Broad-wavelength optical retardation through in-plane optical anisotropy of single crystalline materials

Abstract

In one aspect, the disclosure relates to a variety of crystalline materials that have a 2D crystal structure and an in-plane anisotropy. The crystalline materials can include metals having a partially filled d shell and that undergo a Jahn-Teller distortion. The crystalline materials can include incorporating two organic spacers in the same repeating layers to induced additional out-of-plane heterogeneity. The crystalline materials can exhibit broad wavelength optical retardation. The materials can be used in lenses such as in an achromatic quarter waveplate (A-QWP).

Description

BROAD-WAVELENGTH OPTICAL RETARDATION THROUGH IN-PLANE OPTICAL ANISOTROPY OF SINGLE CRYSTALLINE MATERIALSCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 529,443 filed on July 28, 2023, which is incorporated herein by reference in its entirety.BACKGROUND

[0002] Birefringence is a well-known phenomenon in which an anisotropic crystal exhibits different refractive indices depending on the polarization and propagation direction of the light, that can split an incident light beam into a slow ray and a fast ray. Birefringent crystals serve as the basis for constructing various types of waveplates, including half-waveplates (HWPs) and quarter-waveplates (QWPs). The degree of phase retardation in waveplates is dependent on several factors including incident beam wavelength, crystal birefringence value (An), and crystal thickness, which can be precisely controlled. Waveplates made from a single crystal component face limitations in achieving the desired phase retardation at a specific wavelength, since the amount of phase retardation is directly proportional to the wavelength. The incorporation of multiple birefringent crystals enables the waveplate to effectively operate over a wide range of wavelengths, providing broad-band phase retardation, resulting in an Achromatic-QWP (A-QWP). However, the traditional approach for fabricating A-QWPs involves a complex and high-cost multi- step process with high commercial costs, which requires selecting and incorporating birefringent crystals with optimized thicknesses and birefringence values.

[0003] The recent emergence of 2D materials, such as transition metal dichalcogenides and halide perovskites, presents new opportunities for creating birefringent crystals. The incorporation of organic components in 2D halide perovskites provides a high degree of tunability and programmability in both crystal structure and optical anisotropy. Furthermore, single crystals of 2D halide perovskites can be synthesized in the solution phase, near room temperature, and at atmospheric pressure, and a large crystal flake can be obtained which is favorable for fabricating optical waveplates. This facile wet-chemistry synthesis motivates the production of new- generation optical materials at low cost, high throughput, and improved reproducibility. However, the use of 2D materials in the fabrication of A-QWPs remains unexplored.

[0004] Despite advances in quarter waveplate materials research, there is still a scarcity ofmaterials and processes that are useful for making A-QWPs easily, reproducibly, and at low cost An ideal material would be tunable in terms of crystal structure and optical anisotropy. These needs and other needs are satisfied by the present disclosure.SUMMARY

[0005] In accordance with the purpose(s) of the present disclosure, as embodied and broadly described herein, the disclosure, in various aspects, relates to a crystalline material comprising a chemical structure according to the formula (Li)(L2)MXiY4-i. The materials described in the present disclosure overcome many deficiencies with prior anisotropic crystalline materials, for example can effectively modulate the light polarization across a broad range of wavelengths. In various aspects, the disclosure provides a crystalline material having a chemical structure according to the formula (Li)(L2)MXjY4-i; where Li and l_2are each independent ammonium containing organic ligands; where M is a divalent metal; where X and Y are each independently monovalent anions; and where i is an integer from 0 to 4. In some aspects, the crystalline material comprises single crystals having a thickness of about 50 pm, about 100 pm or about 150 pm to about 250 pm or about 350 pm. In some aspects, the crystalline material exhibits in-plane birefringence factor with An (na-nb) from about 0.02-0.04 for light having a wavelength of 800 - 820 nm and for light having a wavelength of 1000 - 1100 nm. A lens containing a crystalline material described herein is also provided. The lens can be used, for example, for converting a linearly polarized light into a circularly polarized light. A method of converting a linearly polarized light into a circularly polarized light is also provided by exposing the linearly polarized light to a crystalline material according or a lens described herein. The linearly polarized can include both visible light and NIR light.

[0006] Other systems, methods, features, and advantages of the present disclosure will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description, be within the scope of the present disclosure, and be protected by the accompanying claims. In addition, all optional and preferred features and modifications of the described embodiments are usable in all aspects of the disclosure taught herein. Furthermore, the individual features of the dependent claims, as well as all optional and preferred features and modifications of the described embodiments are combinable and interchangeable with one another.BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Many aspects of the present disclosure can be better understood with reference to thefollowing drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.

[0008] FIGs. 1A-1F shows birefringence and optical properties of HCH single crystals. FIG. 1A: Crystal structure of HCH crystals with a schematic illustration of birefringence. FIG. 1B: Transmission spectrum of the HCH crystal from ultraviolet (UV) to NIR wavelengths with insert showing the photograph of a HCH crystal. FIG. 1C: In-plane refractive index from first principles density functional theory (DFT) calculations. FIG. 1 D: Birefringence Ar? (na-nb) factor from DFT calculations. FIG. 1 E: Schematic diagram of the configuration of a polarized optical microscopy setup. FIG. 1F: Polarized optical microscope image of the HCH crystal (164 pm) as a function of different analyzer angles, the scale bar in the image is 5 pm. Top row (left to right): golden yellow, orange, lemon yellow, yellow-green. Bottom row (left to right): yellow-green, rust, warm red, orange. Retardation scale: 0 and 180 ° orange, lemon yellow at 40 °, green at 80 to 90 °, rust to red-orange / warm red at 100 °.

[0009] FIGs. 2A-2D show polarization measurement of HCH as an A-QWP. FIG. 2A: Schematic diagram of the laser polarization modulation measurement setup. FIG. 2B: The transmitted laser intensity change with the laser modulation setup without a sample at 600 - 650 nm. FIG. 2C: The transmitted laser intensity change with commercial quartz / MgF QWP at 600 - 650 nm; FIG. 2D: Transmitted laser intensity change with HCH crystal in between HWP and an analyzer (540-600 nm, 600 - 650 nm, 805 - 820 nm, 1000 - 1060 nm from left to right).

[0010] FIGs. 3A-3D show thickness-dependent single crystal structural analysis. FIG. 3A: Schematic diagram that shows the formation of out-of-plane mosaicity between thin and thick single crystals. GI-WAXS measurement for the HCH crystals with varied thicknesses FIG. 3B: 3 pm, FIG. 3C: 5 pm, and FIG. 3D: 164 pm.

[0011] FIGs. 4A-4F show thermally-induced optical anisotropy. FIG. 4A: CPOM image (the angle between polarizer and analyzer is 90°) of PEA2CuCl4 crystal upon heating (303 to 438 K) and cooling (438 to 303 K); FIGs. 4B-4D: Transmitted laser intensity with laser modulation setup of PEA2CuCl4 crystal under 298 K, 330 K, and cooling down to 298 K (600 - 610 nm); FIGs. 4E-4F: Fourier-transform infrared spectroscopy (FTIR) of PEA2CUCI4 crystal under 300 K, 358 K, 413 K, and 433 K.

