Rare earth borates for nonlinear optics in the ultraviolet region, methods of making the same

Abstract

Disclosed herein is a single nonlinear optical crystal having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; and wherein n is 1 to 14. Also disclosed are devices comprising the same and methods of making the same.

Description

Attorney Docket No.11196-117WO1 RARE EARTH BORATES FOR NONLINEAR OPTICS IN THE ULTRAVIOLET REGION, METHODS OF MAKING THE SAME, AND DEVICES COMPRISING THE SAME CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of priority to U.S. Provisional Application No.63 / 685,080, filed August 20, 2024, which is incorporated by reference herein in its entirety. STATEMENT OF GOVERNMENT SUPPORT

[0002] This invention was made with government support under Grant Nos. DMR2011839, DMR2039351 and DMR2210933 awarded by the National Science Foundation. The Government has certain rights in the invention. TECHNICAL FIELD

[0003] This application relates generally to single crystals with nonlinear optical (NLO) properties that allow their use in high-power visible or UV-C 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] Nonlinear optical crystals are the essential components of high-power lasers for frequency conversion through nonlinear optical phenomena such as second harmonic generation (SHG), sum frequency, and difference frequency. For commercial utilization, a potential NLO material should have a broad transparency window, low birefringence, stability in the ambient chemical environment, high NLO coefficient, high laser-induced surface damage threshold (LISDT), and ease of facile growth into large single crystals. Traditional NLO materials such as β-BaB2O4 (BBO) and KH2PO4 (KDP) are not suitable for the desired applications because of the laser damage threshold (LDT) and low environmental stability. The development of high-Attorney Docket No.11196-117WO1 power visible and UV-C laser systems demands novel NLO crystals with superior optical properties.

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

[0007] In some aspects, disclosed herein is a single nonlinear optical crystal having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; wherein n is 1 to 14; and wherein the crystal exhibits a second harmonic generation (SHG) coefficient of from 0.2 pm / V to 200 pm / V.

[0008] In some aspects, also disclosed herein is a single nonlinear optical crystal having a formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; wherein n is 1 to 14; and wherein at least a portion of RnBa3(B3O6)3 exhibits a metastable low symmetry (M) phase.

[0009] In some aspects, also disclosed herein is a laser comprising any of the disclosed single nonlinear optical crystals.

[0010] In some aspects, disclosed herein is a quantum light emitter comprising any of the disclosed nonlinear optical single crystals.

[0011] In some aspects, also disclosed herein is a device comprising any of the disclosed single nonlinear optical crystals, any of the disclosed lasers, or any of the disclosed quantum light emitters.

[0012] In some aspects, also disclosed herein is a method of forming any of the disclosed single nonlinear optical crystals, the method comprising growing the single crystal from a polycrystalline material having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; and wherein n is 1 to 14.

[0013] In some aspects, also disclosed herein is a method of forming any of the disclosed single nonlinear optical crystals, the method comprising shrinking a crystallographic c-axis of a single crystal having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from any combination of La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu; and wherein n is 1 to 14.Attorney Docket No.11196-117WO1

[0014] Other systems, methods, features and / or advantages will be or may become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features and / or advantages be included within this description and be protected by the accompanying claims. BRIEF DESCRIPTION OF DRAWINGS

[0015] FIGURES 1A-1E depict EuBa3B9O18 (EBBO). FIG. 1A shows phonon dispersion relations for EuBa3B9O18 (EBBO). Unstable modes are shown in red. FIG.1B shows the structure of the experimentally determined P6^ phase showing thedisplacive disorder of the barium atoms. FIG.1C shows the structure of the P3 phase showing the atomic displacements with respect to the centrosymmetric P63 / m phase. The dark and clear balls represent the atoms in the P3 and in the P63 / m phase, respectively. FIGS.1D-1E show the same, for the P63 phase (FIG.1D) and the P1^phase.

[0016] FIGURES 2A-2C depict characterization of EBBO crystals. FIG.2A shows powder XRD pattern of polycrystalline EBBO. FIG.2B is an optical image of EBBO crystals grown using the floating-zone technique. FIG. 2C shows XRD patterns measured on the surface of a representative EBBO crystal.

[0017] FIGURES 3A-3C depict further characterization of EBBO. FIG.3A shows a transmittance spectrum of a single crystal EBBO. FIG.3B shows a Tauc plot of EBBO, indicating a direct bandgap of 5.56eV. Inset: Absorption coefficient of EBBO obtained from a polycrystalline pellet using ellipsometry. FIG.3C shows the complex ordinary and extraordinary refractive index of EBBO. The blue and orange curves represent the real and imaginary components, respectively.

[0018] FIGURES 4A-4C depict SHG characterization of EBBO. FIG.4A shows a schematic of the SHG polarimetry geometry. (b) Polar plots of p-polarized and s- polarized SHG intensities measured in normal reflection geometry at 800nm fundamental wavelength for extracting the ratio of d11 / d22 and the absolute values. The black curves are the theoretical fit based on point group 6^. FIG.4C shows SHG power dependency of EBBO crystal, confirming the detected signal was generated from the SHG process.Attorney Docket No.11196-117WO1

[0019] FIGURES 5A-5E depict Type I and Type II phase-matching. FIGS.5A-5B show Type I (FIG.5A) and Type II (FIG.5B) phase-matching angles as a function of wavelength. FIG.5C shows the definition of φ. FIG.5D shows deff for Type I and Type II phase-matching conditions as a function of φ at 800nm fundamental wavelength. FIG. 5E shows photoluminescent (PL) spectrum measured using 785 nm laser, showing no obvious PL signal.

