Method and system for patterning a liquid crystal layer

Abstract

To provide a method and system for patterning a liquid crystal layer.SOLUTION: An optical master is created by using a nanoimprint alignment layer to pattern a liquid crystal layer. The nanoimprint alignment layer and the liquid crystal layer constitute the optical master. The optical master is positioned above a photo-alignment layer. The optical master is illuminated, and light propagating through the nanoimprint alignment layer and the liquid crystal layer is diffracted and subsequently strikes the photo-alignment layer. The incident diffracted light causes the pattern in the liquid crystal layer to be transferred to the photo-alignment layer. A second liquid crystal layer is deposited onto the patterned photo-alignment layer, which subsequently is used to align molecules of the second liquid crystal layer.SELECTED DRAWING: Figure 3b

Description

[Technical Field]

[0001] (Priority Claim) This application claims the benefit of priority under 35 U.S.C. §119(e) to U.S. Provisional Application No. 62 / 939,514, filed November 22, 2019. The entire disclosure of this priority document is incorporated herein by reference. (Incorporated by reference)

[0002] This application incorporates by reference in its entirety U.S. Patent Application No. 16 / 171,290, filed October 25, 2018, and published on July 25, 2019 as U.S. Patent Publication No. 2019 / 0227375. This application also incorporates by reference in its entirety U.S. Patent Application No. 15 / 835,108, filed December 7, 2017, and published on June 14, 2018 as U.S. Patent Publication No. 2018 / 0164627.

[0003] The present disclosure relates to methods and systems for patterning liquid crystal layers. [Background technology]

[0004] Liquid crystals can be manipulated to form various patterns, which can be advantageously applied, for example, to form optical devices. For example, liquid crystal molecules within a liquid crystal layer may be oriented to form patterns with regular spacing and orientation, which may be utilized as diffractive optical features. Because the functionality of a liquid crystal layer depends on the pattern formed by the liquid crystal molecules, there is a continuing need for methods and systems for reliably and efficiently forming liquid crystal layers with liquid crystal molecules having desired orientations and patterns. Summary of the Invention [Means for solving the problem]

[0005] According to some implementations, a method is provided for forming a patterned liquid crystal layer. The method includes providing an optical master comprising an alignment layer including surface relief features and a liquid crystal layer over the surface relief features, where liquid crystal molecules of the liquid crystal layer define a liquid crystal pattern. The method further includes providing an optical alignment layer disposed on a substrate and replicating the liquid crystal pattern in the optical alignment layer by propagating light through the optical master and into the optical alignment layer.

[0006] According to some other implementations, a method is provided for forming an optical master. The method includes providing a first optical master comprising an alignment layer including surface relief features and a first liquid crystal layer on the surface relief features, where liquid crystal molecules of the first liquid crystal layer define a liquid crystal pattern. The method further includes providing an optical alignment layer disposed on a substrate, replicating the liquid crystal pattern in the optical alignment layer by propagating light through the optical master to the optical alignment layer, and depositing a second liquid crystal layer on the optical alignment layer, where the molecules of the second liquid crystal layer are aligned by the optical alignment layer, thereby forming a second optical master. The second optical master comprises the second liquid crystal layer, the optical alignment layer, and the substrate.

[0007] According to yet another implementation, a method is provided for forming a patterned liquid crystal layer using a replicated optical master. The method includes providing a first optical master comprising an alignment layer including surface relief features and a first liquid crystal layer on the surface relief features, where liquid crystal molecules of the first liquid crystal layer define a liquid crystal pattern. The method further includes providing an optical alignment layer disposed on a substrate, replicating the liquid crystal pattern in the optical alignment layer by propagating light through the optical master to the optical alignment layer, and depositing a second liquid crystal layer on the optical alignment layer, where the molecules of the second liquid crystal layer are aligned by the optical alignment layer, thereby forming a second optical master. The second optical master comprises a second liquid crystal layer, the optical alignment layer, and the substrate. The method further includes providing a second optical alignment layer on the second substrate, positioning a second optical master over the second optical alignment layer, and replicating the liquid crystal pattern in the second optical alignment layer by propagating light through the second optical master to the second optical alignment layer.

[0008] According to some other implementations, a method is provided for forming a patterned liquid crystal layer. The method includes providing an optical master comprising an alignment layer and a liquid crystal layer on the alignment layer, where liquid crystal molecules of the liquid crystal layer define a liquid crystal pattern. The method further includes providing an optical alignment layer disposed on a substrate, and propagating light through the optical master to the optical alignment layer by moving a collimated light source across the optical master to replicate the liquid crystal pattern in the optical alignment layer.

[0009] Additional examples of various implementations are provided below.

[0010] Example 1 1. A method of forming a patterned liquid crystal layer, comprising: a matching layer including surface relief features; a liquid crystal layer on the surface relief features, liquid crystal molecules of the liquid crystal layer defining a liquid crystal pattern; providing an optical master comprising: providing an optical alignment layer disposed on a substrate; replicating the liquid crystal pattern in the optical alignment layer by propagating light through the optical master into the optical alignment layer; A method comprising:

[0011] Example 2 The method of claim 1 , wherein the matching layer comprises an imprint layer.

[0012] Example 3 The method of claim 1 , wherein the liquid crystal layer comprises a nematic liquid crystal layer.

[0013] Example 4 The method of claim 1 , wherein the surface relief features comprise nanostructures, and the liquid crystal layer is disposed on the alignment layer such that the liquid crystal molecules align with the nanostructures.

[0014] Example 5 The method of claim 4 , wherein the nanostructures comprise imprinted nanostructures.

[0015] Example 6 The method of claim 4 , wherein the nanostructures have an optical phase and a grating period, and the liquid crystal molecules are aligned by the nanostructures to have substantially the same optical phase and grating period.

[0016] Example 7 2. The method of claim 1, wherein the liquid crystal layer has a thickness of about d, where d=λ / (2Δn), where λ is the wavelength of light propagated through the optical master to the optical alignment layer, and Δn is the birefringence of the liquid crystal layer.

[0017] Example 8 8. The method of claim 7, wherein the liquid crystal layer has an optical phase and a grating period, and after replicating the liquid crystal pattern, the optical matching layer has an optical phase that is about twice the optical phase of the liquid crystal layer and a grating period that is about half the grating period of the liquid crystal layer.

[0018] Example 9 The method of claim 7 , wherein the light comprises linear polarization.

[0019] Example 10 10. The method of claim 9, wherein the liquid crystal layer diffracts light into left-handed circularly polarized light and right-handed circularly polarized light, one of the circularly polarized light being a -1 diffraction order light and the other of the circularly polarized light being a +1 diffraction order light.

[0020] Example 11 11. The method of claim 10, wherein the liquid crystal layer diffracts approximately half the light into left-handed circularly polarized light and half the light into right-handed circularly polarized light.

[0021] Example 12 10. The method of claim 1, wherein the liquid crystal layer has a thickness of about d, where d=λ / (4Δn), where λ is the wavelength of light propagated through the optical master, and Δn is the birefringence of the liquid crystal layer.

[0022] Example 13 13. The method of claim 12, wherein the liquid crystal layer has an optical phase and a grating period, and after replicating the liquid crystal pattern, the optical alignment layer has an optical phase and a grating period equal to those of the liquid crystal layer.

[0023] Example 14 The method of claim 12 , wherein the light comprises one of left-handed circular polarization and right-handed circular polarization.

[0024] Example 15 15. The method of claim 14, wherein the liquid crystal layer diffracts the light into left-handed circularly polarized light and right-handed circularly polarized light, one of the left-handed circularly polarized light and the right-handed circularly polarized light being the +1 or −1 diffraction order light, and the other of the left-handed circularly polarized light and the right-handed circularly polarized light being the zero diffraction order light.

[0025] Example 16 16. The method of claim 15, wherein the liquid crystal layer diffracts approximately half of the light into left-handed circularly polarized light and the liquid crystal layer diffracts approximately half of the light into right-handed circularly polarized light.

[0026] Example 17 The method of claim 1 , further comprising depositing a liquid crystal layer directly on the optical alignment layer, wherein molecules of the liquid crystal layer on the optical alignment layer are aligned by the optical alignment layer.

[0027] Example 18 The method of claim 1 , wherein the optical alignment layer comprises at least one of an azo, cinnamic acid, and / or coumarin-based material.

[0028] Example 19 The method of claim 1 , wherein propagating light through the optical master comprises positioning a collimated light source over the optical master that illuminates at least a portion of the optical master.

[0029] Example 20 20. The method of claim 19, wherein the collimated light source comprises a laser, a light emitting diode, or a lamp.

[0030] Example 21 20. The method of claim 19, wherein propagating light through the optical master further comprises moving the collimated light source to different portions of the optical master.

[0031] Example 22 20. The method of claim 19, wherein the collimated light source has a beam power (P) and a beam width (W).

[0032] Example 23 The collimated light source is moved at a scanning speed (S), and the dose is equal to P*W / S, where the dose is 0.5 Joules / cm 2 ~10 joules / cm 2 23. The method of claim 22, wherein:

[0033] Example 24 Dose is 0.5 joules / cm 2 ~1 joule / cm 2 24. The method of claim 23, wherein:

[0034] Example 25 23. The method of claim 22, wherein the collimated light source is moved at a scanning speed (S), the scanning speed providing a total exposure time of less than 1 / 6 second across any portion of the optical alignment layer.

[0035] Example 26 1. A method of forming an optical master, comprising: a matching layer including surface relief features; a first liquid crystal layer on the surface relief features, the liquid crystal molecules of the first liquid crystal layer defining a liquid crystal pattern; providing a first optical master comprising: providing an optical alignment layer disposed on a substrate; replicating the liquid crystal pattern in the optical alignment layer by propagating light through the optical master into the optical alignment layer; depositing a second liquid crystal layer on the optical alignment layer, wherein molecules of the second liquid crystal layer are aligned by the optical alignment layer; forming a second optical master by wherein the second optical master comprises a second liquid crystal layer, an optical alignment layer, and a substrate.