[0012] FIGs. 5A-5B show an atomic force microscopy (AFM) image of PEA2C11CI4 bulk crystal to show surface roughness. FIG. 5A: Height channel. FIG. 5B: Amplitude channel.

[0013] FIGs. 6A-6B show exported red and green values from polarized optical microscope image with HCH crystal. FIG. 6A: R value and FIG. 6B: G value change upon rotating the analyzer angle (Set the polarization angle of the polarizer at the excitation side as 0°).

[0014] FIGs. 7A-7B show polarized optical images with different analyzer polarization directions of FIG. 7A: R-MPhA2CuCl4 crystal (R-MPhA is (R)-(+)-£-Methylphenethylaminium)) and FIG. 7B: BuA2CuCl4 crystal (BuA is N-butylammonium). The scale bar in the image is 5 pm. Top row: overall yellow cast to images with green in center (darker to lighter green from left to right) and increasing amounts of red / orange from left to right. Middle row: from yellow to orange / darker overall cast to images from left to right, with increasing amounts of green in top corners from left to right, and darker orange surrounding a narrow yellow strip at center from left to right. Bottom row: overall green cast to images, with decreasing amount of orange in center from left to right.

[0015] FIG. 8A shows cross-polarized optical image of PEA2PbBr4crystal and glass substrate, the scale bar is 5 pm. FIG. 8B shows optical image and thickness measurement diagram of PEA2PbBr4 single crystal.

[0016] FIG. 9 shows polarized optical images of PEA2CuCI2Br2crystal with different polarization directions at 25 °C.

[0017] FIG. 10A shows a thickness diagram of the HCH crystal with a thickness of 34 pm. FIGs. 10B-1 OK show transmitted laser intensity with PEA2CUCI4 crystal under laser modulation setup from 550 - 1060 nm.

[0018] FIGs. 11A-11C show a tunable incident laser spectrum from OPA at the wavelength of FIG. 11A: 550-650nm, FIG. 11B: 800-820 nm, and FIG. 11C: 1000-1060 nm.

[0019] FIG. 12A shows a 3D thickness distribution image of PEA2CuCl4 crystals with thicknesses 164 pm. FIG. 12B shows a thickness diagram of PEA2CUCI4 crystals with thicknesses of 164 pm.

[0020] FIG. 13A shows a thickness diagram of the HCH crystal with a thickness of 237 pm. FIGs. 13B-13H show transmitted laser intensity of PEA2CuCl4 crystal under the laser modulation setup from I = 550 - 930 nm.

[0021] FIG. 14A shows a schematic diagram of the laser polarization modulation measurement setup by adding an additional QWP after the sample; FIG. 14B shows the transmitted laserintensity changes with laser modulation setup with or without PEA2CUCI4 crystal (164 pm) at the laser wavelength of 1000 -1060 nm.

[0022] FIGs. 15A-15B show a thickness diagram of HCH crystals with thicknesses of FIG. 15A: 3 pm, FIG. 15B: 5 pm.

[0023] FIG. 16 shows an optical image of PEAzCuCU crystal during the heating and cooling down process from 300 K to 425 K.

[0024] FIG. 17 shows cross-polarized optical images of PEA2CuCI2Br2crystal at different temperatures, the scale bar is 5 pm.

[0025] FIG. 18 shows in-situ powder XRD spectra of HCH crystal under different temperatures.

[0026] Additional advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or can be learned by practice of the invention. The advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.DETAILED DESCRIPTION

[0027] Disclosed herein are single crystalline 2D hybrid copper halide (HCH) perovskites that show in-plane optical anisotropy due to the Jahn-Teller (JT) distortion in copper halide octahedral layers. This results in an in-plane birefringence factor about 0.026 from visible to near-infrared (NIR), based on the first principles Density Functional Theory (DFT) calculations. In some aspects, the in-plane birefringence factor can be from about 0.026 to about 0.029, or about 0.026, 0.027, 0.028, or 0.029, or a combination of any of the foregoing values, or a range encompassing any of the foregoing values. It is first shown that the relatively thin (~34 pm) birefringent HCH crystal (PEA2CuCl4, PEA = phenylethylammonium) can be utilized as QWP with a single wavelength of 920 nm to convert linearly polarized light to circularly polarized light or vice versa. Then, the thick (-164 pm) HCH single crystal is shown to function as A-QWP that effectively modulates the light polarization across a broad range of wavelengths from visible to NIR (A = 540- 650 nm, 805-820 nm, and 1000 - 1060 nm) without any complex design. In addition, HCH crystals possess exceptional air stability and forbidden luminescence properties, thereby minimizing artifacts that typically arise from bandgap photoluminescence emission that used to be found in the lead (Pb)-based 2D halide perovskites. Grazing Incidence Wide-Angle X-ray Scattering (Gl-WAXS) experiments revealed that the A-QWP property of HCH crystal results from out-of-plane mosaicity of the stacked inorganic layers. The weak interlayer van der Waals forces between the 2D layered HCH crystal encourages the naturally forming interlayer dislocations and twists. The out-of-plane mosaicity in the inorganic layers of HCH crystals causes each crystal to behave like a combination of multiple birefringent crystals with different fast-axis orientations. As a result, a single HCH crystal can function as A-QWP, eliminating the need for multiple crystals. In addition, the disclosed HCH crystal shows reversible light modulation when subjected to elevated temperatures, due to the nature of its thermochromic effect. These findings indicate that 2D HCH crystals have the potential to enable the development of low-cost single-component A-QWPs for multi-spectral photonic components and optical device applications. In an aspect, the 2D HCH crystals disclosed herein exhibit thermochromism and temperature-controlled birefringence, enabling temperature-controlled optical polarization.

[0028] In one aspect, disclosed herein is a crystalline material having or consisting essentially of a chemical structure of the formula (Li)(l_2)MXiY4-i; where Li and l_2are each independently ammonium containing organic ligands; where M is a divalent metal; where X and Y are each independently monovalent anions; and where i is an integer from 0 to 4. In an aspect, i can be 0, 2, or 4.

[0029] In an aspect, Li and l_2can be the same or different. In a further aspect, M can be a metal that undergoes a Jahn-Teller distortion. In a still further aspect, M can have 1 , 2, 4, 5, 6, 7, or 9 electrons in d orbitals. In some aspects, M can be selected from Cu2+, Cr2+, Fe2+, Pb2+, Sn2+, Mn2+, or Cd2+. In one aspect, M is Cu2+. In another aspect, M can be Pb2+.