[0020] FIGURES 6A-6E depict characterization of parent R1Ba3(B3O6)3 crystals. FIG.6A shows optical microscope images of the R1Ba3(B3O6)3 single crystals grown by the optical floating zone technique (R = Nd, Sm, Tb, Dy, and Er) (the scale bars are 2 mm). FIG. 6B shows powder x-ray diffraction spectrum of crushed single-crystal R1Ba3(B3O6)3 samples compared with the simulated pattern of ErBa3(B3O6)3. FIG.6C shows lattice parameters of R1Ba3(B3O6)3 obtained through the refinements for single- crystal x-ray diffraction data. FIG.6D shows θ-2θ x-ray diffraction spectrum collected from polished parallel slabs of the single crystals. FIG.6E shows the crystallographic structure of DyBa3(B3O6)3 determined from single crystal x-ray diffraction and refinement.

[0021] FIGURES 7A-7B depict further characterization of parent R1Ba3(B3O6)3 crystals. FIG.7A shows transmission of the parallel plate slab of R1Ba3(B3O6)3 crystals characterized by UV-vis and Fourier transform infrared spectroscopy. FIG.7B shows the absorption coefficient of the R1Ba3(B3O6)3 samples calculated through fitting the experimental transmission and reflection data at normal incidence. The labels 1 through 8 correspond to term symbols as follows: 1 ≡4D1 / 2 +4D3 / 2 +4D5 / 2 +2I11 / 2, 2 ≡2G9 / 2 +2D3 / 2 +4G3 / 2 +2K7 / 2, 3 ≡2K5 / 2 +4G7 / 2 +4G9 / 2, 4 ≡4G7 / 2 +4G5 / 2, 5 ≡6F3 / 2, 6 ≡6F9 / 2, 7 ≡6F7 / 2, and 8 ≡6F5 / 2.

[0022] FIGURE 8 depicts an emission spectrum of a R1Ba3(B3O6)3 sample in the range of 380–1000 nm under irradiation of 532 nm Nd:YAG laser.

[0023] FIGURES 9A-9C depict further characterization of R1Ba3(B3O6)3. FIGS.9A- 9B show the real part of ordinary (FIG. 9A) and extraordinary (FIG. 9B) refractive indices for the R1Ba3(B3O6)3 single crystals. FIG. 9C shows Tauc analysis for measuring the direct bandgap. FIG.9D shows the direct bandgap of the constituent borates calculated from the Tauc plot.

[0024] FIGURES 10A-10F depict SHG characterization. FIG. 10A shows the experimental configuration for the second harmonic generation measurement of the SmBa3(B3O6)3 single crystals. FIG.10B shows SHG intensity as a function of incidentAttorney Docket No.11196-117WO1 fundamental 800 nm laser intensity and fitted with quadratic equation. FIG.10C-10D show SHG polarimetry as a function of incident polarization for SmBa3(B3O6)3 (FIG. 10C) and DyBa3(B3O6)3 (FIG. 10D) samples. FIG.10E shows the nonlinear optical coefficient of R1Ba3(B3O6)3 crystal in comparison to other UV-C crystals. FIG. 10F shows Laser-induced surface damage threshold (LISDT) under irradiation of 100-fs, 1-KHz Ti: Sapphire laser compared with commercially utilized β-BaB2O4.

[0025] FIGURES 11A-11D depict Type I and Type II phase-matching of DyBa3B9O18. FIGS.11A-11B show Type-I (FIG.11A) and Type-II (FIG.11B) phase matching angles for the R1BBO single crystals. FIG. 11C is a depiction of the orientation of the angle φ. FIG.11D shows effective nonlinear optical coefficients, deff, for the DyBa3(B3O6)3 sample for both Type-I and Type-II conditions.

[0026] FIGURE 12 depicts the single crystal X-ray diffraction θ−2θ scan of ErBa3(B3O6)3 single crystal indicating the formation of twins.

[0027] FIGURES 13A-13D depict Laue diffraction pattern on the backscattering geometry of TbBa3(B3O6)3 (FIG.13A), ErBa3(B3O6)3 (FIG.13B), DyBa3(B3O6)3 (FIG. 13C), and SmBa3(B3O6)3 (FIG.13D) single crystals. The ErBa3(B3O6)3 single crystals indicate domain formation from the Laue backscattering geometry.

[0028] FIGURE 14 depicts powder X-ray diffraction spectrum (θ-2θ scan) (range of 20° to 70°) of single crystal R1Ba3(B3O6)3 samples compared with simulated data from the crystallographic index file refined using direct x ray method.

[0029] FIGURE 15 depicts an Energy-dispersive X-ray spectroscopy (EDS) spectrum of the R1Ba3(B3O6)3 single crystal sample at low vacuum. The peaks correspond to the X-ray emission energy of the constitutive elements.

[0030] FIGURES 16A-16E depict Energy-dispersive X-ray spectroscopy (EDS) mapping on the NdBa3(B3O6)3 single crystal sample. FIG. 16A shows an electron microscope image. FIG.16B shows boron K. FIG.16C shows neodymium M. FIG. 16D shows oxygen K. FIG.16E shows barium L. The levels are the excitation of the core electrons of the constituent atoms. Oxygen K is the excitation of the 1s core electron of an oxygen atom. The rare earth M shells are higher-energy electrons that transition to fill vacancies in the M-shell of rare earth atoms.

[0031] FIGURES 17A-17E depict Energy-dispersive X-ray spectroscopy (EDS) mapping on the SmBa3(B3O6)3 single crystal sample. FIG. 17A shows an electron microscope image. FIG.17B shows boron K. FIG.16C shows samarium M. FIG.17D shows oxygen K. FIG.17E shows barium L.Attorney Docket No.11196-117WO1

[0032] FIGURES 18A-18E depict Energy-dispersive X-ray spectroscopy (EDS) mapping on the TbBa3(B3O6)3 single crystal sample. FIG. 18A shows an electron microscope image. FIG.18B shows boron K. FIG.18C shows terbium M. FIG.18D shows oxygen K. FIG.18E shows barium L.

