Nonlinear optical mg-iv-v 2 crystals, methods of making the same and devices comprising the same

Abstract

Disclosed herein is a single nonlinear optical crystal having a chemical formula of Mg-IV-V2, wherein IV is selected from Si, Ge, or Sn, and V is selected from P or As, wherein the single nonlinear optical crystal has a chalcopyrite and non-centrosymmetric crystal structure, with a space group of, wherein the non-centrosymmetric crystal structure is defined by unit cell parameters: a between about 5.5 to about 6 Å, c between about 9.5 to about 12.5 Å, and a unit cell volume of about 287 to about 450 Å3, wherein the single nonlinear optical crystal exhibits a refractive index of about 2.770 to about 2.780 and from about 2.800 to about 2.810 for no and ne respectively at a wavelength of 1,550 nm, and a nonlinear coefficient of d eff of SHG from about 80 to about 95 pm / V, wherein the single crystal Mg-IV-V2 is substantially free of impurities.

Description

[0001] Attorney Docket No.11196-079WO1 NONLINEAR OPTICAL Mg-IV-V2 CRYSTALS, METHODS OF MAKING THE SAME AND DEVICES COMPRISING THE SAME CROSS-REFERENCE TO THE RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No.63 / 398,993, filed August 18, 2022, and U.S. Provisional Application No. 63 / 492,080, filed March 24, 2023, the contents of which are incorporated herein by reference in their entirety. STATEMENT OF GOVERNMENT SUPPORT

[0002] This invention was made with government support under Grant Nos. DMR2210933 and DMR2039351, awarded by the National Science Foundation under Grant No. DE-SC0019068, awarded by the Department of Energy and under Grant No. FA9550-19-1-0243 awarded by the U.S. Air Force / AFOSR. The Government has certain rights in the invention. TECHNICAL FIELD

[0003] This application relates generally to single crystals with nonlinear optical (NLO) properties, including large second-order NLO characteristics, Type I and Type II phase-matchability, and low absorption in a wide infrared spectral range, allowing for the application of the NLO crystals in high-power laser systems. BACKGROUND

[0004] The 1961 experimental discovery of optical second harmonic generation (SHG) by Franken et al. and the 1965 theory by Bloembergen (Nobel prize in physics, 1981) launched the field of nonlinear optics (NLO). This discovery of the ability to combine and split photons using nonlinear optical interactions has had a dramatic impact on generating a continuously tunable electromagnetic spectrum towards furthering both fundamental sciences as well as technological applications.

[0005] Infrared lasers with wide tunability and high efficiency are becoming increasingly vital because of their broad applications for many civilian and military applications, including environmental monitoring, countermeasure, and laser Attorney Docket No.11196-079WO1 surgery. Nonlinear optical crystals are the essential components of the high-power lasers for frequency conversion through nonlinear optical phenomena such as second harmonic generation (SHG), sum frequency and difference frequency. The traditional NLO materials such as β-BaB2O4 (BBO), KH2PO4 (KDP) and LiNbO3 are not suitable for broadband infrared applications because of the relatively low conversion efficiency and infrared absorption beyond 4.5-5μm wavelength. The current state of art infrared NLO crystals includes AgGaS2, AgGaSe2, and ZnGeP2. Though these crystals exhibit high optical nonlinearity and wide transparency in IR spectral range, their low laser damage threshold (LDT) values or two-phonon absorption limits their applications. Clearly, the development of infrared laser systems demands novel infrared NLO crystals with superior optical properties.

[0006] These needs and other needs are at least partially satisfied by the present disclosure. SUMMARY

[0007] The present disclosure is directed to a single nonlinear optical crystal having a chemical formula of Mg-IV-V2, wherein IV is selected from Si, Ge, or Sn, and V is selected from P or As, wherein the single nonlinear optical crystal has achalcopyrite and a non-centrosymmetric crystal structure, with a space group of^4^2^; wherein the non-centrosymmetric crystal structure is defined by unit cellparameters: a between about 5.5 to about 6 Å, c between about 9.5 to about 12.5Å, and a unit cell volume of about 287 to about 450 Å3, wherein the single nonlinearoptical crystal exhibits a refractive index of about 2.770 to about 2.780 and from about 2.800 to about 2.810 for no and ne respectively at a wavelength of 1,550 nm, and a nonlinear coefficient of deffof SHG from about 80 to about 95 pm / V, wherein the single nonlinear optical crystal Mg-IV-V2is substantially free of impurities.

[0008] In yet still, further aspects, the nonlinear optical crystal disclosed herein can exhibit a transmittance from about 60 % to less than 100% in a wavelength range from about 0.55 µm to about at least 20 µm.

[0009] In yet still further aspects, single crystal Mg-IV-V2 is uniaxial. Attorney Docket No.11196-079WO1

[0010] Also disclosed herein is a method of forming any of the disclosed herein single nonlinear optical crystals, wherein the method comprises: a) providing a solution comprising a solute comprising a mixture of Mg, IV and V in a molar ratio from about 0.95:0.95:2 to about 1.05:1.05:2 and a solvent; wherein a mass ratio between the solvent and solute is from about 10:1 to about 4:1; b) growing a crystalline composition comprising Mg-IV-V2 at a first temperature from about 950 °C to about 1,200 °C for a first predetermined time; c) centrifugally separating the solvent to form a single nonlinear optical crystal of Mg-IV-V2 having a size from about 0.01 mm to about 10 mm in length, wherein the single nonlinear optical crystal is substantially free of a solvent residue.

[0011] In yet still further aspects, disclosed herein is a method of forming any of the disclosed herein single nonlinear optical crystals, wherein the method comprises: a) sealing a polycrystalline material, comprising the Mg-IV-V2 in a temperature resistant container; b) placing the temperature resistant container in a rocking furnace; c) heating the polycrystalline material to a first temperature at a rate of about 45 °C / h to about 120 °C / h and keeping the mixture at this heating temperature for a first predetermined time; d) placing the temperature-resistant container in a three-zone furnace, wherein the three-zone furnace exhibits a temperature profile defined by an upper / melt zone temperature, a middle / crystallization zone temperature; and a lower / annealing zone temperature; e) translating the temperature-resistant container vertically thereby allowing the temperature-resistant container to arrive at a nucleating temperature to form a self- seeding crystal; f) growing an ingot material from the self-seeding crystal; g) annealing the polycrystalline material to a temperature of about 700 °C to about 850 °C for a second predetermined time; and h) forming the single nonlinear optical crystal Mg-IV-V2, wherein the crystal is substantially free of impurities, defined by a single phase and has a size from about 0.1 mm to about 10 cm in length.

[0012] In still further aspects, the polycrystalline material comprising the Mg-IV-V2 compound used in the disclosed methods is formed by the steps comprising: a) mixing Mg, IV, and V in a molar ratio of about 0.95:0.95:2 to about 1.05:1.05:2 to form a mixture; b) placing the mixture into a sealed container in a furnace; c) Attorney Docket No.11196-079WO1 bringing the mixture to a first heating temperature of about 450 °C to about 550 °C at a rate of about 1 °C / h to 55 °C / h and keeping the mixture at the first heating temperature for about 60 to about 100 hours; d) bringing the mixture to a second heating temperature of about 780° C to about 850 °C at a rate of about 1 °C / h to about 40 °C / h and keeping the mixture at the second heating temperature for about 50 to about 100 hours; e) bringing the mixture to a third heating temperature of about 1,100 °C to about 1,250 °C at a rate of about 20 °C / h to about 40 °C / h and keeping the mixture at the third heating temperature for about 50 to about 100 hours; f) cooling the mixture to a room temperature at a rate of about 50 °C / h to about 150 °C / h; and g) recovering the polycrystalline material comprising Mg-IV-V2, wherein the polycrystalline material is substantially free of impurities and has a substantially single phase.

[0013] Also disclosed herein is an optical parametric oscillator comprising any of the disclosed herein single nonlinear optical crystals.

[0014] In yet still further aspects, disclosed herein is a laser comprising any of the disclosed herein single nonlinear optical crystals.

[0015] Additional advantages 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 aspects described below. The advantages described below will be realized and attained by means of the chemical compositions, methods, and combinations thereof, 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. BRIEF DESCRIPTION OF DRAWINGS

[0016] FIGURES 1A-1E show the state of the art in Nonlinear and Quantum Optics: FIG.1A shows the inverse relationship (grey band) between the second-order optical nonlinearity, dijk, versus the electronic bandgap of various NLO crystals. The red stars (⋆) indicate data obtained in one aspect of the present disclosure, the Attorney Docket No.11196-079WO1 remaining data is obtained from the literature (Ref.9, 30-39). Open symbols are theoretical predictions. FIG.1B shows a single photon nonlinearity (defined in the main text) versus effective defffor optical cavity mode volume of 0.1 (red), 1 (green) and 10(blue) times (^ / ^^)^, where ^ is the wavelength and ^^is the mode index. This indicates that the larger the optical mode volume, the larger the deff desired for single-photon nonlinear frequency conversion for quantum optics. FIG.1C depictsa schematic of Second Order Nonlinear Processes. An NLO medium denoted by^(^) can combine two photons of frequencies ^^ and ^^, to generate ^^ + ^^ calledsum frequency generation or SFG, as well as ^^− ^^called the difference frequency generation or DFG. FIGs.1D and 1E show NLO crystal design considerations. FIG.1D shows the for NLO crystals. FIG.1E depicts transparency windows for design in mid-IR (between ^^^^and ^^^^^^), and in the THz (between ^^^^^^and ^^^^^^^).

[0017] FIGURE 2A shows the lattice structure of MgSiP2 in one aspect. FIGURE 2B shows photographs of MgSiP2 in one aspect.

[0018] FIGURES 3A-3D compare CVT-treated crystals and exemplary crystals according to some aspects of the disclosure.

[0019] FIGURE 4 shows an XRD comparison of CVT-treated crystals and exemplary crystals according to some aspects of the disclosure

[0020] FIGURE 5 depicts the crystal structure of MgSiP2, showing the (101) plane and the [111^] direction.

[0021] FIGURE 6 shows a schematic view of the SHG polarimetry geometry.

[0022] FIGURES 7A-7C show the Crystal structure of MgSiP2 viewed from the

[0120] axis (FIG. 7A) and from the (112) plane, which is highlighted in red (FIG. 7B). The[111^] and [11^0] axes are marked in grey arrows. FIG. 7C shows an image of aMgSiP2 crystal aligned in the same orientation as in Fig.7B, showing the (112) plane. The other facet corresponds to the (101) plane, and the growth direction is along the [111^] axis. Attorney Docket No.11196-079WO1

[0023] FIGURES 8A-8B depict the MgSiP2 crystal structure. FIG.8A shows the XRD pattern collected on the two facets of the MgSiP2 single crystals, confirming the chalcopyrite structure, high crystallinity and plane orientation. Inset: a schematic (top) and an SEM image (bottom) of the crystal showing the (112) and (101) facets. FIG.8B depicts a STEM image taken from the

[0110] axis. Inset: A magnified HAADF-STEM image superimposed with a simulated crystal structure.

[0024] FIGURE 9 shows the real (solid line) and imaginary (dash line) refractive indices of MgSiP2. The blue and red curves represent the ordinary and extraordinary components, respectively.

[0025] FIGURES 10A-10B depict polar plots of p-polarized (FIG.10A) and s- polarized (FIG.10B) SHG intensities. The black curves are the theoretical fit based on a point group 4^2#.

[0026] FIGURE 11A shows the experimental geometry of the SHG polarimetry. FIG.11B shows polar plots of p-polarized (blue) and s-polarized (pink) SHG intensities of MgSiP2 and the theoretical fit (black lines). FIG.11C shows SHG intensities of MgSiP2 crystal versus incident power. The good quadratic fit confirmed the measured signal was from the SHG process. Inset: SHG intensities versus incident power in logarithmic scale. FIG.11D shows a comparison of SHG coefficients and bandgaps among MgSiP2 (red star) and various NLO materials. The highest non-resonant dijk coefficients of the NLO materials are shown. The LDTs of MgSiP2, CdSiP2 and ZnGeP2 are illustrated in the inset. FIG.11E shows the energy-dependent complex d36 coefficient calculated by DFT with internal relaxation and scissor shift (labeled as “full”). The experimental value is shown as a pink star. In the inset, the curve obtained in the anti-resonant approximation (i.e., neglecting the anti-resonant contribution) is also displayed as a dashed line labeled AA.

[0027] FIGURE 12 depicts the definition of the phase matching angle θmand azimuthal angle φ.

[0028] FIGURES 13A-13B depict schematics of the crystal wafer cut at the Type I phase matching direction when |deff,I| is at its maximum. Attorney Docket No.11196-079WO1

[0029] FIGURES 14A-14B depict the Type I and Type II phase-matching angle of MgSiP2 versus the fundamental wavelength.

[0030] FIGURE 15 shows the deff for Type I and Type II phase-matching conditions of MgSiP2 versus the azimuthal angle φ.

[0031] FIGURE 16 shows the Band structure of MgSiP2 with internal relaxation and without scissor shift. All bands are shifted to set the valence band maximum (VBM) at 0 eV.

[0032] FIGURE 17A shows the transmittance spectrum of a single crystal MgSiP2 with a thickness of ~225 μm. FIG.17B shows the experimental complex ordinary (top) and extraordinary (bottom) refractive indices of MgSiP2 compared with results from DFT calculations with internal relaxation and scissor shift. FIG.17C shows the ordinary and extraordinary refractive indices of MgSiP2 and the theoretical Sellmeier fit. The inset enlarges the data in 0.45-1.0 μm to show the good fit.

[0033] FIG.18A shows the energy dependence of the imaginary SHG “intra” 1 and 2 terms and of the xx (ordinary) and zz (extraordinary) components of the linear optical response. The 2^ curve was shifted in accordance with its resonance. FIG. 18B shows the contributions of the different bands to the main peak of the imaginary SHG response for the main terms. Only the 3-bands interactions were considered. The bands are shifted to set the valence band maximum (VBM) at 0 eV.

[0034] FIGURE 19 shows the definition of the phase matching angle θm and azimuthal angle φ.

[0035] FIGURE 20 shows the crystal structure of MgSiP2 viewed from the

[0111] axis, showing the MgP4 and SiP4 tetrahedra are aligned in one direction. P atoms are omitted from the figure for clarity.

[0036] FIGURE 21 shows an image of MgSiP2 single crystals.

[0037] FIGURE 22 shows a crystal image of MgSiP2 after being left in air for two days, showing the beginning of surface degradation. Attorney Docket No.11196-079WO1

[0038] FIGURE 23 shows the band structure of MgSiP2 with internal relaxation and scissor shift. All bands are shifted to set the valence band maximum (VBM) at 0 eV.

[0039] FIGURE 24 shows the complex dielectric constants of MgSiP2 extracted from ellipsometry, showing each oscillator.

[0040] FIGURE 25 shows the birefringence curve (^$− ^^) of MgSiP2.

[0041] FIGURE 26 shows a comparison of the SHG intensities of MgSiP2 and x-cut LiNbO3, normalized to the same incident power.

[0042] FIGURE 27 shows three different contributions to the SHG coefficient of MgSiP2. Only the resonant terms have been considered here.

[0043] FIGURE 28 shows the projected density of states (PDOS) of MgSiP2.

[0044] FIGURES 29A-29F show crystal images of (FIG.29A) MgSiP2, (FIG.29C) CdSiP2and (FIG.29E) ZnGeP2before the laser damage measurements and (FIG. 29B) MgSiP2, (FIG.29D) CdSiP2 and (FIG.29F) ZnGeP2 after the laser damage measurements.