[0030] In an aspect, Li and l_2are independently selected from phenylethylammonium (PEA), (R)-(+)-[3-methylphenethylammonium, butylammonium, 1,2,4-triazolium, ethylammonium, propylammonium, isopropylammonium, pentylammonium, hexylammonium, heptylammonium, benzylammonium, naphthylammonium, pyridinium, imidazolium, pyrrolidinium, piperidinium, morpholinium, quinolinium,. pyrazinium, and quinoxalinium. In a further aspect, Li and L2can both be PEA. In an alternative aspect, Li and L2are independently selected from amino acids having L chirality such as, for example, alanine, cysteine, aspartic acid, glutamic acid, phenylalanine, histidine, isoleucine, lysine, leucine, methionine, asparagine, ornithine, proline, glutamine, arginine, serine, threonine, valine, tryptophan, or tyrosine. In an aspect, Li and L2are independently selected from L-histidine, L-proline, L-lysine, L-ornithine, L-alanine, L- phenylalanine, L-cysteine, or L-leucine.

[0031] In one aspect, X and Y can independently be selected from chloride, bromide, and iodide. In one aspect, X is absent (i.e., i = 0) and Y is chloride. In another aspect, X is chloride and Y is bromide.

[0032] In an aspect, the crystalline material can be PEA2C11CI4 or PEA2CuCl2Br2. In another aspect, the crystalline material can be single crystalline or essentially single crystalline. In a further aspect, the crystalline material includes single crystals having a thickness of from about 50 pm to about 350 pm, or from about 100 pm to about 300 pm, or from about 150 pm to about 250 pm, or about 50, 100, 150, 200, 250, 300, or about 350 pm, or a combination of any of the foregoing values, or a range encompassing any of the foregoing values.

[0033] In yet another aspect, the crystalline material exhibits in-plane birefringence factor with An (na-nb) from about 0.02-0.04 for light having a wavelength of 800 - 820 nm and for light having a wavelength of 1000 -1100 nm. In one aspect, the crystalline material exhibits an in-plane birefringence. In some aspects, the material has a two dimensional crystal structure. In one aspect, in the crystalline material, a mosaic parameter perpendicular to the detector plane (e3) when measured from XRD spectra of a single crystal of the crystalline material is greater than about 1.5.

[0034] Also disclosed herein is a lens including the crystalline material disclosed herein. In another aspect, disclosed herein is a method of converting linearly polarized light into circularly polarized light, the method including at least the step of exposing the linearly polarized light to a disclosed crystalline material or lens. In some aspects, the linearly polarized light includes visible light, near infrared (NIR) light, or both.

[0035] Many modifications and other embodiments disclosed herein will come to mind to one skilled in the art to which the disclosed compositions and methods pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the disclosures are not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. The skilled artisan will recognize many variants and adaptations of the aspects described herein. These variants and adaptations are intended to be included in the teachings of this disclosure and to be encompassed by the claims herein.

[0036] Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

[0037] As will be apparent to those of skill in the art upon reading this disclosure, each of the individual embodiments described and illustrated herein has discrete components and features which may be readily separated from or combined with the features of any of the other several embodiments without departing from the scope or spirit of the present disclosure.

[0038] Any recited method can be carried out in the order of events recited or in any other order that is logically possible. That is, unless otherwise expressly stated, it is in no way intended that any method or aspect set forth herein be construed as requiring that its steps be performed in a specific order. Accordingly, where a method claim does not specifically state in the claims or descriptions that the steps are to be limited to a specific order, it is no way intended that an order be inferred, in any respect. This holds for any possible non-express basis for interpretation, including matters of logic with respect to arrangement of steps or operational flow, plain meaning derived from grammatical organization or punctuation, or the number or type of aspects described in the specification.

[0039] All publications mentioned herein are incorporated herein by reference to disclose and describe the methods and / or materials in connection with which the publications are cited. The publications discussed herein are provided solely for their disclosure prior to the filing date of the present application. Nothing herein is to be construed as an admission that the present invention is not entitled to antedate such publication by virtue of prior invention. Further, the dates of publication provided herein can be different from the actual publication dates, which can require independent confirmation.

[0040] While aspects of the present disclosure can be described and claimed in a particular statutory class, such as the system statutory class, this is for convenience only and one of skill in the art will understand that each aspect of the present disclosure can be described and claimed in any statutory class.

[0041] It is also to be understood that the terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the disclosed compositions and methods belong. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the specification and relevant art and should not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0042] Prior to describing the various aspects of the present disclosure, the following definitions are provided and should be used unless otherwise indicated. Additional terms may be defined elsewhere in the present disclosure.Definitions

[0043] As used herein, “comprising” is to be interpreted as specifying the presence of the stated features, integers, steps, or components as referred to, but does not preclude the presence or addition of one or more features, integers, steps, or components, or groups thereof. Moreover, each of the terms “by”, “comprising,” “comprises”, “comprised of,” “including,” “includes,” “included,” “involving,” “involves,” “involved,” and “such as” are used in their open, non-limiting sense and may be used interchangeably. Further, the term “comprising” is intended to include examples and aspects encompassed by the terms “consisting essentially of” and “consisting of.” Similarly, the term “consisting essentially of” is intended to include examples encompassed by the term “consisting of.

[0044] As used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a metal,” “a monovalent anion,” or “an ammonium containing inorganic ligand,” includes, but is not limited to, mixtures or combinations of two or more such metals, monovalent anions, or ammonium containing inorganic ligands, and the like.

[0045] It should be noted that ratios, concentrations, amounts, and other numerical data can be expressed herein in a range format. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. It is also understood that there are a number of values disclosed herein, and that each value is also herein disclosed as “about” that particular value in addition to the value itself. For example, if the value “10” is disclosed, then “about 10” is also disclosed. Ranges can be expressed herein as from “about” one particular value, and / or to “about” another particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms a further aspect. For example, if the value “about 10” is disclosed, then “10” is also disclosed.

[0046] When a range is expressed, a further aspect includes from one particular value and / or to the other particular value. For example, where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in the disclosure, e.g. the phrase “x to y” includes the range from ‘x’ to ‘y’ as well as the range greater than ‘x’ and lessthan ‘y’. The range can also be expressed as an upper limit, e.g. ‘about x, y, z, or less’ and should be interpreted to include the specific ranges of ‘about x’, ‘about y’, and ‘about z’ as well as the ranges of ‘less than x’, less than y’, and ‘less than z’. Likewise, the phrase ‘about x, y, z, or greater’ should be interpreted to include the specific ranges of ‘about x’, ‘about y’, and ‘about z’ as well as the ranges of ‘greater than x’, greater than y’, and ‘greater than z’. In addition, the phrase “about ‘x’ to ‘y’”, where ‘x’ and ‘y’ are numerical values, includes “about ‘x’ to about ‘y’”.

[0047] It is to be understood that such a range format is used for convenience and brevity, and thus, should be interpreted in a flexible manner to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or subranges encompassed within that range as if each numerical value and sub-range is explicitly recited. To illustrate, a numerical range of “about 0.1 % to 5%” should be interpreted to include not only the explicitly recited values of about 0.1% to about 5%, but also include individual values (e.g., about 1%, about 2%, about 3%, and about 4%) and the sub-ranges (e.g., about 0.5% to about 1.1%; about 5% to about 2.4%; about 0.5% to about 3.2%, and about 0.5% to about 4.4%, and other possible sub-ranges) within the indicated range.