[0033] FIGURES 19A-19E depict Energy-dispersive X-ray spectroscopy (EDS) mapping on the DyBa3(B3O6)3 single crystal sample (arrows indicate region of inhomogeneity of the constituents). FIG.19A shows an electron microscope image. FIG.19B shows boron K. FIG.19C shows dysprosium M. FIG.19D shows oxygen O K. FIG.19E shows barium L.

[0034] FIGURES 20A-20E depict Energy-dispersive X-ray spectroscopy (EDS) mapping on the TbBa3(B3O6)3 single crystal sample. FIG. 20A shows an electron microscope image. FIG.20B shows boron K. FIG.20C shows erbium M. FIG.20D shows oxygen O K. FIG.20E shows barium L.

[0035] FIGURES 21A-21C depict Energy-dispersive X-ray spectroscopy (EDS) mapping on the DyBa3(B3O6)3 single crystal sample displaying two distinct regions of the surface. FIGS.21B-21C are the EDS spectra of the two distinct regions defined in red and blue, respectively.

[0036] FIGURES 22A-22C depict SHG measurements of TbBa3(B3O6)3 and NdBa3(B3O6)3. FIGS. 22A-22B show second harmonic generation polarimetry as a function of incident polarization for TbBa3(B3O6)3 (FIG.22A) and NdBa3(B3O6)3 (FIG. 22B) samples. FIG. 22C shows the experimental configuration for the second harmonic generation measurement of the Tb / NdBa3(B3O6)3 single crystals.

[0037] FIGURES 23A-23D depict effective nonlinear optical coefficient for the NdBa3(B3O6)3 (FIG. 23A), TbBa3(B3O6)3 (FIG. 23B), and DyBa3(B3O6)3 (FIG. 23C) single crystal samples.

[0038] FIGURE 24 depicts second harmonic generation polarimetry as a function of incident polarization for a z-cut LiNbO3 single crystal sample.

[0039] FIGURES 25A-25B depict optical microscope images of the polished DyBa3(B3O6)3 single crystal surface before (FIG. 25A) and after (FIG. 25B) the irradiation of 1Khz 100fs laser (800 GW / cm2intensity) .

[0040] FIGURE 26 depicts a single crystal rod from the floating zone growth of NdBa3(B3O6)3 (the squares have a dimension of 1mm x 1mm).

[0041] FIGURES 27A-27C depict characterization of Ra5, Rb5, and R6crystals. FIG. 27A shows the powder X-ray diffraction pattern of the Ra5Attorney Docket No.11196-117WO1 ((NdTbSmDyEr)0.2Ba3(B3O6)3), Rb5((NdTbSmDyYb)0.2Ba3(B3O6)3), and R6((NdTbGdDyErYb)0.16Ba3(B3O6)3) single crystals. FIG.27B shows the Laue diffraction pattern of R6((NdTbGdDyErYb)0.16Ba3(B3O6)3) single crystal and the fitted crystallographic orientation. FIG. 27C shows EDS spectrum mapping of the R6((NdTbGdDyErYb)0.16Ba3(B3O6)3) single crystal sample. The scale bar on the bottom left is 200 µm.

[0042] FIGURES 28A-28B depict XPS fitting of ((NdTbGdDyErYb)0.16Ba3(B3O6)3) single crystals sample for Er 4d, Dy 4d, Gd 4d, Sm 4d and Nd 4d (FIG.28A), and for B 1s, Yb 4d and Ba 4p (FIG.28B).

[0043] FIGURES 29A-29D depict further characterization of Ra5, Rb5, and R6crystals. FIG.29A shows a transmission spectrum from UV-vis spectroscopy of Ra5((NdTbSmDyEr)0.2Ba3(B3O6)3), Rb5((NdTbSmDyYb)0.2Ba3(B3O6)3), and R6((NdTbGdDyErYb)0.16Ba3(B3O6)3) samples. FIG. 29B shows Tauc plot analysis to delineate the direct bandgap of the high entropy samples. FIG.29C shows real and imaginary parts of the refractive index of the high entropy single crystals. FIG.29D shows the emission spectrum of the high entropy single crystals characterized under 532 nm Nd: YAG laser irradiation.

[0044] FIGURES 30A-30E depict SHG measurements. FIG. 30A shows the experimental configuration for the second harmonic generation measurement of the (NdTbSmDyEr)0.2Ba3(B3O6)3 single crystal sample. FIG. 30C-30D show SHG polarimetry as a function of incident polarization for (NdTbSmDyEr)0.2Ba3(B3O6)3 single crystal.

[0045] FIGURES 31A-31D depict characterization of the DyBa3(B3O6)3 single crystal. FIG.31A shows the SHG enhanced region in the DyBa3(B3O6)3 single crystal and the subsequent SHG mapping. The inset shows the region's optical microscope image. FIG.31B shows a PE loop measurement on the DyBa3(B3O6)3 single crystal showing no saturation polarization. The different datasets were on different samples. FIGS.31C-31D show SHG polarimetry fitting on the reflection geometry for region 1 and region 2 (defined in FIG.31A). In the fitting for region 1, two orthogonal analyzer directions, X and Y, were considered to generate unique fitting conditions.

[0046] FIGURES 32A-32E depict nonlinear optical (NLO) materials in the deep- ultraviolet (UV-C) region evaluated for their spectral properties, design strategies, and functional performance. FIG. 32A shows the traditionally utilized NLO crystals between 100nm and 260nm, with arrows marking the absorption edges. FIG. 32BAttorney Docket No.11196-117WO1 shows the design principles for UV-C NLO single crystals, focusing on transparency, frequency conversion efficiency, ease of growth, and phase matchability. FIG.32C shows the SHG coefficients and laser-induced surface damage thresholds (LISDT) of selected UV-C materials, illustrating the balance between nonlinearity and damage resistance. FIG. 32D shows a crystallographic framework for high-entropy oxides based on a rare-earth borate unit cell, showcasing the motif position variations in a higher configurational entropy system. The Shannon-Prewitt ionic radius for the rare earth in tetrahedral coordination geometry decreases with higher f-orbital occupancy. FIG.32E shows typical laser media between the UV-C and NIR regions, with arrows marking the emission wavelength. In addition, the emission lines observed for the high-entropy borate have been marked with a red arrow indicating multimodal emission potential.

