into a light guide (or waveguide), propagated within the waveguide, and coupled out of the waveguide at different locations to expand the effective pupil. A diffractive optical element can be disposed on the waveguide to couple the image light into or out of the waveguide by diffraction. Expanded pupil light guide (or waveguide) display systems can potentially provide a glasses form factor, a reasonably large field of view ("FOV"), high transmittance, and a large eyepiece frame.

[0123] In a typical light guide (or waveguide) display system or assembly, a light source assembly can generate image light representing a virtual image. An incoupling grating can couple the image light (referred to as input image light) into the light guide as incoupling image light. The incoupling image light can propagate within the light guide toward an outcoupling grating by total internal reflection ("TIR"). Therefore, the incoupling image light is also referred to as TIR-propagated image light. When the incoupling image light propagates within the light guide by TIR, the incoupling image light can be incident on different portions of the outcoupling grating. The outcoupling grating can couple the incoupling image light out of the light guide at different portions as multiple outcoupling (or output) image lights. In this way, the outcoupling grating can replicate the image light received from the light source assembly to expand the effective pupil of the light guide display assembly. The outcoupling grating can provide uniform or constant diffraction efficiency for the incoupling image light (or predetermined polarization components of the incoupling image light) incident on different portions of the outcoupling grating. Therefore, when different parts of the coupled-in image light are coupled out of the light guide at different parts of the outcoupling grating, the intensity of the coupled-in image light propagating inside the light guide can naturally decrease from one part to another. Therefore, the intensity (or illuminance) of the outcoupled image light can naturally decrease in the pupil expansion direction. Therefore, when an outcoupling grating with uniform diffraction efficiency along the pupil expansion direction is used in a conventional light guide display system, the conventional light guide display system may provide non-uniform illuminance on the output side of the light guide due to the above-mentioned natural decrease in light intensity. In other words, the virtual image perceived by the eye at the output side of the light guide may have spatially varying brightness, where different parts of the virtual image may have different brightness. The non-uniform illuminance provided by a conventional light guide display system is generally uncontrolled. Such uncontrolled non-uniform illuminance may provide a poor visual effect to the user.

[0124] The present disclosure provides devices (eg, optical devices) or light guide display assemblies or systems that include one or more disclosed LCPH elements. Figure 5A An xz cross-sectional view of a light guide display system 500 according to an embodiment of the present disclosure is shown, the light guide display system including the disclosed LCPH with nonlinear azimuthal variation. The light guide display system 500 can be implemented in an artificial reality system for VR, AR and / or MR applications. The disclosed light guide display system 500 can be configured to provide not only a uniform angular distribution of controllable illuminance (or brightness) within a predetermined FOV of the system 500, but also a controllable illuminance (or brightness) distribution along the pupil expansion direction. Depending on the application needs, by configuring different amplitudes A that affect the nonlinear azimuthal variation, the controllable illuminance distribution along the pupil expansion direction can be controlled to be uniform or non-uniform (according to a predetermined distribution, such as a Gaussian distribution).

[0125] like Figure 5AAs shown, the light guide display system 500 may include a light source assembly 505, a light guide 510, and a controller 515. The light source assembly 505 may include a light source 520 and a collimating lens 525. The light guide 510 may be coupled to an incoupling element (or input coupler) 535 and an outcoupling element (or output coupler) 545. The light guide 510 coupled to the incoupling element 535 and the outcoupling element 545 may also be referred to as a light guide image combiner.

[0126] In some embodiments, light source 520 may include a display element (also referred to as 520) including a plurality of pixels (not shown) arranged in a pixel array, wherein adjacent pixels may be separated by, for example, a black matrix. Display element 520 may output image light 529 representing a virtual image (having a predetermined image size associated with the linear size of display element 520) to collimating lens 525. Image light 529 may be a divergent image light including a beam of light. For illustrative purposes, Figure 5A A single ray of image light 529 is shown. Collimating lens 525 can transmit image light 529 as image light 530 having a predetermined input FOV (e.g., α) toward the input side of light guide 510. Collimating lens 525 can transform or convert a linear distribution of pixels in a virtual image formed by image light 529 into an angular distribution of pixels in image light 530 having a predetermined input FOV. Each ray in image light 530 can represent a FOV direction of the input FOV. For illustration purposes, Figure 5A A single ray of image light 530 (eg, a central ray) is shown orthogonally incident on the incoupling element 535 and may represent a single FOV direction of the input FOV (eg, a 0° FOV direction).

[0127] The coupling element 535 can couple the image light 530 into the light guide 510 as coupled-in image light 531, which can propagate within the light guide 510 toward the coupling-out element 545 via total internal reflection ("TIR"). The coupling-out element 545 can couple the coupled-in image light 531 out of the light guide 510 as a plurality of output image lights 532 at different locations (or portions) along the longitudinal or pupil expansion direction (e.g., the x-axis direction) of the light guide 510. Each of the plurality of output image lights 532 can have an output FOV (e.g., represented by an angle α) that is substantially the same as the input FOV. For discussion purposes, Figure 5A Three output image lights 532 are shown, each represented by a single ray (e.g., a central ray). Each output image light 532 can include the same image content as the virtual image displayed on the display element 520. Thus, the light guide 510 coupled with the incoupling element 535 and the outcoupling element 545 can replicate the image light 530 at the output side of the light guide 510 to expand the effective pupil of the system 500.

[0128] For the purpose of discussion, Figure 5A Shown along Figure 5A The pupil is expanded in one dimension along the x-axis. Therefore, the pupil expansion direction is the x-axis. In some embodiments, the system 500 can also provide two-dimensional pupil expansion, such as along Figure 5A For example, in some embodiments, the system 500 may further include a redirecting element (or folding element) 540 coupled to the light guide 510, and the redirecting element 540 is configured to redirect the incoupled image light 531 to an outcoupling element 545. The redirecting element 540 may be configured to expand the input image light 530 in a first direction (e.g., the y-axis direction), and the outcoupling element 545 may be configured to expand the input image light 530 in a second, different direction (e.g., the x-axis direction).

[0129] The plurality of image lights 532 can propagate through a plurality of exit pupils 557 located within an eyebox region 559 of the system 500. The plurality of exit pupils 557 can correspond to a spatial region in which a pupil 558 of the user's eye 160 can be located within the eyebox region 559 of the system 500 to perceive the virtual image. The size of a single exit pupil 557 can be larger than and comparable to the size of the pupil 558. The plurality of exit pupils 557 can be sufficiently spaced apart such that when one of the plurality of exit pupils 557 substantially coincides with the location of the pupil 558, the remaining one or more exit pupils 557 can be located outside the location of the pupil 558 (e.g., fall outside the pupil 558). The light guide 510 and the outcoupling element 545 can also transmit light from the real-world environment (not shown) (referred to as real-world light), combine the real-world light with the output image light 532, and deliver the combined light to the eye 160. Thus, eye 160 can observe a virtual scene that is optically combined with a real-world scene.

[0130] In some embodiments, the outcoupling element 545 may include a grating that couples the image light 531 out of the light guide 510 by diffraction. The grating may include an LCPH element as disclosed herein, for example Figure 4A . The LCPH element 400 shown in FIG. The LC molecules 212 (not shown) included in the outcoupling element 545 can be configured to have a nonlinear azimuthal variation along the helical axis of the helical twist structure formed within the volume of the outcoupling element 545. In addition, the LC molecules 212 (not shown) located near the surface of the outcoupling element 545 can be configured to have a nonlinear azimuthal variation along at least one in-plane direction (or in-plane axis) within the surface of the outcoupling element 545.