[0048] As used herein, the terms “about,” “approximate,” “at or about,” and “substantially” mean that the amount or value in question can be the exact value or a value that provides equivalent results or effects as recited in the claims or taught herein. That is, it is understood that amounts, sizes, formulations, parameters, and other quantities and characteristics are not and need not be exact, but may be approximate and / or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding off, measurement error and the like, and other factors known to those of skill in the art such that equivalent results or effects are obtained. In some circumstances, the value that provides equivalent results or effects cannot be reasonably determined. In such cases, it is generally understood, as used herein, that “about” and “at or about” mean the nominal value indicated ±10% variation unless otherwise indicated or inferred. In general, an amount, size, formulation, parameter or other quantity or characteristic is “about,” “approximate,” or “at or about” whether or not expressly stated to be such. It is understood that where “about,” “approximate,” or “at or about” is used before a quantitative value, the parameter also includes the specific quantitative value itself, unless specifically stated otherwise.

[0049] As used herein, the terms “optional” or “optionally” mean that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where said event or circumstance occurs and instances where it does not.

[0050] The “Jahn Teller effect” or “Jahn Teller distortion” as used herein refers to geometrical distortion of molecules and / or ions resulting from specific electron configurations. In a further aspect, in the Jahn-Teller effect, a non-linear molecule or an ion with a degenerate electronic ground state will undergo a geometrical distortion that removes the degeneracy. In one aspect, and without wishing to be bound by theory, the Jahn Teller distortion lowers the overall energy of the molecule or ion. In one aspect, the Jahn Teller effect is often encountered in octahedral complexes of transition metals, especially, but not exclusively, in six-coordinate Cu2+complexes. In a further aspect, the Jahn Teller effect can be observed in some UV-visible spectra of compounds, for example in band splitting.

[0051] “Mosaicity” as used herein is a measure of the spread of crystal plane orientations. In one aspect, a crystal with a high degree of mosaicity may include numerous small perfect crystals that are randomly misoriented.

[0052] “e1,” “e2,” and “e3” values as used herein are defined as follows. When processing XRD data, the software calculates these mosaicity values defined as a reflection profile shape given by the three mosaic parameters (e1 , e2, and e3), where e3 is defined to be perpendicular to the detector plane, whereas e1 and e2 lie in the detector plane. For a normally ordered crystal, e1 and e2 are usually a few tenths of a degree, while e3 depends mostly on the slicing angle.

[0053] Unless otherwise specified, temperatures referred to herein are based on atmospheric pressure (i.e. one atmosphere).

[0054] Now having described the aspects of the present disclosure, in general, the following Examples describe some additional aspects of the present disclosure. While aspects of the present disclosure are described in connection with the following examples and the corresponding text and figures, there is no intent to limit aspects of the present disclosure to this description. On the contrary, the intent is to cover all alternatives, modifications, and equivalents included within the spirit and scope of the present disclosure.ASPECTS

[0055] The present disclosure can be described in accordance with the following numbered aspects, which should not be confused with the claims.

[0056] Aspect 1. A crystalline material comprising a chemical structure according to the formula (Li)(l_2)MXiY4-i;where Li and L2are each independently ammonium containing organic ligands; where M is a divalent metal; where X and Y are each independently monovalent anions; and where i is an integer from 0 to 4.

[0057] Aspect 2. The crystalline material of aspect 1 , wherein Li and l_2 are the same.

[0058] Aspect 3. The crystalline material of aspect 1 or 2, wherein M is a metal that undergoes a Jahn-Teller distortion.

[0059] Aspect 4. The crystalline material of any one of aspects 1-3, wherein M has 1 , 2, 4, 5, 6, 7, or 9 electrons in d orbitals.

[0060] Aspect 5. The crystalline material of any one of aspects 1-4, wherein M is selected from the group consisting of Cu2+, Cr2+, and Fe2+.

[0061] Aspect 6. The crystalline material of aspect 5, wherein M is Cu2+.

[0062] Aspect 7. The crystalline material of any one of aspects 1 and 3-5, wherein Li and l_2are different.

[0063] Aspect 8. The crystalline material of aspect 7, wherein M is selected from the group consisting of Pb2+, Sn2+, Mn2+, and Cd2+.

[0064] Aspect 9. The crystalline material of aspect 8, wherein M is Pb2+.

[0065] Aspect 10. The crystalline material according to any one of aspects 1-9, wherein one or both of Li and L2is each independently selected from the group consisting of phenylethylammonium (PEA), (R)-(+)-p-methylphenethylammonium, butylammonium, 1 ,2,4- triazolium, ethylammonium, propylammonium, isopropylammonium, pentylammonium, hexylammonium, heptylammonium, benzylammonium, naphthylammonium, pyridinium, imidazolium, pyrrolidinium, piperidinium, morpholinium, quinolinium,. pyrazinium, and quinoxalinium.

[0066] Aspect 1 1 . The crystalline material of aspect 10, wherein Li and l_2are both phenylethylammonium.

[0067] Aspect 12. The crystalline material according to any one of aspects 1-9, wherein one or both of Li and l_2is each independently selected from the group consisting of L-histidine, L-proline, L-lysine, L-ornithine, L-alanine, L-phenylalanine, L-cysteine, and L-leucine, or another chiral amino acid.

[0068] Aspect 13. The crystalline material according to any one of aspects 1-10, wherein X and Y are each independently selected from the group consisting of chloride, bromide, and iodide.

[0069] Aspect 14. The crystalline material of aspect 13, wherein Y is chloride.

[0070] Aspect 15. The crystalline material of aspect 13, wherein X is chloride and Y is bromide.

[0071] Aspect 16. The crystalline material according to any one of aspects 1-15, wherein i is0, 2, or 4.

[0072] Aspect 17. The crystalline material of aspect 16 wherein i is 0.

[0073] Aspect 18. The crystalline material of aspect 16, wherein i is 2.

[0074] Aspect 19. The crystalline material of any one of aspects 1-18, wherein the crystalline material is PEA2CuCl4 or PEA2CuCI2Br2.

[0075] Aspect 20. The crystalline material according to any one of aspects 1-19, wherein the crystalline material is single crystalline or essentially single crystalline.

[0076] Aspect 21. The crystalline material according to any one of aspects 1-20, wherein the material consists essentially of the material comprising a chemical structure according to the formula (Li)(L2)MXiY4-i.

[0077] Aspect 22. The crystalline material according to any one of aspects 1-21, wherein the crystalline material comprises single crystals having a thickness of from about 50 pm to about 350 pm.

[0078] Aspect 23. The crystalline material according to any one of aspects 1-22, wherein the material exhibits in-plane birefringence factor with An (na-nb) from about 0.02-0.04 for light having a wavelength of 800 - 820 nm and for light having a wavelength of 1000 -1100 nm.

[0079] Aspect 24. The crystalline material according to any one of aspects 1-23, wherein the crystalline material exhibits an in-plane birefringence.

[0080] Aspect 25. The crystalline material according to any one of aspects 1-24, wherein the material exhibits a 2-dimensional crystal structure.

