Compositions of materials for fabrication of evacuated periodic gratings

Abstract

Compositions, systems, and methods for fabricating a grating are described herein. Grating structures can be formed to have evacuated periodic structures (EPSs) with alternating polymer rich regions and inert fluid rich regions. In an EPS process, a volume grating is formed after a holographic exposure process. This volume grating includes polymer rich regions (e.g. a polymer matrix) surrounding inert substance rich regions. The inert material rich regions are removed to produce high modulation surface relief gratings (SRGs) after the inert material is removed. The SRGs may include a polymer matrix surrounding air gaps.

Description

COM POSITIONS OF MATERIALS FOR FABRICATION OF EVACUATED PERIODIC GRATINGSCROSS-REFERENCES TO RELATED APPLICATIONS

[0001] The current application claims priority to Provisional Application No. 63 / 633,527, filed April 12, 2024, the disclosure of which is incorporated herein by reference.FIELD OF THE INVENTION

[0002] This disclosure generally refers to compositions, systems, and methods for fabricating a grating. Grating structures can be formed to have alternating polymer rich regions and inert fluid rich regions.BACKGROUND

[0003] Waveguides can be referred to as structures with the capability of confining and guiding waves (i.e., restricting the spatial region in which waves can propagate). One subclass includes optical waveguides, which are structures that can guide electromagnetic waves, typically those in the visible spectrum. Waveguide structures can be designed to control the propagation path of waves using a number of different mechanisms. For example, planar waveguides can be designed to utilize diffraction gratings to diffract and couple incident light into the waveguide structure such that the incoupled light can proceed to travel within the planar structure via total internal reflection (TIR).

[0004] Fabrication of waveguides can include the use of material systems that allow for the recording of holographic optical elements within or on the surface of the waveguides. One class of such material includes polymer dispersed liquid crystal (PDLC) mixtures, which are mixtures containing photopolymerizable monomers and liquid crystals. A further subclass of such mixtures includes holographic polymer dispersed liquid crystal (HPDLC) mixtures. Holographic optical elements, such as volume phase gratings, can be recorded in such a liquid mixture by illuminating the material with two or more mutually coherent laser beams. During the recording process, the monomerspolymerize, and the mixture undergoes a photopolymerization-induced phase separation, creating regions densely populated by liquid crystal (LC) micro-droplets, interspersed with regions of clear polymer. The alternating liquid crystal-rich and liquid crystal-depleted regions form the fringe planes of the grating.

[0005] Waveguide optics, such as those described above, can be considered for a range of display systems and sensor applications. In many applications, waveguides containing one or more grating layers encoding multiple optical functions can be realized using various waveguide architectures and material systems, enabling new innovations in near-eye displays for Augmented Reality (AR) and Virtual Reality (VR), compact Heads Up Displays (HUDs) for aviation and road transport, and sensors for biometric and laser radar (LIDAR) applications. As many of these applications are directed at consumer products, there is a growing requirement for efficient low cost means for manufacturing holographic waveguides in large volumes.SUMMARY OF THE INVENTION

[0006] Systems and methods in accordance with some embodiments of the invention are directed to grating structures formed to have alternating polymer rich regions and inert fluid rich regions.

[0007] In some aspects, the techniques described herein relate to a holographic mixture including: a monomer; one or more photoinitiators; and a liquid crystal material including a first component of formula:where n is 3 or more, Y is H or a halogen, R is H, an alkyl, or an alkoxy, and Z is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, SCN, or nitrogen derivatives.

[0008] In some aspects, the techniques described herein relate to a holographic mixture, wherein the first component has the formula:

[0009] In some aspects, the techniques described herein relate to a holographic mixture, wherein the first component has the formula:

[0010] In some aspects, the techniques described herein relate to a holographic mixture, further including a second component selected from the group consisting of amolecule of formula: where n is 2; R is an alkyl; and Z is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen derivatives.

[0011] In some aspects, the techniques described herein relate to a holographic mixture, wherein the second component includes alkyl cyanobiphenyl or alkoxy cyanobiphenyl.

[0012] In some aspects, the techniques described herein relate to a holographic mixture, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is pentyl cyanobiphenyl or pentyloxy cyanobiphenyl.

[0013] In some aspects, the techniques described herein relate to a holographic mixture, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is hexyl cyanobiphenyl or hexyloxy cyanobiphenyl.

[0014] In some aspects, the techniques described herein relate to a holographic mixture, further including a third component of a formula:where X is an ester, an olefinic, an acetylenic, Y is H or a halogen, R is an alkyl or an alkoxy, and Z is an alkyl, an alkoxy, an ester, a halogen, CN, CNS, or nitrogen derivatives.

[0015] In some aspects, the techniques described herein relate to a holographic mixture, wherein the third component has the formula:

[0016] In some aspects, the techniques described herein relate to a holographic mixture, wherein the second component includes: a first molecule of formula:and a second molecule of formula:

[0017] In some aspects, the techniques described herein relate to a holographic mixture, further including a second component of a molecule of formula:, where n is 2; R is an alkyl; and Z is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen derivatives.

[0018] In some aspects, the techniques described herein relate to a holographic mixture, wherein the second component includes alkyl cyanobiphenyl or alkoxy cyanobiphenyl.

[0019] In some aspects, the techniques described herein relate to a holographic mixture, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is pentyl cyanobiphenyl or pentyloxy cyanobiphenyl.

[0020] In some aspects, the techniques described herein relate to a holographic mixture, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is hexyl cyanobiphenyl or hexyloxy cyanobiphenyl.

[0021] In some aspects, the techniques described herein relate to a holographic mixture, further including a third component of a formula:where X is an ester, an olefinic, an acetylenic, Y is H or a halogen, R is an alkyl or an alkoxy, and Z is an alkyl, an alkoxy, an ester, a halogen, CN, CNS, or nitrogen derivatives.

[0022] In some aspects, the techniques described herein relate to a holographic mixture, wherein the third component has the formula:

[0023] In some aspects, the techniques described herein relate to a holographic mixture, wherein the second component includes: a first molecule of formula:and a second molecule of formula:

[0024] In some aspects, the techniques described herein relate to a method of fabricating a grating, the method including: coating a holographic mixture on a surface of a substrate, the holographic mixture including: a monomer; a liquid crystal material including a first component of formula:where n is 3 or more, Y is H or a halogen, R is H, alkyl, or alkoxy, and Z is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen; applying holographic recording beams to the layer to form a volume grating including alternating polymer rich regions and liquid crystal rich regions; and removing at least a portion of the liquid crystal in the liquid crystal rich regions to form a polymer surface relief grating.

[0025] In some aspects, the techniques described herein relate to a method, wherein the polymer surface relief grating includes a Bragg fringe spacing of 0.35pm to 0.8pm and a grating depth of 1 pm to 3pm as examples.

[0026] In some aspects, the techniques described herein relate to a method, wherein the polymer surface relief grating includes a ratio of Bragg fringe spacing to grating depth of 1 :1 to 5:1.

[0027] In some aspects, the techniques described herein relate to a method, wherein the polymer surface relief grating includes a grating depth and a grating pitch and wherein the grating depth is greater than the grating pitch.

[0028] In some aspects, the techniques described herein relate to a method, wherein the holographic mixture includes a low viscosity which is configured to enable ink jet printing.

[0029] In some aspects, the techniques described herein relate to a method, wherein coating the holographic mixture on the surface of the substrate includes inkjet printing the holographic mixture onto the surface of the substrate.

[0030] In some aspects, the techniques described herein relate to a method, wherein the first component has the formula:

[0031] In some aspects, the techniques described herein relate to a method, whereinthe first component has the formula:

[0032] In some aspects, the techniques described herein relate to a method, wherein the liquid crystal material further includes a second component selected from the groupconsisting of a molecule of formula: where n is 2; R is an alkyl; and Z is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen derivatives.

[0033] In some aspects, the techniques described herein relate to a method, wherein the second component includes alkyl cyanobiphenyl or alkoxy cyanobiphenyl.

[0034] In some aspects, the techniques described herein relate to a method, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is pentyl cyanobiphenyl or pentyloxy cyanobiphenyl.

[0035] In some aspects, the techniques described herein relate to a method, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is hexyl cyanobiphenyl or hexyloxy cyanobiphenyl.

[0036] In some aspects, the techniques described herein relate to a method, wherein the liquid crystal material further includes a third component of a formula:where X is an ester, an olefinic, an acetylenic, Y is H or a halogen, R is an alkyl or an alkoxy, and Z is an alkyl, an alkoxy, an ester, a halogen, CN, CNS, or nitrogen derivatives.

[0037] In some aspects, the techniques described herein relate to a method, wherein the third component has the formula:

[0038] In some aspects, the techniques described herein relate to a method, whereinthe second component includes: a first molecule of formula:and a second molecule of formula:

[0039] In some aspects, the techniques described herein relate to a method, wherein the liquid crystal material further includes a second component of a molecule of formula:, where n is 2; R is an alkyl; and Z is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen derivatives.

[0040] In some aspects, the techniques described herein relate to a method, wherein the second component includes alkyl cyanobiphenyl or alkoxy cyanobiphenyl.

[0041] In some aspects, the techniques described herein relate to a method, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is pentyl cyanobiphenyl or pentyloxy cyanobiphenyl.

[0042] In some aspects, the techniques described herein relate to a method, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is hexyl cyanobiphenyl or hexyloxy cyanobiphenyl.