[0131] Different portions of the outcoupling element 545 can employ different azimuthal angle variations, A. The amplitude A can vary along one or more in-plane dimensions, such as along the x-axis and / or y-axis within the film plane of the outcoupling element 545. Thus, the outcoupling element 545 can be configured to provide a predetermined diffraction efficiency distribution, such as a predetermined 1D or 2D diffraction efficiency distribution in the xy plane, to image light 531 incident on different portions of the outcoupling element 545 at the same predetermined incident angle, with the same predetermined incident wavelength, and with the same predetermined polarization. For example, the predetermined diffraction efficiency distribution can include different diffraction efficiencies for different portions of the outcoupling element 545. Thus, the outcoupling element 545 can diffract image light 531 incident on different portions of the light guide 510 with different diffraction efficiencies. For example, the diffraction efficiency can increase along the pupil expansion direction, thereby mitigating the natural decrease in intensity of the image light 531 and providing uniform brightness at the output side of the light guide display system 500.

[0132] In order to provide different diffraction efficiencies in different parts of the outcoupling element 545, in some embodiments, the amplitude A of the nonlinear distribution of azimuth angles in the outcoupling element 545 can be configured to be at least Figure 5A The +x axis direction (i.e., pupil expansion direction) in the image changes. The amplitude A of the change can cause the outcoupling element 545 to change at least along Figure 5A In some embodiments, the amplitude A can be selected to decrease in the +x-axis direction, which can increase the diffraction efficiency of the outcoupling element 545 along the +x-axis direction. Therefore, while the intensity of the image light 531 naturally decreases as the image light 531 propagates along the propagation direction or the pupil expansion direction, the output image light 532 output from different parts of the light guide 510 can become uniform due to the increased diffraction efficiency along the propagation direction or the pupil expansion direction. Therefore, the uniformity of the illumination on the output side of the light guide 510 can be enhanced at least along the +x-axis direction (or the pupil expansion direction).

[0133] although Figure 5A It is shown that the outcoupling element 545 can provide uniform illumination in one pupil expansion direction (e.g., the +x-axis direction), but in some embodiments, the outcoupling element 545 can be configured to provide uniform illumination in two pupil expansion directions (e.g., the x-axis direction and the y-axis direction). For example, in some embodiments, the amplitude A can vary in the x-axis direction and the y-axis direction so that the azimuth angle varies nonlinearly in the x-axis direction and the y-axis direction. Therefore, the outcoupling element 545 can provide a first (e.g., non-uniform) 1D diffraction efficiency distribution in the x-axis direction and a second (e.g., non-uniform) 1D diffraction efficiency distribution in the y-axis direction. Therefore, the uniformity of the illumination of the image light 532 on the output side of the light guide 510 can be improved in both the +x-axis direction and the +y-axis direction.

[0134] In some embodiments, the controllable illumination distribution along the pupil expansion direction on the output side of the light guide display system 500 can be controlled to be non-uniform by configuring different amplitudes A at different portions of the outcoupling element 545. For example, the outcoupling element 545 can be configured to diffract image light to an area outside the eyebox area 559 with a relatively small (e.g., negligible) diffraction efficiency, and to diffract image light to an area within the eyebox area 559 with a relatively large diffraction efficiency. Thus, the loss of image light directed to areas outside the eyebox area 559 can be reduced. Consequently, the power consumption of the light source assembly 505 can be significantly reduced, while the power efficiency of the light guide display system 500 can be significantly improved.

[0135] In some embodiments, the redirecting element 540 may be a grating comprising a LCPH element as disclosed herein, e.g. Figure 4A . The LCPH element 400 shown in FIG. LC molecules 212 (not shown) included in the redirecting element 540 can be configured to have a nonlinear azimuthal variation along the helical axis of the helical twist structure formed within the volume of the redirecting element 540. Furthermore, the LC molecules 212 (not shown) located near the surface of the redirecting element 540 can be configured to have a nonlinear azimuthal variation along at least one in-plane direction (or in-plane axis) within the surface of the redirecting element 540.

[0136] In some embodiments, the amplitude A of the nonlinear azimuthal variation can be a constant value at different portions of the redirecting element 540. In some embodiments, the amplitude A of the nonlinear azimuthal variation can be different values ​​at different portions of the redirecting element 540. When using different values ​​of amplitude A, the amplitude A can vary along a first in-plane direction (e.g., the y-axis direction within the film plane of the redirecting element 540). Thus, the redirecting element 540 can be configured to provide a predetermined (e.g., non-uniform) diffraction efficiency distribution, such as a predetermined 1D diffraction efficiency distribution, in the y-axis direction for image light 531 incident on different portions of the redirecting element 540 at the same predetermined incident angle, with the same predetermined incident wavelength, and with the same predetermined polarization. For example, in some embodiments, the diffraction efficiency of different portions of the redirecting element 540 can increase along the +y-axis direction, while the diffraction efficiency of different portions of the outcoupling element 545 can increase along the +x-axis direction. Consequently, the uniformity of the illumination of the image light 532 at the output side of the light guide 510 can be enhanced in both the +x-axis and +y-axis directions.

[0137] In some embodiments, the light guide display system 500 may include a plurality of light guides 510 ( Figure 5A). At least one (e.g., each) of the plurality of light guides 510 can be coupled to or include one or more diffraction elements (e.g., in-coupling elements, out-coupling elements, and / or guiding elements) that can be configured to direct image light 530 toward the eye 160. In some embodiments, the plurality of light guides 510 arranged in a stacked configuration can be configured to output expanded multi-color image light (e.g., full-color image light). In some embodiments, the light guide display system 500 can include one or more light source assemblies 505 and / or one or more light guides 510. In some embodiments, at least one (e.g., each) of the plurality of light source assemblies 505 can be configured to emit monochromatic image light of a specific wavelength band corresponding to a primary color (e.g., red, green, or blue) and a predetermined FOV (or a predetermined portion of the FOV). In some embodiments, the light guide display system 500 may include three distinct light guides 510 configured to deliver component color images (e.g., primary color images) by respectively coupling in and subsequently coupling out, for example, red light, green light, and blue light in any suitable order. In some embodiments, the light guide display assembly 500 may include two distinct light guides configured to deliver component color images (e.g., primary color images) by respectively coupling in and subsequently coupling out, for example, a combination of red and green light and a combination of green and blue light in any suitable order. In some embodiments, at least one (e.g., each) of the plurality of light source assemblies 505 may be configured to emit multi-color image light (e.g., full-color image light).

[0138] Figure 5B FIG. 5 shows a conventional light guide display system 580 including an outcoupling element 585 that provides uniform diffraction efficiency in the x-axis direction. Figure 5B As shown, as image light 531 propagates within light guide 510 via TIR, multiple portions of image light 531 are diffracted out of light guide 510 by outcoupling element 585 at different locations. Consequently, the intensity of image light 531 naturally decreases along the direction of light propagation, as schematically illustrated by the gradually decreasing thickness of lines 530-1, 530-2, and 530-3. Consequently, the intensity (or illuminance) of output lights 542-1, 542-2, and 542-3 output from light guide 510 gradually decreases. Consequently, on the output side of light guide 510, the illuminance along the pupil expansion direction (e.g., the +x-axis direction) is non-uniform.

[0139] According to an embodiment of the present invention, the disclosed LCPH element with nonlinear azimuth angle variation can improve the illumination uniformity of the output image light at the output side of the light guide. Figure 5C Diffraction of image light 531 by the disclosed light guide display system 500 is shown. Figure 5C Shown in Figure 5A In the disclosed light guide display system 500 shown in , the outcoupling element 545 can be configured to have different nonlinear azimuthal angle changes (for example, by adopting different amplitudes A), so that the outcoupling element 545 can provide a diffraction efficiency that gradually increases along the x-axis direction. For example, in the three exemplary parts N1, N2 and N3 of the outcoupling element 545, the amplitude A of the nonlinear azimuthal angle change can gradually increase. Therefore, the diffraction efficiency of the outcoupling element 545 can gradually decrease. Therefore, at part N1 where the intensity of the image light 531 is the largest, the diffraction efficiency can be the smallest. At part N2, the intensity of the image light 531 can be lower than the intensity at part N1. Therefore, the diffraction efficiency at part N2 can be higher than the diffraction efficiency at part N1. At part N3, the intensity of the image light 531 can be further reduced. Therefore, compared with the diffraction efficiency at part N2, the diffraction efficiency at part N3 can be further increased. Therefore, the diffraction efficiency at part N3 can be the highest. Since different diffraction efficiencies are provided in different parts of the outcoupling element 545, Figure 5B Compared to the conventional configuration shown in , the illuminance (or intensity) of the output image lights 532 - 1 , 532 - 2 , and 532 - 3 on the output side of the light guide 510 may become more uniform.