[0045] FIGURE 30 shows the temperature-dependent thermal conductivity of MgSiP2. DETAILED DESCRIPTION

[0046] The present invention can be understood more readily by reference to the following detailed description, examples, drawings, and claims, and their previous and following description. However, before the present articles, systems, and / or methods are disclosed and described, it is to be understood that this invention is not limited to the specific or exemplary aspects of articles, systems, and / or methods disclosed unless otherwise specified, as such can, of course, vary. 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.

[0047] The following description of the invention is provided as an enabling teaching of the invention in its best, currently known aspect. To this end, those skilled in the relevant art will recognize and appreciate that many changes can be Attorney Docket No.11196-079WO1 made to the various aspects of the invention described herein while still obtaining the beneficial results of the present invention. It will also be apparent that some of the desired benefits of the present invention can be obtained by selecting some of the features of the present invention without utilizing other features. Accordingly, those of ordinary skill in the pertinent art will recognize that many modifications and adaptations to the present invention are possible and may even be desirable in certain circumstances and are a part of the present invention. Thus, the following description is again provided as illustrative of the principles of the present invention and not in limitation thereof. DEFINITIONS

[0048] 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.

[0049] It is appreciated that certain features of the disclosure, which are, for clarity, described in the context of separate aspects, can also be provided in combination in a single aspect. Conversely, various features of the disclosure, which are, for brevity, described in the context of a single aspect, can also be provided separately or in any suitable subcombination.

[0050] As used in the description and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, a reference to “a crystal” includes two or more such crystals, and a reference to “a laser” includes two or more such lasers and the like.

[0051] 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. As used in the specification and in the claims, the term “comprising” can include the aspects “consisting of” and “consisting essentially of.” 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 this invention belongs. In this Attorney Docket No.11196-079WO1 specification and in the claims which follow, reference will be made to a number of terms that shall be defined herein.

[0052] For the terms “for example” and “such as,” and grammatical equivalences thereof, the phrase “and without limitation” is understood to follow unless explicitly stated otherwise.

[0053] Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the disclosure are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contains certain errors necessarily resulting from the standard deviation found in their respective testing measurements. Furthermore, when numerical ranges of varying scope are set forth herein, it is contemplated that any combination of these values, inclusive of the recited values, may be used. Further, ranges can be expressed herein as from “about” one particular value and / or to “about” another particular value. When such a range is expressed, another aspect includes from the one particular value and / or to the other particular value.

[0054] Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another aspect. 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. Unless stated otherwise, the term “about” means within 5% (e.g., within 2% or 1%) of the particular value modified by the term “about.”

[0055] Throughout this disclosure, various aspects of the invention can be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, a description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6, etc., as well as individual numbers within that range, for Attorney Docket No.11196-079WO1 example, 1, 2, 2.7, 3, 4, 5, 5.3, 6 and any whole and partial increments therebetween. This applies regardless of the breadth of the range.

[0056] As used herein, the term “composition” is intended to encompass a product comprising the specified ingredients in the specified amounts, as well as any product which results, directly or indirectly, from a combination of the specified ingredients in the specified amounts.

[0057] References in the specification and concluding claims to parts by weight of a particular element or component in a composition denotes the weight relationship between the element or component and any other elements or components in the composition or article for which a part by weight is expressed. Thus, in a mixture containing 2 parts by weight of component X and 5 parts by weight, components Y, X, and Y are present at a weight ratio of 2:5 and are present in such a ratio regardless of whether additional components are contained in the mixture.

[0058] A weight percent (wt.%) of a component, unless specifically stated to the contrary, is based on the total weight of the formulation or composition in which the component is included.

[0059] It will be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or intervening elements may be present. In contrast, when an element is referred to as being “directly connected” or “directly coupled” to another element, there are no intervening elements present. Other words used to describe the relationship between elements or layers should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” “on” versus “directly on”).

[0060] As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0061] It will be understood that although the terms “first,” “second,” etc., may be used herein to describe various elements, components, regions, layers, and / or sections. These elements, components, regions, layers, and / or sections should not be limited by these terms. These terms are only used to distinguish one element, Attorney Docket No.11196-079WO1 component, region, layer, or section from another element, component, region, layer, or section. Thus, a first element, component, region, layer, or section discussed below could be termed a second element, component, region, layer, or section without departing from the teachings of example embodiments.

[0062] As used herein, the term “substantially” means that the subsequently described event or circumstance completely occurs or that the subsequently described event or circumstance generally, typically, or approximately occurs.

[0063] Still further, the term “substantially” can, in some aspects, refer to at least about 80 %, at least about 85 %, at least about 90 %, at least about 91 %, at least about 92 %, at least about 93 %, at least about 94 %, at least about 95 %, at least about 96 %, at least about 97 %, at least about 98 %, at least about 99 %, or about 100 % of the stated property, component, composition, or other condition for which substantially is used to characterize or otherwise quantify an amount.

[0064] In other aspects, as used herein, the term “substantially free,” when used in the context of a composition or component of a composition that is substantially absent, is intended to refer to an amount that is then about 1 % by weight, e.g., less than about 0.5 % by weight, less than about 0.1 % by weight, less than about 0.05 % by weight, or less than about 0.01 % by weight of the stated material, based on the total weight of the composition.

[0065] As used herein, the terms “substantially identical reference composition,” “substantially identical reference article,” or “substantially identical reference electrochemical cell” refer to a reference composition, article, or electrochemical cell comprising substantially identical components in the absence of an inventive component. In another exemplary aspect, the term “substantially,” in, for example, the context “substantially identical reference composition,” or “substantially identical reference article,” or “substantially identical reference electrochemical cell,” refers to a reference composition, article, or an electrochemical cell comprising substantially identical components and wherein an inventive component is substituted with a common in the art component. Attorney Docket No.11196-079WO1

[0066] While aspects of the present invention can be described and claimed in a particular statutory class, such as the system statutory class, this is for convenience only and one of ordinary skill in the art will understand that each aspect of the present invention can be described and claimed in any statutory class. 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 in 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 the 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.

[0067] The present invention may be understood more readily by reference to the following detailed description of various aspects of the invention and the examples included therein and to the Figures and their previous and following description. NON-LINEAR OPTICAL CRYSTALS AND DEVICES

[0068] As disclosed herein, the current disclosure is directed to a single nonlinear optical crystal having a chemical formula of Mg-IV-V2. In such aspects, a component IV is selected from Si, Ge, or Sn. In other aspects, a component V is selected from P or As. In certain aspects, the disclosed herein single nonlinear optical crystal has a chemical formula of MgSiP2. In yet other aspects, the single nonlinear optical crystal has a chemical formula of MgGeP2. In still further aspects, the single nonlinear optical crystal has a chemical formula of MgSnP2. In yet other aspects, the single nonlinear optical crystal has a chemical formula of MgSiAs2. In yet other aspects, the single nonlinear optical crystal has a chemical formula of MgGeAs2. In still further aspects, the single nonlinear optical crystal has a chemical formula of MgSnAs2. In yet other aspects, In yet still further aspects, the disclosed herein single nonlinear optical crystal has a chalcopyrite and non-centrosymmetric crystal structure. For example, in some aspects, the disclosed herein single Attorney Docket No.11196-079WO1 nonlinear optical crystal has a non-centrosymmetric crystal structure with a space group of ^4^2^. In yet still further aspects, the disclosed herein single nonlinear optical crystal has a point group symmetry 4^2#.

[0069] In still further aspects, the crystal structure is defined by unit cell parametersfrom about 5.5 Å to about 6 Å, including exemplary values of about 5.6 Å, about 5.7Å, about 5.8 Å, and about 5.9 Å; c between about 9.5 to about 12.5 Å, includingexemplary values of about 9.6 Å, about 9.7 Å, about 9.8 Å, about 9.9 Å, about 10.0Å, about 10.1 Å, about 10.2 Å, about 10.3 Å, about 10.4 Å, about 10.5 Å, about 10.6Å, about 10.7 Å, about 10.8 Å, about 10.9 Å, about 11.0 Å, about 11.1 Å, about 11.2Å, about 11.3 Å, about 11.4 Å, about 11.5 Å, about 11.6 Å, about 11.7 Å, about 11.8Å, about 11.9 Å, about 12.0 Å, about 12.1 Å, about 12.2 Å, about 12.3 Å, about 12.4Å; and a unit cell volume of about 287 Å3 to about 450 Å3, including exemplaryvalues of about 288 Å3, about 289 Å3, about 290 Å3, about 291 Å3, about 292 Å3,about 293 Å3, about 294 Å3, about 295 Å3, about 296 Å3, about 297 Å3, about 298Å3, about 299 Å3, about 300 Å3, about 301 Å3, about 302 Å3, about 303 Å3, about304 Å3, about 305 Å3, about 306 Å3, about 307 Å3, about 308 Å3, about 309 Å3,about 310 Å3, about 311 Å3, about 312 Å3, about 313 Å3, about 314 Å3, about 315Å3, about 316 Å3, about 317 Å3, about 318 Å3, about 319 Å3, about 320 Å3, about321 Å3, about 322 Å3, about 323 Å3, about 324 Å3, about 325 Å3, about 326 Å3,about 327 Å3, about 328 Å3, about 329 Å3, about 330 Å3, about 331 Å3, about 332Å3, about 333 Å3, about 334 Å3, about 335 Å3, about 336 Å3, about 337 Å3, about338 Å3, about 339 Å3, about 340 Å3, about 341 Å3, about 342 Å3, about 343 Å3,about 344 Å3, about 345 Å3, about 346 Å3, about 347 Å3, about 348 Å3, about 349Å3, about 350 Å3, about 351 Å3, about 352 Å3, about 353 Å3, about 354 Å3, about355 Å3, about 356 Å3, about 357 Å3, about 358 Å3, about 359 Å3, about 360Å3,about 361 Å3, about 362 Å3, about 363 Å3, about 364 Å3, about 365 Å3, about366 Å3, about 367 Å3, about 368 Å3, about 369 Å3, about 370 Å3, about 371 Å3,about 372 Å3, about 373 Å3, about 374 Å3, about 375 Å3, about 376 Å3, about 377Å3, about 378 Å3, about 389 Å3, about 390 Å3, about 391 Å3, about 392 Å3, about393 Å3, about 394 Å3, about 395 Å3, about 396 Å3, about 397 Å3, about 398 Å3, Attorney Docket No.11196-079WO1about 399 Å3, about 400 Å3, about 401 Å3, about 402 Å3, about 403 Å3, about 404Å3, about 405 Å3, about 406 Å3, about 407 Å3, about 408 Å3, about 409 Å3, about410 Å3, about 411 Å3, about 412 Å3, about 413 Å3, about 414 Å3, about 415 Å3,about 416 Å3, about 417 Å3, about 418 Å3, about 419 Å3, about 420 Å3, about 421Å3, about 422 Å3, about 423 Å3, about 424 Å3, about 425 Å3, about 426 Å3, about427 Å3, about 428 Å3, about 429 Å3, about 430 Å3, about 431 Å3, about 432 Å3,about 433 Å3, about 434 Å3, about 435 Å3, about 436 Å3, about 437 Å3, about 438Å3, about 439 Å3, about 440 Å3, about 441 Å3, about 442 Å3, about 443 Å3, about444 Å3, about 445 Å3, about 446 Å3, about 447 Å3, about 448 Å3, and about 449 Å3.

[0070] In still further aspects, the single nonlinear optical crystal disclosed herein exhibits a refractive index of about 2.770 to about 2.780, including exemplary values of about 2.771, about 2.772, about 2.773, about 2.774, about 2.775, about 2.776, about 2.777, about 2.778, and about 2.779 for no at a wavelength of 1550 nm. In yet still further aspects, the single nonlinear optical crystal disclosed herein exhibits a refractive index of about 2.800 to about 2.810, including exemplary values of about 2.801, about 2.802, about 2.803, about 2.804, about 2.805, about 2.806, about 2.807, about 2.808, and about 2.809 for ne at a wavelength of 1550 nm. In yet still further aspects, the single nonlinear optical crystal exhibits a nonlinear coefficient of deff of SHG from about 80 to about 95 pm / V, including exemplary values of about 81 pm / V, about 82 pm / V, about 83 pm / V, about 84 pm / V, about 85 pm / V, about 86 pm / V, about 87 pm / V, about 88 pm / V, about 89 pm / V, about 90 pm / V, about 91 pm / V, about 92 pm / V, about 93 pm / V, and about 94 pm / V. In yet still in further aspects, the single nonlinear optical crystal Mg-IV-V2 is substantially free of impurities.

[0071] In still further aspects, the disclosed herein single nonlinear optical crystal exhibits a transmittance from about 60% to less than 100%, including exemplary values of about 65%, about 70%, about 75%, about 80%, about 85%, about 90%, about 95%, and about 99% in a wavelength range from about 0.55 µm to at least about 20 µm, including exemplary values of about 0.60 µm, about 0.70 µm, about 0.80 µm, about 0.90 µm, about 1.0 µm, about 2 µm, about 5 µm, about 10 µm, Attorney Docket No.11196-079WO1 about 11 µm, about 12 µm, about 13 µm, about 14 µm, about 15 µm, about 16 µm, about 17 µm, about 18 µm, and about 19 µm.

[0072] In yet still further aspects, the disclosed herein single nonlinear optical crystals and their properties are defined by d14and d36coefficients. In some aspects, the disclosed herein single nonlinear optical crystal has a d14 coefficient from about 80pm / V to about 95pm / V, including exemplary values of about 81 pm / V, about 82 pm / V, about 83 pm / V, about 84 pm / V about 85 pm / V, about 86 pm / V, about 87 pm / V, about 88 pm / V, about 89 pm / V, about 90 pm / V, about 91 pm / V, about 92 pm / V, about 93 pm / V, and about 94 pm / V at a fundamental wavelength of 1550nm. While in other aspects, the disclosed herein single nonlinear optical crystal has a d36 coefficient from about 80 pm / V to about 95 pm / V, including exemplary values of about 81 pm / V, about 82 pm / V, about 83 pm / V, about 84 pm / V, about 85 pm / V, about 86 pm / V, about 87 pm / V, about 88 pm / V, about 89 pm / V, about 90 pm / V, about 91 pm / V, about 92 pm / V, about 93 pm / V, and about 94 pm / V at a fundamental wavelength of 1550nm.

[0073] In still further aspects, the disclosed herein single nonlinear optical crystals exhibit type I and type II phase matching. In such aspects, the disclosed herein single nonlinear optical crystal exhibits |deff,I| at φ=0° greater than about 75 pm / V to about 90 pm / V, including exemplary values of about 76 pm / V, about 77 pm / V, about 78 pm / V, about 79 pm / V, about 80 pm / V, about 81 pm / V, about 82 pm / V, about 83 pm / V, about 84 pm / V, about 85 pm / V, about 86 pm / V, about 87 pm / V, about 88 pm / V, and about 89 pm / V at a fundamental wavelength of about 3.5 μm. While in other aspects, the disclosed herein single nonlinear optical crystal exhibits |deff, II|= at φ=45° greater than about 70 pm / V to about 80 pm / V, including exemplary values of about 71 pm / V, about 72 pm / V, about 73 pm / V, about 74 pm / V, about 75 pm / V, about 76 pm / V, about 77 pm / V, about 78 pm / V, and about 79 pm / V at a fundamental wavelength of 3.5 μm.