[0047] FIGURES 33A-33N depict crystallographic structure and experimental X- ray characterization of high-entropy rare-earth borates, RnBa3(B3O6)3. FIG.33A shows the average unit cell of the high-entropy borate structure, highlighting the presence of an average mirror symmetry element when the Ba site is disordered as shown by split Ba atoms across the average mirror plane. Stochastic fluctuations in this disorder will however break the mirror symmetry on a local scale. FIG.33B shows an alternative projection of the unit cell, emphasizing the spatial arrangement of the constituent atoms. The lower subpanel isolates the boron–oxygen bonding network, revealing planar hexagonal motifs characteristic of the borate layers. FIG. 33C shows the polyhedral representation of the RnBa3(B3O6)3 high-entropy oxide framework, providing insight into the local coordination environments. FIG.33D shows powder X- ray diffraction data for multiple high-entropy borate compositions, alongside simulated patterns derived from structural models. FIG. 33E shows Laue backscattered diffraction pattern demonstrating excellent agreement between experimental and simulated patterns. FIG. 33F shows high-resolution θ-2θ X-ray diffraction data collected from a single-crystal sample with a z-cut orientation. FIG.33G shows lattice parameter of the monolithic compounds compared with the high entropy oxides. FIG. 33H shows reciprocal space mapping (RSM) of the (0008) peak for the R6compound by hard x-ray nano probe experiment. FIG. 33I shows scanning diffraction X-ray microscopy measurement indicating variation of the lattice parameter across 110 µm region to be smaller than 5 × 10−5for single crystal R6compound. FIG.33J shows EDS elemental maps for the rare-earth elements, R, as well as Ba and B, whoseAttorney Docket No.11196-117WO1 spatially uniform intensities attest to the chemical homogeneity. Scale bar is 200 μm. FIG.33K shows an image of the crystal boule with a backdrop of white paper with grids. The scale bar is 3 mm. FIGS.33L-33N show core-level XPS spectra for B 1s, O 1s, Er 4d, Tb 4d, Nd 4d, Sm 4d, Dy 4d; each spectrum is deconvoluted to show individual rare earth peak envelopes.

[0048] FIGURES 34A-34M depict high resolution STEM investigation of the rare earth high entropy oxide depicting crystallography, structure, disorder, and the anisotropic thermal expansion quantified by temperature dependent X-ray. FIG.34A shows atomic-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of a single crystal R6Ba3(B3O6)3 along the [101^0] zone axis. The

[0001] and [1^21^0] directions have been highlighted. FIG.34B shows a magnified view of the boxed region in FIG.34A. FIG.34C shows a simulated high- angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of corresponding region and zone axis in FIG.34B, but based on the structure of DyBa3(B3O6)3. FIG. 34D shows an illustration of the atomic structure of R1Ba3(B3O6)3 projected along the [101^0] zone axis, where R can be replaced by Dy / Nd / Sm / Gd / Er / Yb elements. FIG. 34E shows overlaid FIG. 34A and the corresponding displacement vectors of R-site atomic columns using the Dy atomic columns in the pristine DyBa3(B3O6)3 structure as a zero-displacement reference. The vectors are enlarged by 10 × for enhancing visibility. FIGS.34F-34G show averaged HAADF-STEM images of single Ba atom columns and Ba dumbbell columns extracted from FIG.34A, accompanied by Gaussian fits of the intensity profiles along the

[0001] direction. The full width half maximum (FWHM) values are shown next to the corresponding intensity profiles. FIGS. 34H-34J Integrated intensities of representative reflections for the three high-entropy compositions as the temperature is ramped from 25°C to 600°C. The specular (000l) peaks undergo a pronounced change with temperature, whereas in-plane (h k 0) reflections remain essentially invariant, indicating that the dominant structural response is confined along the c-axis. FIG. 34K shows evolution of the c lattice parameter derived from the (0 0 0 l) reflections, revealing a substantial positive thermal expansion. By contrast, FIG.34L shows that the average in-plane a–b lattice parameter varies only marginally over the same temperature range. FIG. 34M shows the c-axis linear thermal-expansion coefficients of the high-entropy borates with those of their parent compound end-Attorney Docket No.11196-117WO1 members and with the benchmark nonlinear-optical crystal β-BaB2O4 (BBO). The comparable magnitudes highlight a pronounced anisotropy akin to that of BBO.

[0049] FIGURES 35A-35L depict linear optical properties of rare-earth high- entropy borate crystals. FIG.35A shows room temperature transmittance spanning the UV-C to near infrared (≈ 190 nm - 5 μm) shows negligible absorption for high entropy borate across the entire spectral window relevant to nonlinear-optical applications. The result shows an improvement of the transparency for the high entropy compounds in comparison to the parent compounds. FIG.35B shows a Tauc plot to derive the optical bandgap for the high entropy borates using the Kubelka-Munk (K-M) function. FIG.35C shows the bandgap between the parent and the high entropy compounds, showing a decrease in the bandgap relative to a single rare-earth crystal, indicating the possibility for compositional engineering of electronic bandgap tunability. FIGS. 35D-35E show wavelength-dependent ordinary (no) and extraordinary (ne) refractive indices for the three high entropy compositions. In all cases no > ne, confirming a negative-uniaxial character over the measured range. FIGS.35F-35G show the photoluminescence response from the bulk sample in the visible and NIR spectrum shows strong and sharp emission bands originating from the individual rare- earth elements. FIGS.35H-35L show the energy levels of different bands showcase the absorption and emission of the rare earth elements.