[0081] Aspect 26. The crystalline material according to any one of aspects 1-25, wherein a mosaic parameter perpendicular to the detector plane (e3) when measured from an XRD spectra of a single crystal of the crystalline material is greater than about 1 .5.

[0082] Aspect 27. A lens comprising a crystalline material according to any one of aspects 1- 26.

[0083] Aspect 28. A method of converting a linearly polarized light into a circularly polarized light comprising exposing the linearly polarized light to a crystalline material according to any one of aspects 1-26 or a lens according to aspect 27.

[0084] Aspect 29. The method according to aspect 28, wherein the linearly polarized light comprises visible light and NIR light.EXAMPLES

[0085] The following examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and description of how the compounds, compositions, articles, devices and / or methods claimed herein are made and evaluated, and are intended to be purely exemplary of the disclosure and are not intended to limit the scope of what the inventors regard as their disclosure. Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.), but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in °C or is at ambient temperature, and pressure is at or near atmospheric.Example 1 : In-Plane Optical Birefringence in 2D Hybrid Copper Halides

[0086] A high-quality, centimeter-sized crystal flake of HCH (PEA2CUCI4; PEA = phenylethylammonium) was prepared using a standard slow-cooling crystallization method from an aqueous solution. The crystal image can be seen in the inset image of FIG. 1 B. The reported single-crystal X-ray diffraction identified the orthorhombic structure of PEA2CuCl4, which showed a layered structure composed of inorganic octahedra and organic cation layers, as shown in FIG. 1A. The unequally occupied degenerate orbitals of Cu2+3d9give rise to significant JT distortion. As shown in FIG. 1 B, the weak absorption feature induced by the d-d transition of the copperchloride octahedra can be observed in the NIR (800-1000 nm) region, which is caused by the splitting of d-energy levels in a ligand field that experiences JT effects. The JT distortion plays a crucial role in reducing the energy and results in elongated copper-halide octahedra, enabling anisotropic lattice distortion in both out-of-plane and in-plane directions. The in-plane structuralanisotropy is crucial to generate in-plane optical birefringence which is still challenging for common 2D metal halide materials. To quantitatively study the optical birefringence, first- principles calculations were performed to confirm the refractive indices at both in-plane and out- of-plane directions as depicted in FIG. 1C. Notably, the HCH crystal shows in-plane birefringence factor with An (n3-nb value of about 0.026 from visible to NIR region, which is comparable to the birefringence factor from standard QWP materials (Table 1, FIG. 1D).

[0087] Then, cross-polarized optical microscopy (CPOM) was employed to visualize the optical anisotropy and further identify birefringence by monitoring the crystal interference color. FIG. 1E illustrates the CPOM setup, where a polarizer and an analyzer are positioned before and after the sample in the perpendicular direction, respectively. The birefringent crystal sample splits the incident beam into fast and slow rays that are vectorially recombined after passing through the analyzer. The phase retardation between two rays results in destructive interference for certain wavelengths, which leads to interference colors in the CPOM. Therefore, the interference color is controlled by the phase retardation, which is determined by the crystal thickness and birefringence, as described in the equation: R (radian) = 2TT * An x T / A (R is phase retardation, T is thickness, A is wavelength). The HCH crystal with uniform thickness and a smooth surface (FIGs. 5A-5B) showed a uniform bright green color under CPOM (FIG. 1 F). By rotating the analyzer from 0° to 90°, the crystal color changed substantially due to the retardance change, leading to the interference color change from yellow to green to red. To quantify the interference color change, the RGB values of the CPOM microscopy color at different analyzer angles areextracted (Table 2). As the angle difference between the polarizer and analyzer increased from 0 to 180 degrees, both R and G values changed periodically (FIGs. 6A-6B), which further confirmed the in-plane birefringence of the HCH crystal.

[0088] To further explore the origin of the in-plane birefringence of 2D HCH crystal due to JT effects, the in-plane birefringence of hybrid metal halide crystals was studied via chemical structure engineering with various organic ligands, metal cations, and halide ions. When the organic ligands were varied while keeping the same copper halide building blocks, the HCH crystal retained the desirable in-plane birefringence as shown in the CPOM images (FIGs. 7A- 7B). This indicated that the in-plane anisotropy of HCH crystal is not significantly affected by the organic spacer layer in the case of copper chloride-based system. Since the in-plane birefringence should result from the JT distortion of copper-halide inorganic layers, both metal cation and halide ions were engineered to further study the effect of JT distortion. After replacing the copper (Cu) divalent cation with lead (Pb) divalent cation in the inorganic layer, while maintaining the same PEA organic spacer, evidence of in-plane birefringence from the PEA2PbBr4crystal with a thickness of approximately 88 pm was not observed (FIGs. 8A-8B). Since it is known that the Pb2+system does not retain JT distortion, the non-existence of in-plane birefringence further indicates the crucial role of JT distortion to in-plane birefringence in PEA2CUCI4. 50% of Br was then alloyed into the pure chloride-based HCH crystal as PEA2CuCl2Br2, and the Br-alloyed HCH again showed the in-plane birefringence (FIG. 9). However, the interference color showed limited changes when the analyzer angle was rotated, due to reduced in-plane birefringence and strong absorption of the crystal in the visible range. It is believed that the weakening of in-plane birefringence could be related to changes in the degree of JT distortion. Therefore, crystal structure engineering provides strong evidence that in-plane birefringence is mainly impacted by JT distortion in copper halide octahedra layers.Example 2: Broadband Achromatic Quarter-Wave Plates from Hybrid Copper Halide Single Crystal

[0089] The in-plane birefringence is crucial for their use in fabricating waveplates, indicating HCH crystal is a promising candidate for waveplate material. To evaluate the potential of HCH crystals as waveplates, laser modulation measurements were conducted. The laser modulation measurement setup is depicted in FIG. 2A, and a detailed explanation of the setup is in the Methods section. A wavelength-tunable femtosecond laser was used as an incident light source and linearly polarized laser light was directed perpendicular to the in-plane direction of a 2D HCH single crystal. As shown in FIGs. 2B-2C, when the crystal was absent from the beam path, the laser was fully linearly polarized and showed parallel stripes in the 2D colormap graph. When adding a commercial QWP (quartz / MgF) to the beam path, the colormap showed clear circles indicative of waveplate behavior. Initially, the HCH crystal was measured with a thickness of 34 pm, and the clear circles were observed in the color map from 900-940 nm, similar to the commercially available multi-order QWP as illustrated in FIGs. 10A-10K (as demonstrated by the original laser spectrum in FIGs. 11A-11C), indicating that the HCH crystal can function as single wavelength QWP. Subsequently, a thicker HCH crystal with a thickness of 164 pm was measured (FIGs. 12A-12B), and the thicker HCH crystal showed unexpected A-QWP properties over a broad range of wavelengths from visible to NIR, including A= 540-650 nm, 800-820 nm, and 1000- 1060 nm (FIG. 2D). Next, another HCH crystal was analyzed with a thickness of 237 pm (FIGs. 13A-13H), which displayed a slightly distinct wavelength response at A= 550-650 nm, 700-750 nm, and 800-850 nm. These results indicate that the wavelength response range of A-QWP HCH crystal is dependent on crystal thickness. Furthermore, a different laser modulation setup was used to further confirm the QWP properties (FIGs. 14A-14B). A commercialized QWP was placedafter the HCH crystal, and the laser became circularly polarized light after passing through HCH crystal, then after passing through the commercialized QWP, the laser became linearly polarized light again. This measurement provides further evidence of the QWP property of HCH crystal. Such the A-QWP property is unprecedented in mono-structured single crystals and highlights the HCH’s uniqueness and potential for practical applications.