[0074] In still further aspects, the single nonlinear optical crystal Mg-IV-V2 is uniaxial. In still further aspects, the single nonlinear optical crystal of Mg-IV-V2 exhibits a substantially single phase. In such aspects, the single nonlinear optical Attorney Docket No.11196-079WO1 crystal is substantially free of impurities. It is understood that if impurities are present, they can be defined as MgP2 phase impurity, SiP2 phase impurity or MgSi phase impurity. In yet still further aspects, the impurity can comprise MgP2 phase impurity. In yet still further aspects, the impurity can comprise SiP2 phase impurity. \ In yet still further aspects, if the impurities are present, they can be present in an amount less than about 10 wt%, less than about 9 wt%, less than about 8 wt%, less than about 7 wt%, less than about 6 wt%, less than about 5 wt%, less than about 4 wt%, less than about 3 wt%, less than about 2 wt%, less than about 1 wt%, less than about 0.5 wt%, less than about 0.1 wt%, less than about 0.05 wt%, less than about 0.01 wt%. In yet still further aspects, the impurities can be present in an amount not greater than about 0.01 wt%, not greater than about 0.05 wt%, not greater than about 0.1 wt%, not greater than about 0.5 wt%, not greater than about 1 wt%, not greater than about 2 wt%, not greater than about 3 wt%, not greater than about 4 wt%, not greater than about 5 wt%, not greater than about 6 wt%, not greater than about 7 wt%, not greater than about 8 wt%, not greater than about 9 wt%, or not greater than about 10 wt%.

[0075] In still further aspects disclosed herein is an optical parametric oscillator comprising any of the disclosed herein single nonlinear optical crystals. The optical parametric oscillators (OPO) are light sources that use the optical gain in a nonlinear optical medium. The OPOs have two key components: a nonlinear optical crystal and an optical resonator. Any of the disclosed herein nonlinear optical crystals can be present. When traveling through the nonlinear optical crystals of the present disclosure, a pump laser light of frequency ωp can be converted into two waves - signal and idler with lower frequency of ωs and ωi via the second-order NLO effect such that ωp= ωs + ωi. The frequencies of these two waves are dependent on the phase-matching conditions of disclosed herein nonlinear optical crystals and, therefore, can be tuned in a broad spectral range by changing the phase-matching conditions through changing the temperature or orientation of the disclosed herein nonlinear optical crystals.

[0076] In certain aspects, the optical parametric oscillator can comprise a pump laser source having a pump beam in a range of about 1.1 µm to about 4 µm, Attorney Docket No.11196-079WO1 including exemplary values of about 1.2 µm, about 1.5 µm, about 1.7 µm, about 2.0 µm, about 2.2 µm, about 2.5 µm, about 2.7 µm, about 3.0 µm, about 3.2 µm, about 3.5 µm, and about 3.7 µm. In such exemplary aspects, the pump laser source is a liquid laser, gas laser, or semiconductor laser. Yet, in other aspects, the pump laser source can be a pulse laser or a continuous laser.

[0077] In still further aspects, the optical parametric oscillator can comprise an optical resonator comprising a plurality of mirrors. In such aspects, the plurality of mirrors can be arranged in a way that a beam can circulate in a closed path. Any of the disclosed herein nonlinear optical crystals can be placed in the optical resonator, which will resonate the signal and / or idler wave(s). This allows the resonating wave(s) to oscillate in the resonator, compensating for any losses the wave(s) experience. The OPOs have many technical applications. For example, they are used in spectroscopy, especially in the mid-infrared and far-infrared wavelengths, which are challenging to produce by lasers. METHODS

[0078] Also disclosed herein are the methods of forming the disclosed herein single nonlinear optical crystals. In such aspects, the method comprises a step of providing a solution comprising a solute comprising a mixture of Mg, IV and V in a molar ratio from about 0.95:0.95:2 to about 1.05:1.05:2, including exemplary values of about 0.96:0.96:2, about 0.97:0.97:2, about 0.98:0.98:2, about 1.00:1.00:2, about 1.01:1.01:2, about 1.02:1.02:2, about 1.03:1.03:2, and about 1.04:1.04:2 and a solvent. In still further aspects, a mass ratio between the solvent and solute can be from about 10:1 to about 4:1, including exemplary values of about 9:1, about 8:1, about 7:1, about 6:1, and about 5:1.

[0079] In still further aspects, the method comprises a step of growing a crystalline composition comprising Mg-IV-V2 at a first temperature from about 950 °C to about 1,200 °C, including exemplary values of about 960 °C, about 970 °C, about 980 °C, about 990 °C, about 1,000 °C, about 1,010 °C, about 1,020 °C, about 1,030 °C, about 1,040 °C, about 1,050 °C, about 1,060 °C, about 1,070 °C, about 1,080 °C, about 1,090 °C, about 1,100 °C, about 1,110 °C, about 1,120 °C, about 1,130 °C, Attorney Docket No.11196-079WO1 about 1,140 °C, about 1,150 °C, about 1,160 °C, about 1,170 °C, about 1,180 °C, about 1,190 °C, about 1,110 °C, about 1,120 °C, about 1,130 °C, about 1,140 °C, about 1,150 °C, about 1,160 °C, about 1,170 °C, about 1,180 °C, and about 1,190 °C for a first predetermined time. In still further aspects, the first predetermined time is from about 30 hours to about 60 hours, including exemplary values of about 32 hours, about 35 hours, about 38 hours, about 40 hours, about 42 hours, about 45 hours, about 48 hours, about 50 hours, about 52 hours, about 55 hours, and about 58 hours.

[0080] In still further aspects, the methods further comprise centrifugally separating the solvent to form a single nonlinear optical crystal of Mg-IV-V2 having a size from about 0.01 mm to about 10 mm, including exemplary values of about 0.05 mm, about 0.1 mm, about 0.5 mm, about 1.0 mm, about 1.5 mm, about 2.0 mm, about 2.5 mm, about 3.0 mm, about 3.5 mm, about 4.0 mm, about 4.5 mm, about 5.0 mm, about 5.5 mm, about 6.0 mm, about 6.5 mm, about 7.0 mm, about 7.5 mm, about 8.0 mm, about 8.5 mm, about 9.0 mm, and about 9.5 mm in length, and wherein the single nonlinear optical crystal is substantially free of a solvent residue.

[0081] In still further aspects, the solution is cooled down prior to centrifugally separating the solvent. In such aspects, the solution can be cooled down to a temperature in a range from about 750 °C to about 640 °C, including exemplary values of about 740 °C, about 730 °C, about 720 °C, about 710 °C, about 700 °C, about 690 °C, about 680 °C, about 670 °C, about 660 °C, and about 650 °C. In such aspects, the cool-down process can be done at any acceptable range, for example and without limitations, a cool dawn rate can be from about 0.5 °C / h to about 35 °C / h, including exemplary values of about 1 °C / h, about 2 °C / h, about 3 °C / h, about 4 °C / h, about 5 °C / h, about 6 °C / h, about 7 °C / h, about 8 °C / h, about 9 °C / h, about 10 °C / h, about 11 °C / h, about 12 °C / h, about 13 °C / h, about 14 °C / h, about 15 °C / h, about 16 °C / h, about 17 °C / h, about 18 °C / h, about 19 °C / h, about 20 °C / h, about 21 °C / h, about 22 °C / h, about 23 °C / h, about 24 °C / h, about 25 °C / h, about 26 °C / h, about 27 °C / h, about 28 °C / h, about 29 °C / h, about 30 °C / h, about 31 °C / h, about 32 °C / h, about 33 °C / h and about 34 °C / h. Attorney Docket No.11196-079WO1

[0082] In still further aspects, the step of centrifugally separating is performed at a second temperature and a speed of about 1,300 to about 1,500 rpm for a second predetermined time of about 1 min to about 15 min. In such aspects, the second temperature can be anywhere between 650 °C to about 750 °C, including exemplary values of about 660 °C, about 670 °C, about 680 °C, about 690 °C, about 700 °C, about 710 °C, about 720 °C, about 730 °C, and about 740 °C. In yet other aspects, a speed of centrifuge used to separate the solute from the solution can be about 1,300 to about 1,500 rpm, including exemplary values of about 1,310 rpm, about 1,320 rpm, about 1,330 rpm, about 1,340 rpm, about 1,350 rpm, about 1,360 rpm, about 1,370 rpm, about 1,380 rpm, about 1,390 rpm, about 1,400 rpm, about 1,410 rpm, about 1,420 rpm, 1,430 rpm, about 1,440 rpm, about 1,450 rpm, about 1,460 rpm, about 1,470 rpm, about 1,480 rpm, and about 1,490 rpm.

[0083] In still further aspect, the second predetermined time can be from about 1 min to about 15 min, including exemplary values of about 2 min, about 3.0 min, about 4.0 min, about 5.0 min, about 6.0 min, about 7.0 min, about 8.0 min, about 9.0 min, about 10.0 min, about 11 min, about 12 min, about 13 min, and about 14 min. However, it is understood that if needed, the second predetermined time can be greater than 15 min, for example, and without limitations, it can be about 20 min, about 30 min, about 1 h, or even about 5 hours if needed. In yet still further aspects, the second predetermined time can be anywhere between 1 min and 5 min, including exemplary values of about 1.1 min, about 1.2 min, about 1.3 min, about 1.4 min, about 1.5 min, about 1.6 min, about 1.7 min, about 1.8 min, about 1.9 min, about 2.0 min, about 2.1 min, about 2.2 min, about 2.3 min, about 2.4 min, about 2.5 min, about 2.6 min, about 2.7 min, about 2.8 min, about 2.9 min, about 3.0 min, about 3.1 min, about 3.2 min, about 3.3 min, about 3.4 min, about 3.5 min, about 3.6 min, about 3.7 min, about 3.8 min, about 3.9 min, about 4.0 min, about 4.1 min, about 4.2 min, about 4.3 min, about 4.4 min, about 4.5 min, about 4.6 min, about 4.7 min, about 4.8 min, and about 4.9 min.

[0084] In still further aspects, the solvent can comprise Sn or Sb. In yet still in further aspects, the solvent comprises Sb. In yet still further aspects, the solvent Attorney Docket No.11196-079WO1 comprises Sn. In yet still further aspects, the solvent comprises a combination of Sb and Sn.

[0085] In still further aspects, the solution used in this method is formed by mixing Mg, IV and V and the solvent provided in a powdered form and heating to a temperature sufficient to homogeneously mix the solute and solvent. In still further aspects, the single nonlinear optical crystal Mg-IV-V2 grows along

[0111] direction.

[0086] In still further aspects, the formed single nonlinear optical crystal Mg-IV-V2 is uniaxial. In still further aspects, the formed single nonlinear optical crystal of Mg-IV- V2 exhibits a substantially single phase. In such aspects, the single nonlinear optical crystal is substantially free of impurities. It is understood that if impurities are present, they can be defined as MgP2 phase impurity or SiP2 phase impurity or MgSi phase impurity. In yet still further aspects, the impurity can comprise MgP2 phase impurity. In yet still further aspects, the impurity can comprise SiP2 phase impurity. In yet still further aspects, if the impurities are present, they can be present in an amount of less than about 10 wt%, less than about 9 wt%, less than about 8 wt%, less than about 7 wt%, less than about 6 wt%, less than about 5 wt%, less than about 4 wt%, less than about 3 wt%, less than about 2 wt%, less than about 1 wt%, less than about 0.5 wt%, less than about 0.1 wt%, less than about 0.05 wt%, less than about 0.01 wt%. In yet still further aspects, the impurities can be present in an amount not greater than about 0.01 wt%, not greater than about 0.05 wt%, not greater than about 0.1 wt%, not greater than about 0.5 wt%, not greater than about 1 wt%, not greater than about 2 wt%, not greater than about 3 wt%, not greater than about 4 wt%, not greater than about 5 wt%, not greater than about 6 wt%, not greater than about 7 wt%, not greater than about 8 wt%, not greater than about 9 wt%, or not greater than about 10 wt%. In yet still further aspects, the single nonlinear optical crystal formed by the disclosed methods exhibits any of the disclosed above properties.

[0087] In still further aspects, the disclosed herein single nonlinear optical crystals can be formed by additional methods. For example, and without limitations, the Attorney Docket No.11196-079WO1 disclosed herein single nonlinear optical crystal can be formed according to Bridgman methods or float-zone methods.

[0088] In still further aspects, the method of forming the disclosed herein single nonlinear optical crystal can comprise a) sealing a polycrystalline material, comprising a Mg-IV-V2 compound in a temperature resistant container; b) placing the temperature resistant container in a rocking furnace; c) heating the polycrystalline material to a third temperature at a rate of about 45 °C / h to about 120 °C / h and keeping the polycrystalline material at the third temperature for a first predetermined time; d) placing the temperature-resistant container in a three-zone furnace, wherein the three-zone furnace exhibits a temperature profile defined by an upper / melt zone temperature, a middle / crystallization zone temperature; and a lower / annealing zone temperature; e) translating the temperature-resistant container vertically thereby allowing the temperature-resistant container to arrive at a nucleating temperature to form a seeding crystal; f) growing an ingot material from the seeding crystal; g) annealing the ingot material to a temperature of about 700 °C to about 850 °C for a fourth predetermined time; and h) forming the single nonlinear optical crystal Mg-IV-V2, wherein the crystal is substantially free of impurities, defined by a single phase and has a size from about 0.1 mm to about 10 cm in length.

[0089] In still further aspects, the Mg-IV-V2 compound has a molar ratio of Mg, IV, and V in from about 0.95:0.95:2 to about 1.05:1.05:2, including exemplary values of about 0.96:0.96:2, about 0.97:0.97:2, about 0.98:0.98:2, about 1.00:1.00:2, about 1.01:1.01:2, about 1.02:1.02:2, about 1.03:1.03:2, and about 1.04:1.04:2. In yet still further aspects, a total amount of each component can be between 1 g up to about 5 g, including exemplary values of about 2 g, about 2.5 g, about 3 g, about 3.5 g, about 4 g, and about 4.5 g. In yet further aspects, the polycrystalline material is ground prior to the step of sealing; and wherein grinding is performed in an inert atmosphere. Any known in the art methods of grinding can be used. For example, and without limitations, the material can be ground with mortar and pestle or by any other automatic grinding methods. In yet still further aspects, the inert atmosphere Attorney Docket No.11196-079WO1 can comprise an inert gas, such as, for example, and without limitations, argon or nitrogen. In yet still further aspects, the grinding can be performed in a glove box.

[0090] In still further aspects, the ground polycrystalline material is placed into an alumina crucible which is then placed into the temperature-resistant container. In such aspects, the temperature-resistant container can be a quartz tube. It is understood that the alumina crucible can have any shape that would allow the desired outcome. Yet, in some aspects, the alumina crucible can have a tip-shaped form.