[0050] FIGURES 36A-36B depict EDS spectrum of the Ra5, Rb5, and R6compounds at low vacuum where subscripts a and b label two different compositions. The emission energy for the constituent elements is seen in the photoluminescence spectrum.

[0051] FIGURES 37A-37H depict EPMA mapping of the individual elements for the Ra5single crystal samples.

[0052] FIGURES 38A-38H depict EPMA mapping of the individual elements for the Rb5single crystal samples.

[0053] FIGURES 39A-39I depict EPMA mapping of the individual elements for the R6single crystal samples.

[0054] FIGURES 40A-40B depict the X-ray diffraction pattern for the drop-cast and spin-coated films of the R6sample, showing the powder X-ray diffraction pattern for the reference R6 sample compared with the drop-cast and spin-coated films. The data reveals confirms the phase purity of the film and lack of phase segregation upon solution treatment.Attorney Docket No.11196-117WO1

[0055] FIGURES 41A-41C depict processing on the R6single crystal HAADF- STEM imaging, showing a schematic illustration of the process used to generate the A -site displacement vector map.

[0056] FIGUERS 42A-42C depict characterization of R6Ba3(B3O6)3. FIG. 42A shows the intensity of the Bragg reflection for the high-entropy R6Ba3(B3O6)3 powder sample at different temperatures. FIG.42B shows that lattice parameters change as a function of temperature. FIG.42C shows SHG intensity as a function of temperature for the binary and high-entropy compounds.

[0057] FIGURS 43A-43B depict refractive index comparison between the bulk and the M phase. FIG.43A shows the ordinary part of the refractive index for the bulk and the M phase across UV-C and visible range. FIG.43B shows the refractive index of the M phase at different rotation angles with respect to the crystallographic c-axis. The hexagonal crystal system, similar to the parent phase, should have in-plane isotropy, which means the refractive index in the a-b plane should not change. By that implication, a change in index (in plane) is a direct indication of the symmetry lowering. The inset showcases an angle γ, which is the intersection between the plane of incidence and the a-b crystallographic plane. The measurement was conducted for R6Ba3(B3O6)3 ((NdTbGdDyErYb)0.16Ba3(B3O6)3) sample.

[0058] FIGURES 44A-44D depict cross-sectional four-dimensional scanning transmission electron microscopy (4D-STEM) analysis of a laser processed R6Ba3(B3O6)3 ((NdTbGdDyErYb)0.16Ba3(B3O6)3) sample interface sample along the [101^0] zone axis, where A can be replaced by Dy / Nd / Sm / Gd / Er / Yb elements. FIG. 44A shows a virtual dark-field image of the R6Ba3(B3O6)3 ((NdTbGdDyErYb)0.16Ba3(B3O6)3) sample cross section. The region to the right of yellow dotted line indicates the laser-processed area. An amorphous region is observed beneath the crystalline region across the sample, although portion of the beneath region is crystalline structure in the laser-processed part, as indicated by yellow annotations. Scale bar: 500 nm. FIG.44B shows the diffraction pattern from a reference R6Ba3(B3O6)3 sample (unprocessed) along the [101^0] zone axis. FIGS.44C- 44D show diffraction patterns obtained from the most on-zone areas on the left and right sides of the interface sample, respectively. The angles between the

[0001] and [121^0] directions are 89.95°, 89.57°, 89.51° for FIGS.44B-44D, respectively. Scale bars in FIGS.44B-44D: 5 nm-1.Attorney Docket No.11196-117WO1

[0059] FIGURES 45A-45D depict transmission electron microscopy (HAADF- STEM) images of R6Ba3(B3O6)3. FIGURES 45A-45B show atomic-resolution high- angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images of single crystalline of R6Ba3(B3O6)3 along the [101^0] zone axis from the left (no laser) and right (laser-processed) regions of the interface shown in FIG.45A. The

[0001] and [1^21^0] directions have been highlighted. FIGS.45C-45D show overlays of FIGS.45A-45B and the corresponding displacement vectors of A-site atomic columns using the average R-site atomic column locations as a zero-displacement reference. The vectors are enlarged by 30X to enhance visibility. The scale bars in FIGS.45A- 45D are 1 nm.

[0060] FIGURES 46A-46D depict further SHG characterization. FIG.46A shows experimental geometry of the second harmonic generation microscopy from 800nm to 400nm photons. FIG.46B shows SHG mapping of the high entropy compound with an enhanced region identified. FIG.46C shows SHG intensity across the defined line in the panel is missing the enhanced region. FIG.46D shows SHG polarimetry of the unwritten and written regions.

[0061] FIGURES 47A-47C depict experimental configuration for the tabletop SHG measurement of the high entropy single crystal sample. FIGS.47A-47B show SHG polarimetry fitting for different experimental configuration considering the low symmetry M phase. FIG.47C shows the effective nonlinear optical coefficient as a function of bandgap for the UV-C materials.

[0062] FIGURES 48A-48B depict an SHG microscopy image of the large written phase of the bulk high entropy oxide. The white line indicates a 10 µm region. Scale bar is hidden.

[0063] FIGURES 49A-49C depict transmission and transparency characterization. FIG.49A shows UV-Visible spectroscopy showing transmission spectrum for the high entropy and the binary compounds in the spectral range of 200 nm to 2000 nm. FIG. 49B shows the transparency window of the binary and the high entropy compound. The lines showing the spectral ranges at which the samples are transparent. FIG.49C shows an FTIR spectrum of the high entropy oxide showcasing a broad transparency window up to 3500 nm.Attorney Docket No.11196-117WO1 DETAILED DESCRIPTION

[0064] 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 with 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. 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. Methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present disclosure. DEFINITIONS

[0065] 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.

[0066] 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.

[0067] 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.