[0090] Typically, conventional A-QWPs are fabricated by combining multiple birefringent crystals. This is often interpreted by calculating the combined retardation of A / birefringent crystals with a thickness of dj and birefringence value of ni as follows: Rcombined= . In contrast, thepresent A-QWP is based on a single HCH crystal with a layered structure and does not require a heterostructure or multi-component design. The HCH’s broadband retardation is possibly due to dislocation and distortion between the stacked inorganic layers, named out-of-plane mosaicity of copper chloride. The HCH crystals used in the laser modulation measurement had a thickness of approximately 164 pm (FIGs. 12A-12B), and the distance between two copper chloride inorganic layers is estimated to be around 1.9 nm based on the lattice parameter obtained from single crystal X-ray Diffraction. Out-of-plane dislocations and twists are anticipated to appear among the hundreds of copper chloride inorganic layers of thick bulk HCH crystal with weak interlayer Van der Waals interaction, leading to disordered stacked inorganic layers as illustrated in FIG. 3A. However, the A-QWP property was not observed in thinner HCH crystals (34 pm) due to the relatively ordered stacking of the crystals in the out-of-plane direction. Thus, the thick HCH single crystal possesses disordered stacking of inorganic layers, which can be seen as a combination of multiple birefringent HCH crystals. This combination is responsible for the broadband retardation observed in the material.

[0091] To investigate the interlayer packing of the HCH crystal with different thicknesses, Gl- WAXS experiments were performed on crystals with thicknesses ranging from 3 pm (FIGs. 15A- 15B) to 164 pm and monitored the diffraction peak of the (0 0 2) plane and (0 0 4) plane. As shown in FIGs. 3B-3D, the diffraction peaks of the thinnest HCH crystal with a thickness of 3 pm (FIG. 3B) were more elaborate, sharper, and showed less out-of-plane order than the thickest crystal (FIG. 3D), which showed significant streaking of the (0 0 2) reflection along qxy. This provides direct evidence of the less ordered layer stacking arrangement of the thicker HCH crystal, indicating that out-of-plane mosaicity can be responsible for the broadband retardation. It is known that the A-QWPs can be fabricated with the combination of two or more different birefringent crystals, and the broad wavelength laser modulation range could be controlled by theangle between crystal fast axes. Thus, the HCH A-QWPs wavelength range can be affected by the twisted angle between copper halide octahedra (CuCle4-) layers along the c-axis. Also, multiple copper chloride inorganic layers with different twisted angles can lead to a broader achromatic wavelength range.Example 3: Thermal-Induced Reversible Optical Retardation

[0092] Developing an external stimuli-controlled retarder remains a challenge, as it requires the ability to control phase retardation with external stimuli such as magnetic fields, temperature, etc. As shown in FIG. 16, HCH crystals display reversible thermochromism, changing from light yellow to orange as the temperature increases from 300 to 395 K. The thermochromism should contribute to the distorted copper halide octahedra under higher temperatures, and the distorted structure could lead to the change of in-plane birefringence. Then, the in-plane birefringence change of HCH crystal was investigated using CPOM. As shown in FIG. 4A, a reversible color change in CPOM is observed as the temperature increased from 303 to 438 K, providing direct evidence of birefringence change at higher temperatures. In addition, the interference color of the Br-alloyed HCH crystal also showed a color change under higher temperatures and lost its birefringence at 419 K (FIG. 17). Moreover, Fourier-transform infrared spectroscopy (FTIR) was utilized to obtain more information on the structural change that occurs at elevated temperatures (FIGs. 4E-4F). Peaks attributed to C-N and C-H stretching at around 1000 cm-1showed significant changes with increasing temperature, indicating that the packing of the organic cation also changed with temperature, particularly the ethylamine chain close to the copper halide octahedra. On the other hand, the aromatic ring deformation peaks at around 600 and 700 cm-1show limited changes, suggesting that the changes in organic cation packing result from the distortion of the inorganic copper halide layers. Laser modulation measurements were also conducted on the HCH crystal under different temperatures from 298 to 330 K. As shown in FIGs. 4B-4D, after heating the HCH crystal from 298 to 330 K, the transmitted laser changed from circularly to linearly polarized light, which is induced by the change of crystal birefringence. Upon cooling back to 298 K, circularly polarized light is restored, demonstrating that laser modulation of HCH crystal can be controlled by temperature reversibly. All the above-mentioned optical measurements are conducted in an air atmosphere, indicating the robustness of HCH crystals for practical optical applications.

[0093] T o investigate the structural change of the HCH crystal under higher temperatures, in-situ temperature-dependent powder X-ray diffraction (PXRD) was conducted. The PXRD peaks ofHCH crystal show a continuous shift to lower angles with increasing temperature (FIG. 18). The peak shift value increased with increasing temperature, indicating continuous lattice expansion with increasing temperatures according to Bragg's Law. The peak shift from out-of-plane diffraction peaks at higher angles is significantly larger than the in-plane diffraction peaks at lower angles. For example, the (0 0 2) out-of-plane diffraction peak at 4.37° (Table 3) shifted about 0.005° from 300 K to 450 K, while the (1 3 1) in-plane diffraction peak at 38.86° shows a much larger shift of about 0.515° from 300 K to 450 K, indicating a significant in-plane structure distortion upon increasing the temperature. In summary, the in-plane distortion from copper-halide octahedra is likely responsible for the temperature-controlled birefringence and laser modulation of HCH crystal.

[0094] The high-quality large-area anisotropy 2D HCH layered crystal exhibited a desirable birefringence with an in-plane An about 0.026 from visible to NIR wavelengths. The anisotropy is proven to originate from the distortion of copper-halide octahedra layers with JT distortion. The birefringent HCH crystal flake is able to function as a QWP that can modulate linearly polarized light to circularly polarized light or vice versa. In addition, the HCH crystal QWP covers a broad wavelength range from visible to NIR, indicating that HCH crystals can be used as A-QWP. Based on the GI-WAXS results, the disordered stacked inorganic layers are responsible for the A-QWP property of thick HCH single crystals. Furthermore, the A-QWP property of the crystal could be controlled by temperature, and the high-temperature CPOM, FTIR, and XRD further prove the inplane anisotropy of the inorganic layer is responsible for the desirable birefringence value. This work indicates the 2D HCH perovskite is a promising candidate for fabricating economical A- QWPs and other optical devices.Example 4: Methods

[0095] Crystal preparation: PEA2Cu&4: 473.9 mg phenethylammonium chloride (PEACI) and 256.5 mg copper(ll) chloride dihydrate are dissolved with 9 ml_ methanol under 75°C in an oil bath. Upon slow cooling down of the solution at 4°C / hour to 25°C, a yellow PEA2CUCI4 crystal flake is obtained. The crystal is then washed with chloroform three times. PEA2CuCl2Br2: Using the same methods as PEA2CuCl4, the PEA2CuCI2Br2crystal is prepared by replacing 473.9 mg phenethylammonium chloride (PEACI) with 404.18 mg phenethylammonium bromide (PEABr).