[0043] In some aspects, the techniques described herein relate to a method, wherein the liquid crystal material further includes a third component of a formula:where X is an ester, an olefinic, an acetylenic, Y is H or a halogen, R is an alkyl or an alkoxy, and Z is an alkyl, an alkoxy, an ester, a halogen, CN, CNS, or nitrogen derivatives.

[0044] In some aspects, the techniques described herein relate to a holographic mixture, wherein the third component has the formula:

[0045] In some aspects, the techniques described herein relate to a holographic mixture, wherein the second component includes: a first molecule of formula:and a second molecule of formula:

[0046] In some aspects, the techniques described herein relate to a method, wherein the refractive index difference between the polymer rich regions and inert fluid rich regions corresponds to an LC-poor concentration in an isotropic metastable region of a phase diagram and an LC-rich concentration in the isotropic metastable region of the phase diagram.

[0047] In some aspects, the techniques described herein relate to a method, wherein polymer rich regions corresponds to the LC-poor concentration and inert fluid rich regions corresponds the LC-rich concentration which both lie above the isotropic to anisotropic transition line.

[0048] In some aspects, the techniques described herein relate to a method for fabricating a grating, the method including: providing a mixture of monomer and inert fluid; coating a layer of the mixture on a surface of the substrate; and applying holographic recording beams to the layer to form a volume grating including alternating polymer rich regions and inert fluid rich regions, wherein the refractive index difference between the polymer rich regions and inert fluid rich regions is low.

[0049] In some aspects, the techniques described herein relate to a method for fabricating a grating, the method including: providing a mixture of monomer and inert fluid; coating a layer of the mixture on a surface of the substrate; and applying holographic recording beams to the layer to form a volume grating including alternating polymer rich regions and inert fluid rich regions, wherein the refractive index difference between the polymer rich regions and inert fluid rich regions corresponds to an LC-poor concentration in an isotropic metastable region of a phase diagram and an LC-rich concentration in the isotropic metastable region of the phase diagram.

[0050] In some aspects, the techniques described herein relate to a method for fabricating a grating, the method including: providing a mixture of monomer and inert fluid; coating a layer of the mixture on a surface of the substrate; and applying holographic recording beams to the layer to form a volume grating including alternating polymer rich regions and inert fluid rich regions, wherein polymer rich regions corresponds to the LC- poor concentration and inert fluid rich regions corresponds the LC-rich concentration which both lie above the isotropic to anisotropic transition line.

[0051] Additional embodiments and features are set forth in part in the description that follows, and in part will become apparent to those skilled in the art upon examination of the specification or may be learned by the practice of the disclosure. A further understanding of the nature and advantages of the present disclosure may be realized by reference to the remaining portions of the specification and the drawings, which forms a part of this disclosure.BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The description will be more fully understood with reference to the following figures, which are presented as embodiments of the invention and should not be construed as a complete recitation of the scope of the invention, wherein:

[0053] Fig. 1A illustrates a Group 1 liquid crystal material for use in a holographic polymer dispersed liquid crystal (HPDLC) mixture.

[0054] Figs. 1 B-1 to 1 B-5 illustrate various examples of Group 1 liquid crystal material in accordance with various embodiments.

[0055] Fig. 2A illustrates a Group 2 liquid crystal material for use in a HPDLC mixture in accordance with various embodiments.

[0056] Figs. 2B-1 to 2B-4 illustrate various examples of Group 2 liquid crystal material in accordance with various embodiments.

[0057] Fig. 3A illustrates a Group 3 liquid crystal material for use in a HPDLC mixture in accordance with various embodiments.

[0058] Figs. 3B-1 to 3B-2 illustrate various examples of Group 3 liquid crystal material in accordance with various embodiments.

[0059] Fig. 4A illustrates a Group 4 liquid crystal material for use in a HPDLC mixture in accordance with various embodiments.

[0060] Figs. 4B illustrates an example of Group 4 liquid crystal material in accordance with various embodiments.

[0061] Figs. 5A-5D schematically illustrate a process for fabricating deep SRGs or EPSs in accordance with an embodiment.

[0062] Fig. 6 illustrates a method for forming deep SRGs from a HPDLC periodic structure formed on a transparent substrate in accordance with an embodiment.

[0063] Figs. 7A and 7B schematically illustrate a cross sectional view of exemplary embodiments of polymer-air periodic grating structures.

[0064] Fig. 8 illustrates a phase diagram of a typical isotropic mixing of liquid crystal and monomer.

[0065] Fig. 9 illustrates various plots relating free energy (Gibbs free energy) to phase diagram for a typical isotropic mixing case.

[0066] Fig. 10 illustrates a phase diagram including isotropic mixing and nematic contribution in accordance with various embodiments.

[0067] Fig. 11 illustrates a plot of nematic order parameter versus concentration (pi. in accordance with various embodiments.

[0068] Fig. 12 illustrates a phase diagram including isotropic mixing and nematic contribution and cross linking in accordance with various embodiments.

[0069] Fig. 13 illustrates a time-development of phase diagram around a mixture point (P) in accordance with various embodiments.

[0070] Fig. 14 illustrates a liquid crystal polymer cross-linked phase diagram in accordance with various embodiments.DETAILED DESCRIPTION

[0071] Various embodiments of the invention relate to evacuated periodic structures (EPSs) which includes the use of a holographic mixture which may include, among other substances, a monomer and an inert substance. EPSs and various methods of manufacture including descriptions of holographic mixtures are described in U.S. Pat. Pub. No. 20220283376, entitled “Evacuated Periodic Structures and Methods of Manufacturing” and filed Mar. 7, 2022, and U.S. Pat. Pub. No. “Evacuating Bragg gratings and methods of manufacturing” and filed Aug. 28, 2020, which are hereby incorporated by reference in their entireties for all purposes. Examples of holographic mixtures are described in U.S. Pat. Pub. No. 20200271973, entitled “Holographic Polymer Dispersed Liquid Crystal Mixtures with High Diffraction Efficiency and Low Haze” and filed Feb. 24, 2020, which is hereby incorporated by reference in its entirety for all purposes. In an EPS process, a volume grating is formed after a holographic exposure process. This volume grating includes polymer rich regions (e.g. a polymer matrix) surrounding inert substance rich regions.

[0072] The inert material rich regions are removed to produce high modulation surface relief gratings (SRGs) after the inert material is removed. The SRGs may include a polymer matrix surrounding air gaps. The inert material may be a liquid crystal (LC). The LC may include cyanobiphenyls and / or terphenyls with desired substituents or functionalities. It has been discovered that the optical modulation of the recordedholographic mixture structure is not significant to the overall performance of the resulting evacuated periodic structure. Optical modulation may be referred to as An which is the difference between the refractive index between the polymer rich regions and the inert fluid rich regions after exposure. This differs from conventional holographic waveguide processes where high refractive index difference is desirable to create high diffraction efficiency where difference in refractive indices is created by holographic process. In creating an EPS, the inert material is removed and thus the diffraction efficiency is created by the difference in refractive index between the polymer matrix and the resultant air gaps. In some embodiments, the inert material may be tuned to allow for optimal printability using coating techniques such as inkjet printing of the holographic mixture which results in high performance gratings. In some embodiments the composition of the inert material and monomer may be tuned for optimum printability while at the same time providing the optical mixture for phase separation to take place. Ideally phase separation should result in small droplet sizes to minimise surface roughness after inert material removal and to facilitate etching processes used in post curing to modify the shape of the diffracting structures. In some cases, after exposure but before evacuation, the resultant volume grating may have zero or close to zero diffraction efficiency.

[0073] It has been discovered that utilizing an inert substance which creates inert substance rich regions which are of low refractive index difference between the polymer matrix still creates a high diffraction efficiency grating after the subsequent removal of the inert substance. The removal of the inert substance creates alternating polymer matrix regions with air gap regions. The polymer matrix has a high refractive index difference with the air gap. Previous volume Bragg gratings (VBGs) utilize a holographic mixture including a monomer and liquid crystal. After holographic exposure, a volume grating of alternating polymer regions and liquid crystal regions were created. However, these polymer regions and liquid crystal regions have a high refractive index difference to create high diffraction efficiency. This is fundamentally different from the holographic mixture utilized in creating evacuated periodic structures as discussed above. The holographic mixture utilized to create evacuated periodic structures, may include an inert substance (e.g. inert fluid). The inert substance may be utilized to create optimal phase separation with the monomer during holographic exposure. The inert substance may include a liquidcrystal. In many embodiments, the inert substance may include nanoparticles. In many embodiments, the inert substance may not be a full liquid crystal but instead include various liquid crystal singles or monomers. In many embodiments, the inert substance may be tuned to allow for optimal printability of the holographic mixture which results in high performance gratings. It has been discovered that utilizing a holographic mixture which, after holographic exposure, creates a low refractive index difference between the polymer matrix and the inert substance allows homogeneity of the ink and / or high flexibility which makes these inert substances unique candidates for these holographic applications. The inert substance may be utilized to produce good phase separation or have high printability instead of optimized for producing a high refractive index difference after exposure as in conventional holographic processes.

[0074] Thus, the resultant volume grating after exposure may include low refractive index difference between the inert substance rich regions and the polymer matrix regions. Further, typical VBGs include a high film thickness to create a high diffraction efficiency. However, the resultant volume grating after exposure may be of low refractive index difference and resultant high diffraction efficiency of the volume grating has been discovered to be not of importance in waveguide applications. Instead, high diffraction efficiency of the resultant EPS is of more importance. In some embodiments, the high diffraction efficiency EPS structures is thin, with a typical thickness of less than 3 microns as an example. It has been discovered that high diffraction efficiency with the resultant EPS may be achieved without having high thickness which is significantly different from the structure of typical VBGs.