[0068] 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 specification and in the claims which follow, reference will be made to a number of terms that shall be defined herein.

[0069] 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.Attorney Docket No.11196-117WO1

[0070] 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.

[0071] 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.”

[0072] 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 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.

[0073] 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.

[0074] 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 theAttorney Docket No.11196-117WO1 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.

[0075] 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.

[0076] 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”).

[0077] As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0078] 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, 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.

[0079] 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.

[0080] 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.Attorney Docket No.11196-117WO1

[0081] 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.

[0082] 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.

[0083] 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. SINGLE NONLINEAR OPTICAL CRYSTALS

[0084] In some aspects, disclosed herein is a single nonlinear optical crystal having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof.Attorney Docket No.11196-117WO1

[0085] In some aspects, n can be 1 or more (e.g., 2 or more, 3 or more, 4 or more, 5 or more, 6 or more, 7 or more, 8 or more, 9 or more, 10 or more, 11 or more, 12 or more, 13 or more). In some aspects, n can be 14 or less (e.g., 13 or less, 12 or less, 11 or less, 10 or less, 9 or less, 8 or less, 7 or less, 6 or less, 5 or less, 4 or less, 3 or less, 2 or less).

[0086] It is considered that n can be any value ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, n can be 1 to 14 (e.g., 2 to 14, 3 to 14, 4 to 14, 5 to 14, 6 to 14, 7 to 14, 8 to 14, 9 to 14, 10 to 14, 11 to 14, 12 to 14, 1 to 10, 1 to 9, 1 to 8, 1 to 7, 1 to 6, 1 to 5, 2 to 10, 2 to 9, 2 to 8, 2 to 7, 2 to 6, 2 to 5). In some aspects, n can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, or 14.

[0087] In some aspects, n can be 1, and R can be Eu, Nd, Sm, Tb, or Dy.

[0088] In some aspects, n can be greater than 1, and R can be any combination of Nd, Sm, Tb, Dy, Er, Gd, and Yb. For example, in some aspects, n can be 5 and R can be: a) Nd, Tb, Sm, Dy, and Er; or b) Nd, Tb, Sm, Dy, and Yb. As another example, in some aspects, n can be 6 and R can be Nd, Sm, Dy, Gd, Yb, and Er.

[0089] In some aspects, each rare earth element in R can be present in a substantially equal mole fraction (e.g., at least about 80% equal, at least about 85% equal, at least about 90% equal, at least about 91% equal, at least about 92% equal, at least about 93% equal, at least about 94% equal, at least about 95% equal, at least about 96% equal, at least about 97% equal, at least about 98% equal, at least about 99% equal, or about 100% equal).

[0090] In some aspects, the lattice parameters a and / or b can each independently have a length of 7 Å or more (e.g., 7.05 Å or more, 7.1 Å or more, 7.15 Å or more, 7.2 Å or more, 7.25 Å or more, 7.3 Å or more, 7.35 Å or more, 7.4 Å or more, 7.45 Å or more, 7.5 Å or more). In some aspects, the lattice parameters a and / or b can each independently have a length of 7.5 Å or less (e.g., 7.45 Å or less, 7.4 Å or less, 7.35 Å or less, 7.3 Å or less, 7.25 Å or less, 7.2 Å or less, 7.15 Å or less, 7.1 Å or less, 7.05 Å or less, 7 Å or less).

[0091] The lattice parameters a and / or b can each independently have a length ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the lattice parameters a and / or b can each independently have a length of from 7 Å to 7.5 Å (e.g., from 7.05 Å to 7.45 Å, from 7.1 Å to 7.4 Å, from 7.15 Å to 7.35 Å, from 7.2 Å to 7.3 Å, from 7 Å toAttorney Docket No.11196-117WO1 7.25 Å, from 7.05 Å to 7.2 Å, from 7.1 Å to 7.15 Å, from 7.25 Å to 7.5 Å, from 7.3 Å to 7.45 Å, from 7.35 Å to 7.4 Å). In some aspects, the length of the lattice parameters a and / or b can be the same or different.

[0092] In some aspects, the crystal can have a non-centrosymmetric crystal structure. Importantly, this can allow the crystal to exhibit second harmonic generation (SHG). This, in combination with the high bandgap and high laser-induced surface damage threshold (LISDT) of the crystal, allows the crystal to be used for significantly higher power applications than conventional nonlinear optical crystals.

[0093] In some aspects, the crystal can exhibit a second harmonic generation (SHG) coefficient of 0.2 pm / V or more (e.g., 0.3 pm / V or more, 0.4 pm / V or more, 0.5 pm / V or more, 1 pm / V or more, 1.5 pm / V or more, 2 pm / V or more, 3 pm / V or more, 4 pm / V or more, 5 pm / V or more, 10 pm / V or more, 15 pm / V or more, 20 pm / V or more, 30 pm / V or more, 40 pm / V or more, 50 pm / V or more, 60 pm / V or more, 70 pm / V or more, 80 pm / V or more, 90 pm / V or more, 100 pm / V or more, 125 pm / V or more, 150 pm / V or more, 175 pm / V or more, 200 pm / V or more). In some aspects, the crystal can exhibit a SHG coefficient of 200 pm / V or less (e.g., 175 pm / V or less, 150 pm / V or less, 125 pm / V or less, 100 pm / V or less, 90 pm / V or less, 80 pm / V or less, 70 pm / V or less, 60 pm / V or less, 50 pm / V or less, 40 pm / V or less, 30 pm / V or less, 20 pm / V or less, 15 pm / V or less, 10 pm / V or less, 5 pm / V or less, 4 pm / V or less, 3 pm / V or less, 2 pm / V or less, 1.5 pm / V or less, 1 pm / V or less, 0.5 pm / V or less, 0.4 pm / V or less, 0.3 pm / V or less, 0.2 pm / V or less).