[0140] exist Figure 5C In the embodiment of the present invention, it is assumed that the diffraction efficiency of the outcoupling element 545 varies in one dimension. It is understood that the diffraction efficiency of the outcoupling element 545 can vary in two dimensions, namely, the x-axis and the y-axis. The outcoupling element 545 can have any suitable diffraction efficiency distribution in one or two dimensions.

[0141] Figure 5D The diffraction of two image lights 530-1 and 530-2 by the disclosed light guide display system 500 is shown. The two image lights 530-1 and 530-2 can represent the leftmost and rightmost portions of the input FOV of the system 500. The two image lights 530-1 and 530-2 can have different incident angles at the coupling element 535 and can be coupled into the light guide 510 as image lights 531-1 and 531-2, respectively. The image lights 531-1 and 531-2 can have different TIR angles. For the same image light 531-1 or 531-2 propagating along the light guide 510, the diffraction efficiency provided by the coupling element 545 at different positions can vary (e.g., increase) in the +x-axis direction. That is, for the same image light 531-1 or 531-2 propagating along the light guide 510, the diffraction efficiency at different portions of the coupling element 545 can be different.

[0142] At the same portion N1, N2, or N3 of the outcoupling element 545, the outcoupling element 545 can provide substantially the same diffraction efficiency for different image lights 531-1 and 531-2 (having different incident angles, the same incident wavelength, and the same polarization). Therefore, the output image light 532-1, 532-2, or 532-3 diffracted from the same portion N1, N2, or N3 of the outcoupling element 545 can have improved angular illumination uniformity across the entire output FOV associated with the input FOV. As a result, the eye 160 located at the eyebox 559 can perceive substantially uniform brightness or illumination across the entire output FOV associated with the input FOV.

[0143] Figure 6A A schematic diagram of an artificial reality device 600 according to an embodiment of the present disclosure is shown. In some embodiments, the artificial reality device 600 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 600 can be smart glasses. In one embodiment, the artificial reality device 600 can be a near-eye display ("NED"). In some embodiments, the artificial reality device 600 can be in the form of glasses, goggles, a helmet, a visor, or other type of eye-mounted device. In some embodiments, the artificial reality device 600 can be configured to be worn on the user's head (e.g., by having the form of spectacles or eyeglasses, such as Figure 6A ), or included as part of a helmet worn by the user. In some embodiments, the artificial reality device 600 may be configured to be placed in a fixed position near and in front of one or both of the user's eyes, rather than being mounted on the user's head. In some embodiments, the artificial reality device 600 may be in the form of glasses that provide vision correction for the user's vision. In some embodiments, the artificial reality device 600 may be in the form of sunglasses that protect the user's eyes from bright sunlight. In some embodiments, the artificial reality device 600 may be in the form of safety glasses that protect the user's eyes. In some embodiments, the artificial reality device 600 may be in the form of night vision devices or infrared goggles for enhancing the user's vision at night.

[0144] For the purpose of discussion, Figure 6A The artificial reality device 600 is shown to include a frame 605 configured to be mounted to a user's head, and a left-eye display system 610L and a right-eye display system 610R mounted to the frame 605. Figure 6B According to an embodiment of the present disclosure Figure 6A . For discussion purposes, Figure 6BA cross-sectional view associated with left-eye display system 610L is shown. Frame 605 is merely an example structure to which various components of artificial reality device 600 may be mounted. Other suitable types of fixtures may be used in place of or in combination with frame 605.

[0145] In some embodiments, the left-eye display system 610L and the right-eye display system 610R may each include suitable image display components configured to generate image light representing a virtual image. In some embodiments, the left-eye display system 610L and the right-eye display system 610R may each include suitable optical components configured to direct the image light toward the eyebox area 559. For example, in some embodiments, the left-eye display system 610L and the right-eye display system 610R may each include a light guide display system, such as Figure 5A System 500 is shown.

[0146] In some embodiments, the artificial reality device 600 may further include a viewing optical system 624 disposed between the left-eye display system 610L or the right-eye display system 610R and the eyebox area 559. The viewing optical system 624 may be configured to guide image light (representing a computer-generated virtual image) output from the left-eye display system 610L or the right-eye display system 610R to propagate through one or more exit pupils 557 within the eyebox area 559. In some embodiments, the viewing optical system 624 may also be configured to perform appropriate optical adjustments on the image light output from the left-eye display system 610L or the right-eye display system 610R, for example, correcting aberrations in the image light, adjusting the position of the focus of the image light in the eyebox area 559, and the like.

[0147] In some embodiments, as Figure 6B As shown, the artificial reality device 600 may further include an object tracking system 650 (e.g., an eye tracking system and / or a face tracking system). The object tracking system 650 may include an IR light source 651 configured to illuminate an eye 660 and / or a face, a light deflection element 652 configured to deflect the IR light reflected by the eye 660, and an optical sensor 655 configured to receive the IR light deflected by the deflection element 652 and generate a tracking signal. A controller (e.g., similar to Figure 5A The controller 515 shown in FIG) may be included in the artificial reality device 600.

[0148] The present disclosure also provides methods of fabricating LCPH elements or devices having nonlinear azimuthal angle variations. 7A to 7F The figure schematically illustrates a process of manufacturing an LCPH element with nonlinear azimuthal angle variation according to an embodiment of the present disclosure. 7A to 7FThe manufacturing process shown in FIG can include holographically recording an alignment pattern in a photo-alignment film and aligning molecules of an anisotropic material (e.g., LC material) via 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 purposes of discussion, the substrate and various layers, films, or structures formed thereon are shown as having flat surfaces. In some embodiments, the substrate and various layers, films, or structures can have curved surfaces.

[0149] like Figure 7A As shown, a recording medium layer 710 can be formed on a surface (e.g., top surface) of the substrate 705 by distributing (e.g., coating, printing, or depositing) a polarization-sensitive material on the surface of the substrate 705. The recording medium layer 710 may include a polarization-sensitive material, which is an optically recordable and polarization-sensitive material (e.g., a photo-aligned material) that is configured to have light-induced optical anisotropy when exposed to polarized light. The molecules (or fragments) and / or photoproducts of the polarization-sensitive material can be configured to produce orientational order under polarized light irradiation. In some embodiments, the polarization-sensitive material can be dissolved in a solvent to form a solution. The solution can be applied to the substrate 705 using any suitable solution coating process, such as spin coating, slit coating, doctor blade coating, spray coating, or jet (inkjet) coating or printing. The solvent may be removed from the applied solution using a suitable process (eg, drying or heating), thereby leaving the polarization-sensitive material on the substrate 705 to form the recording medium layer 710 .

[0150] After forming the recording medium layer 710 on the substrate 705, as shown in FIG. Figure 7B As shown, the recording medium layer 710 may be exposed to a polarization interference pattern (eg, more than two recording beams) generated based on a plurality of recording beams 721 to 724 (eg, more than two recording beams). Figure 7C 720 shown in FIG). The recording beams 721 to 724 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 7B Four recording beams 721 to 724 are shown for generating polarization interference patterns, for example, two right circularly polarized beams 721 and 722 and two left circularly polarized beams 723 and 724. In some embodiments, although not shown, three recording beams, five recording beams, etc. may be used to generate polarization interference patterns.