[0036] Example 27 The method of claim 26 , wherein the matching layer comprises an imprint layer.

[0037] Example 28 27. The method of claim 26, wherein the liquid crystal layer comprises a nematic liquid crystal layer.

[0038] Example 29 27. The method of claim 26, wherein the surface relief features comprise nanostructures, and the first liquid crystal layer is disposed on the alignment layer such that liquid crystal molecules of the first liquid crystal layer align with the nanostructures.

[0039] Example 30 30. The method of claim 29, wherein the nanostructures comprise imprinted nanostructures.

[0040] Example 31 30. The method of claim 29, wherein the nanostructures have an optical phase and a grating period, and the liquid crystal molecules of the first liquid crystal layer are aligned by the nanostructures to have substantially the same optical phase and grating period.

[0041] Example 32 27. The method of claim 26, wherein the first liquid crystal layer has a thickness of about d, where d=λ / (2Δn), where λ is the wavelength of light propagated through the first optical master to the optical alignment layer, and Δn is the birefringence of the first liquid crystal layer.

[0042] Example 33 33. The method of claim 32, wherein the first liquid crystal layer has an optical phase and a grating period, and after replicating the liquid crystal pattern, the optical matching layer has an optical phase that is approximately twice the optical phase of the first liquid crystal layer and a grating period that is approximately half the grating period of the first liquid crystal layer.

[0043] Example 34 The method of claim 32 , wherein the light comprises linear polarization.

[0044] Example 35 35. The method of claim 34, wherein the first liquid crystal layer diffracts light into left-handed circularly polarized light and right-handed circularly polarized light, one of the circularly polarized light being a -1 diffraction order light and the other of the circularly polarized light being a +1 diffraction order light.

[0045] Example 36 36. The method of claim 35, wherein the first liquid crystal layer diffracts approximately half the light into left-handed circularly polarized light and half the light into right-handed circularly polarized light.

[0046] Example 37 27. The method of claim 26, wherein the first liquid crystal layer has a thickness of about d, where d=λ / (4Δn), where λ is the wavelength of light propagated through the first optical master, and Δn is the birefringence of the first liquid crystal layer.

[0047] Example 38 38. The method of claim 37, wherein the first liquid crystal layer has an optical phase and a grating period, and after replicating the liquid crystal pattern, the optical alignment layer has an optical phase and a grating period equal to those of the first liquid crystal layer.

[0048] Example 39 38. The method of claim 37, wherein the light comprises one of left-handed circular polarization and right-handed circular polarization.

[0049] Example 40 40. The method of claim 39, wherein the first liquid crystal layer diffracts light into left-handed circularly polarized light and right-handed circularly polarized light, one of the left-handed circularly polarized light and the right-handed circularly polarized light being the +1 or −1 diffraction order light, and the other of the left-handed circularly polarized light and the right-handed circularly polarized light being the zero diffraction order light.

[0050] Example 41 41. The method of claim 40, wherein the first liquid crystal layer diffracts approximately half of the light into left-handed circularly polarized light and the second liquid crystal layer diffracts approximately half of the light into right-handed circularly polarized light.

[0051] Example 42 27. The method of claim 26, wherein the optical alignment layer comprises at least one of an azo, cinnamic acid, and / or coumarin-based material.

[0052] Example 43 27. The method of claim 26, wherein propagating light through the first optical master comprises positioning a collimated light source across the first optical master that illuminates at least a portion of the first optical master.

[0053] Example 44 44. The method of claim 43, wherein the collimated light source comprises a laser, a light emitting diode, or a lamp.

[0054] Example 45 44. The method of claim 43, wherein propagating the light through the first optical master further comprises moving the collimated light source to a different portion of the first optical master.

[0055] Example 46 44. The method of claim 43, wherein the collimated light source has a beam power (P) and a beam width (W).

[0056] Example 47 The collimated light source is moved at a scanning speed (S), and the dose is equal to P*W / S, where the dose is 0.5 Joules / cm 2 ~10 joules / cm 2 47. The method of claim 46, wherein:

[0057] Example 48 Dose is 0.5 joules / cm 2 ~1 joule / cm 2 48. The method of claim 47, wherein:

[0058] Example 49 48. The method of claim 47, wherein the scanning speed provides a total exposure time of less than 1 / 6 second across any portion of the photoalignment layer.

[0059] Example 50 1. A method of forming a patterned liquid crystal layer using a replicated optical master, comprising: a matching layer including surface relief features; a first liquid crystal layer on the surface relief features, the liquid crystal molecules of the first liquid crystal layer defining a liquid crystal pattern; providing a first optical master comprising: providing an optical alignment layer disposed on a substrate; replicating the liquid crystal pattern in the optical alignment layer by propagating light through the optical master into the optical alignment layer; depositing a second liquid crystal layer on the optical alignment layer, wherein molecules of the second liquid crystal layer are aligned by the optical alignment layer; forming a second optical master by, wherein the second optical master comprises a second liquid crystal layer, an optical alignment layer, and a substrate; providing a second optical alignment layer on the second substrate; Positioning a second optical master over the second optical alignment layer; replicating the liquid crystal pattern in the second optical alignment layer by propagating light through the second optical master to the second optical alignment layer; A method comprising:

[0060] Example 51 51. The method of claim 50, further comprising depositing a third liquid crystal layer on the second optical alignment layer, wherein the molecules of the third liquid crystal layer are aligned by the second optical alignment layer.

[0061] Example 52 1. A method of forming a patterned liquid crystal layer, comprising: a matching layer; providing an optical master comprising a liquid crystal layer on an alignment layer, the liquid crystal molecules of the liquid crystal layer defining a liquid crystal pattern; providing an optical alignment layer disposed on a substrate; propagating light through the optical master into the optical alignment layer by moving a collimated light source across the optical master to replicate the liquid crystal pattern in the optical alignment layer; A method comprising:

[0062] Example 53 53. The method of claim 52, wherein propagating light through the optical master comprises positioning a collimated light source over the optical master that illuminates at least a portion of the optical master.

[0063] Example 54 54. The method of claim 53, wherein propagating the light through the optical master further comprises moving the collimated light source to different portions of the optical master.

[0064] Example 55 53. The method of claim 52, wherein the collimated light source comprises a laser, a light emitting diode, or a lamp.

[0065] Example 56 53. The method of claim 52, wherein the collimated light source has a beam power (P) and a beam width (W).

[0066] Example 57 The collimated light source is moved at a scanning speed (S), and the dose is equal to P*W / S, where the dose is 0.5 Joules / cm 2 ~10 joules / cm 2 57. The method of claim 56, wherein:

[0067] Example 58 Dose is 0.5 joules / cm 2 ~1 joule / cm 2 58. The method of claim 57, wherein:

[0068] Example 59 58. The method of claim 57, wherein the scanning speed provides a total exposure time of less than 1 / 6 second across any portion of the photoalignment layer.

[0069] Example 60 53. The method of claim 52, wherein propagating light through the optical master comprises positioning a plurality of collimated light sources across the optical master, the collimated light sources illuminating portions of the optical master.

[0070] Example 61 61. The method of claim 60, wherein propagating light through the optical master further comprises moving a plurality of collimated light sources to illuminate different portions of the optical master.

[0071] Example 62 61. The method of claim 60, wherein each of the plurality of collimated light sources comprises a laser, a light emitting diode, or a lamp. The present invention provides, for example, the following. (Item 1) 1. A method of forming a patterned liquid crystal layer, the method comprising: providing an optical master, the optical master comprising: a matching layer including surface relief features; a liquid crystal layer on the surface relief features, the liquid crystal molecules of the liquid crystal layer defining a liquid crystal pattern; and providing an optical alignment layer disposed on a substrate; replicating the liquid crystal pattern in the optical alignment layer by propagating light through the optical master into the optical alignment layer; A method comprising: (Item 2) Item 10. The method of claim 1, wherein the matching layer is formed by imprinting the surface relief features into the matching layer. (Item 3) Item 10. The method of item 1, wherein the surface relief features comprise nanostructures, the liquid crystal layer is disposed on the alignment layer such that the liquid crystal molecules align with the nanostructures, the nanostructures comprising an optical phase and a grating period, and the liquid crystal molecules are aligned by the nanostructures to have substantially the same optical phase and grating period. (Item 4) Item 10. The method of claim 1, wherein the liquid crystal layer has a thickness of about d, where d=λ / (2Δn), where λ is the wavelength of light propagated through the optical master to the optical alignment layer, and Δn is the birefringence of the liquid crystal layer. (Item 5) Item 5. The method of item 4, wherein the liquid crystal layer has an optical phase and a grating period, and after replicating the liquid crystal pattern, the optical alignment layer has an optical phase that is about twice the optical phase of the liquid crystal layer and a grating period that is about half the grating period of the liquid crystal layer. (Item 6) Item 5. The method of item 4, wherein the light has linear polarization and the liquid crystal layer diffracts the light into left-handed circularly polarized light and right-handed circularly polarized light, one of the circularly polarized light being a −1 diffraction order light and the other of the circularly polarized light being a +1 diffraction order light. (Item 7) Item 10. The method of item 1, wherein the liquid crystal layer has a thickness of about d, where d=λ / (4Δn), where λ is the wavelength of light propagated through the optical master and Δn is the birefringence of the liquid crystal layer, the liquid crystal layer having an optical phase and a grating period, and after replicating the liquid crystal pattern, the optical alignment layer has an optical phase and a grating period equal to those of the liquid crystal layer. (Item 8) Item 8. The method of item 7, wherein the light comprises one of left-handed circularly polarized light and right-handed circularly polarized light, and the liquid crystal layer diffracts the light into left-handed circularly polarized light and right-handed circularly polarized light, one of the left-handed circularly polarized light and the right-handed circularly polarized light being a +1 or −1 diffraction order light, and the other of the left-handed circularly polarized light and the right-handed circularly polarized light being a zero diffraction order light. (Item 9) Item 10. The method of claim 1, wherein the optical alignment layer comprises at least one of an azo, cinnamic acid, and / or coumarin-based material. (Item 10) Item 10. The method of item 1, wherein propagating light through the optical master comprises directing collimated light from a collimated light source across the optical master. (Item 11) Item 11. The method of item 10, wherein the collimated light source comprises a laser, a light emitting diode, or a lamp. (Item 12) Item 11. The method of item 10, wherein propagating light through the optical master further comprises moving the collimated light source to a different portion of the optical master. (Item 13) The collimated light source has a beam power (P) and a beam width (W), the collimated light source is moved at a scan speed (S), and the dose is equal to P*W / S, and the dose is 0.5 Joules / cm 2 ~10 joules / cm 2 Item 11. The method according to Item 10, wherein (Item 14) The dose is 0.5 joules / cm 2 ~1 joule / cm 2 Item 14. The method according to Item 13, wherein (Item 15) Item 14. The method of item 13, wherein the collimated light source is moved at a scanning speed (S), the scanning speed providing a total exposure time of less than 1 / 6 second across any portion of the optical alignment layer. (Item 16) Item 11. The method of item 10, wherein propagating light through the optical master includes positioning a plurality of collimated light sources across the optical master. (Item 17) Item 17. The method of item 16, wherein propagating light through the optical master further comprises moving the plurality of collimated light sources to illuminate different portions of the optical master. (Item 18) Item 17. The method of item 16, wherein each of the plurality of collimated light sources comprises a laser, a light emitting diode, or a lamp. (Item 19) and forming a second optical master, the forming of the second optical master comprising: depositing a second liquid crystal layer on the optical alignment layer, the molecules of the second liquid crystal layer being aligned by the optical alignment layer; Item 10. The method of item 1, wherein the second optical master comprises the second liquid crystal layer, the optical alignment layer, and the substrate. (Item 20) providing a second optical alignment layer on the second substrate; Positioning the second optical master over the second optical alignment layer; replicating the liquid crystal pattern in the second optical alignment layer by propagating light through the second optical master to the second optical alignment layer; Item 1, the method of claim 1 further comprising: (Item 21) 21. The method of claim 20, further comprising depositing a third liquid crystal layer on the second optical alignment layer, wherein the molecules of the third liquid crystal layer are aligned by the second optical alignment layer. [Brief explanation of the drawings]