[0075] In some embodiments the refractive index difference between the polymer rich regions and the inert substance rich regions is 0.01 to 0.2. In some embodiments, the refractive index difference between the polymer rich regions and the inert substance rich regions is 0.05 to 0.2. This difference may create a low diffraction efficiency. By comparison, the refractive index difference between the polymer matrix and the air gaps of the resultant EPS may be 0.25 to 0.4. This difference may create a high diffraction efficiency in the EPS.

[0076] Specific inert materials have been discovered. These inert materials may include various liquid crystal materials. The liquid crystal materials may include one or more liquid crystal singles or monomers.

[0077] Fig. 1 A illustrates a liquid crystal material for utilization in a holographic polymer dispersed liquid crystal (HPDLC) mixture in accordance with an embodiment of the invention. In this liquid crystal material: n is 2; R is an alkyl (e.g. CnH2n+i); Y is hydrogen (H); Z is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, SCN, or nitrogen derivatives. For the purposes of this disclosure, this liquid crystal material will be labeled Group 1.

[0078] Figs. 1 B-1 , 1 B-2, 1 B-3, 1 B-4, and 1 B-5 are various specific examples of the liquid crystals of Fig. 1A in accordance with embodiments of the invention. In one example, R is H or alkyls (e.g. CnH2n+i). Z is alkyl, alkoxy, ester, halogens, CN, NCS, SCN, nitro. One example may be pentyl cyanobiphenyl. Other examples may include homologues of pentyl cyanobiphenyl or functionalized / substituted with various alkyl chains or their derivatives.

[0079] In each of the groups discussed in this disclosure, type of alkyl chain and other substituents / functionalities are selected based on their compatibility with rest of the formulation, phase transition characteristics, molecular weight, and efficacy to phase separate during photopolymerization.

[0080] Fig. 2A illustrates a liquid crystal material for utilization in a HPDLC mixture in accordance with an embodiment of the invention. In this liquid crystal material: n is 2; R is H or alkyls (e.g. CnH2n+i); Z is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen derivatives. For the purposes of this disclosure, this liquid crystal material will be labeled Group 2.

[0081] Figs. 2B-1 , 2B-2, 2B-3, and 2B-4 are a specific example of the liquid crystal material of Fig. 2A. In Fig. 2B-1 , R is attached to an oxygen which produces OCeH . This example is hexyloxy cyanobiphenyl. Other examples may include homologues of hexyloxy cyanobiphenyls or functionalized / substituted biphenyls with various alkyl chains. In Figs. 2B-1 to 2B-4, R is H or alkyls (e.g. CnH2n+i); Z is alkyl, alkoxy, ester, halogens, CN, NCS, SCN, or nitrogen derivatives.

[0082] Fig. 3A illustrates a liquid crystal material for utilization in a HPDLC mixture in accordance with an embodiment of the invention. In this liquid crystal material, n is 3 ormore; Y is H or a halogen; R is H, an alkyl (e.g. CnH2n+i), or an alkoxy (OCnH2n+i); Z is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, SCN, or nitrogen derivatives. There may be other derivatives and variants of the core structure. For the purposes of this disclosure, this liquid crystal material will be labeled Group 3.

[0083] Figs. 3B-1 and 3B-2 are specific examples of the liquid crystals of Fig. 3A. In one of the examples, R is an alkyl (-C3H7). This example includes substituted terphenyls having propyl or one or more homologues with various alkyl chains substitutes and other substituents may include halogens like fluoro and / or cyano groups. One example may be 2'-fluoro-4"-propyl-[1 ,1 ':4',1"-terphenyl]-4-carbonitrile. One example may be 4"-pentyl- [1 , 1 ' : 4' , 1 "-terphenyl]-4-carbonitrile.

[0084] Fig. 4A illustrates a liquid crystal material for utilization in a HPDLC mixture in accordance with an embodiment of the invention. In this liquid crystal material, A and B are phenyl and / or cyclohexyl; n is 1 or more; X is an ester, an olefinic, or an acetylenic; Y is a halogen; R is alkyl or alkoxy; Z is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, ora nitrogen derivative. There may be other derivatives and variants of this core structure. For the purposes of this disclosure, this liquid crystal material will be labeled Group 4.

[0085] Fig. 4B illustrates a specific example of the liquid crystal material of Fig. 4A. In this example, the linking group is an ester (-COO- linking groups). This example may include substituted phenyls having alkyl chain. Substitutes can be halogens like fluoro, and / or cyano groups. One example may include 4-cyano-3-fluorophenyl 4-butylbenzoate.

[0086] Phenyl groups in LCs are known to facilitate K-K staking of aromatic groups. This property is commonly used in Calamitic LCs where conjugated aromatic groups provide rigid core structures leading aggregated LC clusters, also known as LC ‘droplets’. Nematic phase is a type of calamitic LCs and commonly used in HPDLCs. Other types of Calamitic LCs are smectic and cholesteric types. Alkyl groups in nematic LCs provide tail end or flexible phase in these LCs. Packing of aromatic groups creates stacked & rigid structures almost like crystalline phases, but flexible alkyl chains are structural building blocks to enable mobile or liquid phases in these LCs. Combinations of aromatic and alkyl chains are commonly used in Calamitic to tune micro-structures and phase transition characteristics.

[0087] As discussed above, the holographic mixture may be utilized to produce a polymer surface relief grating. The polymer surface relief grating may be considered an evacuated periodic structure (EPS). Examples of EPSs are disclosed in U.S. Pat. Pub. No. 2021 / 0063634, entitled “Evacuating Bragg gratings and methods of manufacturing” and filed Aug. 28, 2020, PCT Pub. No. WO 2022015878, entitled “Nanoparticle-based holographic photopolymer materials and related applications” and filed Jul. 14, 2021 , and U.S. Pat. Pub. No. 2022 / 0283376, entitled “Evacuated Periodic Structures and Methods of Manufacturing” and filed Mar. 7, 2022, which are hereby incorporated by reference in their entirety.

[0088] Periodic structures (e.g. gratings) may be utilized on waveguides in order to provide a variety of functions. These periodic structure may include angle multiplexed gratings, color multiplexed gratings, fold gratings, dual interaction gratings, rolled K-vector gratings, crossed fold gratings, tessellated gratings, chirped gratings, gratings with spatially varying refractive index modulation, gratings having spatially varying grating thickness, gratings having spatially varying average refractive index, gratings with spatially varying refractive index modulation tensors, and gratings having spatially varying average refractive index tensors. In specific examples, gratings for diffraction of various polarizations of light (e.g. S-polarized light and P-polarized light) may be beneficial. It may be specifically advantageous to have a grating which diffracts either S-polarized light or P-polarized light. Specific applications for this technology include waveguide-based displays such as augmented reality displays and virtual reality displays. One example is input gratings which may be used to input one or both of S-polarized light or P-polarized light into the waveguide. However, in many cases, it may be advantageous to have a grating which can diffract either S-polarized light and P-polarized light. For example, waveguide displays using unpolarized light sources such as organic light emitting diodes (OLEDs) as light sources produce both S-polarized and P-polarized light and thus it would be advantageous to have gratings which can diffract both S-polarized and P-polarized light.

[0089] Surface relief gratings (SRGs) may be used to diffract either P-polarized light or S-polarized light which may lead to a 50% efficiency loss with unpolarized light sources such as OLEDs and light emitting diodes (LEDs). Combining a mixture of S-polarizationdiffracting and P-polarization diffracting gratings may provide a theoretical 2x improvement over waveguides using P-diffracting gratings only. Thus, it would be advantageous to have a high efficiency S-polarization diffraction grating. In many embodiments, an S-polarization diffracting grating can be provided by a periodic structure formed in a holographic photopolymer. One periodic structure includes a grating such as a Bragg grating.

[0090] The EPSs may form deep SRGs which have superior S-polarization diffraction efficiency. Deep SRGs may be configured to provide high efficiency for both S- polarization and P-polarization light. HPDLC periodic structures formed using typical LC and monomer material components may have LC molecular structures that are preferentially aligned for high P diffraction efficiency. After the LC has been removed, the polarization dependence of the resulting SRG may depend on properties of the resulting polymer grating. The relative efficiencies for S-polarization and P-polarization light may be tuned to provide high S-polarization or P-polarization diffraction efficiency or high diffraction efficiency at both polarizations based on grating thickness.

[0091] The deep SRGs may exhibit high S-diffraction efficiency (up to 99%) and low P-diffraction efficiency and may be implemented as input gratings for waveguides. The EPSs may be evacuated Bragg gratings (EBGs). Such periodic structures can be formed by removing the liquid crystal from HPDLC periodic structures formed from holographic phase separation of a liquid crystal and monomer mixture. Deep SRGs formed by such a process typically have a thickness in the range 1 -3 micrometers with a fringe spacing 0.35 to 0.80 micrometers. In some embodiments, a fringe spacing may be less than 0.35 micrometers. In some embodiments, the ratio of grating depth to fringe spacing may be 1 :1 to 5:1. As can readily be appreciated, such gratings can be formed with different dimensions depending on the specific requirements of the given application.