[0151] The recording light beams 721 to 724 may have wavelengths within the absorption band of the recording medium layer 710, such as ultraviolet ("UV") light beams, violet light beams, blue light beams, or green light beams. In some embodiments, the recording light beams 721 to 724 may be laser beams, such as UV laser beams, violet laser beams, blue laser beams, or green laser beams. In some embodiments, the superposition of the recording light beams 721 to 724 may result in 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 the spatial region where the recording light beams 721 to 724 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 721 to 724 interfere with each other.

[0152] The superposition of the recording beams 721 to 724 can produce a Figure 2C The polarization interference pattern 720 is shown. The polarization interference pattern 720 can also be referred to as a pattern of spatially varying orientations (or polarization directions) of the linear polarization of the superimposed waves, or a pattern of varying linear polarization of the superimposed waves. Figure 7C As shown, the orientation (or polarization direction) of the linear polarization can be periodically or non-periodically changed along at least one in-plane direction 728 within the surface of the recording medium layer 710 with a pitch of P O In some embodiments, the pitch P of the polarization interference pattern 720 is O The distance along the in-plane direction 728 over which the orientation (or polarization direction) of the linear polarization is rotated by 180° may be referred to as the distance along which the in-plane direction 728 (or polarization direction) is rotated by 180°. Figure 7C It is shown that in the polarization interference pattern 720, the orientations (or polarization directions) of the linear polarizations are arranged at a constant pitch P along the in-plane direction 728. O Changes periodically.

[0153] In some embodiments, the angles between the recording beams 721 to 724 can be configured so that the polarization interference pattern 720 has a single pitch P. O The orientation (or polarization direction) of the linear polarization can be configured to rotate in a predetermined nonlinear manner along the in-plane direction 728. For example, in a single pitch P of the polarization interference pattern 720 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 728 can be configured to vary in a predetermined nonlinear manner (or according to a predetermined nonlinear function) along the in-plane direction 728. For the purpose of discussion, the polarization interference pattern 720 can be referred to as a nonlinear polarization interference pattern 720.

[0154] In some embodiments, the nonlinear polarization interference pattern 720 can be generated by superposition of the following: a first linear polarization interference pattern generated based on the right-handed circularly polarized recording beam 721 and the left-handed circularly polarized recording beam 723; and a second linear polarization interference pattern generated based on the right-handed circularly polarized recording beam 722 and the left-handed circularly polarized recording beam 724. For example, referring to Figure 7B , the right-handed circularly polarized recording beam 721 and the left-handed circularly polarized recording beam 723 can interfere with each other to generate a first linear polarization interference pattern having a first pitch P1 in the in-plane direction 728. At a single first pitch P1 of the first linear polarization interference pattern, the angle of the orientation of the linear polarization relative to the in-plane direction 728 (or polarization direction) can be configured to vary along the in-plane direction 728 in a first predetermined linear manner (or according to a first predetermined linear function). In addition, the right-handed circularly polarized recording beam 722 and the left-handed circularly polarized recording beam 724 can interfere with each other to generate a second linear polarization interference pattern having a second pitch P2 in the in-plane direction 728. At a single second pitch P2 of the second linear polarization interference pattern, the angle of the orientation of the linear polarization (or polarization direction) relative to the in-plane direction 728 can be configured to vary along the in-plane direction 728 in a second predetermined linear manner (or according to a second predetermined linear function).

[0155] In some embodiments, the first angle formed between the right-handed circularly polarized recording beam 721 and the left-handed circularly polarized recording beam 723 can be configured to be different from the second angle formed between the right-handed circularly polarized recording beam 722 and the left-handed circularly polarized recording beam 724. 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 the following: Figure 7C Nonlinear polarization interference pattern 720 is shown.

[0156] refer to Figure 7B and Figure 7CWhen the recording medium layer 710 is exposed to a polarized interference pattern 720 generated based on recording light beams 721 to 724 during a polarized interference exposure process, the recording medium layer 710 can be optically patterned. The orientation pattern of the optical axis of the recording medium layer 710 can be defined by the polarized interference pattern 720. In some embodiments, the recording medium layer 710 can include extended anisotropic photosensitive units (e.g., fragments of small molecules or polymer molecules). After sufficient exposure to the polarized interference pattern 720, the polarized interference pattern 720 can induce a local alignment direction of the anisotropic photosensitive units in the recording medium layer 710, thereby causing an alignment pattern (or in-plane modulation) of the optical axis of the recording medium layer 710 due to the optical alignment of the anisotropic photosensitive units. After the recording medium layer 710 is optically patterned under the polarized interference pattern 720, the recording medium layer 710 can be referred to as a patterned recording medium layer having an alignment pattern.

[0157] like Figure 7D As shown, after forming the patterned recording medium layer 710, a first optically anisotropic film 715a can be formed on the patterned recording medium layer 710 by dispensing a birefringent medium on the patterned recording medium layer 710. For example, the birefringent medium can be dissolved in a solvent to form a solution. An appropriate amount of the solution can be dispensed (e.g., by coating, printing, or spraying) on ​​the patterned recording medium layer 710 to form the first optically anisotropic film 715a. In some embodiments, the solution containing the birefringent medium can be dispensed on the patterned recording medium layer 710 using a suitable process, such as spin coating, slit coating, doctor blade coating, spray coating, or inkjet coating or printing.

[0158] The birefringent medium may include a host birefringent material having intrinsic birefringence, such as 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 helically twisted 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.

[0159] The patterned recording medium layer 710 can be configured to provide surface alignment to the LC molecules in the first optically anisotropic film 715a, at least partially aligning the LC molecules near the patterned recording medium layer 710 in a predetermined non-uniform in-plane alignment pattern. For example, the LC molecules near the patterned recording medium layer 710 can be at least partially aligned along the local alignment direction of the anisotropic photosensitive elements in the patterned recording medium layer 710 to form a predetermined non-uniform in-plane alignment pattern. Thus, the alignment pattern recorded in the patterned recording medium layer 710 (or the in-plane alignment pattern of the optical axis of the recording medium layer 710) can be transferred to the LC molecules near the patterned recording medium layer 710. Consequently, the LC molecules near the patterned recording medium layer 710 can exhibit a nonlinear azimuthal variation along the in-plane direction 728. The patterned recording medium layer 710 can act as a photo-alignment material (PAM) layer for the LC molecules near the patterned recording medium layer 710. This alignment process can be referred to as surface-mediated photo-alignment.

[0160] like Figure 7E As shown, after forming a first optical anisotropic film 715a on the patterned recording medium layer 710, a second optical anisotropic film 715b may be formed on the first optical anisotropic film 715a. The first optical anisotropic film 715a and the second optical anisotropic film 715b may be made based on similar birefringent media, which include a host birefringent material and a chiral dopant. Figure 7D and Figure 7E The chiral dopant contained in the optically anisotropic film 715a or 715b may have a helical twisting power (HTP) (unit: μm -1 ), which 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 helical pitch P of the helical twist structure formed in the optically anisotropic film 715a or 715b is h The helical pitch P of the helical twist structure formed in the optically anisotropic film 715a or 715b 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 can be 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, a larger HTP of the chiral dopant can cause a shorter helical pitch P of the helical twist structure. hWhen the HTP of the chiral dopant is constant, a larger weight concentration (or mole fraction) of the chiral dopant in the host birefringent material can induce a short helical pitch P of the helical twist structure. h .

[0161] In some embodiments, the chiral dopants included in the first optically anisotropic film 715a and the second optically anisotropic film 715b may be configured to have a difference in at least one of HTP or weight concentration, so that the helical twisted structures formed in the first optically anisotropic film 715a and the second optically anisotropic film 715b may have different helical pitches P. h In some embodiments, when the first optically anisotropic film 715a and the second optically anisotropic film 715b are manufactured to have the same predetermined thickness, due to the spiral pitch P h Due to the difference in thickness, the first optically anisotropic film 715a and the second optically anisotropic film 715b may exhibit different amounts of changes in the azimuth angles of the LC molecules at the same predetermined thickness.