[0072] [Figure 1a]FIG. 1a is a cross-sectional side view of an example of surface relief features for forming an optical master, according to some implementations of the present disclosure.

[0073] [Figure 1b] FIG. 1b is a cross-sectional side view of an example optical master according to some implementations of the present disclosure.

[0074] [Figure 2] 2a and 2b are perspective views of the surface relief features and optical master of FIGS. 1a and 1b, respectively.

[0075] [Figure 3a] FIG. 3a is a cross-sectional side view of an example optical master according to some implementations of the present disclosure.

[0076] [Figure 3b] FIG. 3b is a cross-sectional side view of an example of light propagating through the optical master of FIG. 3a and replicating a pattern in an optical alignment layer, according to some implementations of the present disclosure.

[0077] [Figure 4a] FIG. 4a is a cross-sectional side view of an example optical master according to some implementations of the present disclosure.

[0078] [Figure 4b] FIG. 4b is a cross-sectional side view of an example of light propagating through the optical master of FIG. 4a and replicating a pattern in an optical alignment layer, according to some implementations of the present disclosure.

[0079] [Figure 5] FIG. 5 is a cross-sectional side view of an example structure with replicated liquid crystal patterns, according to some implementations of the present disclosure.

[0080] [Figure 6] FIG. 6 is a perspective view of an example system for forming replicated liquid crystal patterns, according to some implementations of the present disclosure.

[0081] [Figure 7a] FIG. 7a is a schematic side view of the system of FIG.

[0082] [Figure 7b] FIG. 7b is a schematic top-down view of various beam positions of light output by the systems of FIGS. 6 and 7a, according to some implementations of the present disclosure.

[0083] [Figure 8a] FIG. 8a illustrates a cross-sectional side view of an example set of stacked waveguides, each including an internally coupled optical element usable in an augmented reality (AR) system, according to some implementations of the present disclosure.

[0084] [Figure 8b] FIG. 8b illustrates an example of a perspective view of multiple stacked waveguides of FIG. 8a that can be used in an augmented reality (AR) system, according to some implementations of the present disclosure.

[0085] [Figure 8c] FIG. 8c illustrates a top-down plan view of an example of the multiple stacked waveguides of FIGS. 8a and 8b that can be used in an augmented reality (AR) system, according to some implementations of the present disclosure.

[0086] [Figure 8d] FIG. 8d illustrates an example of a wearable display system according to some implementations of the present disclosure.

[0087] [Figure 9] FIG. 9 illustrates an example of an imaging system comprising a front-facing camera configured to image a wearer's eye using a liquid crystal off-axis mirror formed using an optical master, according to some implementations of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0088] Detailed Description Geometric phase holograms (GPHs) may be used for various applications, such as lenses and polarization conversion systems. GPHs may be formed by three-dimensional patterns of liquid crystal molecules. Examples of GPHs are disclosed in U.S. Patent Publication No. 2019 / 0227375, the entire disclosure of which is incorporated herein by reference.

[0089] One approach to fabricating GPHs involves the use of an optically patterned, photo-aligned material. A liquid crystal layer is deposited on the patterned photo-aligned material, which aligns the liquid crystal molecules in the liquid crystal layer based on the interaction between the liquid crystal molecules and the pattern in the photo-aligned material. Patterning the photo-aligned material can involve the use of two beams of collimated light, complex optics, a highly coherent light source, and rigorous mechanical stability (e.g., high levels of vibration isolation). As a result, forming GPHs, especially those that extend across large areas, can undesirably require complex and highly constrained systems and can occur with low throughput.

[0090] Advantageously, in some implementations, methods and systems are provided for forming GPHs with relaxed manufacturing constraints and high throughput. Additionally, the methods and systems may utilize easily created optical masters, which can be formed with high precision and facilitate replication of "sub" masters. Both the master and the submaster may be utilized to pattern an optical alignment layer, which may in turn be utilized to align liquid crystal molecules. Thus, in some implementations, easily formed and easily replicated optical masters may be utilized to form GPHs with relaxed manufacturing constraints and high throughput over large areas using the present systems.

[0091] In some implementations, the optical master includes surface relief features and, preferably, an overlying liquid crystal layer in contact with the surface relief features. The surface relief features may be sized, shaped, and formed from a suitable material to align liquid crystal molecules in the liquid crystal layer with the surface relief features. In some implementations, the surface relief features may be imprinted nanostructures. In some implementations, the surface relief features form a pattern, and the liquid crystal molecules may align to adopt the same pattern. Advantageously, forming the surface relief features by imprinting may more easily provide high accuracy and repeatability compared to forming the optical master using multiple beams of light.

[0092] It should be understood that after being aligned to form a particular pattern, the liquid crystal molecules may be polymerized (e.g., by application of heat and / or irradiation with light, such as by UV illumination). Upon polymerization, the individual liquid crystal molecules retain their orientation relative to one another, but upon polymerization, they become linked (e.g., covalently bonded). For ease of explanation herein, and as will be clear from the context, the term "liquid crystal molecule" may refer to both discrete, unlinked liquid crystal molecules and also to those same liquid crystal molecules after they have been linked. That is, the term "liquid crystal molecule" may refer to a corresponding portion of a larger network of linked liquid crystal material formed by previously unlinked liquid crystal molecules.

[0093] In some implementations, optically patterning an optical alignment layer formed from an optical alignment material involves illuminating the optical master such that light propagates through the optical master into the optical alignment material and patterns the optical alignment material. Light passing through the optical master is diffracted, forming two beams of light that then impinge on the optical alignment layer. Without being limited by theory, it is believed that interference between the two beams of light in the optical alignment layer forms a pattern in the optical alignment layer, which causes an overlying layer of liquid crystal molecules to align so that the liquid crystal molecules adopt a desired pattern. This desired pattern preferably substantially replicates the pattern of liquid crystal molecules in the optical master.

[0094] It has been found that the thickness of the liquid crystal layer of the optical master can affect the diffraction of light illuminating the optical master. Advantageously, by appropriately selecting the thickness of the liquid crystal layer, the pitch of the features of the replicated liquid crystal pattern can be modified. In some implementations, this allows the optical master, with easily formed large-pitch features, to provide a replicated liquid crystal pattern having half the pitch of the optical master liquid crystal pattern. In some other implementations, the thickness of the optical master liquid crystal layer may be selected so that the replicated liquid crystal pattern and the optical master liquid crystal pattern have substantially the same pitch, which can be advantageous when replicating patterns with a significant amount of zero-diffraction-order light, as discussed herein.

[0095] In some implementations, propagating light through an optical master to pattern a target optical matching layer may include illuminating all of the optical master corresponding to the entire target optical matching layer such that the light propagates through the optical master and simultaneously impinges on the entire target optical matching layer. However, such a scheme undesirably requires a large, collimated beam of light, which may involve complex optics and a high level of vibration isolation. In some implementations, rather than illuminating the entire target optical matching layer, the beam of light is moved relative to the optical matching layer such that only one or more portions of the optical matching layer receive the incident light at any given time. For example, the incident light may be scanned and / or stepped across the optical matching layer, and / or the optical matching layer may be moved relative to the incident light. Advantageously, using a narrow beam of light relaxes requirements on the incident beam, and the relative movement between the incident light and the optical matching layer reduces the susceptibility of the patterning process to vibrations. For example, the speed of light movement (e.g., the speed at which an incident light beam is moved across an optical alignment layer) preferably exceeds the speed of vibrations expected for the manufacturing system to reduce the effects of any such vibrations.