[0092] Periodic structures of any complexity can be made using interference or master and contact copy replication. In some embodiments, after removing the LC, the SRGs can be back filled with a material with different properties to the LC. This allows a periodic structure with modulation properties that are not limited by the grating chemistry needed for grating formation.

[0093] In some embodiments, the backfill material may not be a LC material. In some embodiments, the backfill material may have a higher index of refraction than air which may increase the angular bandwidth of a waveguide. The backfill material may have an index (based on ordinary or extraordinary indices in the case of birefringent materials) higher or lower than the polymer matrix. The backfill material may provide planarization of the grating structure. This may be advantageous for deposition of optical coatings. In several embodiments, the deep SRGs can be partially backfilled with LC to provide a hybrid SRG / periodic structure. Alternatively, in some embodiments, the refill step can be avoided by removing just a portion of the LC from the LC rich regions of the HPDLC to provide a hybrid SRG / periodic structure. The refill approach has the advantage that a different LC can be used to form the hybrid periodic structures. The materials can be deposited using an inkjet deposition process.

[0094] In some embodiments, the methods described herein may be used to create photonic crystals. Photonic crystals may be implemented to create a wide variety of diffracting structures including periodic structures such as Bragg gratings. Periodic structures may be used as diffraction gratings to provide functionality including but not limited to input gratings, output gratings, beam expansion gratings, and gratings for diffracting more than one primary color. A photonic crystal can be a three-dimensional lattice structure that can have diffractive capabilities not achievable with basic periodic structures (such as Bragg gratings formed from alternating high index and low index lamina). Photonic crystals can include many structures including all 2-D and 3-D Bravais lattices. Recording of such structures may benefit from more than two recording beams. Photonic crystals may include polymer diffracting elements (such as rods) immersed in air or, alternatively, elongated voids in a polymer matrix. The structures may have more complex geometries depending on the recording arrangement and number of interfering beams. In many cases, the structure resulting from exposure and phase separation may be modified using etching processes.

[0095] In some embodiments, waveguides incorporating photonic crystals can be arranged in stacks of waveguides, each having a grating prescription for diffracting a unique spectral bandwidth or angular bandwidth. In many embodiments, a photonic crystal formed by liquid crystal extraction provides a deep SRG. In many embodiments,a deep SRG formed using a liquid crystal extraction process can typically have a thickness in the range 1-3 micron with a fringe spacing 0.35 micron to 0.80 micron. The fringe spacing may be a Bragg fringe spacing. In many embodiments, the condition for a deep SRG is characterized by a high grating depth to fringe spacing ratio. In some embodiments the condition for the formation of a deep SRG is that the grating depth can be approximately twice the grating period. It should be emphasized here that, although S-polarization diffracting deep SRGs are described in the present application, deep SRGs can, as will be discussed below, provide a range of polarization response characteristics depending on the thickness of the grating prescription and, in particular, the grating depth. Deep SRGs can also be used in conjunction with conventional Bragg gratings to enhance the color, uniformity and other properties of waveguide displays.

[0096] The disclosure provides a method for making a surface relief grating that can offer very significant advantages over nanoimprint lithographic process particularly for slanted gratings. Periodic structures of any complexity can be made using interference or master and contact copy replication. In some embodiments after removing the LC the SRG can be back filled with a material with different properties to the LC. This allows a periodic structure with modulation properties that are not limited by the grating chemistry needed for grating formation. In some embodiments the SRGs can be partially backfilled with LC to provide a hybrid SRG / periodic structure. Alternatively, in some embodiments, the refill step can be avoided by removing just a portion of the LC from the LC rich regions of the HPDLC to provide a hybrid SRG / periodic structure. The refill approach has the advantage that a different LC can be used to form the hybrid grating. The materials can be deposited using an inkjet process. In some embodiments, the refill material may have a higher index of refraction than air which may increase diffraction efficiency of the periodic structure.

[0097] While this disclosure has been made in the context of fabricating deep SRGs, it is appreciated that many other grating structures may be produced using the techniques described herein. For example, any type of SRG including SRGs in which the grating depth is smaller than the grating frequency (e.g. Raman-Nath gratings) may be fabricated as well.

[0098] Figs. 5A-5D schematically illustrate a process for fabricating deep SRGs or EPSs in accordance with an embodiment. Fig. 5A illustrates a first step of a method for fabricating an EPS in which a mixture 191 of monomer and liquid crystal is deposited on a transparent substrate 192 and exposed to holographic exposure beams 193, 194. The holographic exposure beams 193, 194 may be deep UV beams. In some examples, the mixture 191 may also include at least one of a photoinitiator, a coinitiator, a multifunctional thiol, adhesion promoter, surfactant, and / or additional additives. In some embodiments, the mixture may be deposited with a spatial variation of composition and / or layer thickness across the substrate. In some embodiments, the mixture may contain additives for providing a spatial variation of average refractive index across the finished grating.

[0099] The mixture 191 may include nanoparticles. The mixture 191 may include photoacids. The mixture 191 may be a monomer diluted with a non-reactive polymer. The mixture 191 may include more than one monomer. In some embodiments, the monomer may be isocyanate-acrylate based or thiolene based. In some embodiments, the liquid crystal may be a full liquid crystal mixture or a liquid crystal single. A liquid crystal single may only include a portion of a full liquid crystal mixture. Various examples of liquid crystal singles or monomers may include one or all of cyanobiphenyls, alkyl, alkoxy, cyanobiphenyls, and / or terphenyls with or without substitutions on phenyl groups. The liquid crystal mixture may include a cholesteric liquid crystal. The liquid crystal mixture may include chiral dopants which may control the grating period. The liquid crystal mixture may include photo-responsive and / or halogen bonded liquid crystals. Examples of the liquid crystal in the holographic mixture 191 are discussed above.

[0100] In some embodiments, liquid crystal may be replaced with another substance that phase separates with the monomer during exposure to create polymer rich regions and substance rich regions. Advantageously, the substance and liquid crystal singles or monomers may be a cost-effective substitute to full liquid crystal mixtures which are removed at a later step as described below.

[0101] In some embodiments, the liquid crystal in the mixture 191 may have a difference between an extraordinary refractive index and an ordinary refractive index of less than 0.01. In some embodiments, the liquid crystal in the mixture 191 may have a difference between an extraordinary refractive index and an ordinary refractive index ofless than 0.025. In some embodiments, the liquid crystal in the mixture 191 may have a difference between an extraordinary refractive index and an ordinary refractive index of less than 0.05.

[0102] Fig. 5B conceptually illustrates the result from Fig. 5A which includes an HPDLC Bragg grating 195 formed on a transparent substrate using the holographic exposure beams. The holographic exposure beams may transform the monomer into a polymer in some areas. The holographic exposure beams may include intersecting recording beams and include alternating bright and dark illumination regions. A polymerization-driven diffusion process may cause the diffusion of monomers and liquid crystal in opposite directions, with the monomers undergoing gelation to form polymer- rich regions (in the bright regions) and the liquid crystal becoming trapped in a polymer matrix to form liquid crystal rich regions (in the dark regions).

[0103] Fig. 5C conceptually illustrates a step for fabricating a polymer surface relief grating 196 or EPS in which the liquid crystal is removed from an HPDLC periodic structure of Fig. 8B to form a polymer surface relief grating. Advantageously, a polymer surface relief grating 196 may include a large depth with a comparatively small grating period in order to form a deep SRG. The liquid crystal may be removed by washing with a solvent such as isopropyl alcohol (IPA) or similar which can solvate LC molecules to facilitate their removal from polymer network. The solvent may be strong enough to wash away the liquid crystal but weak enough to maintain the polymer structure. In some embodiments, the solvent may be chilled below room temperature before washing the grating. In some embodiments, the liquid crystal molecules are used for creating phase separated domains. The phase separated domains remain after the liquid crystal molecules are removed.

[0104] In some embodiments, a further post treatment of the EPSs might be used to remove more of the weak polymer network regions. In some embodiments, a plasma ashing may be performed, to reduce or eliminate vestigial polymer networks. In some embodiments the plasma ashing may be used to remove the initial inert fluid such that inert fluid may be removed without the use of a solvent but merely by plasma ashing.

[0105] In some embodiments, post coating the EPSs with a very thin atomic layer of high index material can enhance the diffractive properties (e.g. the refractive indexmodulation) of the grating. The coating may be a metallic layer or a dielectric layer. One such process, Atomic Layer Deposition (ALD), involves coating the gratings with TiO2 or ZnO2 or similar high refractive index metal oxides.

[0106] In some embodiments, after curing, removal of the inert material to form the polymer grating, and ashing, thermal reflow may be used to modify the geometry and surface quality of the etched feature. The thermal reflow may include modification of the shape of the grating structure using polymer melting and mass transport. When heated over its glass transition temperature, the polymer changes into a viscous state. A surface of least energy (surface of minimum area) is formed under surface tension forces. This process typically occurs at high temperatures but may also take place at moderate temperatures if the polymer melt is sufficiently viscous. Reflow may result in a curving of the faces of the polymer structure. The resulting curved diffractive elements are potentially useful for expanding the angular response of the grating structure.

[0107] In some embodiments, a protective layer is applied after the fabrication of the EPS. Fig. 5D illustrates an example step of a method for fabricating a polymer surface relief grating in which the polymer surface relief grating is covered with a protective layer 197.