[0162] For example, reference Figure 2H and Figure 7E , the first optical anisotropic film 715a and the second optical anisotropic film 715b may be manufactured to have the same predetermined thickness of 0.25*P B μm. The azimuth angle of the LC molecules in the first optically anisotropic film 715a may vary from 0° to 63° along the helical axis from the lower surface of the first optically anisotropic film 715a to the interface between the first and second optically anisotropic films 715b. The azimuth angle of the LC molecules in the first optically anisotropic film 715a may vary from 63° to 90° along the helical axis from the interface between the first and second optically anisotropic films 715a, 715b to the upper surface of the second optically anisotropic film 715b.

[0163] For the purpose of discussion, Figure 7E Only two optically anisotropic films 715a and 715b are shown; additional optically anisotropic films may be formed continuously on the second optically anisotropic film 715b. For example, the azimuth angle of the LC molecules in the third optically anisotropic film may 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 may be configured to vary from 117° to 180° along the helical axis, and so on. Multiple optically anisotropic films may form an optically anisotropic layer, within which a nonlinear azimuth angle variation of the LC molecules may be established.

[0164] In some embodiments, as Figure 7FAs shown, the first and second optically anisotropic films 715a, 715b can be exposed to polymerizing radiation 744 to form a polymerized optically anisotropic layer 729, thereby stabilizing the nonlinear azimuthal angle variation. In some embodiments, the exposure of the first and second optically anisotropic films 715a, 715b to the polymerizing radiation 744 can be performed in air; an inert atmosphere formed, for example, by nitrogen, argon, or carbon dioxide; or a vacuum. The polymerizing radiation 744 can have a wavelength within the absorption band of the photoinitiator, thereby activating the photoinitiator to produce a polymerization-initiating species. In some embodiments, the polymerizing radiation 744 can be ultraviolet ("UV") radiation.

[0165] For example, Figure 7F As shown, the first optically anisotropic film 715a and the second optically anisotropic film 715b can be exposed to a UV beam (also referred to as 744 for discussion purposes). Upon sufficient exposure to the UV beam 744, the birefringent material (e.g., RM monomer) in the first and second optically anisotropic films 715a, 715b 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 715a can first be exposed to polymerizing radiation 744 to form a first polymerized optically anisotropic film. Then, the second optically anisotropic film 715b can be formed on the first polymerized optically anisotropic film and exposed to polymerizing radiation 744 to form a second polymerized optically anisotropic film.

[0166] Figure 7F Also shown is an xz view of an LCPH element 700 including a polymeric optically anisotropic layer 729. The LCPH element 700 may be a PVH element, and the polymeric optically anisotropic layer 729 may be a PVH layer, such as a PVH layer similar to Figure 2A . In some embodiments, the substrate 705 and / or the alignment structure 710 can be used to manufacture, store, or transport the manufactured LCPH element 700. In some embodiments, the substrate 705 and / or the alignment structure 710 can be separated or removed from the manufactured LCPH element 700 after the LCPH element 700 is manufactured or transported to another location or device. That is, the substrate 705 and / or the alignment structure 710 can be used during manufacturing, transportation, and / or storage to support the LCPH element 700 disposed thereon, and when the LCPH element 700 is manufactured, or when the LCPH element 700 is to be implemented in an optical device, the substrate 105 and / or the alignment structure 710 can be separated or removed from the LCPH element 700. In some embodiments, the substrate 705 and / or the alignment structure 710 may not be separated from the LCPH element 700.

[0167] Figure 8A and Figure 8B Schematically illustrates a process for manufacturing an LCPH element with nonlinear azimuthal angle variation according to an embodiment of the present disclosure. Figure 8A and Figure 8B The fabrication process shown in can include holographic recording and volume-mediated photoalignment (also called volume recording). Figure 8A and Figure 8B The manufacturing process shown in the 7A to 7F Similar steps are shown in . Figure 8A and Figure 8B The LCPH components manufactured by the process shown may include similar 7A to 7F The components of the LCPH component manufactured by the process shown in FIG. The description of similar steps and similar components, structures or functions can refer to the above combined 7A to 7F Although the substrate and layers are shown as having flat surfaces, in some embodiments, the substrate and layers formed thereon may include curved surfaces.

[0168] and Figure 7A and Figure 7B Similar to the embodiment shown in, Figure 8A and Figure 8B The process shown in can include dispensing (e.g., coating, depositing, etc.) a recording medium on a surface (e.g., top surface) of a substrate 705 to form a recording medium layer 810. The recording medium can be a polarization-sensitive recording medium. The recording medium can include an optically recordable and polarization-sensitive material (e.g., a photo-aligned material) that is configured to have light-induced optical anisotropy when exposed to polarized light irradiation. Under polarized light irradiation, molecules (or fragments) and / or photoproducts of the optically recordable and polarization-sensitive material can produce an anisotropic angular distribution in the film plane of the recording medium layer. In some embodiments, the recording medium can include or be mixed with other components, such as a solvent in which the optically recordable and polarization-sensitive material can be dissolved to form a solution, and a photosensitizer. The solution can be dispensed on the substrate 705 using a suitable process, such as spin coating, slit coating, doctor blade coating, spray coating, or jet (inkjet) coating or printing. The solvent may be removed from the applied solution using a suitable process (eg, drying or heating), thereby leaving the recording medium on the substrate 705 .

[0169] like Figure 8BAs shown, after forming a recording medium layer 810 on a substrate 705, the recording medium layer 810 can be exposed to a polarization interference pattern generated based on four recording light beams 721 to 724. 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, the recording medium layer 810 can be optically patterned. The polarization interference pattern can be used to define the orientation pattern of the optical axis of the recording medium layer 810 in the exposure area.

[0170] exist Figure 8A and Figure 8B In the embodiment shown in , 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 polymer backbone or polymer side chains. During the polarization interference exposure process of the recording medium layer 810, the photoalignment of the polarization-sensitive photoreactive groups may be performed within the volume of the recording medium layer 810 (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 721 to 724 can be directly recorded within the volume of the recording medium layer 810 (or in the volume, inside the volume). Figure 8A and Figure 8B In the embodiment shown in , the 3D orientation pattern of the optical axis can be directly recorded in the recording medium layer 810 by bulk-mediated photoalignment in the exposed area. The step of providing an additional optically anisotropic layer on the patterned recording medium layer 810 can be omitted. The patterned recording medium layer 810 can serve as the LCPH element 800.

[0171] Figure 8B The alignment process shown can be called bulk-mediated photoalignment. Figure 8B The bulk-mediated photoaligned recording medium layer 810 shown can be compared to 7A to 7F The surface-mediated photoalignment recording medium layer 710 shown in FIG is relatively thicker. Figure 8B The recording medium having the bulk-mediated photoaligned recording medium layer 810 shown in FIG. 8 is referred to as a volume recording medium or bulk PAM.

[0172] In some embodiments, the photosensitive polymer included in the recording medium layer 810 may include an amorphous polymer or an LC polymer, etc. The molecules of the photosensitive polymer may include one or more polarization-sensitive photoreactive groups embedded in the polymer backbone or polymer side chains. In some embodiments, the polarization-sensitive photoreactive groups may include azobenzene groups, cinnamate groups, or coumarin groups, etc. 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., light-induced) 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 light-induced optical anisotropy. In some embodiments, the photosensitive polymer may be an LC polymer having polarization-sensitive cinnamate groups embedded in polymer side chains. In some embodiments, when the recording medium layer 810 includes an LC polymer, the patterned recording medium layer 810 may be heat-treated (e.g., annealed) within a temperature range corresponding to the liquid crystal state of the LC polymer to enhance the light-induced optical anisotropy ( Figure 8B not shown).