[0096] Thin layer PEA2CuCl4 crystal preparation with space-confinement method: PEA2CUCI4 crystal solutions are prepared by directly dissolving washed crystals. The solution concentration is 200 mg / mL dissolving with dimethyl sulfoxide / y-Butyrolactone mixed solvent (7:3 volume ratio). Glass slides are cleaned for 15 mins in an ultrasonic cleaner with water, 2-Propanol, then acetone respectively. Petri dishes, glass slides, spacers (microscope slide covers), and PEA2CuCl4 crystal solutions are preheated on a hotplate for 10 mins at 70°C. Spacers are placed on both edges of the glass slide, and 10 uL crystal solution (preheated for 10 mins) is dropped in the middle of the glass slide. Then another preheated glass slide is placed on top. Another small petri dish is placed on top of the glass slide(s) filled with 5ml_ chloroform. The petri dish (containing the glass and small petri dish) is closed and wrapped in foil for about 3 days to afford the thin crystal on the glass.

[0097] Characterizations: The UV-Vis-NIR absorption is measured by the Hitachi U4100 from UV-VIS-NIR Spectroscopy from Hitachi High Technologies. Grazing-incidence wide-angle X-ray scattering (GI-WAXS) experiments are performed on a Xenocs Xeuss 3.0 SAXS / WAXS equipped with a GeniX 3D Cu HFVLF microfocus X-ray source utilizing Cu Ka radiation (A = 0.154 nm). The sample-to-detector distance is 370 mm and calibrated using a silver behenate standard, and the incident angle was 0.2°. Two-dimensional scattering patterns are obtained using a Dectris EIGER 4M detector and processed using the XSACT software package. The laser modulation measurement setup is shown in FIG. 2A. The laser is generated from the Astrella-F-1 K one-box femtosecond amplifier of Coherent company with an optical parametric amplifier system. The polarizer, half waveplate, and QWP are purchased from Thorlabs, and the thin film polarizer works as an analyzer is purchased from Newport. The H RS-300 spectrometer with a PyLoN camera system from Princeton Instruments is used to detect the transmitted laser intensity. The in situ heating PXRD is measured by the Rigaku Miniflex 6G Benchtop Powder XRD with a Cu Ka radiation source. The temperature is controlled with a BTS 500 - benchtop heating stage. Samplesare ground into powder and filled in a 0.2mm depth stage for measurements. The sample is heated in the air.

[0098] Laser modulation measurement: At first, the femtosecond pulsed laser passes through a linear polarizer, followed by a half-waveplate that can tune the polarization direction. Then, the highly polarized light with tunable direction will pass through the PEA2CuCl4 crystal. If the PEA2CuCl4 crystal can function as a QWP, the light can be modulated to be circularly or elliptically polarized light when the angle difference between the laser fast axes and crystal fast axes is 45° or between 45° and 0°. Here, the half waveplate has rotated a total of 90°, which means the laser fast axes angle changed 180°. As the laser fast axes angle changes, the transmitted light will change from linear to elliptical and circularly polarized light if the PEA2CUCI4 crystal can function as a QWP, followed by an analyzer to detect the laser polarization direction. The transmitted light intensity is monitored when rotating the analyzer. When rotating the analyzer, the circularly polarized light intensity will show negligible change, the elliptical light intensity will show small change, and the linearly polarized laser will show tremendous change. A two-dimensional color map is obtained by recording the transmitted laser intensity upon half waveplate and the analyzer angle change. As shown in FIGs. 2B-2C, the laser is fully linearly polarized without the crystal on the beam path, which exhibits parallel stripes in the 2D colormap graph. While with a commercial A-QWP in the beam path, the colormap shows clear circles.

[0099] First principles density functional theory calculations are performed using the Vienna Ab- initio Simulation Package (VASP) code with projector augmented-wave potentials. An energy cutoff value of 400 eV is adopted to expand the wavefunctions and the Gamma-centered 2x2*1 k mesh is considered when sampling the Brillouin zone. The experimental lattice parameters were used and the atomic coordinates were relaxed using the Perdew-Burke-Ernzerhof functional with a force tolerance of 0.01 eV / A. The DFT+U scheme with an effective U value of 7.28 eV for Cu was employed.