[0108] Fig. 6 is a flowchart of a method for forming deep SRGs from a HPDLC periodic structure formed on a transparent substrate in accordance with an embodiment of the invention. As shown, a method 250 of forming deep SRGs or EPSs is provided. Referring to the flow diagram, the method 250 includes providing (251 ) a mixture of at least one monomer and at least one liquid crystal. The mixture is previously described in detail. The at least one monomer may include an isocyanate-acrylate monomer or thiolene. For example, the mixture may include a liquid crystal and a thiolene based photopolymer. In some embodiments, the mixture may include a liquid crystal and an acrylate-based photopolymer. In some embodiments, at least one liquid crystal may be a full liquid crystal mixture or may be a liquid crystal single which may include only a portion of the liquid crystal mixture such as a single component of the liquid crystal mixture. In some embodiments, at least one liquid crystal may be substituted for a solution which phase separates with the monomer during holographic exposure. The criteria for such a solution may include the ability to phase separate with the monomer during exposure, ease ofremoval after curing and during washing, and ease of handing. Example substitute solutions include solvents, non-reactive monomers, inorganics, and nanoparticles.

[0109] Providing the mixture of the monomer and the liquid crystal may also include mixing one or more of the following with the at least one monomer and the liquid crystal: initiators such as photoinitiators or coinitiators, acrylates, methacrylates, multifunctional thiols, or thio-esters, dye, adhesion promoters, surfactants and / or wetting agents, and / or additional additives such as other cross linking agents. This mixture may be allowed to rest in order to allow the coinitiator to catalyze a reaction between the monomer and the thiol. The rest period may occur in a dark space or a space with red light (e.g. infrared light) at a cold temperature (e.g. 20°C) for a period of approximately 8 hours. After resting, additional monomers may be mixed into the monomer. This mixture may be then strained or filtered through a filter with a small pore size (e.g. 0.45pm pore size). After straining, this mixture may be stored at room temperature in a dark space or a space with red light before coating.

[0110] Next, a transparent substrate is provided (252). In certain embodiments, the transparent substrate may be a glass substrate or a plastic substrate. In some embodiments, the transparent substrate may be a flexible substrate to facilitate roll to roll processing. In some embodiments, the EPS may be manufactured on a flexible substrate through a roll to roll process and then peeled off and adhered to a rigid substrate. In some embodiments, the EPS may be manufactured on a flexible substrate and a second flexible release layer may be peeled off and discarded which would leave the EPS on a flexible layer. The flexible layer may be then bonded to another rigid substrate.

[0111] A layer of the mixture can be deposited or coated (253) onto a surface of the substrate. The layer of mixture may be deposited using inkjet printing. In some embodiments, the mixture is sandwiched between the transparent substrate and another substrate using glass spacers to maintain internal dimensions. A non-stick coating may be applied to the other substrate before the mixture is sandwiched. The non-stick coating may include a fluoropolymer such as OPTOOL UD509, Fluoropel, and EC200. Holographic recording beams can be applied (254) to the mixture layer. Holographic recording beams may be a two-beam interference pattern which may cause phase separation of the inert fluid and the polymer. In response to the holographic recordingbeam, the monomer and inert components diffuse in opposite directions under the change in chemical potential resulting from polymerization. The liquid monomer changes to a solid polymer to form a polymer-rich region in the high intensity fringes of the interference pattern whereas the neutral, inert fluid (e.g., LC) or non-reactive substance becomes mainly confined to a LC-rich region in the low intensity fringes of the interference pattern. While LC may be one implementation of the neutral, non-reactive substance, other substances may also be used. The substance and the monomer may form a miscible mixture prior to the holographic exposure and become immiscible upon holographic exposure.

[0112] After applying the holographic recording beams, the mixture may be cured. The curing process may include leaving the mixture under low-intensity white light for a period of time until the mixture fully cures. The low intensity white light may also cause a photobleaching of the dye. Thus, a HPDLC periodic structure having alternating polymer rich and inert fluid rich regions can be formed (255). In some embodiments, the curing process may occur in two hours or less. After curing, one of the substrates may be removed exposing the HPDLC periodic structure. Advantageously, the non-stick coating may allow the other substrate to be removed while the HPDLC periodic structure remains.

[0113] HPDLC periodic structure may include alternating sections of inert fluid rich regions and polymer regions. The inert fluid in the inert fluid rich regions can be removed (256) to form polymer surface relief gratings or EPSs which may be used as deep SRGs. The inert fluid may be removed by gently immersing the grating into a solvent such as IPA. The IPA may be chilled and may be kept at a temperature lower than room temperature while the grating is immersed in the IPA. The periodic structure may be then removed from the solvent and dried. In some embodiments, the periodic structure is dried using a high flow air source such as compressed air. After the LC is removed from the periodic structure, a polymer-air surface relief grating is formed.

[0114] As shown in Fig. 5D, the formed surface relief grating can further be covered with a protective layer 197. In some instances, the protective layer may be a moisture and oxygen barrier with scratch resistance capabilities. In some instances, the protective layer may be a coating that does not fill in air gap regions where LC that was removed once existed. The coating may be deposited using a low temperature process. In someimplementations, the protective layer may have anti-reflective (AR) properties. The coating may be a silicate or silicon nitride. The coating process may be performed by a plasma assisted chemical vapor deposition (CVD) process such as a nanocoating process. The coating may be a parylene coating. The protective layer may be a glass layer. A vacuum or inert gas may fill the gaps where LC that was removed once existed before the protective layer is applied. In some embodiments, the coating process may be integrated with the inert fluid removal process (256). For example, a coating material may be mixed with the solvent which is used to wash the inert fluid from the periodic structure.

[0115] Further details of EPS structures and fabrication methods are disclosed in U.S. Pat. Pub. No. 2023 / 0078253, entitled “Evacuated Gratings and Methods of Manufacturing” and filed Sept. 12, 2022, U.S. Pat. Pub. No. 2023 / 0266512, entitled “Nanoparticle-Based Holographic Photopolymer Materials and Related Applications” and filed Jan. 13, 2023, and U.S. Pat. Pub. No. 2022 / 0283376, entitled “Evacuated Periodic Structures and Methods of Manufacturing” and filed Mar. 7, 2022, which are hereby incorporated by reference in their entirety for all purposes. An EPS or a volume grating can also be configured as a grating operating in the Raman-Nath regime. Unlike Bragg gratings which diffract with high efficiency into the first order, Raman Nath gratings are characterized by higher orders. While a Raman-Nath grating is often physically thin, the transition from Raman-Nath and Bragg regimes also depends on index modulation and may occur for relatively large grating thicknesses.

[0116] Fig. 7A illustrates a cross sectional schematic view of an exemplary embodiment of a polymer-air periodic structure 3000 implemented on a waveguide 3002. The polymer-air periodic structure 3000 includes periodic polymer sections 3004a. Adjacent polymer sections 3004a sandwich air sections 3004b. The air sections 3004b are sandwiched by polymer sections 3004a. The air sections 3004b and polymer sections 3004a have different indexes of refraction. Advantageously, the polymer-air periodic structure 3000 may be formed with a high grating depth 3006a to Bragg fringe spacing 3006b ratio which may create a deep SRG. As illustrated, the polymer sections 3004a and the air sections 3004b extend all the way to the waveguide 3002 to directly contact the waveguide 3002. As illustrated, there may be no bias layer between the polymer sections 3004a and the air sections 3004b and the waveguide 3002. As discussedpreviously, deep SRGs may exhibit many beneficial qualities such as high S-diffraction efficiency which may not be present within the typical SRGs.

[0117] In one example, a polymer-air periodic structure 3000 may have a Bragg fringe spacing 3006b of 0.35pm to 0.8pm and a grating depth of 1 pm to 3pm. in some embodiments, a grating depth of 1 pm to 3 pm may be too thick for most EPS (with ashing and ALD) for fold and output gratings for waveguide applications, where leaky structures are needed. Values in the ranges of 0.1 pm to 0.5 pm might be more suitable for leaky structures, particularly when modulation is increased with ashing and ALD. For example, input structures may include a depth in the range of 0.4 pm up to 1 pm. Structures with a depth from 1 pm to 3 pm may be advantageous for display cases, and structures even taller may be advantageous for non-display applications. Structures with half period (e.g. a critical dimension) to height ratio of 7:1 or even 8:1 have been demonstrated with advantageous effects.

[0118] In some embodiments, the polymer sections 3004a may include at least some residual liquid crystal when the liquid crystal is not completely removed during step 256 described in connection with Fig. 6. In some embodiments, the presence of residual LC within the polymer rich regions may increase refractive index modulation of the final polymer SRG. In some embodiments, the air sections 3004b may include some residual liquid crystal if the liquid crystal is not completely removed during step 256 from these air sections 3004b. In some embodiments, by leaving some residual liquid crystal within the air sections 3004b, a hybrid grating may be created.

[0119] Fig. 7B illustrates a cross sectional schematic view of a polymer-air periodic structure 3000a in accordance with an embodiment of the invention. The polymer-air periodic structure 3000a includes many identically numbered components with the polymer-air periodic structure 3000 of Fig. 7A. In some embodiments, an optical layer 3008 may also exist between the polymer sections 3004a and the air sections 3004b and the waveguide 3002. The optical layer 3008 may be a bias layer between the polymer sections 3004a and the air sections 3004b and the waveguide 3002. The description of these components is applicable with the polymer-air periodic structure 3000a described in connection with Fig. 7B and this description will not be repeated in detail. As illustrated, an optical layer 3008 is positioned between the polymer sections 3004a and the airsections 3004b and the waveguide 3002. The waveguide may include a waveguide 3002 and an optical layer 3008 (e.g. the bias layer) sandwiched by the waveguide 3002 and the polymer periodic structure and wherein the polymer periodic structure extends all the way to the optical layer to directly contact the optical layer. The polymer periodic structure includes the polymer sections 3004a and the air sections 3004b.