[0173] Figures 9A to 9C Schematically illustrates a process for fabricating an LCPH element with nonlinear azimuthal angle variation according to an embodiment of the present disclosure. Figures 9A to 9C The fabrication process shown in can include holographic recording and surface-mediated photoalignment. Figures 9A to 9C The manufacturing process shown in the figure may include 7A to 7F Similar steps are shown in . Figures 9A to 9C The LCPH components manufactured by the process shown may include 7A to 7F 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 7A to 7F Although the substrate and layers are shown as having flat surfaces, in some embodiments, the substrate and layers formed thereon may include curved surfaces.

[0174] and Figure 7A and Figure 7B Similar to the embodiment shown in, Figure 9A The process shown in FIG. 7 may include dispensing (e.g., coating, depositing, etc.) a recording medium on a surface (e.g., top surface) of a substrate 705 to form a recording medium layer 710. The recording medium layer 710 may be exposed to a nonlinear polarization interference pattern generated based on a plurality of recording beams 921 to 923. The recording beams 921 to 923 may be similar to Figure 7BFor example, the recording beams 921 to 923 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. Figure 9A Three recording beams 921 to 923 are shown for generating a nonlinear polarization interference pattern, for example, two right-handed circularly polarized beams 921 and 922 and one left-handed circularly polarized beam 923. In some embodiments, although not shown, four recording beams, five recording beams, etc., may be used to generate a nonlinear polarization interference pattern.

[0175] In some embodiments, the nonlinear polarization interference pattern generated based on the recording beams 921 to 923 can be generated by superposition of the following: a first linear polarization interference pattern generated based on the right-handed circularly polarized recording beam 921 and the left-handed circularly polarized recording beam 923; and a second linear polarization interference pattern generated based on the right-handed circularly polarized recording beam 922 and the left-handed circularly polarized recording beam 923. For example, referring to Figure 7B , the right-handed circularly polarized recording beam 921 and the left-handed circularly polarized recording beam 923 can interfere with each other to generate a first linear polarization interference pattern having a first pitch P1 in the in-plane direction 728. At a single first pitch P1 of the first linear polarization interference pattern, the angle of the orientation of the linear polarization relative to the in-plane direction 728 (or polarization direction) can be configured to vary along the in-plane direction 728 in a first predetermined linear manner (or according to a first predetermined linear function). In addition, the right-handed circularly polarized recording beam 922 and the left-handed circularly polarized recording beam 923 can interfere with each other to generate a second linear polarization interference pattern having a second pitch P2 in the in-plane direction 728. At a single second pitch P2 of the second linear polarization interference pattern, the angle of the orientation of the linear polarization (or polarization direction) relative to the in-plane direction 728 can be configured to vary along the in-plane direction 728 in a second predetermined linear manner (or according to a second predetermined linear function).

[0176] In some embodiments, the first angle formed between right-handed circularly polarized recording beam 921 and left-handed circularly polarized recording beam 923 can be configured to be different from the second angle formed between right-handed circularly polarized recording beam 922 and left-handed circularly polarized recording beam 923. 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.

[0177] and Figure 7D The process is similar to that shown in Figure 9BThe process shown in FIG. 7 may include forming an optically anisotropic layer 915 on the patterned recording medium layer 710 by dispensing a birefringent medium onto the patterned recording medium layer 710. The birefringent medium forming the optically anisotropic layer 915 may be the same as the birefringent medium forming the patterned recording medium layer 710. Figure 7D The birefringent medium of the optically anisotropic film 715a shown in FIG. For example, the birefringent medium may include a host birefringent material having intrinsic birefringence (e.g., a non-polymerizable LC or a polymerizable LC (e.g., RM)) and a photoresponsive chiral dopant 902. The patterned recording medium layer 710 may be configured to provide surface alignment to the LC molecules in the optically anisotropic layer 915. As a result, the LC molecules located near the patterned recording medium layer 710 may exhibit a nonlinear azimuthal angle variation along the in-plane direction 728.

[0178] The photo-responsive chiral dopant 902 can distort the LC molecules in the host birefringent material to form a helically twisted structure. Due to the photoisomerization of the photo-responsive chiral dopant 902, the photoresponsive chiral dopant 902 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 902 changes, the HTP of the photoresponsive chiral dopant 902 can change (e.g., increase, decrease, or reverse handedness). In some embodiments, the photoisomerization of the photoresponsive chiral dopant 902 can be reversible. Light irradiation that changes the HTP of the photoresponsive chiral dopant 902 (or to which the photoresponsive chiral dopant 902 is sensitive) can be referred to as stimulating irradiation.

[0179] The stimulating irradiation may only activate the stimuli-responsive chiral dopant 902 to change the HTP, and may not activate the photoinitiator (if the photoinitiator is contained in the birefringent medium) to produce a polymerization-initiating species. Depending on the type of photoresponsive chiral dopant, 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. In some embodiments, the photoresponsive chiral dopant 902 may undergo different degrees of photoisomerization in response to stimulating irradiation having different light intensities. In some embodiments, the photoresponsive chiral dopant 902 may include azobenzene, diarylethene transition olefin, spirooxazine, fulgide, α-unsaturated ketone, β-unsaturated ketone, naphthopyran, or a combination thereof.

[0180] like Figure 9BAs shown, the optically anisotropic layer 915 can be exposed to an intensity interference pattern generated based on two recording beams 951 and 952. The recording beams 951 and 952 can be coherent polarized beams having the same polarization. For example, the recording beams 951 and 952 can be two linearly polarized beams having the same linear polarization direction, or two circularly polarized beams having the same handedness. The recording beams 951 and 952 can have a wavelength range to which the photoresponsive chiral dopant 902 is sensitive. In some embodiments, within the spatial region where the recording beams 951 and 952 interfere with each other, the interference of the recording beams 951 and 952 can generate an intensity interference pattern having a spatially constant polarization and a spatially varying intensity. In other words, the intensity interference pattern can exhibit a 3D intensity variation within the spatial region where the recording beams 951 and 952 interfere with each other. The intensity interference pattern having a 3D intensity variation can serve as a stimulating illumination for the photoresponsive chiral dopant 902.

[0181] During exposure to the intensity interference pattern of the optically anisotropic layer 915, the photoresponsive chiral dopant 902 distributed within the volume of the optically anisotropic layer 915 may undergo varying degrees of photoisomerization in response to the intensity interference pattern having a 3D intensity variation, thereby causing a variation in the 3D helical twisting force of the photoresponsive chiral dopant 902 within the volume of the optically anisotropic layer 915. Assuming a constant weight concentration of the photoresponsive chiral dopant 902 across the optically anisotropic layer 915, the variation in the 3D helical twisting force of the photoresponsive chiral dopant 902 may cause a variation in the 3D helical pitch of the helical twisted structure within the volume of the optically anisotropic layer 915. In some embodiments, by configuring the two recording beams 951 and 952, the variation in the 3D helical pitch of the helical twisted structure within the volume of the optically anisotropic layer 915 may be configured, which may induce a predetermined nonlinear azimuthal variation in the LC molecules along the helical axis of the helical twisted structure.

[0182] In some embodiments, as Figure 9C As shown, after the intensity interference pattern exposure, the optically anisotropic layer 915 can be exposed to polymerizing radiation 744 to form a polymerized optically anisotropic layer 929, thereby stabilizing the nonlinear azimuthal angle variation. Figure 9B and Figure 9C, the polymerization radiation 744 may be different from the stimulation radiation generated by the recording light beams 951 and 952. The stimulation radiation may only activate the photoresponsive chiral dopant 902 to change its HTP, but may not activate the photoinitiator to produce a polymerization-initiating species. 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 915. The polymerization radiation 744 may only activate the photoinitiator to produce a polymerization-initiating species, and may not activate the photoresponsive chiral dopant 902 to change its HTP. That is, the photoresponsive chiral dopant 902 may not respond to the polymerization radiation, and the polymerization radiation may not change the HTP of the photoresponsive chiral dopant 902.