[0096] The resulting structure, having a patterned optical alignment layer and a liquid crystal layer having a pattern replicating the liquid crystal pattern of the optical master, may be utilized as a submaster to form another GPH in some implementations. In some other implementations, the resulting structure may form an optical structure that can be integrated into an optical device such as a display. For example, the resulting structure may be utilized as part of an optical system associated with in-coupling and / or out-coupling optical elements in one or more waveguides forming an eyepiece for a head-mounted display. Alternatively, the resulting structure may be an entirely separate layer used to image the eye, or a portion thereof, as part of an eye-tracking system. For example, the GPH may be used as a mirror to provide a view of the eye to an eye-tracking camera. An example of an eye-tracking system is disclosed in U.S. Patent Publication No. US2018 / 0164627, the entire disclosure of which is incorporated herein by reference.

[0097] Reference is now made to the drawings, wherein like reference numerals refer to like parts throughout.

[0098] FIG. 1a is a cross-sectional side view of an example of surface relief features for forming an optical master, according to some implementations.

[0099] 1a, an optically transmissive (e.g., transparent) substrate 1312 is provided. A layer of imprint resist (e.g., a polymer layer) may be deposited on the substrate 1312 and then imprinted with a pattern to form an imprint layer 3004 of the intermediate structure 3000A.

[0100] It should be understood that layer 3004 may be imprinted with a pattern by contacting layer 3004 with a nano-imprint template (not shown) having a negative of the desired pattern for layer 3004. The nano-imprint template may have predetermined topological features configured to form an alignment pattern for LC molecules in the subsequently formed LC layer 2704 ( FIG. 1 b), e.g., at least for the bottom LC molecules in LC layer 2704 closest to substrate 1312. The template may then be pressed into an imprint resist layer. In some implementations, the imprint resist layer may include a polymer that is thermoplastic under a certain temperature, e.g., above the glass transition temperature of the polymer, thereby transferring the pattern of the template into the softened resist layer to form imprint layer 3004. After cooling, the template is separated from imprint layer 3004, which then has an alignment pattern having a predetermined topological pattern including surface relief features configured to align LC molecules in the subsequently formed LC layer 2704 ( FIG. 1 b). In some other implementations, after being pressed into the base polymer layer, the matching layer 3004 is solidified by cross-linking under UV light.

[0101] In some other implementations, the imprint resist may be deposited on a nanoimprint mold (not shown) having a negative of the desired pattern. The imprint resist may then be solidified, and the mold may be removed after solidifying the imprint resist. The substrate 1312 may be attached to the imprint layer 3004 before removing the mold.

[0102] In some implementations, the imprint resist may be deposited by jet deposition, for example, by dispensing the imprint resist out of one or more nozzles. Such jet deposition allows for the formation of imprint layers having different resist compositions in different locations, which may have advantages for forming different surface relief patterns in different areas and / or for providing imprint layers with different material properties in different locations.

[0103] The matching layer 3004 may include subwavelength features in one or more dimensions (e.g., one or more dimensions less than the wavelength of light expected to be incident on the features). For example, the matching layer 3004 may include features having dimensions (e.g., length, width, and / or depth) of about a few nanometers, hundreds of nanometers, and / or a few microns. As another example, the matching layer 3004 may include features having lengths greater than or equal to about 20 nm and less than or equal to about 100 nm. As yet another example, the matching layer 3004 may include features having widths greater than or equal to about 20 nm and less than or equal to about 100 nm. As yet another example, the matching layer 3004 may include features having depths greater than or equal to about 10 nm and less than or equal to about 100 nm. In various implementations, the length and / or width of a feature may be greater than the depth of the feature. However, in some implementations, the depth may be approximately equal to the length and / or width of the feature. The features of each domain of the matching layer 3004 may be arranged to form a complex geometric pattern within each domain, in which the direction and / or periodicity between successive features varies along length scales of about a few nanometers, hundreds of nanometers, and / or a few microns.

[0104] 1a to form the matching layer 3004, implementations are not so limited. In some other implementations, the matching layer 3004 may be fabricated using other patterning techniques, including lithography and etching. Additionally, while the matching layer 3004 is described as being formed from a polymeric material, implementations are not so limited, and in various other implementations, the matching layer 3004 may comprise a dielectric material, such as a silicon or glass material.

[0105] Referring now to FIG. 1b, a cross-sectional side view of an example of an optical master is illustrated, according to some implementations. After forming the matching layer 3004, an unpolymerized LC layer 2704, e.g., a layer of reactive mesogens, is deposited thereon. Without being bound by any theory, the matching layer 3004 acts as a matching layer, causing the LC molecules of the LC layer 2704 to align according to the pattern of the matching layer 3004. For example, the elongation direction of the LC molecules within a domain may generally align parallel to the local elongation direction of the nanostructures within the matching layer 3004. Without being bound by any theory, the alignment of the LC molecules with the pattern of the matching layer 3004 may be due to steric interactions with the liquid crystal molecules and / or anchoring energy imparted by the matching layer 3004 on the deposited LC molecules. Still referring to the intermediate structure 3000B of FIG. 1b, the LC layer 2704 may be further processed according to different implementations. For example, the liquid crystal molecules of LC layer 2704 may be polymerized and / or multiple LC layers may be stacked such that LC layer 2704 has multiple constituent LC sub-layers. The resulting structure may be understood as an optical master.

[0106] In some implementations, an optical master may be used to pattern the optical alignment layer. In these implementations, the optical master includes a liquid crystal pattern, which may diffract light. The optical master may be placed in front of the optical alignment layer, which may be supported on a substrate. The optical master may be illuminated such that incident light propagating through the optical master is diffracted by the pattern. The diffracted light may be used to illuminate the optical alignment layer and thus expose and pattern it. This will be further discussed with respect to Figures 3b and 4b.

[0107] 2a and 2b, which illustrate perspective views of the surface relief features and optical master of FIGS. 1a and 1b, respectively. Substrate 202 (corresponding to substrate 1312 in FIGS. 1a and 1b) includes alignment layer 204 (corresponding to alignment layer 3004 in FIGS. 1a and 1b), which includes surface relief pattern 205. As shown, surface relief pattern 205 may include surface relief features 205a with a grating period Λ(x,y) and an optical phase φ(x,y), which may create a diffraction pattern. As further shown, liquid crystal layer 206 (corresponding to liquid crystal layer 2704 in FIGS. 1a and 1b) is disposed on surface relief pattern 205 such that surface relief features 205a align liquid crystal molecules of liquid crystal layer 206 and form pattern 208 within liquid crystal layer 206. The pattern 208 is based on the alignment of liquid crystal molecules 208a, which are aligned by the surface relief features 205a. The pattern 208 has the same grating period Λ(x,y) and optical phase φ(x,y) as those of the surface relief pattern 205.

[0108] In some implementations, the pattern 208 in the liquid crystal layer 206 creates the GPH. In some implementations, the liquid crystal layer 206 may be a nematic liquid crystal layer.

[0109] Referring now to FIG. 3a, a cross-sectional side view of an embodiment of optical master 200a is illustrated. Optical master 200a includes substrate 202 and alignment layer 204. Details of the shared features from FIGS. 2a and 2b will not be repeated in detail. FIG. 3a further includes liquid crystal layer 206a, which is understood to be similar to layer 206 and to have a liquid crystal pattern (not shown) similar to pattern 208 (FIG. 2b). The liquid crystal layer has a birefringence Δn and an approximate thickness d, which can vary depending on the light illuminating optical master 200a. The light 308 illuminating optical master 200a has a wavelength λ. Equation 1 can be used to determine the approximate thickness d of liquid crystal layer 206b, which depends on the liquid crystal birefringence Δn and the wavelength λ of the light illuminating optical master 200a. Preferably, in some implementations, the thickness of liquid crystal layer 206a is within ±5% of the value of d provided by Equation 1.

[0110] Equation 1: d=λ / (2Δn)

[0111] When Equation 1 is satisfied and light 308 has a wavelength λ, the pattern 208 in the liquid crystal layer 206a diffracts linearly polarized light 308 into left-handed and right-handed circularly polarized light. Depending on the polarization of the light 308 illuminating the optical master 200a, one of the circularly polarized light is −1 diffraction order light 306b and the other circularly polarized light is +1 diffraction order light 306a. When the light 308 is linearly polarized, the −1 diffraction order light 306b can be right-handed circularly polarized light and the +1 diffraction order light 306a can be left-handed circularly polarized light. Alternatively, this can be switched depending on the orientation of the pattern 208, such that the −1 diffraction order light 306b can be left-handed circularly polarized light and the +1 diffraction order light 306a can be right-handed circularly polarized light.

[0112] FIG. 3b illustrates a cross-sectional view of the optical master 200a and replicated optical matching structure 300a of FIG. 3a. The replicated structure 300a includes an optical matching layer 304a, which is disposed on a substrate 302. The optical matching layer 304a is between the optical master 200a and the substrate 302. As discussed above in the discussion of FIG. 3a, when the optical master 200a is illuminated with light 308 of wavelength λ, the light diffracts into either left-handed or right-handed circularly polarized light, which is −1 diffraction order light 306b, and into either right-handed or left-handed circularly polarized light, which is +1 diffraction order light 306a. It should be understood that approximately half of the light is diffracted into −1 diffraction order light 306b and approximately half of the light is diffracted into +1 diffraction order light 306a. The liquid crystal layer 206a includes a pattern 208, and the −1 diffraction order light 306b and the +1 diffraction order light 306a will also cause the pattern 208 to be replicated in the optical matching layer 304a. As discussed herein, the pattern 208 includes a grating period Λ(x,y) and an optical phase φ(x,y). It has been found that when light is diffracted into the −1 diffraction order light 306b and the +1 diffraction order light 306a, the grating period is half that of the pattern 208 and the optical phase is twice that of the pattern 208. In other words, the grating period of the pattern replicated in the optical matching layer 304a is equal to 0.5*Λ(x,y), and the optical phase of the pattern replicated in the optical matching layer 304a is equal to 2φ(x,y). Advantageously, the grating period or pitch of optical matching layer 304a is half the size of the grating period or pitch of pattern 208, so the feature size of pattern 208 can be twice the size of the features replicated in optical matching layer 304a. It should be appreciated that smaller nanostructures contained within surface relief features can be more difficult to achieve, and therefore it can be beneficial to utilize larger surface relief features to form relatively small replicated features in optical matching layer 304a.