[0091] In still further aspects, the third temperature can be from about 900 °C to about 1,300 °C, including exemplary values of about 950 °C, about 1,000 °C, about 1,050 °C, about 1,100 °C, about 1,150 °C, about 1,200 °C, and about 1,250 °C. In still further aspects, the heating can be done at a rate of about 45 °C / h to about 120 °C / h, including exemplary values of about 50 °C / h, about 55 °C / h, about 60 °C / h, about 65 °C / h, about 70 °C / h, about 75 °C / h, about 80 °C / h, about 85 °C / h, about 90 °C / h, about 95 °C / h, about 100 °C / h, about 105 °C / h, about 110 °C / h, and about 115 °C / h. In still further aspects, the third predetermined time is from about 5 h to about 12 hours, including exemplary values of about 6 h, about 7 h, about 8 h, about 9 h, about 10 h, and about 11 h. In yet still further aspects, the polycrystalline material is rocked within the rocking furnace at the third temperature to form a homogeneous mixture. In still further aspects, the method comprises obtaining a temperature profile of a three-zone Bridgman furnace. The three-zone furnace is defined by an upper / melt zone temperature, a middle / crystallization zone temperature, and a lower / annealing zone temperature. In such aspects, the temperature profile is achieved with the required gradient temperature of about 1 °C to about 15 °C, including exemplary values of about 2 °C, about 3 °C, about 4 °C, about 5 °C, about 6 °C, about 7 °C, about 8 °C, about 9 °C, about 10 °C, about 11 °C, about 12 °C, about 13 °C, and about 14 °C at the crystallization zone. In still further aspects, the upper / melt zone temperature is set to about 1,050 °C to about 1,200 °C, including exemplary values of about 1,060 °C, about 1,070 °C, about 1,080 °C, about 1,090 °C, about 1,100 °C, about 1,110 °C, about 1,120 °C, about Attorney Docket No.11196-079WO1 1,130 °C, about 1,140 °C, about 1,150 °C, about 1,160 °C, about 1,170 °C, about 1,180 °C and about 1,190 °C. In other aspects, the middle / crystallization zone temperature is set to about 950 °C to about 1,100 °C, including exemplary values of about 960 °C, about 970 °C, about 980 °C, about 990 °C, about 1,000 °C, about 1,010 °C, about 1,020 °C, about 1,030 °C, about 1,040 °C, about 1,050 °C, about 1,060 °C, about 1,070 °C, about 1,080 °C and about 1,090 °C. In yet still further aspects, the lower / annealing zone temperature is set to about 750 °C to about 900 °C, including exemplary values of about 760 °C, about 770 °C, about 780 °C, about 790 °C, about 800 °C, about 810 °C, about 820 °C, about 830 °C, about 840 °C, about 850 °C, about 860 °C, about 870 °C, about 880 °C and about 890 °C.

[0092] In still further aspects, the sealed temperature-resistant container can be placed at a location where the temperature is above the melting point of the polycrystalline material. For example, and without limitations, if the polycrystalline material comprises MgSiP2, such a location will have a temperature greater than about 1,130 °C, greater than about 1,140 °C, greater than about 1,150 °C, greater than about 1,160 °C, or greater than about 1,170 °C. In some aspects, the temperature is greater than about 1,132 °C. Yet, in other aspects, the temperature is greater than about 1,173°C. In still further aspects, the polycrystalline material is brought to the described temperatures in the disclosed zones in about 3 to about 12 hours, including exemplary values of about 4 h, about 5 h, about 6 h, about 7 h, about 8 h, about 9 h, about 10 h, and about 11 h. In yet other aspects, the polycrystalline material is further dwelled at those temperatures for a fifth predetermined time. In such aspects, the fifth predetermined time can be anywhere between 1 h and about 24 h, including exemplary values of about 2 h, about 3 h, about 4 h, about 5 h, about 6 h, about 7 h, about 8 h, about 9 h, about 10 h, about 11 h, about 12 h, about 13 h, about 14 h, about 15 h, about 16 h, about 17 h, about 18 h, about 19 h, about 20 h, about 21 h, about 22 h, and about 23 h.

[0093] In still further aspects, the step of translating the sealed temperature- resistant container vertically can comprise raising the container from about 50 to about 300 mm, including exemplary values of about 60 mm, about 70 mm, about Attorney Docket No.11196-079WO1 80 mm, about 90 mm, about 100 mm, about 110 mm, about 120 mm, about 130 mm, about 140 mm, about 150 mm, about 160 mm, about 170 mm, about 180 mm, about 190 mm, about 200 mm, about 210 mm, about 220 mm, about 230 mm, about 240 mm, about 250 mm, about 260 mm, about 270 mm, about 280 mm, and about 290 mm with a translation rate of about 0.1 mm / h to about 1 mm / h, including exemplary values of about 0.2 mm / h, about 0.3 mm / h, about 0.4 mm / h, about 0.5 mm / h, about 0.6 mm / h, about 0.7 mm / h, about 0.8 mm / h, and about 0.9 mm / h.

[0094] In yet still further aspects, at these conditions, the sealed temperature- resistant container can pass through the nucleation temperature to form a seeding crystal. For example, in aspects where MgSiP2 crystal is formed, the nucleation temperate can be about 1,100 °C to about 1,200 °C, including exemplary values of about 1,110 °C, about 1,120 °C, about 1,130 °C, about 1,140 °C, about 1,150 °C, about 1,160 °C, about 1,170 °C, about 1,180 °C and about 1,190 °C.

[0095] In still further aspects, prior to the annealing step, the upper / melt zone temperature, the middle / crystallization zone temperature, and the lower / annealing zone temperature reduced to a fourth temperature at a first predetermined cooling rate. In such aspects, the fourth temperature can be from about 900 °C to about 700 °C, including exemplary values of about 890 °C, about 880 °C, about 870 °C, about 860 °C, about 850 °C, about 840 °C, about 830 °C, about 820 °C, about 810 °C, about 800 °C, about 790 °C, about 780 °C, about 770 °C, about 760 °C, about 750 °C, about 740 °C, about 730 °C, about 720 °C, and about 710 °C. Wherein the first predetermined cooling rate is from about 1 °C / h to about 90 °C / h, including exemplary values of about 2 °C / h, about 3 °C / h, about 4 °C / h, about 5 °C / h, about 6 °C / h, about 7 °C / h, about 8 °C / h, about 9 °C / h, about 10 °C / h, about 11 °C / h, about 12 °C / h, about 13 °C / h, about 14 °C / h, about 15 °C / h, about 16°C / h, about 17 °C / h, about 18 °C / h, about 19 °C / h, about 20 °C / h, about 21 °C / h, about 22 °C / h, about 23 °C / h, about 24 °C / h, about 25 °C / h, about 26 °C / h, about 27 °C / h, about 28 °C / h, about 29 °C / h, about 30 °C / h, about 31 °C / h, about 32 °C / h, about 33 °C / h, about 34 °C / h, about 35 °C / h, about 36 °C / h, about 37 °C / h, about 38 °C / h, about 39 °C / h, about 40 °C / h, about 41 °C / h, about 42 °C / h, about 43°C / h, Attorney Docket No.11196-079WO1 about 44 °C / h, about 45 °C / h, about 46 °C / h, about 47 °C / h, about 48 °C / h, about 49 °C / h, about 50 °C / h, about 51 °C / h, about 52 °C / h, about 53 °C / h, about 54 °C / h, about 55 °C / h, about 56 °C / h, about 57 °C / h, about 58 °C / h, about 59 °C / h, about 60 °C / h, about 61°C / h, about 62 °C / h, about 63 °C / h, about 64 °C / h, about 65 °C / h, about 66 °C / h, about 67 °C / h, about 68 °C / h, about 69 °C / h, about 70 °C / h, about 71 °C / h, about 72 °C / h, about 73 °C / h, about 74 °C / h, about 75 °C / h, about 76 °C / h, about 77 °C / h, about 78°C / h, about 79 °C / h, about 80 °C / h, and about 81 °C / h, about 82 °C / h, about 83 °C / h, about 84 °C / h, about 85 °C / h, about 86 °C / h, about 87 °C / h, about 88 °C / h, and about 89 °C / h.

[0096] In still further aspects, the annealing of the ingot material is at a temperature of about 700 °C to about 850 °C, including exemplary values of about 710 °C, about 720 °C, about 730 °C, about 740 °C, about 750 °C, about 760 °C, about 770 °C, about 780 °C, about 790 °C, about 800 °C, about 810 °C, about 820 °C, about 830 °C, and about 840°C, for a fourth predetermined time. Wherein the fourth predetermined time is from about 10 min to about 12 h, including exemplary values of about 30 min, about 1 h, about 2 h, about 3 h, about 4 h, about 5 h, about 6 h, about 7 h, about 8 h, about 9 h, about 10 h, and about 11 h.

[0097] In still further aspects, the ingot material is cooled after annealing to room temperature at a second predetermined cooling rate, wherein the second predetermined cooling range is from about 1 °C / h to about 90 °C / h, including exemplary values of about 2 °C / h, about 3 °C / h, about 4 °C / h, about 5 °C / h, about 6 °C / h, about 7 °C / h, about 8 °C / h, about 9 °C / h, about 10 °C / h, about 11 °C / h, about 12 °C / h, about 13 °C / h, about 14 °C / h, about 15 °C / h, about 16°C / h, about 17 °C / h, about 18 °C / h, about 19 °C / h, about 20 °C / h, about 21 °C / h, about 22 °C / h, about 23 °C / h, about 24 °C / h, about 25 °C / h, about 26 °C / h, about 27 °C / h, about 28 °C / h, about 29 °C / h, about 30 °C / h, about 31 °C / h, about 32 °C / h, about 33 °C / h, about 34 °C / h, about 35 °C / h, about 36 °C / h, about 37 °C / h, about 38 °C / h, about 39 °C / h, about 40 °C / h, about 41 °C / h, about 42 °C / h, about 43°C / h, about 44 °C / h, about 45 °C / h, about 46 °C / h, about 47 °C / h, about 48 °C / h, about Attorney Docket No.11196-079WO1 49 °C / h, about 50 °C / h, about 51 °C / h, about 52 °C / h, about 53 °C / h, about 54 °C / h, about 55 °C / h, about 56 °C / h, about 57 °C / h, about 58 °C / h, about 59 °C / h, about 60 °C / h, about 61°C / h, about 62 °C / h, about 63 °C / h, about 64 °C / h, about 65 °C / h, about 66 °C / h, about 67 °C / h, about 68 °C / h, about 69 °C / h, about 70 °C / h, about 71 °C / h, about 72 °C / h, about 73 °C / h, about 74 °C / h, about 75 °C / h, about 76 °C / h, about 77 °C / h, about 78°C / h, about 79 °C / h, about 80 °C / h, and about 81 °C / h, about 82 °C / h, about 83 °C / h, about 84 °C / h, about 85 °C / h, about 86 °C / h, about 87 °C / h, about 88 °C / h, and about 89 °C / h.

[0098] In still further aspects, the formed single nonlinear optical crystal has a size from about 0.1 mm to about 10 cm, including exemplary values of about 0.5 mm, about 1 mm, about 5 mm, about 10 mm, about 1.5 cm, about 2 cm, about 2.5 cm, about 3 cm, about 3.5 cm, about 4 cm, about 4.5 cm, about 5 cm, about 5.5 cm, about 6 cm, about 6.5 cm, about 7 cm, about 7.5 cm, about 8 cm, about 8.5 cm, about 9 cm, and about 9.5 cm in length.

[0099] In still further asepcts, the polycrystalline materials used in the methods of forming the disclosed single nonlinear optical crystals can be formed by the steps comprising: a) mixing Mg, IV, and V in a molar ratio of about 0.95:0.95:2 to about 1.05:1.05:2 to form a mixture; b) placing the mixture into a sealed container in a furnace; c) bringing the mixture to a first heating temperature of about 450 °C to about 550 °C at a rate of about 45 °C / h to 55 °C / h and keeping the mixture at the first heating temperature for about 60 to about 100 hours; d) bringing the mixture to a second heating temperature of about 780° C to about 850 °C at a rate of about 20 °C / h to about 40 °C / h and keeping the mixture at the second heating temperature for about 50 to about 100 hours; e) bringing the mixture to a third heating temperature of about 1,100 °C to about 1,250 °C at a rate of about 20 °C / h to about 40 °C / h and keeping the mixture at the third heating temperature for about 50 to about 100 hours; f) cooling the mixture to a room temperature at a rate of about 50 °C / h to about 150 °C / h; g) recovering the polycrystalline material comprising Mg-IV- V2, wherein the polycrystalline material is substantially free of impurities and has a substantially single phase. Attorney Docket No.11196-079WO1

[0100] In certain aspects, the Mg:IV:V molar ratio can be from 0.95:0.95:2 to about 1.05:1.05:2, including exemplary values of about 0.96:0.96:2, about 0.97:0.97:2, about 0.98:0.98:2, about 1.00:1.00:2, about 1.01:1.01:2, about 1.02:1.02:2, about 1.03:1.03:2, and about 1.04:1.04:2.

[0101] In yet still further aspects, the first heating temperature of about 450 °C to about 550 °C, including exemplary values of about 460 °C, about 470 °C, about 480 °C, about 490 °C, about 500 °C, about 510 °C, about 520 °C, about 530 °C, and about 540 °C, is achieved at a rate of about 1 °C / h to 55 °C / h, including the exemplary values of about 5 °C / h, about 10 °C / h, about 15 °C / h, about 20 °C / h, about 25 °C / h, about 30 °C / h, about 35 °C / h, about 40 °C / h, about 45 °C / h, and about 50 °C / h. In yet still further aspects, the mixture can be kept at the first heating temperature for about 60 to about 100 hours, including exemplary values of about 65 h, about 70 h, about 75 h, about 80 h, about 85 h, about 90 h, and about 95 h.

[0102] In yet still further aspects, the second heating temperature of about 780° C to about 850 °C, including exemplary values of about 790 °C, about 800 °C, about 810 °C, about 820 °C, about 830 °C, and about 840 °C is achieved at a rate of about 1 °C / h to about 40 °C / h, including exemplary values of about 5 °C / h, about 10 °C / h, about 15 °C / h, about 20 °C / h, about 25 °C / h, about 30 °C / h, and about 35 °C / h. In yet still further aspects, the mixture can be kept at the second heating temperature for about 50 to about 100 hours, including exemplary values of about 55 h, about 60 h, about 65 h, about 70 h, about 75 h, about 80 h, about 85 h, about 90 h, and about 95 h.

[0103] In yet still further aspects, the third heating temperature of about 1,100 °C to about 1,250 °C, including exemplary values of about 1,110 °C, about 1,120 °C, about 1,130 °C, about 1,140 °C, about 1,150 °C, about 1,160 °C, about 1,170 °C, about 1,180 °C, about 1,190 °C, about 1,200 °C, about 1,210 °C, about 1,220 °C, about 1,230 °C, and about 1,240 °C is achieved at a rate of about 20 °C / h to about 40 °C / h, including exemplary values of about 22 °C / h, about 25 °C / h, about 28 °C / h, about 30 °C / h, about 32 °C / h, about 35 °C / h, and about 38 °C / h. In yet still Attorney Docket No.11196-079WO1 further aspects, the mixture can be kept at the third heating temperature for about 50 to about 100 hours, including exemplary values of about 55 h, about 60 h, about 65 h, about 70 h, about 75 h, about 80 h, about 85 h, about 90 h, and about 95 h.

[0104] In still further aspects, the cooling to the room temperature is achieved at a rate of 50 °C / h to about 150 °C / h, including exemplary values of about 60 °C / h, about 70 °C / h, about 80 °C / h, about 90 °C / h, about 100 °C / h, about 110 °C / h, about 120 °C / h, about 130 °C / h, and about 140 °C / h.