[0183] Figure 10A and Figure 10B is a flow chart illustrating various methods for fabricating an LCPH element with nonlinear azimuthal angle variation according to various embodiments of the present disclosure. Figure 10A FIG. 1 is a flow chart illustrating a method 1000 for fabricating an LCPH element with nonlinear azimuthal angle variation according to an embodiment of the present disclosure. Figure 10A As shown, method 1000 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 1010). Method 1000 may also include exposing a polarization-sensitive recording medium to the polarization interference pattern, wherein optically anisotropic molecules in the polarization-sensitive recording medium that has been exposed to the polarization interference pattern form an in-plane alignment pattern (step 1015). In some embodiments, within an in-plane spacing of the in-plane alignment pattern, the azimuthal angle of the optically anisotropic molecules varies nonlinearly along a predetermined in-plane direction of the in-plane alignment pattern.

[0184] 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-aligned 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-aligned material.

[0185] Figure 10B1030 is a flow chart illustrating a method 1030 for fabricating an LCPH element with nonlinear azimuthal angle variation according to an embodiment of the present disclosure. Method 1030 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 1035). Method 1030 may also include exposing a polarization-sensitive recording medium to the polarization interference pattern (step 1040). Method 1030 may also include forming an optically anisotropic film on the polarization-sensitive recording medium exposed to the polarization interference pattern, wherein the optically anisotropic film includes a mixture of a host birefringent material and a chiral dopant (step 1045).

[0186] 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 in the first mixture may have a first helical twisting force and a first weight concentration. Method 1030 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 in the second mixture may have a second helical twisting force and a second weight concentration. The first chiral dopant and the second chiral dopant may be configured to have at least one difference between: a first helical twisting force and a second helical twisting force; or a first weight concentration and a second weight concentration. In some embodiments, method 1030 may also include exposing the first and second optically anisotropic films to polymerizing radiation.

[0187] In some embodiments, the chiral dopant may include a photoresponsive chiral dopant, and the plurality of polarized light beams may be a first plurality of polarized light beams. Method 1030 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 generate an intensity interference pattern within the spatial region where the optically anisotropic film is disposed. Method 1030 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.

[0188] In some embodiments, the present disclosure provides a device. The device includes: a light guide configured to provide total internal reflection for a first light propagating in the light guide; and an optical film coupled to the light guide, wherein the azimuth angles of the optically anisotropic molecules in the optical film are configured to change nonlinearly along the helical axis of the helical structure formed in the optical film. The optical film is configured to reflect the first light from multiple positions of the optical film into multiple second lights at multiple different reflection efficiencies. In some embodiments, in the optical film, on the helical pitch of the helical structure, the azimuth angles of the optically anisotropic molecules vary according to the amplitude parameter A, the Bragg period P of the optical film, and the amplitude parameter A. B The position of the optically anisotropic molecule along the helical axis varies as a nonlinear function of the distance z from the starting point of the helical pitch, and the amplitude parameter A is configured to have a plurality of different values ​​at a plurality of positions of the optical film.

[0189] In some embodiments, in an optical film, the azimuth angle of an optically anisotropic molecule at the helical pitch of the helical structure is configured 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 molecule is located. The helical pitch is the distance along the helical axis over which the azimuth angle of the optically anisotropic molecule varies by a predetermined value. In some embodiments, at the helical pitch of the helical structure, the azimuth angle of the optically anisotropic molecule at the starting point of the helical pitch is zero degrees, and the predetermined value associated with the helical pitch is 180 degrees. In some embodiments, at the helical pitch of the helical structure, the azimuth angle of the optically anisotropic molecule varies according to the following function: 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 along the helical axis where the optically anisotropic molecule is located, and 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°. In some embodiments, the nonlinear function for And the function for In some embodiments, the plurality of second lights output from the plurality of positions of the optical film are distributed along the pupil expansion direction of the device, and the amplitude parameter A of the nonlinear function is configured to decrease along the pupil expansion direction of the device.

[0190] In some embodiments, the optical film includes a reflective polarizer hologram layer, and the optically anisotropic molecules located near 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, where the in-plane spacing is defined as the distance along the predetermined in-plane direction over which the azimuth angle of the optically anisotropic molecules located near the surface of the optical film varies by 180°. In some embodiments, the in-plane spacing is a constant spacing or a varying spacing. In some embodiments, over the in-plane spacing of the non-uniform in-plane orientation pattern, the azimuth angle of the optically anisotropic molecules located near the surface of the optical film is configured to vary non-linearly 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. In some embodiments, over 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. In some embodiments, over the in-plane spacing of the non-uniform in-plane orientation pattern, the azimuth angle of the optically anisotropic molecules located near the surface of the optical film varies according to the following function: in, is the azimuth angle of the optically anisotropic molecule, x is the distance from the starting point of the in-plane spacing to the local point where the optically anisotropic molecule is located along the predetermined in-plane axis, and P in is the in-plane spacing, is a linear function of x, is a nonlinear function of x, A is an amplitude parameter of the nonlinear function and is a positive value less than or equal to 360°. In some embodiments, the nonlinear function for And the function for In some embodiments, the plurality of second lights output from the plurality of positions of the optical film are distributed along the pupil expansion direction of the device, and the amplitude parameter A of the nonlinear function is configured to decrease along the pupil expansion direction of the device.

[0191] In some embodiments, the optical film is configured to couple the first light out of the lightguide as a plurality of second lights by reflection. In some embodiments, the device further comprises an outcoupling element coupled to the lightguide, the optical film is configured to reflect the first light as a plurality of second lights that propagate toward the outcoupling element, and the outcoupling element is configured to couple the plurality of second lights out of the lightguide as a plurality of third lights. In some embodiments, the optical film comprises a cholesteric liquid crystal ("CLC") layer, and the optically anisotropic molecules located near a surface of the optical film are configured in a uniform in-plane orientation pattern.

[0192] In some embodiments, the present disclosure provides a method. The method includes generating 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. The method also includes exposing a polarization-sensitive recording medium to the polarization interference pattern. Optically anisotropic molecules in the polarization-sensitive recording medium exposed to the polarization interference pattern form an in-plane alignment pattern, and the azimuth angles of the optically anisotropic molecules vary nonlinearly along a predetermined in-plane direction of the in-plane alignment pattern.

[0193] In some embodiments, the at least three circularly polarized 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.

[0194] In some embodiments, a polarization-sensitive recording medium includes a surface photoalignment material, and after exposing the polarization-sensitive recording medium to a 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 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.

[0195] In some embodiments, 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: 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 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.

[0196] In some embodiments, the present disclosure provides a device. The device includes: a light guide configured to guide a first light beam to propagate within the light guide; and an optical film coupled to the light guide, wherein a plurality of optically anisotropic molecules in the optical film are configured with an in-plane orientation pattern. The azimuth angles of the plurality of optically anisotropic molecules are configured to vary nonlinearly along a predetermined in-plane direction of the in-plane orientation pattern. The optical film is configured to diffract the first light beam into a plurality of second lights at a plurality of predetermined different diffraction efficiencies at a plurality of locations of the optical film. In some embodiments, the optical film includes a polarization volume hologram. In some embodiments, the azimuth angles of the optically anisotropic molecules are configured to vary according to a nonlinear function of an amplitude parameter A, an in-plane spacing of the in-plane orientation pattern, and the position of the optically anisotropic molecules, and the amplitude parameter A is configured to have a plurality of different values ​​at the plurality of locations of the optical film. In some embodiments, the plurality of second lights are distributed along a pupil expansion direction of the device, the amplitude parameter A of the nonlinear function is configured to decrease along the pupil expansion direction, and the plurality of predetermined different diffraction efficiencies are configured to increase along the pupil expansion direction.