[0113] In some implementations, the optical matching layer 304a may include one of an azo-, cinnamate-, and / or coumarin-based material. In some implementations, the light 308 may be substantially collimated light produced by a collimated light source, such as one or more lasers, light-emitting diodes (LEDs), or lamps. The separation distance between the liquid crystal layer 206a and the optical matching layer 304a may be short (e.g., on the order of tens to hundreds of microns and less than 1 mm). Preferably, the light source provides a spatial coherence length that exceeds the separation between the liquid crystal layer 206a and the optical matching layer 304a. Thus, the ability of the optical master to closely space the liquid crystal layer 206a and the optical matching layer 304a reduces the need for a long spatial coherence length, which advantageously reduces the demands on the light source.

[0114] Referring now to FIG. 4a, a cross-sectional side view of an example of an optical master 200b according to some other implementations is illustrated. Optical master 200b shares various features with optical masters 200, 200a of FIGS. 2b and 3a-3b, and these features will not be repeated in detail. Continuing with FIG. 4a, optical master 200b includes liquid crystal layer 206b, which has a pattern (not shown) corresponding to pattern 208 (FIG. 2b). Liquid crystal layer 206b has a birefringence Δn and an approximate thickness d that depends on the light illuminating optical master 200b. Liquid crystal layer 206b is similar to liquid crystal layer 206a, except that the approximate thickness of liquid crystal layer 206b depends on Equation 2 rather than Equation 1. Preferably, in some implementations, the thickness of liquid crystal layer 206b is within ±5% of the value of d provided by Equation 2.

[0115] Equation 2: d=λ / (4Δn)

[0116] When Equation 2 is satisfied and the circularly polarized light 308 has a wavelength λ, the light is diffracted by the pattern 208 in the liquid crystal layer 206b into left-handed and right-handed circularly polarized light. One of the left-handed and right-handed circularly polarized light is the +1 or −1 diffraction order light, and the other of the left-handed and right-handed circularly polarized light is the zero diffraction order light. The incident light 208 may be either left-handed or right-handed circularly polarized. When the light 208 is left-handed circularly polarized, the +1 or −1 diffraction order light 310a is right-handed circularly polarized, and the zero diffraction order light is left-handed circularly polarized. When the light 208 is right-handed circularly polarized, the +1 or −1 diffraction order light 310a is left-handed circularly polarized, and the zero diffraction order light is right-handed circularly polarized. It should further be appreciated that approximately half of the light is diffracted into the +1 or -1 diffraction order 310a, and approximately half of the light is diffracted into the zero diffraction order 310b.

[0117] FIG. 4b illustrates a cross-sectional view of the optical master 200b and replicated optical matching structure 300b of FIG. 4a. The replicated structure 300b includes an optical matching layer 304b, which is disposed on a substrate 302. The optical matching layer 304a is between the optical master 200a and the substrate 302. As described above with respect to FIG. 4a, when the optical master 200a is illuminated with light 308 of wavelength λ, the light diffracts into either left-handed or right-handed circularly polarized light, which is the −1 or +1 diffraction order light 310a, and into either right-handed or left-handed circularly polarized light, which is the zero diffraction order light 310b. It should be understood that approximately half of the light is diffracted into the −1 or +1 diffraction order light 310a, and approximately half of the light is diffracted into the zero diffraction order light 310b. The liquid crystal layer 206b includes a pattern 208, and the −1 or +1 diffraction order light 310a and the zero diffraction order light 310b will replicate the pattern 208 in the optical matching layer 304b. Therefore, the −1 or +1 diffraction order light 310a and the zero diffraction order light 310b will replicate the pattern 208 in the optical matching layer 304b.

[0118] As discussed above, pattern 208 includes features with a grating period Λ(x,y) and an optical phase φ(x,y). It has been found that when light is diffracted into −1 or +1 diffraction order light 310a and zero diffraction order light 310b, the grating period and optical phase of pattern 308 will be identical to those of pattern 208. In other words, the grating period of the pattern replicated on optical matching layer 304b will be equal to Λ(x,y), and the optical phase of the pattern replicated on optical matching layer 304b will be equal to φ(x,y). The feature size of pattern 208 will be approximately equal to the features replicated in optical matching layer 304b. Therefore, there is no reduction in the pitch of the features of the pattern replicated on optical matching layer 304b. However, it has been found that optical master 200a in FIG. 3b may have leakage of zero diffraction order light, and such leakage may be significant when the feature size is small. Therefore, for small feature sizes, it may be advantageous to use an optical master 200b that already assumes the presence of zero diffraction order light 310b.

[0119] Referring now to FIG. 5, a cross-sectional side view of an example structure with a replicated liquid crystal pattern is illustrated. The replicated structure 500 includes a liquid crystal layer 502, an optical alignment layer 304, and a substrate 302. The replicated structure 500 shares various features with the replicated structures 300a, 300b of FIGS. 4a and 4b, and these overlapping features will not be repeated in detail. The optical alignment layer 304 may be the optical alignment layer 304a of FIG. 3b or the optical alignment layer 304b of FIG. 4b. The liquid crystal layer 502 may be deposited on the optical alignment layer 304, which aligns the liquid crystal molecules in the liquid crystal layer 502 based on the pattern in the optical alignment layer 304. In some implementations, the liquid crystal layer 502 may be formed from nematic or cholesteric liquid crystals.

[0120] In some implementations, the replicated structure 500 may be used as a replicated optical master, i.e., a "sub" master, to replicate the pattern of the liquid crystal layer into other optical alignment layers. When the replicated structure 500 is used as a replicated optical master, the liquid crystal layer 502 may be aligned by the optical alignment layer 304 as described herein.

[0121] The replicated structure 500 may be used to replicate the pattern of the optical alignment layer 304 into a second optical alignment layer (not shown), which may be disposed on a second substrate. The replicated optical master 500 may be positioned such that the second optical alignment layer (not shown) is between the replicated optical master 500 and the second substrate. The second optical master 500 is illuminated with light to replicate the pattern in the liquid crystal layer 502 into the second optical alignment layer. Additionally, another liquid crystal layer may be deposited on the second optical alignment layer to align the second optical alignment layer with the molecules of the other liquid crystal layer.

[0122] Referring now to FIG. 6, a perspective view of an embodiment of a system for forming replicated liquid crystal patterns is illustrated. In some implementations, optical master 200 may correspond to optical masters 200a, 200b described above in FIGS. 2a-4. In some implementations, replicated structure 300 may correspond to replicated structures 300a, 300b described above in FIGS. 3b and 4b, i.e., replicated structure 300 may include an optical alignment layer supported on a substrate, in which the liquid crystal pattern of optical master 200 is replicated by propagation of light from optical master 200 to the optical alignment layer. The illumination system also includes a light source 602, which may be a collimated light source as described with respect to FIGS. 3a, 3b, 4a, and 4b. Light source 602 may output light 604, which may be light 308 of FIGS. 3a, 3b, 4a, and 4b. In some implementations, the light source 602 may include an actuator configured to move the light output aperture of the light source 600 relative to the optical master 200. In some other implementations, the optical master 200 and the replicated structures 300 may be coupled to an actuator (e.g., may rest on a surface attached to the actuator) that moves the optical master 200 and the replicated structures 300 relative to the light output aperture of the light source 602. In some other implementations, the light source 602 and the optical master 200 and the replicated structures 300 may both have associated actuators configured to provide relative movement of the light source 602 with the optical master 200 and the replicated structures 300.

[0123] The light source 602 may scan the surface of the optical master 200 to expose the optical alignment layer of the replicated structures 300 to light diffracted by the optical master 200. The light source 602 may scan the entire surface of the optical master 200, or alternatively, it may selectively scan the surface of the optical master 200 where the pattern 208 is located. It should be understood that a smaller light source 602 may be used when the light source is scanning, as opposed to a large light source that illuminates the entire surface of the optical master 200 without scanning. Advantageously, a smaller light source may have lower cost and energy usage than a larger light source, and may have lower demands on optical properties such as coherence and peak point than a larger light source. As shown in FIG. 6 , the light source 602 may scan the surface of the optical master 200 in both vertical and horizontal directions. Furthermore, the light source 602 may be multiple light sources, each of which may illuminate a different portion of the optical master 300. Multiple light sources may scan and illuminate different portions of the optical master.

[0124] 6, in some implementations, the scanning may be a line scan or a beam scan. In some implementations, the light source 602 may provide a line of light that extends substantially across the width or length of the optical matching layer of the replicated structure 300, providing a line scan. In some other implementations, the light source 602 may provide a discrete beam of light that extends over an area that is less than the entire width or length of the optical matching layer of the replicated structure 300.

[0125] In some implementations, the light source 602 moves continuously relative to the replicated structure 300. For example, in some implementations, the light source 602 may move smoothly at a constant speed, raster scanning different portions of the optical master 300. Alternatively, the relative movement of the light source 602 and the replicated structure 300 may be stepwise, and thus turned off and on while moving to different portions of the optical master 300.

[0126] Referring now to Figure 7a, a schematic side view of the system of Figure 6 is illustrated. Overlapping features of Figures 7a and 6 will not be repeated in detail. Figure 7a further illustrates that light 604 from light source 602 has a beam width W. Furthermore, optical master 200 and replicated structure 300 are separated by a distance D. Light 604 has a beam power P. In some implementations, the system scans light 604 as it is moved at a scan speed S across replicated structure 300. Thus, it can be understood that the light dose on a portion of replicated structure 300 is equal to P*W / S, and the exposure time is equal to W / S.