[0120] In some examples, an optical layer 3008 may be formed when gratings are formed using Nano Imprint Lithography (NIL). The grating pattern may be imprinted in a resin leaving a thin layer underneath the period structure which is a few microns thick. This optical layer 3008, which may be a few microns in thickness, may reside between the waveguide (e.g. glass) substrate and the period grating layer and may not be removed without damaging the NIL grating structure. When the bias refractive index is lower than that of the waveguide substrate the bias layer may confine light for some field angles (furthest from TIR in the waveguide) to the high index substrate which may be analogous to cladding on an optical fiber core. This may cause the field supported in the waveguide to be clipped and hence not supported by the waveguide. Elimination of the bias layer can offer grating coupling from a high index substrate with a grating structure of lower index than the substrate which may not be possible with the bias layer present.

[0121] In formation of EPSs, since the phase separation process leading to grating formation may take place through the entire holographic recording material layer, gratings may be formed throughout the volume of the cell gap resulting in no optical layer 3008. The elimination of the optical layer 3008 can allow wider fields of view to be realized when using high index waveguide substrates. Wide field of view angular content may be propagated with lower refractive index grating structures. EPSs may deliver similar optical performance characteristics to nanoimprinted SRGs by offering taller structures albeit at lower peak refractive index. This may open up the possibility of low-cost fabrication of diffractive structures for high efficiency waveguides.

[0122] Although the elimination of the optical layer 3008 from a waveguide grating device can offer the field of view benefits as discussed above, in some embodiments, an optical layer 3008 may be present in EPSs. The present disclosure allows for waveguide grating devices with or without the optical layer 3008.

[0123] In some embodiments, having the optical layer 3008 can be an advantage as the evanescent coupling between the waveguide and the grating is a function of the indices of the gratings structure (e.g. the grating depth the angles of the faces making up the structure and the grating depth), the waveguide core, and the optical layer 3008 (if present). In some embodiments, the optical layer 3008 may be used as a tuning parameter for optimizing the overall waveguide design for better efficiency and bandwidth. Unlike nanograting SRGs, a bias layer used with an EPS may not be of the same index as the grating structure. The optical layer 3008 may be made of the same material as the polymer sections 3004a such that the polymer sections 3004a and the optical layer 3008 form one homogenous structure. The optical layer 3008 may also be a different material than the polymer sections 3004a.

[0124] Exposed and evacuated gratings were manufactured utilizing various combinations of liquid crystal singles or monomers which were described in connection with Figs. 1 -4 with the processes described and illustrated in connection with Figs. 5 and 6 to create the gratings illustrated in Figs. 7A and 7B. The grating included alternating regions of polymer network with air gaps. It has been discovered that specific LC singles and / or their combinations may be used to control optical response (e.g. s-polarization diffraction efficiency; DE) as illustrated. The liquid crystal may be removed from the liquid crystal rich regions using solvents to form polymer surface relief gratings.Examples Including Different Combinations of LC Singles

[0125] The initial HPDLC mixtures include 42% LC concentration and the weight percentage amount of the deposited HPDLC mixture was the same. It has been discovered that the resultant gratings from some formulations do not result in appreciable diffraction efficiency (DE). The LC types in the formulations may alter the height of the resultant polymer surface relief grating. Different holographic exposures may create nonslanted or slanted gratings. The different formulations include different weight percentages of the Group 1 , Group 2, Group 3, and Group 4 LC singles described above. The Group 1 LC is described in connection with Figs. 1A, 1 B-1 , 1 B-2, 1 B-3, 1 B-4, and / or 1 B-5. The Group 2 LC is described in connection with Figs. 2A, 2B-1 , 2B-2, 2B-3, 2B-4,and / or 2B-5. The Group 3 LC is described in connection with Figs. 3A, 3B-1 , and / or 3B- 2. The Group 4 LC is described in connection with Figs. 4A and / or 4B.

[0126] In one example, slanted and unslanted gratings were manufactured utilizing an HPDLC mixture that includes LC including Group 1. The LC in the HPDLC mixture includes 100% Group 1. It was observed that the unslanted grating produces a 15-20% s-polarization diffraction efficiency with a height of 300nm. The slanted grating includes a low and almost unappreciable diffraction efficiency (<2%) with a height of 245nm.

[0127] In one example, slanted and unslanted gratings were manufactured utilizing an HPDLC mixture that includes LC including Group 1 and Group 2. The LC in the HPDLC mixture includes weight percents of 50% Group 1 and 50% Group 2. It was observed that the unslanted grating produces a 20-25% s-polarization diffraction efficiency with a height of 320nm. The slanted grating includes a low and almost unappreciable diffraction efficiency (<2%) with a height of 260nm.

[0128] In one example, slanted and unslanted gratings manufactured utilizing an HPDLC mixture that includes LC including Group 4. The LC in the HPDLC mixture includes 100% Group 4. The unslanted grating includes a low and almost unappreciable diffraction efficiency (<2%) with a height of 390nm. The slanted grating includes a low and almost unappreciable diffraction efficiency (<2%) with a height of 320nm.

[0129] It has been discovered that using terphenyl LCs (Group 3 LC) improves the phase separation in both slanted and unslanted grating structures. It is understood that improved phase separation creates increased diffraction efficiency in the evacuated structures. In one example, slanted and unslanted gratings manufactured utilizing an HPDLC mixture that includes Group 1 , Group 2, Group 3, and Group 4. In some embodiments, the LC in the HPDLC mixture includes weight percents of 20%-40% Group 1 , 10%-30% Group 2, 20%-50% Group 3, and 5%-15% Group 4. The unslanted grating structure may include a height of 480nm and a peak diffraction efficiency of s-polarized light of between 35% to 50%. The slanted grating structure may include a height of 500nm with a slant angle of 30 degrees and a peak DE of S-polarized light of 85% to 90%.

[0130] It has been discovered that different relative proportions of these LC groups produce different final grating structures. Group 3 LCs have been discovered to provide advantageous phase separation when compared to Group 1 , Group 2, and Group 4.However, Terphenyls LCs in Group 3 may be solid at room temperature. In some examples, Group 3 LCs are less than or up to 50% with remaining components from biphenyl LCs of Group 1 or similar acting as ‘carriers’ to solubilize Group 3. Thus, the combination of Group 3 with Group 1 , Group 2, and / or Group 4 LC singles may provide an inkjet printable HPDLC mixture. Pentyl cyanobiphenyl from Group 1 may be a low- melting LC with a nematic LC phase at lower temperatures (such as ~25 °C) and with a clearing point (nematic to isotropic) slightly above ambient temperatures (such as ~35 °C). Relative concentration may depend on deposition methods. Solids in Group 3 benefit from ‘carriers’ or low viscosity components to keep the viscosity low enough near ambient temperatures for inkjet printing.

[0131] It has been discovered that higher concentrations of Group 3 can result in long term formulation stability issues resulting in precipitation, making them unusable for inkjet printing application without solvents. Including solvents can minimize formulation instability issues and can be used with Group 3 LCs in cases where higher concentrations of terphenyls are included.

[0132] Inclusion of the terphenyl LCs produces a previously unachievable diffraction efficiency for slanted gratings. The LC mixture includes the terphenyl type LCs along with other types, which may enable fabrication of grating structures with different slant angles. The LC concentration in the HPDLC mixture may be about 42%. At concentrations of about 42% high optical performance acceptable formulation stability may be achieved at room temperature without including solvents.

[0133] The 42% concentration is merely exemplary and other concentrations of LC components in the HPDLC mixture may be included. The concentration of 42% may keep acceptable formulation stability at room temperature without using solvents. Phenyl groups in LCs may facilitate 71-71 stacking of aromatic groups. This property is commonly used in calamitic LCs where conjugated aromatic groups provide rigid core structures leading to aggregated LC clusters, also known as LC ‘droplets.’ Nematic phase is a type of calamitic LCs and commonly used in HPDLCs. Other types of Calamitic LCs are smectic and cholesteric types. Alkyl groups in nematic LCs provide tail end or flexible phase in these LCs. Packing of aromatic groups creates stacked & rigid structures almost like crystalline phases, but flexible alkyl chains are structural building blocks to enablemobile or liquid phase in these LCs. Combinations of aromatic and alkyl chains are commonly used in Calamitic LCs to tune micro-structures and phase transition characteristics.

[0134] In the holographic mixture, the inert fluid may be an LC which may include various liquid crystal singles or monomers. It has been discovered that each liquid crystal single plays a different role in the formulation for inkjet printable HPDLC mixtures (inks) providing high index modulation for volume Bragg grating (VBG) waveguides and high modulation EPSs after LC removal. The following properties may be included in the LC- based holographic material which may make it adapted for inkjet printing:• Monodispersed LC in monomer mixture as a homogeneous solution with no precipitates and at acceptable particulate level of typically <0.5 microns;• High degree of LC solubility in monomer mixture;• Ink to be liquid at inkjet printing temperature;• Viscosity and Surface Tension of HPDLC mixture to conform to print head characteristics e.g., nozzle size, drop volume, operating temperature;• Rheology of the HPDLC mixture to confide to drop shape, size and homogeneity control;• Low drop latency and high degree of recoverability;• Limited aggregation or no precipitation leading to nozzle not clogging;• High degree of materials compatibility with print head.