[0197] In some embodiments, the azimuth angle of the optically anisotropic molecules is configured to vary 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 over the in-plane spacing of the in-plane alignment pattern. In some embodiments, the in-plane spacing is defined as the distance over which the azimuth angle of the optically anisotropic molecules varies by 180 degrees along the predetermined in-plane direction, and the azimuth angle of the optically anisotropic molecules located at the starting point of the in-plane spacing is zero degrees. In some embodiments, the azimuth angle of the optically anisotropic molecules varies over the in-plane spacing of the in-plane alignment pattern according to the following function: is the azimuth angle of the optically anisotropic molecule, x is the distance from the starting point of the in-plane spacing to the local point, P in is the in-plane spacing, is a linear function of x, is a nonlinear function of x, A is an amplitude parameter of the nonlinear function and is a positive value less than or equal to 360°. In some embodiments, the nonlinear function for And the function for

[0198] In some embodiments, a plurality of optically anisotropic molecules form a plurality of helical structures within the volume of the optical film, and the azimuth angles of the plurality of optically anisotropic molecules are configured to vary nonlinearly along the helical axis of the helical structure. In some embodiments, the azimuth angles of the optically anisotropic molecules vary according to the amplitude parameter A, the Bragg period P of the optical film, and the optical period P of the optical film. B and the position of the optically anisotropic molecule along the helical axis, and the amplitude parameter A is configured to have multiple different values ​​at multiple locations in the optical film. In some embodiments, the azimuth angle of the optically anisotropic molecule over the helical pitch of the helical structure is configured 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 molecule is located. In some embodiments, the helical pitch is the distance along the helical axis over which the azimuth angle of the optically anisotropic molecule varies 360°, and the azimuth angle of the optically anisotropic molecule located at the starting point of the helical pitch is zero degrees. In some embodiments, the azimuth angle of the optically anisotropic molecule over the helical pitch of the helical structure varies according to the following function: 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, 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°. In some embodiments, the nonlinear function for And the function for

[0199] In some embodiments, the optical film is configured to diffract the first light from the light guide as a plurality of second lights. In some embodiments, the device further comprises an outcoupling element coupled to the light guide, wherein the optical film is configured to diffract the first light into a plurality of second lights that propagate toward the outcoupling element, and wherein the outcoupling element is configured to couple the plurality of second lights out of the light guide as a plurality of third lights.

[0200] In some embodiments, the present disclosure provides a method. The method includes: 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. The method includes: exposing a polarization-sensitive recording medium to the polarization interference pattern to align a plurality of optically anisotropic molecules in the polarization-sensitive recording medium to form an in-plane orientation pattern, wherein the azimuth angles of the aligned plurality of optically anisotropic molecules vary nonlinearly along a predetermined in-plane direction of the in-plane orientation pattern. In some embodiments, the at least three circularly polarized 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.

[0201] Any of the multiple 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 module is implemented using a computer program product comprising a computer-readable medium comprising computer program code that can be executed by a computer processor to perform any or all of the multiple steps, operations, or processes described. In some embodiments, the hardware module can include hardware components such as devices, systems, optical elements, controllers, circuits, logic gates, and the like.

[0202] Furthermore, when an embodiment shown in a drawing shows a single element, it is understood that the embodiment, or embodiments 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 is understood that the embodiment, or embodiments 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 stated, the 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 shown 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.

[0203] 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 implemented 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: a light guide configured to guide first light to propagate within the light guide; as well as an optical film coupled to the light guide, a plurality of optically anisotropic molecules in the optical film being configured with an in-plane alignment pattern having an in-plane pitch along a predetermined in-plane direction, wherein, within the in-plane spacing of the in-plane alignment pattern, the azimuth angles of the plurality of optically anisotropic molecules are configured to change nonlinearly along the predetermined in-plane direction, and The optical film is configured to diffract the first light into a plurality of second lights at a plurality of predetermined different diffraction efficiencies at a plurality of positions of the optical film.

2. The device according to claim 1, wherein The optical film includes a polarizer hologram.

3. The device according to claim 1 or 2, wherein: The azimuth angles of the plurality of optically anisotropic molecules are configured to vary nonlinearly and periodically along the predetermined in-plane direction of the in-plane alignment pattern; Within the in-plane spacing of the in-plane alignment pattern, the azimuth angles of the optically anisotropic molecules are configured to vary according to a nonlinear function of a parameter A, the in-plane spacing, and the positions of the optically anisotropic molecules, and The parameter A is configured to have a plurality of different values ​​at the plurality of locations of the optical film.

4. The device according to claim 3, wherein The plurality of second lights are distributed along the pupil expansion direction of the device, The parameter A of the nonlinear function is configured to decrease along the pupil expansion direction, and The plurality of predetermined different diffraction efficiencies are configured to increase along the pupil expansion direction.

5. The apparatus according to claim 3, wherein The position of the optically anisotropic molecule is associated with the distance from the starting point of the in-plane spacing to the local point where the optically anisotropic molecule is located along the predetermined in-plane direction; and preferably, wherein, The in-plane spacing is defined as a distance along the predetermined in-plane direction where the orientation angle of the optically anisotropic molecules changes by 180 degrees, and The azimuth angle of the optically anisotropic molecules located at the starting point of the in-plane spacing is zero degrees.

6. The device according to claim 5, wherein Within the in-plane spacing of the in-plane alignment pattern, the azimuthal angles of the optically anisotropic molecules vary according to the following function: is the azimuth angle of the optically anisotropic molecule, x is the distance from the starting point of the in-plane spacing to the local point, P in is the in-plane spacing, is a linear function of x, is a nonlinear function of x, and the parameter A is a positive value less than or equal to 360°; And preferably, wherein the nonlinear function for And the function for 7. A method according to any one of the preceding claims, wherein The plurality of optically anisotropic molecules form a plurality of helical structures within the volume of the optical film, and The azimuthal angles of the plurality of optically anisotropic molecules are configured to vary nonlinearly along a helical axis of the helical structure.

8. The apparatus according to claim 7, wherein The azimuth angle of the optical anisotropic molecules is determined by the parameters A, the Bragg period P of the optical film, and the B and the optical anisotropy of the molecules varies as a nonlinear function of their position along the helical axis, and The parameter A is configured to have a plurality of different values ​​at the plurality of locations of the optical film.

9. The apparatus according to claim 7 or 8, wherein Within the helical pitch of the helical structure, the azimuthal angle of the optically anisotropic molecule is configured to vary non-linearly 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 molecule is located.

10. The apparatus according to claim 9, wherein The helical pitch is the distance along the helical axis over which the azimuthal angle of an optically anisotropic molecule varies by 360°, and The azimuth angle of the optically anisotropic molecule located at the starting point of the helical pitch is zero degrees.

11. The device according to claim 10, in, Within the helical pitch of the helical structure, the azimuthal angle of the optically anisotropic molecule varies according to the following function: 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, P B is the Bragg cycle, is a linear function of z, is a nonlinear function of z, and the parameter A is a positive value less than or equal to 360°; And preferably, wherein the nonlinear function for And the function for 12. Apparatus according to any one of the preceding claims, wherein The optical film is configured to diffract the first light out of the light guide as a plurality of second lights.

13. The apparatus according to any one of the preceding claims, further comprising: an outcoupling element coupled to the light guide, wherein the optical film is configured to diffract the first light into the plurality of second lights propagating toward the outcoupling element, and The outcoupling element is configured to couple the plurality of second lights out of the light guide as a plurality of third lights.

14. A method comprising: 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; and The polarization-sensitive recording medium is exposed to the polarization interference pattern to align a plurality of optically anisotropic molecules in the polarization-sensitive recording medium to form an in-plane alignment pattern.

15. The method according to claim 14, wherein The at least three circularly polarized 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; and / or wherein the polarization-sensitive recording medium comprises a bulk photoalignment material, and exposing the polarization-sensitive recording medium to the polarization interference pattern causes the polarization interference pattern to be recorded in the bulk photoalignment material; and / or Wherein, within the in-plane spacing of the in-plane alignment pattern, the azimuth angles of the aligned plurality of optically anisotropic molecules change nonlinearly along a predetermined in-plane direction of the in-plane alignment pattern.

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