[0127] To reduce the effects of environmental noise, such as vibrations, that may occur during exposure, the scanning speed is preferably fast and the exposure time is preferably short, i.e., the scanning speed is fast while still maintaining an adequate dose and adequately exposing the replicated structures 300. In some implementations, P*W / S(dose) is 0.5 Joules / cm 2 ~10 joules / cm 2 or 0.5 joules / cm 2 ~1 joule / cm 2 The dose may be selected based on various factors, such as the pattern 208 in the liquid crystal layer 206 (FIG. 2b) of the optical master 200, the exposure wavelength of the light 604, and the material properties of the liquid crystal layer 206 of the optical master 200 and the optical alignment layer 304 of the replicated structure 300.

[0128] 7b, an example of a schematic diagram of a first beam position 604a and a second beam position 604b of light 604, with a beam width W, is illustrated. As shown, the first beam position 604a and the second beam position 604b have an overlap O. It should be understood that the overlap may be included to compensate for non-uniformity of the light 604 produced by the light source 602 when the light beam 604 is moved in discrete steps across the optical matching layer. The light source 602 may produce light 604 with a Gaussian or non-square beam shape, which may lead to non-uniform intensity with respect to the center as opposed to the edges of the beam. The overlap O may mitigate the effects of the non-uniform intensity. Exemplary Augmented Reality System

[0129] As discussed herein, it should be understood that the replicated GPH disclosed herein may be utilized as part of an eyepiece for a display system, such as a virtual reality or augmented reality (AR) display system.

[0130] The AR system may display virtual content to a user or viewer while still allowing the user to see the world around them. Preferably, this content is displayed on a head-mounted display, for example, as part of eyewear, that projects image information into the user's eyes. In addition, the display may also transmit light from the surrounding environment to the user's eyes, allowing a view of that surrounding environment. As used herein, it should be understood that a "head-mounted" or "head-mountable" display is a display that can be mounted on the viewer's or user's head.

[0131] In some AR systems, multiple waveguides may be configured to form virtual images at multiple virtual depth planes (also simply referred to herein as "depth planes"). Different waveguides of the multiple waveguides may have different refractive powers and may be formed at different distances from the user's eyes. The display system may also include multiple lenses that provide, or additionally provide, refractive power. The refractive power of the waveguides and / or lenses may output light with different amounts of wavefront divergence and provide images at different virtual depth planes. In some implementations, the replicated GPH disclosed herein may advantageously be applied to the waveguides or as a separate, stand-alone layer and function as a lens. Alternatively, one type of replicated GPH may be formed as a wavelength-selective mirror that can be used to image a portion on or within the eye as part of an eye tracking system, as discussed herein.

[0132] Referring now to FIG. 8a, in some embodiments, light impinging on a waveguide may need to be redirected to incouple the light into the waveguide. An incoupling optical element may be used to redirect and incoupling the light into its corresponding waveguide. FIG. 8a illustrates a cross-sectional side view of an example of a plurality or set 660 of stacked waveguides, each including an incoupling optical element. The waveguides may each be configured to output light of one or more different wavelengths or one or more different wavelength ranges.

[0133] The illustrated set 660 of stacked waveguides includes waveguides 670, 680, and 690. Each waveguide includes an associated internal coupling optical element (which may also be referred to as the light input area on the waveguide), for example, internal coupling optical element 700 is disposed on a major surface (e.g., the upper major surface) of waveguide 670, internal coupling optical element 710 is disposed on a major surface (e.g., the upper major surface) of waveguide 680, and internal coupling optical element 720 is disposed on a major surface (e.g., the upper major surface) of waveguide 690. In some implementations, one or more of the internal coupling optical elements 700, 710, 720 may be disposed on the bottom major surface of the respective waveguides 670, 680, 690 (particularly, one or more of the internal coupling optical elements is a reflective polarizing optical element). As shown, the internal coupling optical elements 700, 710, 720 may be disposed on the upper major surface of the respective waveguide 670, 680, 690 (or on top of the next lower waveguide), and in particular, the internal coupling optical elements are transmissive turning optical elements. In some implementations, the internal coupling optical elements 700, 710, 720 may be disposed within the body of the respective waveguide 670, 680, 690. In some implementations, as discussed herein, the internal coupling optical elements 700, 710, 720 are wavelength selective, selectively redirecting one or more wavelengths of light while transmitting other wavelengths of light. While illustrated on one side or corner of the respective waveguide 670, 680, 690, it should be understood that the internal coupling optical elements 700, 710, 720 may be disposed within other areas of the respective waveguide 670, 680, 690 in some implementations.

[0134] As shown, the in-coupling optical elements 700, 710, 720 may be laterally offset from one another. In some implementations, each in-coupling optical element may be offset to receive light without that light passing through another in-coupling optical element.

[0135] Each waveguide also includes an associated optically dispersive element, for example, optically dispersive element 730 is disposed on a major surface (e.g., the top major surface) of waveguide 670, optically dispersive element 740 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and optically dispersive element 750 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some other implementations, optically dispersive elements 730, 740, 750 may be disposed on the bottom major surfaces of associated waveguides 670, 680, 690, respectively. In some other implementations, optically dispersive elements 730, 740, 750 may be disposed on both the top and bottom major surfaces of associated waveguides 670, 680, 690, respectively, or optically dispersive elements 730, 740, 750 may be disposed on different ones of the top and bottom major surfaces in different associated waveguides 670, 680, 690, respectively.

[0136] The waveguides 670, 680, 690 may be spaced apart and separated, for example, by gas, liquid, and / or solid layers of material. For example, as shown, layer 760a may separate waveguides 670 and 680, and layer 760b may separate waveguides 680 and 690. In some implementations, layers 760a and 760b are formed from a low refractive index material (i.e., a material having a lower refractive index than the material forming the immediately adjacent waveguides 670, 680, 690). Preferably, the refractive index of the material forming layers 760a, 760b is more than 0.05 or less than 0.10 relative to the refractive index of the material forming waveguides 670, 680, 690. Advantageously, the lower refractive index layers 760a, 760b may function as cladding layers that promote total internal reflection (TIR) ​​of light through the waveguides 670, 680, 690 (e.g., TIR between the top and bottom major surfaces of each waveguide). In some implementations, the layers 760a, 760b are formed from air. Although not shown, it should be understood that the top and bottom of the illustrated set of waveguides 660 may include immediate cladding layers.

[0137] Preferably, for ease of manufacturing and other considerations, the materials forming waveguides 670, 680, 690 are similar or the same, and the materials forming layers 760a, 760b are similar or the same. In some implementations, the materials forming waveguides 670, 680, 690 may differ between one or more waveguides, and / or the materials forming layers 760a, 760b may differ while still maintaining the various refractive index relationships discussed above.

[0138] 8a, light rays 770, 780, 790 enter the set of waveguides 660. It should be understood that light rays 770, 780, 790 may be launched into the waveguides 670, 680, 690.

[0139] In some implementations, light rays 770, 780, 790 have different properties, such as different wavelengths or different wavelength ranges, which may correspond to different colors. Each of the in-coupling optical elements 700, 710, 720 deflects incident light such that the light propagates through a respective one of the waveguides 670, 680, 690 by TIR. In some implementations, each of the in-coupling optical elements 700, 710, 720 selectively deflects one or more particular wavelengths of light while transmitting other wavelengths to the underlying waveguide and associated in-coupling optical element.

[0140] For example, in-coupling optical element 700 may be configured to selectively deflect light ray 770 having a first wavelength or wavelength range while transmitting light rays 780 and 790 having different second and third wavelengths or wavelength ranges, respectively. Transmitted light ray 780 impinges on and is deflected by in-coupling optical element 710, which is configured to selectively deflect light of the second wavelength or wavelength range. Light ray 790 is deflected by in-coupling optical element 720, which is configured to selectively deflect light of the third wavelength or wavelength range.

[0141] Continuing with reference to FIG. 8a, deflected light rays 770, 780, 790 are deflected to propagate through corresponding waveguides 670, 680, 690. That is, the in-coupling optical element 700, 710, 720 of each waveguide deflects the light into its corresponding waveguide 670, 680, 690, in-coupling the light into the corresponding waveguide. Light rays 770, 780, 790 are deflected at an angle that causes the light to propagate through the respective waveguides 670, 680, 690 by TIR. Light rays 770, 780, 790 propagate through the respective waveguides 670, 680, 690 by TIR until they impinge on the waveguide's corresponding optical dispersive element 730, 740, 750.

[0142] Referring now to Figure 8b, a perspective view of the multiple stacked waveguide embodiment of Figure 8a is illustrated. As described above, in-coupled light rays 770, 780, 790 are deflected by in-coupling optical elements 700, 710, 720, respectively, and then propagate by TIR within waveguides 670, 680, 690, respectively. Light rays 770, 780, 790 then impinge on optically dispersive elements 730, 740, 750, respectively. Optically dispersive elements 730, 740, 750 deflect light rays 770, 780, 790 to propagate toward out-coupling optical elements 800, 810, 820, respectively.