[0105] In yet still further aspects, the polycrystalline material is substantially free of impurities and has a substantially single phase. It is understood that if impurities are present, they can be defined as Mg-V2 phase impurity of IV-V2 phase impurity or Mg-IV phase impurity. In yet still further aspects, if the impurities are present, they can be present in an amount of less than about 10 wt%, less than about 9 wt%, less than about 8 wt%, less than about 7 wt%, less than about 6 wt%, less than about 5 wt%, less than about 4 wt%, less than about 3 wt%, less than about 2 wt%, less than about 1 wt%, less than about 0.5 wt%, less than about 0.1 wt%, less than about 0.05 wt%, less than about 0.01 wt%. In yet still further aspects, the impurities can be present in an amount not greater than about 0.01 wt%, not greater than about 0.05 wt%, not greater than about 0.1 wt%, not greater than about 0.5 wt%, not greater than about 1 wt%, not greater than about 2 wt%, not greater than about 3 wt%, not greater than about 4 wt%, not greater than about 5 wt%, not greater than about 6 wt%, not greater than about 7 wt%, not greater than about 8 wt%, not greater than about 9 wt%, or not greater than about 10 wt%. In yet still further aspects, the single nonlinear optical crystal formed by the disclosed methods exhibits any of the disclosed above properties.

[0106] By way of a non-limiting illustration, examples of certain aspects of the present disclosure are given below. EXAMPLES

[0107] 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 Attorney Docket No.11196-079WO1 evaluated and are intended to be purely exemplary and are not intended to limit the 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 degrees C or is at ambient temperature, and pressure is at or near atmospheric. EXAMPLE 1

[0108] The lack of high-performance NLO single crystals is limiting the development of new laser technologies, especially in the ultraviolet (below 400nm wavelength), mid-IR (2-25μm) and far-IR / THz (above 25μm). High-performance commercial nonlinear optical crystals are a handful: LiNbO3, β-BaB2O4, and KTiOPO4 (KTP) are the most popular in the visible. The dearth of nonlinear crystals is even more severe in the infrared and in the ultraviolet (see Fig.1A). The current disclosure addresses second-order nonlinearity characterized by tensor coefficients, dijk that combine two photons to create a third photon; all three photons can have different frequencies (colors), thus generating new light colors. One typically desires a large transparency range (hence a large bandgap Eg) and a large dijkto maximize the frequency conversion efficiency. However, as seen in Fig.1A, Eg and dijk are inversely related to each other. While larger electronic gaps do indeed lead to smaller linear and nonlinear electronic polarizabilities, a grand challenge is to find outliers that can best optimize Egand dijkbeyond the grey band in Fig.1A.

[0109] Quantum optics demands strong nonlinear optical effects, particularly at the single-photon and few-photon levels, which represents the ultimate efficiency of nonlinear optics, and underlies crucially many important quantum photonic functionalities such as photon blockade and single-photon transistor, deterministic quantum logic gating, on-demand generation and manipulation of quantum entanglement, high-efficiency single-photon conversion and detection, to name a few. In general, the strength of second-order nonlinear optical interaction can be quantified by the single-photon nonlinearity, given by

[0110] %&= √ℏ^^ / ^^eff- ^^^*+^, , Attorney Docket No.11196-079WO1

[0111] where deffis an effective second-order nonlinear coefficient (in pm / V; it is a combination of various dijk for a given measurement geometry), w is the resonance frequency of optical cavity mode (in s-1), nois the refractive index of the opticalmedium, and V is the mode volume of nonlinear optical interactions (in.m3), and eo is the vacuum permittivity (in C / Vm). Of particular interest is the strongcoupling regime where gd > k, where k is the loss rate, and where even a single photon can produce a very significant nonlinear effect.

[0112] As Fig.1B shows, for practical cavity mode volumes, this requires a large non-resonant (low loss) second-order nonlinearity of deff > ~50pm / V. The consequence of strong single-photon nonlinearity is very profound. With the required energy of ~0.1 attoJoules for a single photon in the telecom band, this would result in orders of magnitude improvement in energy efficiency, making nonlinear optical switching a real compelling technique in photonic signal processing. However, new nonlinear crystals are required to crack open this field of single photon strong nonlinearity regime.

[0113] The disclosure aims to synthesize and characterize promising nonlinear optical single crystals (outliers above the grey band in Fig.1A that optimize the highest second-order nonlinear optical coefficients with the largest bandgap (Eg>2eV) towards efficient frequency conversion.

[0114] Light-matter interaction is classically described by the polarization response of a material to an electric field ( / 0) given by,

[0115] 1^= +2^^0(^) / 0+ ^(^)^03 / 0 / 3+ ⋯extending to higher order terms).

[0116] (Note that dijk =1 / 2 ^(^)^03where the dummy subscripts keep track of the polarization directions of interacting photons). The complex linear susceptibility tensor ^^0(^)sets the complex refractive index, n as ^^^0 = 1 + ^^0(^).

[0117] However, under intense electric fields of order effects become important, which collectively form the field of non-linear optics (NLO). For example, through the second-order term, ^(^), an electric field / ~ cos ^9 (^ is the frequency of light, determining its color, and it is time) will give rise to a nonlinear polarization, Attorney Docket No.11196-079WO1

[0118] 1~^(^)cos^^9 = (^(^)⁄ 2) (cos 0^9 + cos 2^9).).

[0119] of light are generated by the crystal, namely generation, SHG) and ω-ω=0 (called optical rectification). SHG is a special case of sum frequency generation (SFG), and the rectification is a special case of difference frequency generation (DFG), as shown in Fig.1C. Multiple photons of different colors can combine in various ways to give a single photon (called SFG), or multiple photons of different colors can interact through the NLO crystal to create photons corresponding to their frequency difference (called DFG). DFG is particularly useful to create lower energy infrared photons starting from a higher frequency incident photon. Conversely, SFG can create infrared photons starting from a CO2 laser at 10.6μm or ultraviolet light from visible. As understood by the skilled practitioner, an important aspect of frequency conversion is phase-matching, where different nonlinear waves involved in a process must travel with the same phase velocity inside the crystal for efficient frequency conversion. The emerging field of quantum photonics also depends on NLO materials and their ability to generate pairs of entangled photons through spontaneous parametric down-conversion. In this example, the inventors have focused on the second-order NLO process, ^(^).

[0120] The requirements for efficient NLO crystals are summarized below and shown in Figs.1D and 1E.

[0121] One of the requirements is non-centrosymmetry, i.e., the material must lack a center of inversion symmetry. Further, a large non-linear susceptibility, i.e. ^(^),or in tensor form, d (=1 / 2 ^(^)ijk ^03) is desired; For mid-infrared wavelengths (^ > 1.#),^$<<>20-100pm / V and for the ultraviolet (^~150 − 40^#), a ^$<<>3-10pm / V isdesired at a minimum.

[0122] Further, a large transparency range in the wavelength of interest, such as^~0.8 − 15.# and beyond for DFG in the infrared and ^~0.1 − 0.4.# for SFG inthe visible / ultraviolet. This requires large electronic bandgaps of / ^>1.5eV for the DFG in the infrared and >2eV for the SFG in the visible / ultraviolet. It also requires the energy at which multiphonon absorption begins to be small (e.g., Attorney Docket No.11196-079WO1 / ^^^^^^<60meV). The transparency window for a photon of energy E is defined as / ^ > / > / ^^^^^^ (Figs. 1D-1E).

[0123] Still further, a moderate birefringence of Δ^~0.05-0.2 for dispersion phase- matching is required. This is a process of momentum conservation between photons that leads to high NLO efficiency.

[0124] Yet still further chemical and thermal stability and ease of large crystal growth are needed. Congruent compositions are the easiest to grow, but they may have non-stoichiometric defects.

[0125] Also, efficient NLO crystals are needed to build a laser with a high laser damage threshold (LDT): i.e., the laser power density at which damage or thermal lensing occurs must be large. This typically scales with Eg and lower physical and chemical defects.

[0126] Tradeoffs abound, such as large band gaps, Eg, correlate with large LDT's but smaller NLO dijk coefficients (see Fig.1A). High LDT also requires very low defect concentrations to minimize absorption and thermal lensing of the laser beam. Too small a birefringence cannot lead to phase-matching, while too large a birefringence leads to a “beam walk-off” problem that reduces the distance over which the photons interact within the crystal and thus limits the NLO efficiency.

[0127] Consider the classical theory of an electron in a nonlinear potential given by A = (1⁄2 )B^C^+ (1⁄3 )E#C^+ ⋯

[0128] where B^is a spring constant reflecting the binding energy of the electron of mass m and charge e, x is the displacement of this spring under an incident light field, E, of frequency ^, and A reflects the nonlinearity of the anharmonic potential well. Ignoring the tensor notation for the moment, the second-order non-resonant optical constants, ^, in the total polarization 1 = +2^ / + ^(^) / ^+ ⋯ can then be derived as: +^^ = F$G^⁄ #(^^^− ^^) and 2^ = ^(^)= (#E+^^⁄ F$^G^)^^(^)^(2^). Here, F$is the density of electron springs of resonant frequency ^^, and optical absorption is excluded for simplicity. Attorney Docket No.11196-079WO1

[0129] Even in this classical approach, one can immediately conclude the basicdesign principles: (1) Large non-resonant linear optical susceptibilities ^(2^) and^(^) give rise to large non-resonant SHG nonlinear susceptibility, ^(^); hence largerefractive indices are desired, which in turn depend on a resonance with a large pair density of states (PDOS). As will be seen below, lower motifs (weakly bonded 0D polyhedra, 1D chains, 2D sheets etc.) within a 3D crystal can give flat bands and larger PDOS.

[0130] (2) Larger the anharmonicity of the potential well that the electron sees(parameter A above), the larger is the nonlinear coefficient d. In ferroelectrics, ^ ∝I12, where 12 is the spontaneous ferroelectric polarization that breaks inversionsymmetry and the I~I^03^is a fourth-rank tensor in the paraelectric phase. Thus, a strong ferroelectric polarization should enhance ^.

[0131] In the examples of the present disclosure, chalcopyrites, MgSiP2 and MgGeP2 were synthesized. Chalcopyrites for NLO possess diamond-like non- centrosymmetric structures with I4^2^ space group that permits nonzero d14=d25 and d36 second-order NLO coefficients that are, in principle, phase-matchable. Recently, high throughput and density functional theory (DFT) calculations have explored Mg–IV–V2 (IV=Si, Ge, Sn; V=P, As) using the first-principles theory. Fig. 1A depicts that of these, the predicted d36 values of MgSiP2 are close to two times that of the benchmark AgGaSe2. The predicted value of MgGeP2 is almost three to four times that of AgGaSe2. However, no single-crystal optical studies have been performed so far to determine their complete tensors or phase-matching conditions. The d36 values increase dramatically in the regions dominated by Si, Ge-p and P -p orbitals of the anionic units [IV–V2]2-. The stronger covalent characters of Si-V and Ge–V bonds enhance the interband dipole moment and hence leads to a stronger SHG response. The MgSiP2 single crystals were successfully synthesized, as shown in Example 2.

[0132] Initial optical SHG measurements from 1.55.m fundamental to 0.775.m fundamental wavelengths, obtained in this example, suggest a giant nonlinear coefficient of deff ~85pm / V (see Fig.1A), which significantly exceeds the theory Attorney Docket No.11196-079WO1 prediction above, indicating that d14, the other non-zero coefficient might also be huge. If so, and if it is phase-matchable, then a 2-3 times increase in d coefficient can lower the incident power by 4-9 times, thus reducing the laser damage issues.

[0133] In addition to a large bandgap and large nonlinear coefficients, one requires phase-matching for efficient frequency conversion. The basic idea is that different colors of light interacting in a crystal need to travel with the same phase velocity for the highest efficiency of NLO frequency conversion. There are two approaches for achieving this: Dispersion phase-matching and quasi-phase matching. In the former, in crystals with moderate birefringence, one can find conditions where different nonlinear waves propagate with the same phase velocity. In the latter, one artificially creates a domain grating that compensates for a specific phase- mismatch.

[0134] Determination of the conditions for dispersion phase matching in NLO requires accurate determination of ^J^0(^)as a function of temperature. This can be arranged by exploiting the indices of the crystal. For a negative uniaxial crystal (^^(^) > ^$(^)), Type I phase matching in the SHG process aims to find a crystal orientation where ^$(2^) = ^^(^), while Type II phase matching aims to find the condition where 2^$(2^) = ^^(^) + ^$(^). These dispersion phase-matching conditions can be determined using cutting and polishing to take advantage of this phase-matching condition and tested in an optical parametric oscillator cavity.

[0135] Where dispersion phase matching is not possible, quasi-phase-matching can be employed.

[0136] In pursuit of the vision of single photon nonlinearity posed in Fig.1B, resonant microcavities from the most promising NLO crystals with the largest deff (>50 pm / V) and lowest optical losses were designed. High Q ring cavities can be created, and modal phase matching can be achieved between fundamental and second harmonic waves. The single photon nonlinearity, gd, was quantified by measuring the efficiency of the process of a single 2^ photon down-converted to two ^ photons. There are two ways the present application explores this. First, by Attorney Docket No.11196-079WO1 modal dispersion phase matching, a lower order 2^ optical cavity mode can be made to phase match with a higher order ^ optical cavity mode. Second, if thecavity itself is periodically poled, such that the period of poling, Λ = 2Lr, as follows:Λ = 2L⁄ (B^M − 2BM) , where k are the wavevectors for the fundamental mode at thetwo frequencies, then a quasi-phase-matched cavity can be used for sum or difference frequency generation. EXAMPLE 2

[0137] Generally, for practical use, and as disclosed above, the infrared NLO materials should satisfy the following requirements: large second-order nonlinearity (large SHG coefficients), broad transparency window, phase matchability, high LDT values, and good crystal growth habit. The main challenge of NLO crystal discovery is balancing the SHG coefficients and the bandgap since large bandgaps generally lead to high LDT values but small SHG coefficients. Fig.1A shows the SHG coefficients vs. bandgap for some well-known NLO crystals. It depicts a general trend that an increase in the bandgap of a crystal can result in a decrease in the SHG coefficient.

[0138] The diamond-like structure can be derived from the diamond structure and consists of vertex-sharing tetrahedra, which are aligned along the same direction. The aligned tetrahedra lead to not only the intrinsic noncentrosymmetric nature but also the superposition of the NLO effects from each microscopic building unit and, therefore, a large macroscopic SHG response.

[0139] In this example, the disclosed NLO crystal is represented by MgSiP2, which is a metal pnictide with the chalcopyrite structure similar to ZnGeP2. MgSiP2 exhibits giant second-order nonlinearity and phase-matchability, promising for high-efficiency laser applications.

[0140] In addition to the nonlinear optical frequency conversion application mentioned above, these crystals in the family Mg-IV-V2 (IV=Si, Sn and Ge, and V=P and As) exhibit superior electro-optic coefficients. Electro-optics is the phenomenon where the refractive index of the material changes in response to an electric field. This is crucial to powering the internet, where the conversion between electrical Attorney Docket No.11196-079WO1 and optical signals is performed by electro-optic crystals. The current industry standard is LiNbO3. However, the above family of crystals could also have large electro-optic coefficients; these properties will be addressed in the present application.

[0141] Finally, in addition to second-order optical nonlinearities, third-order nonlinearities leading to the third harmonic generation and nonlinear absorption and nonlinear refraction are also superior.