[0094] The crystal can exhibit a SHG coefficient ranging from any of the minimum values described above. For example, in some aspects, the crystal can exhibit a SHG coefficient of from 0.2 pm / V to 200 pm / V (e.g., from 0.3 pm / V to 175 pm / V, from 0.4 pm / V to 150 pm / V, from 0.5 pm / V to 125 pm / V, from 1 pm / V to 100 pm / V, from 1.5 pm / V to 90 pm / V, from 2 pm / V to 80 pm / V, from 3 pm / V to 70 pm / V, from 4 pm / V to 60 pm / V, from 5 pm / V to 50 pm / V, from 10 pm / V to 40 pm / V, from 15 pm / V to 30 pm / V, from 0.2 pm / V to 20 pm / V, from 0.3 pm / V to 15 pm / V, from 0.4 pm / V to 10 pm / V, from 0.5 pm / V to 5 pm / V, from 1 pm / V to 4 pm / V, from 1.5 pm / V to 3 pm / V, from 20 pm / V to 200 pm / V, from 30 pm / V to 175 pm / V, from 40 pm / V to 150 pm / V, from 50 pm / V to 125 pm / V, from 60 pm / V to 100 pm / V, from 70 pm / V to 90 pm / V).

[0095] In some aspects, the SHG coefficient of the crystal can be greater than an SHG coefficient of a commercially available BaB2O4 crystal. This can occur for a variety of crystals described herein, and has particularly been observed for crystalsAttorney Docket No.11196-117WO1 exhibiting an M phase, potentially because the M phase lacks barium positional disorder. Instead, the barium atoms in different unit cells appear to displace in an ordered manner in the same direction, which can induce a large nonlinear polarization, leading to large SHG enhancement.

[0096] In some aspects, the SHG coefficient of the crystal can be 10 or more times greater (e.g., 20 or more, 30 or more, 40 or more, 50 or more, 60 or more, 70 or more, 80 or more, 90 or more, 100 or more) than an SHG coefficient of a commercially available BaB2O4 crystal. In some aspects, the SHG coefficient of the crystal can be 100 or less times greater (e.g., 90 or less, 80 or less, 70 or less, 60 or less, 50 or less, 40 or less, 30 or less, 20 or less, 10 or less) than an SHG coefficient of a commercially available BaB2O4 crystal

[0097] The SHG coefficient of the crystal can be any amount greater than an SHG coefficient of a commercially available BaB2O4 crystal ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the SHG coefficient of the crystal can be 10 to 100 times greater (e.g., from 20 to 90, from 30 to 80, from 40 to 70, from 50 to 60, from 10 to 60, from 20 to 50, from 30 to 40, from 50 to 100, from 60 to 90, from 70 to 80) than an SHG coefficient of a commercially available BaB2O4 crystal.

[0098] In some aspects, RnBa3(B3O6)3 can have a bandgap of 4 eV or more (e.g., 4.25 eV or more, 4.5 eV or more, 4.75 eV or more, 5 eV or more, 5.25 eV or more, 5.5 eV or more, 5.75 eV or more, 6 eV or more, 6.25 eV or more, 6.5 eV or more). In some aspects, RnBa3(B3O6)3 can have a bandgap of 6.5 eV or less (e.g., 6.25 eV or less, 6 eV or less, 5.75 eV or less, 5.5 eV or less, 5.25 eV or less, 5 eV or less, 4.75 eV or less, 4.5 eV or less, 4.25 eV or less, 4 eV or less).

[0099] RnBa3(B3O6)3 can have a bandgap ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, RnBa3(B3O6)3 can have a bandgap of from 4 eV to 6.5 eV (e.g., from 4.25 eV to 6.25 eV, from 4.5 eV to 6 eV, from 4.75 eV to 5.75 eV, from 5 eV to 5.5 eV, from 4 eV to 5.25 eV, from 4.25 eV to 5 eV, from 4.5 eV to 4.75 eV, from 5.25 eV to 6.5 eV, from 5.5 eV to 6.25 eV, from 5.75 eV to 6 eV).

[0100] In some aspects, RnBa3(B3O6)3 can exhibit a laser-induced surface damage threshold (LISDT) of 400 GW / cm2or more (e.g., 450 GW / cm2or more, 500 GW / cm2or more, 550 GW / cm2or more, 600 GW / cm2or more, 650 GW / cm2or more, 700 GW / cm2or more, 750 GW / cm2or more, 800 GW / cm2or more, 850 GW / cm2or more,Attorney Docket No.11196-117WO1 900 GW / cm2or more, 950 GW / cm2or more, 1000 GW / cm2or more) for laser pulses of from 100 fs to 300 fs wide in a wavelength range of from 300 nm to 3000 nm. In some aspects, RnBa3(B3O6)3 can exhibit a LISDT of 1000 GW / cm2or less (e.g., 950 GW / cm2or less, 900 GW / cm2or less, 850 GW / cm2or less, 800 GW / cm2or less, 750 GW / cm2or less, 700 GW / cm2or less, 650 GW / cm2or less, 600 GW / cm2or less, 550 GW / cm2or less, 500 GW / cm2or less, 450 GW / cm2or less, 400 GW / cm2or less) for laser pulses of from 100 fs to 300 fs wide in a wavelength range of from 300 nm to 3000 nm.

[0101] RnBa3(B3O6)3 can exhibit a LISDT ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, RnBa3(B3O6)3 can exhibit a LISDT of from 400 GW / cm2to 1000 GW / cm2(e.g., from 450 GW / cm2to 950 GW / cm2, from 500 GW / cm2to 900 GW / cm2, from 550 GW / cm2to 850 GW / cm2, from 600 GW / cm2to 800 GW / cm2, from 650 GW / cm2to 750 GW / cm2, from 400 GW / cm2to 700 GW / cm2, from 450 GW / cm2to 650 GW / cm2, from 500 GW / cm2to 600 GW / cm2, from 700 GW / cm2to 1000 GW / cm2, from 750 GW / cm2to 950 GW / cm2, from 800 GW / cm2to 900 GW / cm2) for laser pulses of from 100 fs to 300 fs wide in a wavelength range of from 300 nm to 3000 nm.