[0143] In some implementations, the optically dispersive elements 730, 740, 750 are orthogonal pupil expanders (OPEs). In some implementations, the OPEs deflect or disperse light into the out-coupling optical elements 800, 810, 820, and in some implementations, may also increase the beam or spot size of this light as it propagates into the out-coupling optical elements. In some implementations, the optically dispersive elements 730, 740, 750 may be omitted, and the in-coupling optical elements 700, 710, 720 may be configured to deflect light directly into the out-coupling optical elements 800, 810, 820. For example, with reference to FIG. 8B , the optically dispersive elements 730, 740, 750 may be replaced with the out-coupling optical elements 800, 810, 820, respectively. In some implementations, the outcoupling optical elements 800, 810, 820 are exit pupils (EPs) or exit pupil expanders (EPEs) that direct light toward the viewer's eyes. It should be understood that an OPE may be configured to increase the size of the eyebox in at least one axis, and that the EPE may increase the eyebox in an axis that intersects the axis of the OPE, e.g., orthogonal to the axis of the OPE. For example, each OPE may be configured to redirect a portion of the light striking the OPE to an EPE of the same waveguide while allowing the remaining portion of the light to continue propagating down the waveguide. Upon striking the OPE, again, another portion of the remaining light is redirected to the EPE, and the remainder of that portion continues to propagate further down the waveguide, etc. Similarly, upon striking the EPE, a portion of the impinging light is directed out of the waveguide toward the user, and the remaining portion of that light continues to propagate through the waveguide until it again strikes an EP, at which point another portion of the impinging light is directed out of the waveguide, etc. As a result, a single beam of internally coupled light may be "replicated" each time a portion of that light is redirected by an OPE or EPE, thereby forming a cloned beam field of light. In some implementations, the OPE and / or EPE may be configured to modify the size of the beam of light.

[0144] 8a and 8b, in some implementations, a waveguide set 660 includes, for each primary color, waveguides 670, 680, 690, in-coupling optical elements 700, 710, 720, optically dispersive elements (e.g., OPEs) 730, 740, 750, and out-coupling optical elements (e.g., EPs) 800, 810, 820. The waveguides 670, 680, 690 may be stacked with an air gap / cladding layer between each one. The in-coupling optical elements 700, 710, 720 redirect or deflect incident light into that waveguide (with different in-coupling optical elements receiving light of different wavelengths). The light then propagates at an angle that will result in TIR within the individual waveguides 670, 680, 690. In the example shown, light ray 770 (e.g., blue light) is deflected by the first in-coupling optical element 700 in the manner described above, then continues bouncing down the waveguide, interacting with the optically dispersive element (e.g., OPE) 730 and then the out-coupling optical element (e.g., EP) 800. Light rays 780 and 790 (e.g., green and red light, respectively) pass through the waveguide 670, with light ray 780 impinging on and being deflected by the in-coupling optical element 710. Light ray 780 will then, via TIR, bounce down the waveguide 680, to its optically dispersive element (e.g., OPE) 740 and then the out-coupling optical element (e.g., EP) 810. Finally, light ray 790 (e.g., red light) passes through the waveguide 690 and impinges on the optically in-coupling optical element 720 of the waveguide 690. The light in-coupling optical element 720 deflects the light ray 790 so that it propagates by TIR to the light dispersive element (e.g., OPE) 750 and then by TIR to the out-coupling optical element (e.g., EP) 820. The out-coupling optical element 820 then finally out-couples the light ray 790 to a viewer, who also receives the out-coupled light from the other waveguides 670, 680.

[0145] FIG. 8c illustrates a top-down plan view of the multiple stacked waveguide embodiment of FIGS. 8a and 8b. As shown, waveguides 670, 680, 690 may be vertically aligned, along with each waveguide's associated optically dispersive element 730, 740, 750 and associated out-coupling optical elements 800, 810, 820. However, as discussed herein, the in-coupling optical elements 700, 710, 720 are not vertically aligned. Rather, the in-coupling optical elements are preferably non-overlapping (e.g., laterally spaced apart, as seen in the top-down views). As discussed further herein, this non-overlapping spatial arrangement facilitates the injection of light from different sources into different waveguides on a one-to-one basis, thereby allowing a specific light source to be uniquely coupled to a specific waveguide. In some implementations, arrays including non-overlapping, spatially separated in-coupling optical elements may be referred to as shifted-pupil systems, and the in-coupling optical elements in these arrays may correspond to sub-pupils.

[0146] Advantageously, the GPHs disclosed herein may be utilized as part of or in addition to the various optical elements described above (e.g., in-coupling optical elements 700, 710, 720, light dispersive elements 730, 740, 750, and / or out-coupling optical elements 800, 810, 820) to provide desired optical functionality. For example, the GPHs may function as lenses and overlay the out-coupling optical elements 800, 810, 820 to provide desired optical power.

[0147] Referring now to FIG. 8d, an example of a wearable display system 60 is illustrated, into which the various waveguide and associated systems disclosed herein may be integrated. The display system 60 includes a display 70 and various mechanical and electronic modules and systems to support the functionality of the display 70. The display 70 may be coupled to a frame 80, which is wearable by a display system user or viewer 90 and configured to position the display 70 directly in front of the user's 90 eye. The display 70 may, in some implementations, be considered an eyepiece. In some implementations, a speaker 100 is coupled to the frame 80 and configured to be positioned adjacent to the user's 90 ear canal (in some implementations, another speaker, not shown, may also optionally be positioned adjacent the user's other ear canal to provide stereo / shapeable sound control). The display system 60 may also include one or more microphones 110 or other devices to detect sound. In some implementations, the microphone may be configured to allow a user to provide input or commands to the system 60 (e.g., selecting voice menu commands, natural language questions, etc.) and / or enable audio communication with other persons (e.g., other users of similar display systems). The microphone may also be configured as an ambient sensor to collect audio data (e.g., sounds from the user and / or the environment). In some implementations, the display system may also include an ambient sensor 120a, which may be separate from the frame 80 and mounted on the body of the user 90 (e.g., the head, torso, limbs, etc. of the user 90). The ambient sensor 120a, in some implementations, may be configured to obtain data characterizing a physiological state of the user 90. For example, the sensor 120a may be an electrode.

[0148] Continuing with reference to FIG. 8d, display 70 is operably coupled to local data processing module 140 by a communication link 130, such as wired or wireless connectivity, which may be mounted in a variety of configurations, such as fixedly attached to frame 80, fixedly attached to a helmet or hat worn by the user, embedded within headphones, or otherwise removably attached to user 90 (e.g., in a backpack-style configuration, in a belt-linked configuration). Similarly, sensor 120a may be operably coupled to local processor and data module 140 by a communication link 120b, such as wired or wireless connectivity. Local processing and data module 140 may comprise a hardware processor and digital memory, such as non-volatile memory (e.g., flash memory or a hard disk drive), both of which may be utilized to aid in processing, caching, and storing data. Optionally, local processing and data module 140 may include one or more central processing units (CPUs), graphics processing units (GPUs), dedicated processing hardware, etc. The data may include a) data captured from sensors (such as image capture devices (cameras, etc.), microphones, inertial measurement units, accelerometers, compasses, GPS units, wireless devices, gyroscopes, and / or other sensors disclosed herein (e.g., which may be operatively coupled to frame 80 or otherwise attached to user 90)) and / or b) data obtained and / or processed using remote processing module 150 and / or remote data repository 160 (including data related to virtual content), possibly for passage to display 70 after processing or retrieval. Local processing and data module 140 may be operatively coupled to remote processing module 150 and remote data repository 160 by communication links 170, 180, such as via wired or wireless communication links, such that these remote modules 150, 160 are operatively coupled to each other and available as resources to local processing and data module 140.In some implementations, local processing and data module 140 may include one or more of an image capture device, a microphone, an inertial measurement unit, an accelerometer, a compass, a GPS unit, a wireless device, and / or a gyroscope. In some other implementations, one or more of these sensors may be attached to frame 80 or may be freestanding structures that communicate with local processing and data module 140 by wired or wireless communication paths.

[0149] Continuing with reference to FIG. 8d, in some implementations, remote processing module 150 may comprise one or more processors configured to analyze and process data and / or image information, and may include, for example, one or more central processing units (CPUs), graphics processing units (GPUs), dedicated processing hardware, etc. In some implementations, remote data repository 160 may comprise a digital data storage facility, which may be available through the Internet or other networking configuration in a “cloud” resource configuration. In some implementations, remote data repository 160 may include one or more remote servers, which provide information, for example, information for generating augmented reality content, to local processing and data module 140 and / or remote processing module 150. In some implementations, all data is stored and all computations are performed in the local processing and data module, allowing for fully autonomous use from the remote module. Optionally, an external system (e.g., one or more processors, one or more computer systems), including a CPU, GPU, etc., may perform at least a portion of the processing (e.g., generating image information, processing data) and provide information to and receive information from modules 140, 150, 160, e.g., via a wireless or wired connection. Exemplary Eye Tracking System

[0150] FIG. 9 illustrates an example of an eye tracking system 2300 employing a liquid crystal reflector (LCR), e.g., a cholesteric liquid crystal reflector. Preferably, the liquid crystal reflector is a wavelength-selective LCR 1150 configured to image a viewer's eye 1302 according to various implementations. In some implementations, the LCR 1150 may be disposed on a surface of a waveguide (e.g., one of the waveguides 670, 680, 690 of FIGS. 8a-8b). Eye tracking may be an important feature within interactive vision or control systems, including wearable displays, e.g., the wearable display system 60 of FIG. 8d, for virtual / augmented / mixed reality display applications, among other applications. To achieve good eye tracking, it may be desirable to acquire images of the eye 1302 at a low gaze angle, and thus, to position the eye tracking camera 702b near the center of the viewer's eye. However, such a position of the camera 702b may interfere with the user's view. Alternatively, the eye tracking camera 702b may be positioned lower or to the side. However, such a camera position may increase the difficulty of obtaining robust and accurate eye tracking because eye images are captured at a steeper angle. By configuring the LCR 1150 to selectively reflect infrared (IR) light 2308 (e.g., having a wavelength of 850 nm) from the eye 302 while transmitting visible light 2304 from the world, the camera 702b may be positioned away from the user's view while capturing eye images at a normal or low gaze angle. Such a configuration does not interfere with the user's view because visible light is not reflected. The same LCR 1150 may also be configured as an IR illumination source 2320, as shown. The low gaze angle of the IR illuminator may result in less occlusion from eyelashes, for example, and the configuration allows for more robust detection of specular reflections.