[0142] The single nonlinear optical crystals MgSiP2 were synthesized using the flux method. Mg turnings, Si powder, and P powder with a molar ratio of 1:1:2 were put into an alumina crucible. The Sb powder was added to the alumina crucible and formed an 83.4 mass percent solution with the raw materials. The alumina crucible was inserted into a quartz tube and sealed under a vacuum. The sealed ampoule was placed inside a muffle furnace and heated to 1100 °C in 48 hours to ensure homogeneous melt, followed by slow cooling at a rate of 3 °C / h to 650°C. The excessive Sb flux was then removed by centrifugation. The red transparent needle- like MgSiP2 single crystals were well separated from the flux, with typical dimensions of 0.3-0.5mm (width) × 0.3-0.4 mm (thickness) × 2-6 mm (length). X-ray diffraction (XRD) and transmission electron microscopy (TEM) analysis confirmed the crystal structure was the same as the reported one of MgSiP2. The composition analyses using an energy dispersive spectrometer (EDS) also confirmed the obtained crystals have compositions close to the expected stoichiometric composition in MgSiP2.

[0143] The CVT method was used to mimic the vacuum distillation method previously used to form MgSiP2 crystals. The flux-grown crystals and Sb flux were sealed in quartz tubes under a high vacuum. No transport agents, such as I2, were added. The sealed quartz tubes were then put into a CVT furnace. The hot end temperature was set to 700 °C, and the cold end temperature was set to 600 °C. The tubes were heated for 1 week to ensure the total removal of Sb flux. The remaining part is the MgSiP2 crystals with black color, as shown in Fig.3B. CVT (vacuum distillation) grown crystals are darker compared to the crystals grown Attorney Docket No.11196-079WO1 according to the methods disclosed herein (flux (centrifugal) grown crystals), as can be seen from the crystal image shown in Figs.3B and 3D. SEM images also suggest that CVT-grown crystals have dirty surfaces compared to the crystals obtained by the disclosed herein methods. (Figs.3A and 3C, respectively). Large amount of oxygen element was detected in the CVT-treated crystals, and no oxygen was detected in the flux (centrifugal) grown crystals, as shown in Figs.3A and 3C, respectively. The XRD measurements of the CVT-treated crystal and polycrystalline samples obtained accordingly to the disclosed methods show that the CVT-treated sample exhibits phase impurities not observed in the r polycrystalline sample (Fig.4).

[0144] MgSiP2 was also investigated using first-principles calculations. Its conventional tetragonal cell has one internal parameter x associated with the position of P atoms (8d Wyckoff sites). all the simulations were performed with the ABINIT software in the framework of density-functional theory (DFT) for the ground- state (GS) calculations and the density-functional perturbation theory (DFPT) for the response functions. The wavefunctions were expanded on a plane-wave basis set using a kinetic energy cutoff of 42 Ha, in combination with scalar relativistic Optimized Norm-Conserving Vanderbilt Pseudopotentials (ONCVPSP) from the PseudoDojo. The DFT and DFPT calculations adopted the local-density approximation (LDA) for the exchange-correlation energy. As an alternative, the Perdew-Burke-Ernzerhof generalized-gradient approximation was also tested for the ground-state calculations, but it did not lead to any significant changes.

[0145] All relaxations were performed using a 10 × 10 × 10 Monkhorst-Pack k-point mesh to sample the Brillouin zone. The structure was optimized until the maximum force on each atom was lower than 2.5 meV / Å. The relaxation of the tetragonal cell parameters (a and c) resulted in an excellent agreement with their experimental values: OP$Q^ − PRSTO=OV$Q^ − VRSTO= Attorney Docket No.11196-079WO1 Table 1 summarizes the conditions used for the synthesis of MgSiP2 according to the methods with a CVT treatment and centrifugal treatment. Flux removal CVT (vacuum distillation) Centrifugal a s P2 Attorney Docket No.11196-079WO1 Flux removal CVT (vacuum distillation) Centrifugal th d t l o sampling of the Brillouin zone, a 16 × 16 × 16 Monkhorst-Pack k-point mesh was adopted for all the calculations other than the relaxations. For the optical properties, a scissor shift was systematically applied on all conduction bands to match the experimental bandgap of 2.34 eV.

[0147] The static high-frequency (clamped-ions) dielectric and SHG tensors were first computed within DFPT using ABINIT. Thanks to the Optic utility of ABINIT, their frequency-dependent counterparts were calculated in the independent-particle approximation with a sum-over-states approach as developed by Hughes and Sipe. The inclusion of the anti-resonant terms results from an unpublished modification of the Optic utility. A total of 60 empty conduction bands (i.e., all the bands up to 25 eV above the valence band maximum) were included in the computation. Divergences were avoided by smoothing the spectrum with a broadening of 0.002 Ha (54 meV). The dielectric function provides the refractive index and extinction coefficients following the usual relations. Attorney Docket No.11196-079WO1

[0148] The crystal structure was first fully relaxed, adopting the local-density approximation (LDA) for the exchange-correlation (XC) energy. The MgSiP2 assynthesized herein has a crystal structure defined by unit cell parameters a=5.721Å, c=10.037 Å, C = 0.207, and a unit cell volume of 330.4 Å3, wherein the singlenonlinear optical crystal exhibits a refractive index of about 2.776 to about 2.778 and from about 2.806 to about 2.808 for no and ne respectively at a wavelength of 1,550 nm, and a nonlinear coefficient of deff of SHG from about 80 to about 95 pm / V. Calculated and experimental cell and internal parameters were found to be in excellent agreement with a difference below 1%. Finally, a relaxation of the internal parameter was also performed while keeping the cell parameters a and c fixed totheir experimental values. This led to C = 0.207 and a distortion parameter X = ^Y +&^ ^Z[\] _&`a\]^^ = 0.293 in accordance with previous investigations. The resultingstructure was used in all subsequent computations unless stated otherwise.

[0149] The band structure, shown in Fig.16, was computed in the same framework. The predicted 1.17 eV bandgap is direct and greatly underestimates the experimental value of 2.34 eV. Such a discrepancy is inherent to DFT when using local or semi-local functionals for the XC energy. Since optical properties are directly related to the bandgap, the latter was systematically corrected to match the experimental gap by applying a scissor shift to all conduction bands. The band structures with internal relaxation and scissor shift are shown in Fig.23. EXAMPLE 3

[0150] In this example, the linear optical properties of MgSiP2 were investigated. The infrared transparency of MgSiP2 was determined using Fourier transform infrared (FTIR) spectroscopy equipped with a 15×objective to ensure that the beam was focused on an area with uniform thickness. The transmittance spectrum shown in Fig.2A and Fig.17A was collected on the (112) plane of a single crystal with a thickness of ~225 μm in the spectral range of 1-25 μm at room temperature. It was found that MgSiP2 is transparent up to ~10.35 μm. Given that its bandgap is 2.34 eV (~0.53 μm), MgSiP2 has a large transparency window of 0.53-10.35 μm. Though AgGaS2, AgGaSe2 and ZnGeP2 are transparent further into the infrared region Attorney Docket No.11196-079WO1 (13.2 μm, 13.22 μm and 10.7 μm respectively), it is better than CdSiP2 (9.5 μm), allowing broadband tunability.

[0151] The anisotropic complex linear optical constants ^J = ^ + cB were determined using spectroscopic ellipsometry (Woollam M-2000F). Since MgSiP2 belongs to the tetragonal crystal system, it is a uniaxial crystal with two distinct complex refractive indices: ordinary ^J^in the plane perpendicular to the 4-fold rotation axis, and extraordinary ^J$along the 4-fold rotation axis.

[0152] The measurement was performed on the (101) plane of MgSiP2 in two different orientations where the orientation [111^] was parallel and perpendicular to the plane of incidence. Fig.5 illustrates the (101) plane and the [111^] direction of MgSiP2 and how they relate to the a, b, and c axes. The ellipsometric spectra collected from 0.200μm to 1μm were fitted with the Gaussian oscillators. The constants ^J^and ^J$can then be extracted by simultaneously fitting the two sets of ellipsometry data with the Gaussian oscillators (Figs.24A-24B), whose fit parameters are listed in Table 2. The dielectric functions and the complex refractive indices were also computed from first principles within DFT-LDA, which show excellent qualitative and quantitative agreement with the experiments, as shown in Fig.2B and Fig.17B. From the extrapolation of the experimental result using the Urbach absorption equation B = B2G(d_de) / df(detailed parameters are shown in Table 3), the experimental extinction coefficient k in the crystals is currently 0.05 at 1550nm and ~0.03 at wavelengths above 3 μm; however, the first principles calculations show that k is 0.02 at 1550nm and 7×10-4above 3 μm. This indicates that the absorption can be improved if the crystals have higher purity and lower defects with better synthesis.

[0153] In the process of second harmonic generation (SHG), two photons of frequency ω are combined into one photon of frequency 2ω (ω+ω=2ω) when traveling in a nonlinear optical medium. The nonlinear polarization can be expressed as 1^^M= ^^03 / 0M / 3M, where ^^03is the second-order optical susceptibility, E is the electric fields of light, and the subscripts i,j,k are dummy variables describing the polarization of the various photons of light. Attorney Docket No.11196-079WO1 Table 2. The parameters of each Gaussian oscillator for the anisotropic linear optical properties. n E^^g^^ / ^^E$^g^$ / ^$9 6 6 7 2 9 7

[0154] Table 3. The parameters of Urbach absorption equations for extinction coefficients. B B2 / h(eV) / 2(eV) B$0.078 1.189 0.946

[0155] It is necessary to ensure the SHG process only involves virtual transitions such that the absorption loss is minimized and the process is non-resonant. Since the bandgap of MgSiP2 is 2.24V, the fundamental wavelength was chosen to be 1550nm, and the wavelength of the SHG was 775nm.

[0156] The SHG measurement was performed in reflection geometry, shown in Fig. 6 and Fig.11A. The 1,550 nm fundamental laser beam was generated by Coherent Attorney Docket No.11196-079WO1 Libra Amplified Ti:Sapphire Laser (85fs, 2kHz). At an incident angle of α= -30°, the fundamental electric field Eω was linear polarized and rotated by an angle of ψ with respect to lab axis X. A wedged crystal with a crystal plane (112) was oriented such that the i111j and i110j crystal axes coincide with the lab axes X and Y, respectively. The advantage of using a wedge sample is that only the SHG generated from the front surface needs to be considered, which has proven robustness in extracting the SHG tensor. The relationship between these two directions and the a, b, c axes can be viewed from Fig.7B. The reflected SHG field was decomposed into p-polarized (∥) and s-polarized (⊥) by an analyzer and detected by a photo-multiplier tube.

[0157] For the point group 42#, the d tensor in Voigt notation is: 00 0 ^^Y 0 0^ = m0 0 0 0 ^^Y0 o 00 0 0 0 ^^n

[0158] The theoretical expressions for the SHG intensity in normal reflection geometry were generated by the modeling tool ♯SHAARP:^^M = 1.501 × 10_q(1. + cos 2 )^ ^p r ^^Y^n (for conversion from 1550nm to 775nm) and that of the rotation matrix that transforms the crystal physics coordinates (Z1, Z2, Z3) to the experimental coordinate system (X, Y, Z).

[0160] The full analytical expressions for LiNbO3 and MgSiP2 are generated using ♯SHAARP.si package. The X-cut LiNbO3 (112^0) is oriented with the c axis parallel to the lab X direction labeled as w^. Lab Y and Z are labeled as w^and w^respectively. At normal incidence, the extraordinary wave and ordinary waves at ^ Attorney Docket No.11196-079WO1 +MRzRz 0 0 (^M ^^ ) 0 0+RM^x = y0 +RM^R^0| = y0 (^^M)^0 | |^

[0161] The both ordinary and extraordinary waves at their corresponding frequencies are / $,M= (1,0,0); ^$$<,M< =^+RMzRz; / ^,M= (0,1,0); ^$^<,M< =^+RM^R^R^

[0162] in agreement with Fresnel coefficients, ^2 cos ^ / ,$,M = ( , 0,0)0)where superscript T, e, o wave and ordinary wave, respectively. Azimuthal angle ^ describes the rotation of incident polarization, as shown in the SHG polarimetry. The resulting SHG tensor in the lab coordinate system and nonlinear polarizations are thus expressed as, ^^^ ^^^ ^^^ 0 0 0o 0 Attorney Docket No.11196-079WO1 4(co )^1^,$$,^M = ^1R^,$$,^M ^^,$$,^M ^,$$,^M s ^ ^^^+2z, 1R, 1R{^ = (^, 0,0)^1 + ^+M ^ ()^ ( ^1^,^^,^M = ^1R^,^^,^M ^^,^^,^M ^,^^,^M 4 sin ^ ^^^+2 4 sin ^) ^^^+2z, 1R, 1R{^ = (^,^, 0)^1 + ^+MR^R^ ^ ^1 + ^+MR^R^ ^ 1^,$^,^M = 8 sin ^ cos ^ ^^1 ^R^,$^,^M +z, 1R^^,$^,^M , 1R^,$^,^M q 2{^ = (0,MM, 0)here, using two extraordinary waves, two ordinary waves or mixtures of extraordinary waves and extraordinary waves. The corresponding electric fields generated by the nonlinear polarizations are thus calculated as shown below, ^^,$$,^M = ^^R^R^^,$$,^M ^R^,$$,^M 1^,$$,^M^,$$,^M ^ = Rz LiNbO3 are shown below using boundary conditions at 2^ frequency, Attorney Docket No.11196-079WO1 / R^,^M2^^,$$,^M ^M − M + ^M ^M − M ^M ^ + ^,^^,^M ^M + ^M ^M − M − M ^MR ) plane of MgSiP2 is (112) and the direction perpendicular to the plane of incidence is [11^0]. The dielectric tensors in the lab coordinate system at both ^ and 2^ frequencies are shown below, +M MRzRz 0 +RzR{M=+M^^^ electric field directions and effective refractive indices for both ordinary and extraordinary waves at their corresponding frequencies are written below, Attorney Docket No.11196-079WO1 / $,M= (−^^^ ^{^{, 0,^^z^{);$,M _^^ ^ ^^z^{ ^ ^^^ ^^z^z ^^{^{^^ ^ ^ ^ ^ ^ ^^$<<=^^^^; agreement with Fresnel coefficients, 2cos ^ 2+MR R cos ^ / ^,$,M = ( , 0, − z { )where ordinary wave, respectively. Azimuthal angle ^ describes the rotation of incident polarization, as shown in the SHG polarimetry. The resulting SHG tensor in the lab coordinate system and nonlinear polarizations are thus expressed as, ^ 0.61^^Y + 0.31^^n −0.78^^n −0.61^^Y + 0.47^^n 0 −0.148^^Y − 0.38^^n 0^Y Attorney Docket No.11196-079WO1 1^,$$,^M= ^1R^,$$,^M, 1R^^,$$,^M, 1R^,$$,^M^ (cos ^)^^^−2.45^+RM ^R ^ + 1.08+RMR+RMR+ 2.45^+RM ^R ^ ^ ^^Y+ ^1.90^+RM ^R ^ + 3.05+RMR+RMR+ 1.22^+RM ^R ^ ^ ^^n^ +2) formed using two extraordinary waves, two ordinary waves or mixtures of extraordinary waves and extraordinary waves. The corresponding electric fields generated by the nonlinear polarizations are thus calculated as shown below,

[0002] Attorney Docket No.11196-079WO1 ^^,$$,^M= ^^R^,$$,^Mz , ^R^^,$$,^M, ^R^,$$,^M{ ^ | MgSiP2 is shown below using boundary conditions at 2^ frequency, / R^,^Mz )^)

[0003] Attorney Docket No.11196-079WO1 / R^^,^M^ )^) demonstration, as all the constants will be cancelled out by comparing the intensity between LiNbO3 and MgSiP2. EXAMPLE 4

[0170] To obtain the dij coefficients of MgSiP2, the polar plots were fitted to the equation for ^s^M(Figs.10A-10B, Fig.11B) and compared with that measured on a wedged reference under the same experimental conditions (Fig.26). From ^p^M, the ratio of d14 / d36=1.05±0.05 was obtained, and thus the two non-zero SHG are practically equal, confirming the Kleinman symmetry and the non-resonant SHG process. The SHG coefficients d14 and d36 were extracted to be from about 80 pm / V to about 95 pm / V, surpassing the commercial NLO crystals AgGaS2, AgGaSe2 and ZnGeP2. To ensure that the detected signal was from the second-order NLO effect, the SHG intensities were measured as a function of incident power, as shown in Fig.11C. The SHG response demonstrates a clear quadratic dependence on the input power. When it is plotted in the logarithmic scale, the slope is 2.08±0.08, confirming that the signal measured was generated by the second-order NLO effect.