[0100] It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications may be made to the abovedescribed embodiment(s) without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.REFERENCES Asensio Y, et al. Magnetic Properties of Layered Hybrid Organic- Inorganic Metal-Halide Perovskites: Transition Metal, Organic Cation and Perovskite Phase Effects. Adv. Funct. Mater., (2022). Beckers, J. Achromatic linear retarders. Applied Optics 10, 973-975 (1971). Bldchl, P. E. Projector augmented-wave method. Physical Review B 50, 17953-17979, (1994). Boulbry, B., et al. Polarization errors associated with zero-order chromatic quarter-wave plates in the whole visible spectral range. Opt. Express 9, 225-235 (2001). Chen X, et al. Solution-processed inorganic perovskite crystals as achromatic quarter-wave plates. Nature Photonics 15, 813-816, (2021). Choi Y, et al. A vertically oriented two-dimensional Ruddlesden-Popper phase perovskite passivation layer for efficient and stable inverted perovskite solar cells. Energy & Environ. Sci. 15, 3369-3378 (2022). Delly, J. G. The Michel-Levy interference color chart-microscopy’s magical color key. Modern Microsc. J (2003). Dudarev, S. L, et al. Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B 57, 1505 (1998). Ermolaev G, et al. Giant optical anisotropy in transition metal dichalcogenides for nextgeneration photonics. Nat. Commun. 12, 854, (2021). Ermolaev, G. A. et al. Giant optical anisotropy in transition metal dichalcogenides for nextgeneration photonics. Nat. Commun. 12, 854, (2021). Fan F, et al. Magnetically Induced Terahertz Birefringence and Chirality Manipulation in Transverse-Magnetized Metasurface. Adv. Opt. Mater. 9, 2101097, (2021). Halcrow, M. A. Jahn-Teller distortions in transition metal compounds, and their importance in functional molecular and inorganic materials. Chem. Soc. Rev. 42, 1784-1795 (2013). Holbourn, A. Angular momentum of circularly polarised light. Nature 137, 31-31 (1936). Hu D, et al. Tunable Modal Birefringence in a Low-Loss Van Der Waals Waveguide. Adv. Mater. 31 , 1807788, (2019).Huang W, et al. A Hybrid Halide Perovskite Birefringent Crystal. Angew Chem Int Ed Engl 2022: e202202746. Kim J, et al. Anisotropic mosaicity and lattice-plane twisting of an m-plane GaN homoepitaxial layer. CrystEngComm 21 , 4036-4041 (2019). Kim WJ, et al. Geometric frustration of Jahn-Teller order in the infinite-layer lattice. Nature, 1- 7 (2023). Kozlov, A. N.-E. S. M., et al. Electronic-structure-based chemical descriptors: (in) dependence on self-interaction and Hartree-Fock exchange. Phys. Rev. B 54, 11169-11186 (1996). Kresse, G. et al. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15-50 (1996). McIntyre, C. M. et al. Achromatic wave plates for the visible spectrum. JOSA 58, 1575-1580 (1968). Munkhbat, B., et al. Optical Constants of Several Multilayer Transition Metal Dichalcogenides Measured by Spectroscopic Ellipsometry in the 300-1700 nm Range: High Index, Anisotropy, and Hyperbolicity. ACS Photonics 9, 2398-2407, (2022). Patel SN, et al. Morphology controls the thermoelectric power factor of a doped semiconducting polymer. Sci. Adv. 3, e1700434, (2017). Pedrotti, F. L, et al. Introduction to optics. (Cambridge University Press, 2017). Perdew, J. P., et al. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996). Polyakov, A. O. et al. Coexisting Ferromagnetic and Ferroelectric Order in a CuCI4-based Organic-Inorganic Hybrid. Chem. Mater. 24, 133-139, (2011). Saha, A., et al. Achromatic quarter-wave plate using crystalline quartz. Appl. Opt. 51 , 1976- 1980 (2012). Sanz-Ortiz, M. N. et al. Photoluminescence properties of Jahn-Teller transition-metal ions. J. Chem. Phys. 131 , 124512, (2009). Saparov, B. et al. Organic-Inorganic Perovskites: Structural Versatility for Functional Materials Design. Chem. Rev. 116, 4558-4596 (2016).Sun B, et al. Reversible Thermochromism and Strong Ferromagnetism in Two-Dimensional Hybrid Perovskites. Angew Chem Int Ed Engl 59, 203-208, (2020). Valiente, R. et al. Comment on “Copper-Substituted Lead Perovskite Materials Constructed with Different Halides for Working (CH3NH3)2CuX4-Based Perovskite Solar Cells from Experimental and Theoretical View”. ACS Appl Mater Interfaces 12, 37807-37810, (2020). Wang J, et al. Unusual ferroelectric-dependent birefringence in 2D trilayered perovskite-type ferroelectric exploited by dimensional tailoring. Matter 2022, 5(1): 194-205. Wang S, et al. Large piezoelectric response in a Jahn-Teller distorted molecular metal halide. Nature Communications 2023, 14(1): 1852. Watson, J. N., et al. Temperature dependence of electric field-gradient induced birefringence in carbon dioxide and carbon disulfide. Chem. Phys. Lett. 274, 1-6 (1997). Wu J, et al. Mosaic growth induced magnetic anisotropy in double perovskite PrBaCo2O5+b thin films. Acta Mater. 234: 118040(2022). Xu, H. et al. Magnetically tunable and stable deep-ultraviolet birefringent optics using two- dimensional hexagonal boron nitride. Nat. Nanotechnol. 17, 1091-1096 (2022). Yuan, M. et al. Perovskite energy funnels for efficient light-emitting diodes. Nat. Nanotechnol.11 , 872-877 (2016).

Claims

CLAIMSWhat is claimed is:

1. A crystalline material comprising a chemical structure according to the formula (Li)(L2)MXiY4.i; where Li and L2are each independently ammonium containing organic ligands; where M is a divalent metal; where X and Y are each independently monovalent anions; and where i is an integer from 0 to 4.

2. The crystalline material of claim 1 , wherein Li and l_2are the same.

3. The crystalline material of claim 1 , wherein M is a metal that undergoes a Jahn-Teller distortion.

4. The crystalline material of claim 1 , wherein M has 1 , 2, 4, 5, 6, 7, or 9 electrons in d orbitals.

5. The crystalline material of claim 1 , wherein M is selected from the group consisting ofCu2+, Cr2+, and Fe2+.

6. The crystalline material of claim 5, wherein M is Cu2+.

7. The crystalline material of claim 1 , wherein Li and l_2are different.

8. The crystalline material of claim 7, wherein M is selected from the group consisting of Pb2+, Sn2+, Mn2+, and Cd2+.

9. The crystalline material of claim 8, wherein M is Pb2+.

10. The crystalline material according to claim 1, wherein one or both of Li and L2is each independently selected from the group consisting of phenylethylammonium (PEA), (R)- (+)-3-methylphenethylammonium, butylammonium, 1 ,2,4-triazolium, ethylammonium, propylammonium, isopropylammonium, pentylammonium, hexylammonium, heptylammonium, benzylammonium, naphthylammonium, pyridinium, imidazolium, pyrrolidinium, piperidinium, morpholinium, quinolinium,. pyrazinium, and quinoxalinium.

11. The crystalline material of claim 10, wherein Li and L2are both phenylethylammonium.

12. The crystalline material according to claim 1, wherein one or both of Li and L2is each independently selected from the group consisting of L-histidine, L-proline, L-lysine, L-ornithine, L-alanine, L-phenylalanine, L-cysteine, and L-leucine, or another chiral amino acid.

13. The crystalline material according to claim 1, wherein X and Y are each independently selected from the group consisting of chloride, bromide, and iodide.

14. The crystalline material of claim 13, wherein Y is chloride.

15. The crystalline material of claim 13, wherein X is chloride and Y is bromide.

16. The crystalline material according to claim 1 , wherein i is 0, 2, or 4.

17. The crystalline material of claim 16 wherein i is 0.

18. The crystalline material of claim 16, wherein i is 2.

19. The crystalline material of claim 1, wherein the crystalline material is PEA2CuCl4 or PEA2CuCI2Br2.

20. The crystalline material according to claim 1 , wherein the crystalline material is single crystalline or essentially single crystalline.

21. The crystalline material according to claim 1 , wherein the material consists essentially of the material comprising a chemical structure according to the formula (Li)(L2)MX 4-i.

22. The crystalline material according to claim 1 , wherein the crystalline material comprises single crystals having a thickness of from about 50 pm to about 350 pm.

23. The crystalline material according to claim 1, wherein the material exhibits in-plane birefringence factor with An (na-nb) from about 0.02-0.04 for light having a wavelength of 800 - 820 nm and for light having a wavelength of 1000 -1100 nm.

24. The crystalline material according to claim 1 , wherein the crystalline material exhibits an in-plane birefringence.

25. The crystalline material according to claim 1 , wherein the material exhibits a 2-dimensional crystal structure.

26. The crystalline material according to claim 1 , wherein a mosaic parameter perpendicular to the detector plane (e3) when measured from an XRD spectra of a single crystal of the crystalline material is greater than about 1.5.

27. A lens comprising a crystalline material according to any one of claims 1-26.

28. A method of converting a linearly polarized light into a circularly polarized light comprising exposing the linearly polarized light to a lens according to claim 27.

29. The method according to claim 28, wherein the linearly polarized light comprises visible light and NIR light.

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