[0151] 9 , according to various implementations, the LCR 1150 may comprise one or more cholesteric liquid crystal (CLC) layers each comprising a plurality of chiral structures, each chiral structure comprising a plurality of liquid crystal molecules extending in a layer depth direction (e.g., z-direction) and sequentially rotated in a first rotation direction, as described in U.S. Patent Publication No. 2018 / 0164627 (the entirety of which is incorporated herein by reference). The alignment of the liquid crystal molecules of the chiral structures varies periodically in a lateral direction perpendicular to the layer depth direction such that the one or more CLC layers are configured to substantially Bragg-reflect a first incident light having a first wavelength (λ1) while substantially transmitting a second incident light having a second wavelength (λ2). Each of the one or more CLC layers may be configured to substantially Bragg reflect first and second incident elliptically or circularly polarized light beams having a polarization handedness that matches a first rotation direction when viewed in the layer depth direction, while substantially transmitting first and second incident elliptically or circularly polarized light beams having a polarization handedness that is opposite to the first rotation direction when viewed in the layer depth direction. According to some implementations, the periodically varying alignment of the liquid crystal molecules in the lateral direction is arranged with a period in the lateral direction such that the ratio between the first wavelength and the period is about 0.5 to about 2.0. According to some implementations, the first wavelength is in the near-infrared range of about 600 nm to about 1.4 μm, e.g., about 850 nm, and the second wavelength is in the visible range having one or more colors. According to some implementations, the liquid crystal molecules in the chiral structure are pre-tilted with respect to a direction normal to the layer depth direction. The one or more CLC layers may be configured such that the first incident light is incident at a depth of about 50° relative to the layer depth. o , about 60 o , about 70 o , or about 80 o The angle (θ R ) may be configured to be reflected by

[0152] 9, the eye 1302 of a head mounted display (HMD) wearer may be imaged using a reflective off-axis liquid crystal reflector 1150, which may provide a view of the eye 1302 to camera 702B, which may also reflect eye illumination light from light source 2320. The resulting image may be used to track one or both eyes, image the retina, reconstruct eye shape in three dimensions, extract biometric information (e.g., iris identification) from the eye, etc.

[0153] Certain features described herein in the context of separate implementations may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented separately in multiple implementations or in any suitable subcombination. Furthermore, while features may be described above as operative in a combination and may even be initially claimed as such, one or more features from the claimed combination may, in some cases, be deleted from the combination, and the claimed combination may be directed to a subcombination or variation of the subcombination. No single feature or group of features is required or essential to every implementation.

[0154] It should be understood that conditional statements used herein, such as "can," "could," "might," "may," "eg," and the like, in particular, are generally intended to convey that certain implementations include certain features, elements, and / or steps, while other implementations do not, unless specifically stated otherwise or understood otherwise within the context as used. Thus, such conditional statements are generally not intended to imply that features, elements, and / or steps are in any way required for one or more implementations, or that one or more embodiment implementations necessarily include logic for determining whether those features, elements, and / or steps should be included or performed in any particular implementation, with or without authorial input or prompting. The terms "comprising," "including," "having," and the like, are synonymous and used inclusively in a non-limiting manner and do not exclude additional elements, features, acts, operations, etc. Also, the term "or" is used in its inclusive sense (and not its exclusive sense); thus, for example, when used to connect a list of elements, the term "or" means one, some, or all of the elements in the list. Additionally, the articles "a," "an," and "the," as used in this application and the appended claims, should be interpreted to mean "one or more" or "at least one," unless otherwise specified. Similarly, while operations may be depicted in the figures in a particular order, it should be recognized that such operations need not be performed in the particular order shown, or in sequential order, or that all of the depicted operations need not be performed, to achieve desirable results. Furthermore, the figures may diagrammatically depict one or more exemplary processes in the form of a flowchart. However, other operations not depicted may be incorporated within the diagrammatically depicted exemplary methods and processes.For example, one or more additional operations may be performed before, after, simultaneously with, or between any of the illustrated operations. Additionally, operations may be rearranged or reordered in other implementations. In some situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems may generally be integrated together in a single software product or packaged into multiple software products. Additionally, other implementations are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results.

[0155] Thus, the claims are not intended to be limited to the implementations shown herein but are to be accorded the widest scope consistent with the present disclosure, the principles, and novel features disclosed herein.

Claims

1. 1. A method of forming an optical master, the method comprising: disposing an optical alignment layer on a substrate; propagating light through a first optical master to the optical alignment layer, the first optical master comprising an alignment layer including surface relief features and a first liquid crystal layer on the surface relief features, liquid crystal molecules of the first liquid crystal layer defining a liquid crystal pattern, the liquid crystal pattern being replicated in the optical alignment layer by propagating the light through the first optical master to the optical alignment layer, and a replica of the liquid crystal pattern being formed in the optical alignment layer by interference of the beam of light in the optical alignment layer; forming the optical master by depositing a second liquid crystal layer on the optical alignment layer, wherein liquid crystal molecules of the second liquid crystal layer are aligned by the optical alignment layer, and the optical master comprises the second liquid crystal layer, the optical alignment layer, and the substrate; Including, The method, wherein propagating light through the first optical master includes positioning a collimated light source over the first optical master such that the collimated light source illuminates at least a portion of the first optical master.

2. 1. A method of forming an optical master, the method comprising: disposing an optical alignment layer on a substrate; propagating light through a first optical master to the optical alignment layer, the first optical master comprising an alignment layer including surface relief features and a first liquid crystal layer on the surface relief features, liquid crystal molecules of the first liquid crystal layer defining a liquid crystal pattern, the liquid crystal pattern being replicated in the optical alignment layer by propagating the light through the first optical master to the optical alignment layer, and a replica of the liquid crystal pattern being formed in the optical alignment layer by interference of the beam of light in the optical alignment layer; forming the optical master by depositing a second liquid crystal layer on the optical alignment layer, wherein liquid crystal molecules of the second liquid crystal layer are aligned by the optical alignment layer, and the optical master comprises the second liquid crystal layer, the optical alignment layer, and the substrate; Including, The first liquid crystal layer has a thickness of d, where d=λ / (2Δn), and λ is the is the wavelength of light propagated through the optical master to the optical alignment layer, and Δn is the birefringence of the first liquid crystal layer.

3. 1. A method of forming an optical master, the method comprising: disposing an optical alignment layer on a substrate; propagating light through a first optical master to the optical alignment layer, the first optical master comprising an alignment layer including surface relief features and a first liquid crystal layer on the surface relief features, liquid crystal molecules of the first liquid crystal layer defining a liquid crystal pattern, the liquid crystal pattern being replicated in the optical alignment layer by propagating the light through the first optical master to the optical alignment layer, and a replica of the liquid crystal pattern being formed in the optical alignment layer by interference of the beam of light in the optical alignment layer; forming the optical master by depositing a second liquid crystal layer on the optical alignment layer, wherein liquid crystal molecules of the second liquid crystal layer are aligned by the optical alignment layer, and the optical master comprises the second liquid crystal layer, the optical alignment layer, and the substrate; Including, the first liquid crystal layer has a thickness of d, where d=λ / (4Δn), where λ is the wavelength of light propagated through the first optical master, and Δn is the birefringence of the first liquid crystal layer.

4. The method of any one of claims 1 to 3, wherein the matching layer comprises an imprint layer.

5. The method of any one of claims 1 to 3, wherein the first and second liquid crystal layers comprise nematic liquid crystal layers.

6. 4. The method of claim 1, wherein the surface relief features comprise nanostructures, and the first liquid crystal layer is disposed on the alignment layer such that the liquid crystal molecules of the first liquid crystal layer align with the nanostructures.

7. The method of claim 6 , wherein the nanostructures comprise imprinted nanostructures.

8. 7. The method of claim 6, wherein the nanostructures comprise an optical phase and a grating period, and the liquid crystal molecules of the first liquid crystal layer are aligned by the nanostructures to comprise substantially the same optical phase and grating period.

9. The method of claim 2 , wherein the light comprises linear polarization.

10. 10. The method of claim 9, wherein the first liquid crystal layer diffracts the light into left-handed circularly polarized light and right-handed circularly polarized light, one of the left-handed circularly polarized light and the right-handed circularly polarized light being a −1 diffraction order light, and the other of the left-handed circularly polarized light and the right-handed circularly polarized light being a +1 diffraction order light.

11. 11. The method of claim 10, wherein the first liquid crystal layer diffracts half the light into left-handed circularly polarized light and half the light into right-handed circularly polarized light.

12. 4. The method of claim 3, wherein the first liquid crystal layer has an optical phase and a grating period, and after replicating the liquid crystal pattern, the optical alignment layer has an optical phase and a grating period equal to the optical phase and the grating period of the first liquid crystal layer.

13. The method of claim 3 , wherein the light comprises one of left-handed and right-handed circular polarization.

14. The first liquid crystal layer diffracts the light into left-handed circularly polarized light and right-handed circularly polarized light, and one of the right-handed circularly polarized light is a +1 or −1 diffraction order light, and the other of the left-handed circularly polarized light and the right-handed circularly polarized light is a zero diffraction order light.

15. 15. The method of claim 14, wherein the first liquid crystal layer diffracts half the light into left-handed circularly polarized light and the second liquid crystal layer diffracts half the light into right-handed circularly polarized light.

16. The method of claim 1 , wherein propagating light through the first optical master further comprises moving the collimated light source to a different portion of the first optical master.

17. The collimated light source has a beam power (P) and a beam width (W), the collimated light source is moved at a scanning speed (S), and the dose provided by the collimated light source is equal to P*W / S, the dose being 0.5 Joules / cm ２ ~10 joules / cm ２ 17. The method of claim 16, wherein:

18. 20. The method of claim 17, wherein the scanning speed provides a total exposure time of less than 1 / 6 second across any portion of the photoalignment layer.

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