[0171] MgSiP2 belongs to the space group ^42^ (point group 42#) and has the chalcopyrite structure closely related to the zinc blende structure except that the unit cell is twice larger (Fig.7A). Similar to other chalcopyrite structured crystals, it comprises of aligned MgP4 and SiP4 units (Fig.20), allowing the superposition of the microscopic SHG response generated from these tetrahedra, which results in overall strong SHG performance. Each P3-anion is bonded with two Si4+and two Mg2+cations, while both the Si4+and Mg2+cations are coordinated with four anions with different Si-P and Mg-P bond lengths, leading to distortion of the anion Attorney Docket No.11196-079WO1 sublattice. As shown in Fig.21, the as-grown crystals are needle-like with typical dimensions of 0.3-0.5mm (width) × 0.3-0.4 mm (thickness) × 2-6 mm (length).The MgSiP2 single crystals have a similar growth habit as ZnSiP2 and CdSiP2: they grow along the

[0111] direction, with two natural facets corresponding to the (112) and (101) planes. Fig.7C shows an image of a MgSiP2 single crystal with labeled facets and growth direction. The planes were also verified by XRD by measuring each facet of the MgSiP2 crystal, as shown in Fig.8A. The crystals are air-sensitive but stable in water. When left in the ambient atmosphere for two days, the surface of the crystal starts to degrade, as shown in Fig.22; hence for eventual applications, the crystal surfaces will need to be sealed against air exposure. Additionally, the XRD pattern confirmed its 4^2# crystal structure and phase purity. Fig.8B shows the atomic resolution high angle annular dark field (HAADF)-STEM image taken along the

[0110] axis. The STEM image also illustrates that the as- grown MgSiP2 crystal possesses the same structure as the previously reported structure (Fig.7A).

[0172] Fig.8A XRD pattern of the MgSiP2 single crystals confirmed the phase- purity and plane orientation. (b) STEM image is taken from the

[0110] axis. Inset: A magnified HAADF-STEM image superimposed with a simulated crystal structure confirmed the phase and structure.

[0173] The ordinary and extraordinary refractive indices in the spectral range of 0.2μm to 1μm were extracted by simultaneously fitting the two sets of ellipsometry data measured on (101) surface with the Gaussian oscillators, as shown in Fig.9.

[0174] Since MgSiP2 has a large transparency window of 0.53-10.35 μm (Figure 17A), the dispersion is small in 1-4 μm. Therefore the refractive indices ^ from 0.45 μm to 1 μm were fitted to the Sellmeier equation ^^= A +^and extrapolated to 4 μm for the SHG analysis and phase-matching (Fig.17C). The parameters of the Sellmeier equations are shown in Table 4. The birefringence is also calculated and shown in Fig.25.

[0175] In real applications, phase-matching is one of the most crucial criteria for efficient high-power nonlinear conversion. When the crystal achieves the phase- Attorney Docket No.11196-079WO1 matching conditions, the fundamental wave and the SHG wave travel at the same speed; in other words, ^M= ^^M. This can only be realized in anisotropic crystalswith a large enough birefringence. Since MgSiP2 is a positive uniaxial crystal (^^ <^$), the Type-I phase-matching condition is ^^,^M = ^$,M(^^) and the Type-II phase-matching condition is ^^M+ ^$M(^^) = 2^^^M(^^), where ^^is the angle between the optical axis and the wave vector. Using the above-mentioned Sellmeier equations for the refractive indices, the phase-matching conditions of MgSiP2 can thus be calculated, as shown in Figs.14A-14B. The effective d coefficient for Type I and Type II can be expressed as deff,I= d36sin(2θm) cos(2φ) and deff,II=−d36sin(θm) sin(2φ), where φ is the azimuthal angle as defined in Fig.12 and Fig.19. In practical applications, the crystal will be cut into a wafer such that the angle between the surface normal and the optical axis equals the phase-matching angle (Figs.13A-13B). Using Miller’s rule, one can estimate the value of d36 at other wavelengths. For example, d36 ≈ 81.6 pm / V at 3.5μm and therefore |deff,I| is greater than about 75 pm / V to about 90 pm / V at φ=0° and |deff,II| is greater than about 70 pm / V to about 80 pm / V at φ=45° as shown in Fig.15. Table 4. The parameters of Sellmeier equations for ordinary and extraordinary refractive indices. ^ A B C (μm2) ^^ 7.43 0.5686 0.06685^$ 7.622 0.4774 0.08485EXAMPLE 5

[0176] To further understand the high NLO susceptibility, first-principles calculations within DFT-LDA were carried out. The static SHG tensor ^^0was computed within density-functional perturbation theory (DFPT). As expected from the small structural difference, both the fully and the internally relaxed structures yield similar results with ^^ n = 27 pm / V and ^^ n = 29 pm / V, respectively. However, a difference in the cell parameters of less than 1% results in a change of the SHG coefficient of 6%. This demonstrates the high sensitivity of SHG to structural variations. Without Attorney Docket No.11196-079WO1 any scissor shift, ^^ n increases to 54.859 pm / V and 57.519 pm / V for both structures, respectively. This shows the importance of the bandgap (and, more generally, of linear optics) in nonlinear optical calculations, as summarized by Miller's rule. Following a sum-over-states approach, the dispersion of the SHG tensor was also calculated. As illustrated in the inset of Fig.11E, from 0 to 1.24 eV, the inclusion of anti-resonant terms is shown to affect exclusively the low-energy range of the real component by doubling its static value. This slightly increases the discrepancy with its DFPT counterpart, but the agreement with the experimental result at 1550 nm (0.8 eV) is improved despite a clear underestimation of the SHG component.

[0177] In order to physically understand the origin of the large SHG coefficient, the total response was decomposed into three different terms originating from 1) the interband transitions; 2) the intraband transitions; and 3) the modulation of the interband terms by intraband terms. In the following, they will respectively be called “inter,” “intra,” and “mod.” Their definition directly originates from the Genkin- Mednis approach in the mathematical treatment applied to the Hamiltonian when developing the sum-over-states equation. There is no straightforward way to relate the “inter,” “intra,” and “mod” terms to distinct features of the electronic band structure. However, by simplifying the different sums, it is possible to identify the bands that contribute the most to each of these terms, as will be shown below. From Fig.27, it can be seen that, in MgSiP2, the total real response (resonant terms only) in the low energy range primarily originates from the "intra" term and, more precisely, from its 2ω resonance. According to the following sum rule, ^^ ^2 ^ ^^(^)(−2^, ^, ^)^

[0178] the responsible for its real value in the static limit. In the present case, it appears that the high positive peak of ^^^(^)(−2^, ^, ^)^around 2.27 eV constitutes the main feature of interest (see Fig.27). Its is also the "intra" 2^ resonant term, as expected from the above equation. Attorney Docket No.11196-079WO1

[0179] When shifting the 2^ term in accordance with its resonance, as shown in Fig.18A, the imaginary “intra” curves can be seen as modulations of the absorption one. This is perfectly in line with what Sipe and Ghahramani proposed originally. It once again proves the importance of linear optics for the emergence of nonlinear optical phenomena, as emphasized by Miller's rule. One can indeed assume that a large or abrupt absorption could favor this “intra” contribution, leading, in turn to an important real value at low frequencies. This assumption and the required interpretation of the “intra” term should be explored in further investigations.

[0180] In all the above, the “inter,” “intra,” and “mod” terms are a sum over two- or three-band contributions. Similar to the band-resolved analysis introduced by Lee et al., the valence and conduction bands with the largest SHG contribution were identified by summing over the bands in two different ways. The results of this analysis in the case of the main ^peak of ^ ^^(^)(−2^, ^, ^)^ are illustrated in Fig. 18B. Only the “intra” 2^ and “inter” 2^ since they largely dominate the other terms (see Fig.27) in this frequency range. As shown by the pie charts in the figure, the SHG mainly comes from the interaction between five bands at the top of the valence band and four bands at the bottom of the conduction band. From the projected density of states (PDOS) of Fig.28, the top of the valence band corresponds to P-p orbitals, while the bottom of the conduction band can be attributed to Si-s, Si-p, and P-p orbitals. This emphasizes the importance of the [SiP4] tetrahedral units as well as their geometrical arrangement.

[0181] Fig.11D compares the highest non-resonant SHG coefficient MgSiP2 and some well-known NLO crystals. It also illustrates the general trend that the NLO susceptibility anticorrelates with the electronic bandgap of a material. Compared with AgGaSe2 and ZnGeP2, MgSiP2 possesses both a large SHG coefficient and a larger bandgap, whereas compared to CdSiP2 (84pm V-1at 4.56μm fundamental wavelength and 93pm V-1at 1550nm fundamental wavelength by Miller’s rule), it has a slightly smaller bandgap (5%) and comparable SHG coefficient considering the error bar. Attorney Docket No.11196-079WO1 EXAMPLE 6

[0182] The LDT value of MgSiP2 was also assessed, as it is a critical requirement for high-power laser applications. The thermal conductivity measurements were conducted on pressed polycrystalline material. Polycrystalline material was ground into a fine powder and then pressed into a bar (10mm x 3mm x 1.65mm). This bar was then annealed under a vacuum at 850℃ for 48 hours. Gold-plated copper leads were attached to the sample using silver epoxy. Thermal conductivity was measured from 5- 300 K using the thermal transport option in a Quantum Design Physical Property Measurement System using a standard 4 lead method.

[0183] The evaluation was performed on the as-grown (112) plane of the crystal without polishing and without any antireflection coating the surfaces. A femtosecond laser system (1550nm, 1kHz, 100fs) was used to generate high peak power laser pulses (up to 50 GW). During the measurement, the beam size (diameter of ~70µm) was kept the same while the incident power was gradually increased. The surface of the crystal was inspected with an optical microscope for each trial until apparent damages appeared. MgSiP2 has a giant LDT value of 684 GW cm-2. For comparison, we also measured the LDTs of ZnGeP2 and CdSiP2 (provided by BAE Systems) using the same laser system, which are 115 GW cm-2and 198 GW cm-2, respectively. The obtained LDT of ZnGeP2 is in excellent agreement with the previously reported value. The LDT of MgSiP2 is ~six times greater than ZnGeP2 and ~three times greater than CdSiP2, as illustrated in the inset of Fig.11D. The detailed parameters are shown in Table 5. Though its thermal conductivity is lower than that of CdSiP2 (Supplementary Information), its LDT is significantly larger. The combination of large phase-matchable SHG coefficients and LDT makes MgSiP2 an excellent material for high-power laser applications.

[0184] The temperature-dependent thermal conductivity of MgSiP2 is shown in Fig. 30. The room temperature thermal conductivity of MgSiP2 is 1.46 W m-1K-1, which is comparable with AgGaS2 and BaGaS7 and slightly higher than AgGaSe2 and BaGaSe7. A comparison between MgSiP2 and some well-known NLO crystals is Attorney Docket No.11196-079WO1 given in Table 5. It is worth mentioning that high thermal conductivity generally leads to high LDT, but this statement is not always accurate since many other factors can affect the LDT value, such as bandgap and defects. For example, ZnGeP2 has much higher thermal conductivity than CdSiP2, yet its LDT is only half that of CdSiP2, likely because of the smaller bandgap and two-photon absorption.

[0185] FIGs.29A-29F show crystal images of MgSiP2, CdSiP2, and ZnGeP2 before and after the laser damage measurements. Table 5. The experimental parameters of the LDT measurements. Wavelength Beam size (μm) LDT (GW / cm2) MgSiP2 1550nm 70 684 CdSiP2 1550nm 102 198 ZnGeP2 1550nm 102 115 PROPHETIC EXAMPLES

[0186] The vertical Bridgeman and floating-zone methods will be used to synthesize cm-sized single crystals. To perform Bridgman and floating-zone growths, one may synthesize polycrystalline MgSiP2 materials through a solid-state reaction method, as disclosed below. Elements of Mg, Si and red phosphorus can be used as source materials. Mixture of Mg, Si and P with a stoichiometric molar ratio can be sealed into a quartz tube. The quartz tube loaded with mixed source materials can be heated in a step-like mode to avoid possible explosion caused by the high vapor pressure of P: the material will first be heated to 525°C and stay at this temperature for 24 hours, then heated to 830°C and dwell at this temperature for 35 hours, followed by increasing the temperature to 1160°C to get homogeneous melt. After waiting for 3 hours at 1160°C, the melt can be cooled down gradually at a rate of 100°C / h. At 525°C and 830°C. EXAMPLE 7

[0187] The polycrystalline MgSiP2 has been synthesized according to the following conditions. Attorney Docket No.11196-079WO1

[0188] Magnesium turnings, silicon powder and phosphorus powder were mixed in the stoichiometric ratio and loaded into a pyrolytic Boron Nitride (PBN) crucible. The PBN crucible was put into a quartz tube which was then sealed under a vacuum. The quartz tube was put into the programmable muffle furnace. The temperature was raised from room temperature to 525°C at a rate of 50°C / hr and then kept at this temperature for 72 hours. The temperature was further increased to 830°C at 30°C / hr and dwelled for 60 hours to ensure the complete reaction of Mg and P. Afterward, the tube was heated to 1150°C at 30°C / hr and held for 60 hours. Finally, it was cooled to room temperature at 100°C / hr. The polycrystalline MgSiP2 was grounded into powder and confirmed the phase purity using x-ray diffraction (XRD).

[0189] The typical mass of individual pieces of crystals ranges from 1mg to 5mg. The total mass of crystals from a batch depends on not only the amount of source materials used for growth but also the cooling rate during the growth and many other factors. The total crystal mass of a batch typically ranges from ~10 mg to ~100 mg.

[0190] Sn flux: Stoichiometric quantities of high-purity Mg turnings, Si powder, and P powder were put into alumina crucibles. Sn powder was added to the alumina crucible and formed a 10 molar percent solution with the raw materials. The alumina crucible was then put in a quartz tube and sealed under a vacuum. The ampoule was then heated to 1100 °C for 24 hours, followed by slow cooling to 400 °C for 240 hours. Centrifugation was used to remove Sn flux when the temperature reached 400 °C. EXEMPLARY ASPECTS

[0191] Example 1. A single nonlinear optical crystal having a chemical formula of Mg-IV-V2, wherein IV is selected from Si, Ge, or Sn, and V is selected from P or As, wherein the single nonlinear optical crystal has a chalcopyrite and non- centrosymmetric crystal structure, with a space group of , wherein the non- centrosymmetric crystal structure is defined by unit cell parameters: a between about 5.5 to about 6 Å, c between about 9.5 to about 12.5 Å, and a unit cell volume Attorney Docket No.11196-079WO1 of about 287 to about 450 Å3, wherein the single nonlinear optical crystal exhibits a refractive index of about 2.770 to about 2.780 and from about 2.800 to about 2.810 for no and ne respectively at a wavelength of 1,550 nm, and a nonlinear coefficient of deff of SHG from about 80 to about 95 pm / V, wherein the single crystal Mg-IV-V2 is substantially free of impurities.