[0135] In some embodiments, the holographic mixture has viscosity in the range 10- 12m Pa ■ s, a surface tension in the range 28-35mN / m and drop volume in the range 5- 20pl as ink requirements for respective industrial inkjet heads. The liquid crystal material may be formulated such that applying holographic recording beams to a layer of the material results in a volume grating including alternating polymer rich regions and inert substance rich regions. The refractive index difference between the polymer rich regions and inert fluid rich regions of the volume grating may be low and thus the DE of the volume grating may be low. However, the evacuated structure may have a high refractive index difference. The volume grating may have a low thickness.Phase Diagrams Representation of Grating Formation

[0136] As discussed above, HPDLC gratings may be used as an interim step in EPS formation. In EPS formation, the LC is flushed out after the polymer structure has formed. Using phase diagrams, an established tool for representing the thermodynamic conditions for phase separation, illustrates that a low LC concentration / low DE is advantageous.

[0137] The most basic model of HPDLC phase separation assumes that the free energy of the system can be characterized in terms of initially isotropically-mixed monomer and LC. This may be adequate for low modulation VBGs. A more rigorous model includes nematic alignment and polymer elasticity contributions to the free energy. Phase diagrams may only describe part of the grating formation process; even though a phase diagram might point to phase separation being thermodynamically possible, the latter can only take place if the kinetic factors governing polymer growth are favourable. In many cases, phase separation and polymer growth (i.e. , conversion of monomer into a polymer network) may be seen as competing processes.

[0138] The phase diagrams provide key features of different grating formation systems. Phase diagrams may vary significantly with mixture components and may depend on the location of the mixture point in the interference pattern. The position of a mixture point relative to the phase diagrams changes as polymerization proceeds.

[0139] Fig. 8 is a phase diagram of a typical isotropic mixing of liquid crystal and monomer. The isotropic (completely mixed phase) and the region of phase separation are separated by the Binodal Curve. The region of phase separation includes Metastable and Spinodal (thermodynamically unstable) regions separated by a Spinodal Curve. Metastable phase separation is based on initial nucleation at discrete points followed by growth. Overcoming the nucleation barrier entails building up sufficient monomer concentration for phase separation, which results in a time lag. Metastable phase separation typically produces a range of LC droplet sizes.

[0140] Phase separation in the spinodal region arises spontaneously from tiny fluctuations (smaller than those required for metastable growth). There may be no nucleation; the process takes place everywhere simultaneously. As the initial spatial variation of chemical potential reaches equilibrium (constant chemical potential), segregation into LC-rich and LC-poor regions occurs. The resulting structures may include complex geometry. In some cases, interfacial tensions may cause the structureto break up into spherical droplets. The detailed mechanics of phase separation in the metastable and spinodal regions may be controlled by diffusion. Although the spinodal region is not ideal for grating formation it may contribute to haze. Coexistence of binodal and spinodal phases may account for grating roughness. The structures formed in the spinodal region may be regular, suggesting that that under certain conditions it may be possible to form photonic crystal structures, offering an alternative to >2 beam recording setups.

[0141] Fig. 9 are various plots relating free energy (Gibbs free energy) to phase diagram for isotropic mixing case. The upper plot shows the variation of free energy versus liquid crystal concentration. The lower plot is a phase diagram corresponding to the free energy plot. Following a common convention, the latter comprise reaction temperature plotted against liquid crystal concentration (in some cases the vertical axis may be the reaction temperature normalized by the nematic transition temperature). The two plots illustrate how free energy maps to a phase diagram for the isotropic mixing case discussed in connection with Fig. 8. The thermodynamically unstable spinodal phase corresponds to the edges of the local maximum in the free energy plotted for a constant temperature, T. The minima of the free energy (mixture points P1 ,P2) define the binodal curve, which separates the region of phase separation from the completely mixed phase. The minima lie on a tangential line corresponding to the change in chemical potential (A / J). Since mixture points P1 and P2 lie on the same line, A is the same for both phases. P1 and P2 become the boundaries between completely mixed and phase separated regions at the temperature T. The phase diagram is completed by considering other temperatures. The common peak of the binodal and spinodal curves define a critical temperature usually referred to as the upper critical solution temperature (UCST) in the literature. In HPDLC grating formation processes, such as the ones disclosed here, the phase separation occurs at temperatures below the critical temperature.

[0142] Fig. 10 is a phase diagram including isotropic mixing and nematic contribution. Adding the nematic contribution to the phase diagram essentially overlaps the symmetrical isotropic mixing function with the nematic-isotropic transition curve of the LC and pushes the phase diagram upwards. The metastable regions and spinodal regions become asymmetrical, each having isotropic and anisotropic regions. Generally, theanisotropic regions are found to the right of anisotropic / anisotropic transition line, as shown in Fig 10. A nematic region (pure liquid crystal) exists at the higher liquid crystal concentrations.

[0143] In conventional HPDLC, recording a higher LC concentration (ideally, an LC continuum) increases the order parameter, leading to higher diffraction efficiency. Fig. 11 is a plot of nematic order parameter versus concentration q>L. The plot, which may be computed using the well-known Maier-Saupe theory of nematic ordering, assumes a nematic transition temperature TNI - 365Kand a mixture temperature T - 300K. The order parameter is zero up to LC concentrations around 0.8 and does not increase significantly beyond that point, even allowing from some uncertainty in the average alignment direction.

[0144] As discussed previously, good phase separation is valued over high diffraction efficiency in the EPS process. Good phase separation results in more uniform grating morphology with low surface roughness and the absence of residual polymer networks between the polymer diffracting features. Where etching is used for further processing of the gratings, a smoother surface is more desirable. High volume uniformity and surface uniform are desirable for achieving low haze in the finished grating. Further, the EPS process does not require high concentration (modulation) or anisotropy for the intermediate grating. Thus, the LC concentration may be well outside the region of high nematic alignment. This suggests that the isotropic mixing phase diagram described in connection with Fig. 8 may be an adequate description of the grating formation process.

[0145] Simply segregating LC and polymer does not account for the anisotropy of VBGs. The nematic ordering within droplets accompanied by macroscopic ordering of droplet symmetry axes produces the anisotropic grating (with polymer elastic free energy playing a key role). Another factor to consider is LC solubility in the resulting polymer matrix, which determines the percentage of the LC that is able to remain phase separated. As illustrated in Fig. 10, The LC content affects not only the size of the domains but also the trajectory of the blend as it is moved through thermodynamic phase space by the polymerization.

[0146] Fig. 12 illustrates a phase diagram including isotropic mixing and nematic contribution and cross linking. Adding crosslinking to the phase diagram pushes themetastable region upwards. The phase diagram changes with increasing cross linking. There may also be more subtle interplay between the polymer structure and the nematic phase with partial orientational ordering of the polymer by the leading to a new stable nematic phase depending on the polymer chain lengths and stiffness.

[0147] Figs.8-12 do not illustrate how the phase diagram evolves in time. Fig. 13 is a time-development of phase diagram around a mixture point (P). Photo-polymerization induced phase separation, as used in the recording of VBGs, starts with a homogeneous mixture of LC, multi-functional monomer, and photo-initiator. After photoinitiation and free radical reaction, the rapid formation of a cross-linked polymer matrix thrusts the mixture into thermodynamic instability. This is similar to the commonly used thermal quench phase separation process in which a mixture point (e.g. a LC concentration point) that initially lies in an isotropic regions at a given temperature enters a metastable region at a lower temperature. As the polymerization continues, the crosslinking of the polymer matrix halts the phase separation of the LC upon the complete gelation of the matrix.

[0148] The phase diagram changes due to the increasing molecular weight of the network (resulting in changes to the molecular interaction parameter (x). Polymerization may not be described by a single phase diagram. Consider the point P representing the mixture at LC concentration q>i_ and temperature T. As polymerization advances, the binodal curve moves upward asymmetrically towards the region of higher LC concentration. At t=0 P is in the fully mixed isotropic region. At t= t-, P enters a metastable region. At t= t2 P enters the thermodynamically unstable spinodal region. Hence, the starting composition and polarization rate determines how quickly P crosses the boundary of the metastable region.

[0149] LC solubility in the resulting polymer matrix determines the percentage of the LC that is able to remain phase separated. The LC content affects not only the size of the domains but also the trajectory of the mixture as it is translated through thermodynamic phase space by the polymerization. Other important factors are monomer functionality, polymerization rate, solubility of LC in the polymer matrix.

[0150] Fig. 14 is a liquid crystal polymer cross-linked phase diagram. Some embodiments include low modulation VBGs used in EPS recording where the inert component is evacuated from the grating after exposure too for an air immersed surfacerelief grating. The use of a low modulation VBG is not an obvious approach as Bragg gratings and thin Bragg gratings in particular ordinarily require high modulation for high DE. The phase diagram shows typical mixture points (A,B) for high modulations may extend from the isotropic metastable region to at least the anisotropic metastable region. In contrast, gratings for EPS may target phase separation points such as C and D which are confined to the isotropic metastable region (e.g., above the Isotropic / Anisotropic Transition Line). Gratings formed in the latter regime may have more even morphology due to lower macroscopic anisotropy, which is desirable for further processing of the intermediate VBG which may be evacuated to produce an EPS.