[0192] Example 2. The single nonlinear optical crystal of any examples herein, particularly example 1, wherein the single nonlinear optical crystal is MgSiP2.

[0193] Example 3. The single nonlinear optical crystal of any examples herein, particularly example 1 or 2, exhibiting a transmittance from about 60% to less than 100% in a wavelength range from about 0.55 to about at least 20 µm.

[0194] Example 4. The single nonlinear optical crystal of any examples herein, particularly examples 1-3, wherein a d14 coefficient is from about 80 pm / V to about 95 pm / V at a fundamental wavelength of 1,550 nm.

[0195] Example 5. The single nonlinear optical crystal of any examples herein, particularly examples 1-4, wherein a d36 coefficient is from about 80 pm / V to about 95 pm / V at a fundamental wavelength of 1,550 nm.

[0196] Example 6. The single nonlinear optical crystal of any examples herein, particularly examples 1-5, exhibiting type I and type II phase matching, wherein |deff,I| at φ=0° is greater than about 75 pm / V to about 90 pm / V and |deff,II|= at φ=45° is greater than about 70 pm / V to about 80 pm / V at a fundamental wavelength of 3.5 μm.

[0197] Example 7. The single nonlinear optical crystal of any examples herein, particularly examples 1-6, wherein the single crystal Mg-IV-V2 is uniaxial.

[0198] Example 8. The single nonlinear optical crystal of any examples herein, particularly examples 1-7, wherein the single crystal of Mg-IV-V2 exhibits a substantially single phase.

[0199] Example 9. A method of forming the single nonlinear optical crystal of any one of clauses 1-8, wherein the method comprises: (a) providing a solution comprising a solute comprising a mixture of Mg, IV and V in a molar ratio from Attorney Docket No.11196-079WO1 about 0.95:0.95:2 to about 1.05:1.05:2 and a solvent; wherein a mass ratio between the solvent and solute is from about 10:1 to about 4:1; (b) growing a crystalline composition comprising Mg-IV-V2 at a first temperature from about 950 °C to about 1,200 °C for a first predetermined time; and (c) centrifugally separating the solvent to form a single crystal of Mg-IV-V2 having a size from about 0.1 mm to about 10 mm in length, wherein the single crystal is substantially free of a solvent residue.

[0200] Example 10. The method of any examples herein, particularly example 9, wherein before step c) the crystalline composition is cooled to a temperature of about 750 °C to about 640 S°C at a rate from about 0.5 °C / h to about 35 °C / h.

[0201] Example 11. The method any examples herein, particularly examples 9 or 10, wherein the step of centrifugally separating is performed at a second temperature and a speed of about 1,300 to about 1,500 rpm for a second predetermined time of about 1 min to about 15 min.

[0202] Example 12. The method of any examples herein, particularly examples 9- 11, wherein the solvent comprises Sb, Sn, or a combination thereof.

[0203] Example 13. The method of any examples herein, particularly examples 9- 12, wherein the solution is formed by mixing Mg, IV, V, and the solvent provided in a powdered form and heating to a temperature sufficient to homogeneously mix the solute and solvent.

[0204] Example 14. The method of any examples herein, particularly examples 9- 13, wherein the single crystal Mg-IV-V2 grows along

[0111] direction.

[0205] Example 15. A method of forming the single nonlinear optical crystal of any examples herein, particularly examples 1-8, wherein the method comprises: (a) sealing a polycrystalline material, comprising a Mg-IV-V2 compound in a temperature-resistant container; (b) placing the temperature-resistant container in a rocking furnace; (c) heating the polycrystalline material to a third temperature at a rate of about 45 °C / h to about 120 °C / h and keeping the polycrystalline material at a third temperature for a third predetermined time; (d) placing the temperature- Attorney Docket No.11196-079WO1 resistant container in a three-zone furnace, wherein the three-zone furnace exhibits a temperature profile defined by an upper / melt zone temperature, a middle / crystallization zone temperature; and a lower / annealing zone temperature; (e) translating the temperature-resistant container vertically, thereby allowing the temperature-resistant container to arrive at a nucleating temperature to form a seeding crystal; (f) growing an ingot material from the seeding crystal; (g) annealing the ingot material at a temperature of about 700 °C to about 850 °C for a fourth predetermined time; and (h) forming the single nonlinear optical crystal Mg-IV-V2, wherein the single nonlinear optical crystal is substantially free of impurities, defined by a single phase and has a size from about 0.1 mm to about 10 cm in length.

[0206] Example 16. The method of any examples herein, particularly example 15, wherein the polycrystalline material is ground prior to the step of sealing and wherein grinding is performed in an inert atmosphere.

[0207] Example 17. The method of any examples herein, particularly example 15 or 16, wherein the polycrystalline material is rocked within the rocking furnace at the third temperature to form a homogeneous mixture.

[0208] Example 18. The method of any examples herein, particularly examples 15- 17, further comprising dwelling the polycrystalline material at the upper / melt zone temperature, the middle / crystallization zone temperature, and the lower / annealing zone temperature for a fifth predetermined time.

[0209] Example 19. The method of any examples herein, particularly examples 15- 18, wherein prior to the annealing step, the upper / melt zone temperature, the middle / crystallization zone temperature, and the lower / annealing zone temperature are reduced to a fourth temperature at a first predetermined cooling rate.

[0210] Example 20. The method of any examples herein, particularly examples 15- 19, wherein the polycrystalline material is cooled after annealing to a room temperature at a second predetermined cooling rate.

[0211] Example 21. The method of any examples herein, particularly examples 15- 20, wherein the polycrystalline material comprising the Mg-IV-V2 compound is Attorney Docket No.11196-079WO1 formed by the steps comprising: (a) mixing Mg, IV, and V in a molar ratio of about 0.95:0.95:2 to about 1.05:1.05:2 to form a mixture; (b) placing the mixture into a sealed container in a furnace; (c) bringing the mixture to a first heating temperature of about 450 °C to about 550 °C at a rate of about 1 °C / h to 55 °C / h and keeping the mixture at the first heating temperature for about 60 to about 100 hours; (d) bringing the mixture to a second heating temperature of about 780 °C to about 850 °C at a rate of about 1 °C / h to about 40 °C / h and keeping the mixture at the second heating temperature for about 50 to about 100 hours; (e) bringing the mixture to a third heating temperature of about 1,100 °C to about 1,250 °C at a rate of about 20 °C / h to about 40 °C / h and keeping the mixture at the third heating temperature for about 50 to about 100 hours; (f) cooling the mixture to a room temperature at a rate of about 50 °C / h to about 150 °C / h; (g) recovering the polycrystalline material comprising Mg-IV-V2, and wherein the polycrystalline material is substantially free of impurities and has a substantially single phase.

[0212] Example 22. An optical parametric oscillator comprising the single nonlinear optical crystal of any examples herein, particularly examples 1-8.

[0213] Example 23. The optical parametric oscillator of any examples herein, particularly example 22, further comprising a pump laser source having a pump beam in a range of about 1.1 to about 4 micrometers.

[0214] Example 24. The optical parametric oscillator of any examples herein, particularly example 23, wherein the pump laser source is a liquid laser, gas laser, or semiconductor laser.

[0215] Example 25. The optical parametric oscillator of any examples herein, particularly example 24 or 24, wherein the pump laser source is a pulse laser or a continuous laser.

[0216] Example 26. The optical parametric oscillator of any examples herein, particularly examples 22-25, further comprises an optical resonator comprising a plurality of mirrors. Attorney Docket No.11196-079WO1

[0217] Example 27. A laser comprising the single nonlinear optical crystal of any examples herein, particularly examples 1-8.

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Claims

Attorney Docket No.11196-079WO1 CLAIMS 1. A single nonlinear optical crystal having a chemical formula of Mg-IV-V2, wherein IV is selected from Si, Ge, or Sn, and V is selected from P or As, wherein the single nonlinear optical crystal has a chalcopyrite and non- centrosymmetric crystal structure, with a space group of ^4^2^, wherein the non- centrosymmetric crystal structure is defined by unit cell parameters: a between about 5.5 to about 6 Å, c between about 9.5 to about 12.5 Å, and a unit cell volume of about 287 to about 450 Å3, wherein the single nonlinear optical crystal exhibits a refractive index of about 2.770 to about 2.780 and from about 2.800 to about 2.810 for noand nerespectively at a wavelength of 1,550 nm, and a nonlinear coefficient of deff of SHG from about 80 to about 95 pm / V, wherein the single crystal Mg-IV-V2 is substantially free of impurities.

2. The single nonlinear optical crystal of claim 1, wherein the single nonlinear optical crystal is MgSiP2.

3. The single nonlinear optical crystal of claim 1 or 2, exhibiting a transmittance from about 60% to less than 100% in a wavelength range from about 0.55 to about at least 20 µm.

4. The single nonlinear optical crystal of any one of claims 1-3, wherein a d14 coefficient is from about 80 pm / V to about 95 pm / V at a fundamental wavelength of 1,550 nm.

5. The single nonlinear optical crystal of any one of claims 1-4, wherein a d36 coefficient is from about 80 pm / V to about 95 pm / V at a fundamental wavelength of 1,550 nm.

6. The single nonlinear optical crystal of any one of claims 1-5, exhibiting type I and type II phase matching, wherein |deff,I| at φ=0° is greater than about 75 pm / V to about 90 pm / V and |deff,II|= at φ=45° is greater than about 70 pm / V to about 80 pm / V at a fundamental wavelength of 3.5 μm.

7. The single nonlinear optical crystal of any one of claims 1-6, wherein the single crystal Mg-IV-V2 is uniaxial.Attorney Docket No.11196-079WO1 8. The single nonlinear optical crystal of any one of claims 1-7, wherein the single crystal of Mg-IV-V2 exhibits a substantially single phase.

9. A method of forming the single nonlinear optical crystal of any one of claims 1-8, wherein the method comprises: a) providing a solution comprising a solute comprising a mixture of Mg, IV and V in a molar ratio from about 0.95:0.95:2 to about 1.05:1.05:2 and a solvent; wherein a mass ratio between the solvent and solute is from about 10:1 to about 4:1; b) growing a crystalline composition comprising Mg-IV-V2 at a first temperature from about 950 °C to about 1,200 °C for a first predetermined time; and c) centrifugally separating the solvent to form a single crystal of Mg-IV-V2 having a size from about 0.01 mm to about 10 mm in length, wherein the single crystal is substantially free of a solvent residue.

10. The method of claim 9, wherein before step c) the crystalline composition is cooled to a temperature of about 750 °C to about 640 °C at a rate from about 0.5 °C / h to about 35 °C / h.

11. The method of claim 9 or 10, wherein the step of centrifugally separating is performed at a second temperature and a speed of about 1,300 to about 1,500 rpm for a second predetermined time of about 1 min to about 15 min.

12. The method of any one of claims 9-11, wherein the solvent comprises Sb, Sn, or a combination thereof.

13. The method of any one of claims 9-12, wherein the solution is formed by mixing Mg, IV, V, and the solvent provided in a powdered form and heating to a temperature sufficient to homogeneously mix the solute and the solvent.

14. The method of any one of claims 9-13, wherein the single crystal Mg-IV-V2 grows along [111] direction.Attorney Docket No.11196-079WO1 15. A method of forming the single nonlinear optical crystal of any one of claims 1- 8, wherein the method comprises: a) sealing a polycrystalline material, comprising a Mg-IV-V2 compound in a temperature-resistant container; b) placing the temperature-resistant container in a rocking furnace; c) heating the polycrystalline material to a third temperature at a rate of about 45 °C / h to about 120 °C / h and keeping the polycrystalline material at a third temperature for a third predetermined time; d) placing the temperature-resistant container in a three-zone furnace, wherein the three-zone furnace exhibits a temperature profile defined by an upper / melt zone temperature, a middle / crystallization zone temperature; and a lower / annealing zone temperature; e) translating the temperature-resistant container vertically, thereby allowing the temperature-resistant container to arrive at a nucleating temperature to form a seeding crystal; f) growing an ingot material from the seeding crystal; g) annealing the ingot material at a temperature of about 700 °C to about 850 °C for a fourth predetermined time; and h) forming the single nonlinear optical crystal Mg-IV-V2, wherein the single nonlinear optical crystal is substantially free of impurities, defined by a single phase and has a size from about 0.1 mm to about 10 cm in length.

16. The method of claim 15, wherein the polycrystalline material is ground prior to the step of sealing and wherein grinding is performed in an inert atmosphere.

17. The method of claim 15 or 16, wherein the polycrystalline material is rocked within the rocking furnace at the third temperature to form a homogeneous mixture.Attorney Docket No.11196-079WO1 18. The method of any one of claims 15-17, further comprising dwelling the polycrystalline material at the upper / melt zone temperature, the middle / crystallization zone temperature, and the lower / annealing zone temperature for a fifth predetermined time.

19. The method of any one of claims 15-18, wherein prior to the annealing step, the upper / melt zone temperature, the middle / crystallization zone temperature, and the lower / annealing zone temperature are reduced to a fourth temperature at a first predetermined cooling rate.

20. The method of any one of claims 15-19, wherein the polycrystalline material is cooled after annealing to a room temperature at a second predetermined cooling rate.

21. The method of any one of claims 15-20, wherein the polycrystalline material comprising the Mg-IV-V2 compound is formed by the steps comprising: a) mixing Mg, IV, and V in a molar ratio of about 0.95:0.95:2 to about 1.05:1.05:2 to form a mixture; b) placing the mixture into a sealed container in a furnace; c) bringing the mixture to a first heating temperature of about 450 °C to about 550 °C at a rate of about 1 °C / h to 55 °C / h and keeping the mixture at the first heating temperature for about 60 to about 100 hours; d) bringing the mixture to a second heating temperature of about 780° C to about 850 °C at a rate of about 1 °C / h to about 40 °C / h and keeping the mixture at the second heating temperature for about 50 to about 100 hours; e) bringing the mixture to a third heating temperature of about 1,100 °C to about 1,250 °C at a rate of about 20 °C / h to about 40 °C / h and keeping the mixture at the third heating temperature for about 50 to about 100 hours;Attorney Docket No.11196-079WO1 f) cooling the mixture to a room temperature at a rate of about 50 °C / h to about 150 °C / h; g) recovering the polycrystalline material comprising Mg-IV-V2, and wherein the polycrystalline material is substantially free of impurities and has a substantially single phase.

22. An optical parametric oscillator comprising the single nonlinear optical crystal of any one of claims 1-8.

23. The optical parametric oscillator of claim 22, further comprising a pump laser source having a pump beam in a range of about 1.1 to about 4 micrometers.

24. The optical parametric oscillator of claim 23, wherein the pump laser source is a liquid laser, gas laser, or semiconductor laser.

25. The optical parametric oscillator of claim 24 or 24, wherein the pump laser source is a pulse laser or a continuous laser.

26. The optical parametric oscillator of any one of claims 22-25, further comprises an optical resonator comprising a plurality of mirrors.

27. A laser comprising the single nonlinear optical crystal of any one of claims 1-8.

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