[0151] The vertical scale is temperature. The reaction temperature for lines C,D and A,B may be the same but have been shown as separated for explanation purposes. The phase diagram shows that LC concentration ranges such as A,B and C,D are thermodynamically allowed (but achieving the concentration range (phase separation) shown depends on diffusion / gelation processes, which are formulation dependent). A,B formulations may be preferable for a high modulation volume Bragg grating. However, the low modulation line C,D may result in a better grating for etching as it does not enter the anisotropic metastable region and hence may not suffer from roughness due to LC droplets. The liquid crystal mixtures discussed above phase separate in such a manner that they operate in the C,D line which is confined to the isotropic metastable region. Thus, they have low diffraction efficiency but may produce high phase separation which makes them useful for EPS.

[0152] In some embodiments, a method for fabricating a grating includes providing a mixture of monomer and inert fluid; coating a layer of the mixture on a surface of the substrate; and applying holographic recording beams to the layer to form a volume grating comprising alternating polymer rich regions and inert fluid rich regions, wherein the refractive index difference between the polymer rich regions and inert fluid rich regions is low. The refractive index difference between the polymer rich regions and inert fluid rich regions corresponds to an LC-poor concentration in the isotropic metastable region of the phase diagram and an LC-rich concentration in the isotropic metastable region of the phase diagram. The refractive index difference between the polymer rich regions and inert fluid rich regions corresponds to both the LC-poor concentration and the LC-richconcentration lying above the isotropic to anisotropic transition line. The grating may be an intermediate grating which may be subsequently evacuated. The previously description of formulation include formulations which may exhibit relatively low modulation.DOCTRINE OF EQUIVALENTS

[0153] While the above description contains many specific embodiments of the invention, these should not be construed as limitations on the scope of the invention, but rather as an example of one embodiment thereof. It is therefore to be understood that the present invention may be practiced in ways other than specifically described, without departing from the scope and spirit of the present invention. Thus, embodiments of the present invention should be considered in all respects as illustrative and not restrictive. Accordingly, the scope of the invention should be determined not by the embodiments illustrated, but by the appended claims and their equivalents.

Claims

WHAT IS CLAIMED IS:1 . A holographic mixture comprising: a monomer; one or more photoinitiators; and a liquid crystal material comprising a first component of formula:where n is 3 or more,Y is H or a halogen,R is H, an alkyl, or an alkoxy, andZ is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, SCN, or nitrogen derivatives.

2. The holographic mixture of claim 1 , wherein the first component has the formula:

3. The holographic mixture of claim 1 , wherein the first component has the formula:

4. The holographic mixture of claim 1 , further comprising a second component selected from the group consisting of a molecule of formula:where n is 2;R is an alkyl; andZ is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen derivatives.

5. The holographic mixture of claim 4, wherein the second component comprises alkyl cyanobiphenyl or alkoxy cyanobiphenyl.

6. The holographic mixture of claim 5, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is pentyl cyanobiphenyl or pentyloxy cyanobiphenyl.

7. The holographic mixture of claim 5, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is hexyl cyanobiphenyl or hexyloxy cyanobiphenyl.

8. The holographic mixture of claim 4, further comprising a third component of a formula:where X is an ester, an olefinic, an acetylenic,Y is H or a halogen,R is an alkyl or an alkoxy, andZ is an alkyl, an alkoxy, an ester, a halogen, CN, CNS, or nitrogen derivatives.

9. The holographic mixture of claim 8, wherein the third component has the formula:

10. The holographic mixture of claim 8, wherein the second component comprises: a first molecule of formula:a second molecule of formula:

11. The holographic mixture of claim 1 , further comprising a second component of a molecule of formula:where n is 2;R is an alkyl; andZ is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen derivatives.

12. The holographic mixture of claim 11 , wherein the second component comprises alkyl cyanobiphenyl or alkoxy cyanobiphenyl.

13. The holographic mixture of claim 12, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is pentyl cyanobiphenyl or pentyloxy cyanobiphenyl.1 . The holographic mixture of claim 12, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is hexyl cyanobiphenyl or hexyloxy cyanobiphenyl.

15. The holographic mixture of claim 11 , further comprising a third component of a formula:where X is an ester, an olefinic, an acetylenic,Y is H or a halogen,R is an alkyl or an alkoxy, andZ is an alkyl, an alkoxy, an ester, a halogen, CN, CNS, or nitrogen derivatives.

16. The holographic mixture of claim 15, wherein the third component has the formula:

17. The holographic mixture of claim 15, wherein the second component comprises:a first molecule of formula: anda second molecule of formula:

18. A method of fabricating a grating, the method comprising: coating a holographic mixture on a surface of a substrate, the holographic mixture comprising: a monomer; a liquid crystal material comprising a first component of formula:where n is 3 or more,Y is H or a halogen,R is H, alkyl, or alkoxy, andZ is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen;applying holographic recording beams to the layer to form a volume grating comprising alternating polymer rich regions and liquid crystal rich regions; and removing at least a portion of the liquid crystal in the liquid crystal rich regions to form a polymer surface relief grating.

19. The method of claim 18, wherein the polymer surface relief grating comprises a Bragg fringe spacing of 0.35pm to 0.8pm and a grating depth of 1 pm to 3pm.

20. The method of claim 18, wherein the polymer surface relief grating comprises a ratio of Bragg fringe spacing to grating depth of 1 : 1 to 5: 1 .

21. The method of claim 18, wherein the polymer surface relief grating comprises a grating depth and a grating pitch and wherein the grating depth is greater than the grating pitch.

22. The method of claim 18, wherein the holographic mixture comprises a low viscosity which is configured to enable inkjet printing.

23. The method of claim 18, wherein coating the holographic mixture on the surface of the substrate comprises inkjet printing the holographic mixture onto the surface of the substrate.

24. The method of claim 18, wherein the first component has the formula:

25. The method of claim 18, wherein the first component has the formula:

26. The method of claim 18, wherein the liquid crystal material further comprises a second component selected from the group consisting of a molecule of formula:where n is 2;R is an alkyl; andZ is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen derivatives.

27. The method of claim 26, wherein the second component comprises alkyl cyanobiphenyl or alkoxy cyanobiphenyl.

28. The method of claim 27, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is pentyl cyanobiphenyl or pentyloxy cyanobiphenyl.

29. The method of claim 27, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is hexyl cyanobiphenyl or hexyloxy cyanobiphenyl.

30. The method of claim 26, wherein the liquid crystal material further comprises a third component of a formula:where X is an ester, an olefinic, an acetylenic,Y is H or a halogen,R is an alkyl or an alkoxy, andZ is an alkyl, an alkoxy, an ester, a halogen, CN, CNS, or nitrogen derivatives.

31. The method of claim 30, wherein the third component has the formula:

32. The method of claim 30, wherein the second component comprises:a first molecule of formula: anda second molecule of formula:

33. The method of claim 18, wherein the liquid crystal material further comprises a second component of a molecule of formula:where n is 2;R is an alkyl; andZ is an alkyl, an alkoxy, an ester, a halogen, CN, NCS, or nitrogen derivatives.

34. The method of claim 33, wherein the second component comprises alkyl cyanobiphenyl or alkoxy cyanobiphenyl.

35. The method of claim 34, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is pentyl cyanobiphenyl or pentyloxy cyanobiphenyl.

36. The method of claim 34, wherein the alkyl cyanobiphenyl or alkoxy cyanobiphenyl is hexyl cyanobiphenyl or hexyloxy cyanobiphenyl.

37. The method of claim 33, wherein the liquid crystal material further comprises a third component of a formula:where X is an ester, an olefinic, an acetylenic,Y is H or a halogen,R is an alkyl or an alkoxy, andZ is an alkyl, an alkoxy, an ester, a halogen, CN, CNS, or nitrogen derivatives.

38. The holographic mixture of claim 37, wherein the third component has the formula:

39. The holographic mixture of claim 37, wherein the second component comprises:a first molecule of formula: anda second molecule of formula:

40. The method of claim 18, wherein the refractive index difference between the polymer rich regions and inert fluid rich regions corresponds to an LC-poor concentration in an isotropic metastable region of a phase diagram and an LC-rich concentration in the isotropic metastable region of the phase diagram.

41. The method of claim 18, wherein polymer rich regions corresponds to the LC- poor concentration and inert fluid rich regions corresponds the LC-rich concentration which both lie above the isotropic to anisotropic transition line.

42. A method for fabricating a grating, the method comprising: providing a mixture of monomer and inert fluid; coating a layer of the mixture on a surface of the substrate; and applying holographic recording beams to the layer to form a volume grating comprising alternating polymer rich regions and inert fluid rich regions, wherein the refractive index difference between the polymer rich regions and inert fluid rich regions is low.

43. A method for fabricating a grating, the method comprising: providing a mixture of monomer and inert fluid; coating a layer of the mixture on a surface of the substrate; and applying holographic recording beams to the layer to form a volume grating comprising alternating polymer rich regions and inert fluid rich regions, wherein the refractive index difference between the polymer rich regions and inert fluid rich regions corresponds to an LC-poor concentration in an isotropic metastable region of a phase diagram and an LC-rich concentration in the isotropic metastable region of the phase diagram.

44. A method for fabricating a grating, the method comprising: providing a mixture of monomer and inert fluid; coating a layer of the mixture on a surface of the substrate; and applying holographic recording beams to the layer to form a volume grating comprising alternating polymer rich regions and inert fluid rich regions, wherein polymer rich regions corresponds to the LC-poor concentration and inert fluid rich regions corresponds the LC-rich concentration which both lie above the isotropic to anisotropic transition line.

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