[0102] In some aspects, RnBa3(B3O6)3 can exhibit a LISDT of from 400 GW / cm2to 1000 GW / cm2for laser pulses of 100 fs or more wide (e.g., 125 fs or more, 150 fs or more, 175 fs or more, 200 fs or more, 225 fs or more, 250 fs or more, 275 fs or more, 300 fs or more) in a wavelength range of from 300 nm to 3000 nm. In some aspects, RnBa3(B3O6)3 can exhibit a LISDT of from 400 GW / cm2to 1000 GW / cm2for laser pulses of 300 fs or less wide (e.g., 275 fs or less, 250 fs or less, 225 fs or less, 200 fs or less, 175 fs or less, 150 fs or less, 125 fs or less, 100 fs or less) in a wavelength range of from 300 nm to 3000 nm.

[0103] RnBa3(B3O6)3 can exhibit a LISDT of from 400 GW / cm2to 1000 GW / cm2for laser pulses of a width ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, In some aspects, RnBa3(B3O6)3 can exhibit a LISDT of from 400 GW / cm2to 1000 GW / cm2for laser pulses of from 100 fs to 300 fs wide (e.g., from 125 fs to 275 fs, from 150 fs to 250 fs, from 175 fs to 225 fs, from 100 fs to 200 fs, from 125 fs to 175 fs, from 200 fs to 300 fs, from 225 fs to 275 fs) in a wavelength range of from 300 nm to 3000 nm.

[0104] In some aspects, RnBa3(B3O6)3 can exhibit a LISDT of from 400 GW / cm2to 1000 GW / cm2for laser pulses of from 100 fs to 300 fs wide in a wavelength range ofAttorney Docket No.11196-117WO1 300 nm or more (e.g., 350 nm or more, 400 nm or more, 450 nm or more, 500 nm or more, 600 nm or more, 700 nm or more, 800 nm or more, 900 nm or more, 1000 nm or more, 1250 nm or more, 1500 nm or more, 1750 nm or more, 2000 nm or more, 2500 nm or more, 3000 nm or more). In some aspects, RnBa3(B3O6)3 can exhibit a LISDT of from 400 GW / cm2to 1000 GW / cm2for laser pulses of from 100 fs to 300 fs wide in a wavelength range of 3000 nm or less (e.g., 2500 nm or less, 2000 nm or less, 1750 nm or less, 1500 nm or less, 1250 nm or less, 1000 nm or less, 900 nm or less, 800 nm or less, 700 nm or less, 600 nm or less, 500 nm or less, 450 nm or less, 400 nm or less, 350 nm or less, 300 nm or less).

[0105] RnBa3(B3O6)3 can exhibit a LISDT of from 400 GW / cm2to 1000 GW / cm2for laser pulses of from 100 fs to 300 fs wide in a wavelength range from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, RnBa3(B3O6)3 can exhibit a LISDT of from 400 GW / cm2to 1000 GW / cm2for laser pulses of from 100 fs to 300 fs wide in a wavelength range of from 300 nm to 3000 nm (e.g., from 350 nm to 2500 nm, from 400 nm to 2000 nm, from 450 nm to 1750 nm, from 500 nm to 1500 nm, from 600 nm to 1250 nm, from 700 nm to 1000 nm, from 800 nm to 900 nm, from 300 nm to 900 nm, from 350 nm to 800 nm, from 400 nm to 700 nm, from 450 nm to 600 nm, from 800 nm to 3000 nm, from 900 nm to 2500 nm, from 1000 nm to 2000 nm, from 1250 nm to 1750 nm).

[0106] In some aspects, RnBa3(B3O6)3 can exhibit a LISDT that is higher than a LISDT of a commercially available BaB2O4 crystal. This high LISDT allows the crystals to be used in applications where higher laser damage threshold is needed without damage, which can improve the utility and efficiency of the crystals (particularly for frequency conversion and parametric amplification).

[0107] In some aspects, RnBa3(B3O6)3 can exhibit a LISDT that is 2 or more times higher (e.g., 2.5 or more, 3 or more, 3.5 or more, 4 or more, 4.5 or more, 5 or more, 5.5 or more, 6 or more) than a LISDT of a commercially available BaB2O4 crystal. In some aspects, RnBa3(B3O6)3 can exhibit a LISDT that is 6 or less times higher (e.g., 5.5 or less, 5 or less, 4.5 or less, 4 or less, 3.5 or less, 3 or less, 2.5 or less, 2 or less) than a LISDT of a commercially available BaB2O4 crystal.

[0108] RnBa3(B3O6)3 can exhibit a LISDT that is higher than a LISDT of a commercially available BaB2O4 crystal by any amount ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, RnBa3(B3O6)3 can exhibit a LISDT that is from 2 to 6 timesAttorney Docket No.11196-117WO1 higher (e.g., from 2.5 to 5.5, from 3 to 5, from 3.5 to 4.5, from 2 to 4, from 2.5 to 3.5, from 4 to 6, from 4.5 to 5.5) than a LISDT of a commercially available BaB2O4 crystal.

[0109] In some aspects, RnBa3(B3O6)3 can have an absorption coefficient α (1 / mm) of less than 0.3 (e.g., less than 0.29, less than 0.28, less than 0.27, less than 0.26, less than 0.25, less than 0.24, less than 0.23, less than 0.22, less than 0.21, less than 0.2, less than 0.19, less than 0.18, less than 0.17, less than 0.16, less than 0.15, less than 0.14, less than 0.13, less than 0.12, less than 0.11, less than 0.1, less than 0.09, less than 0.08, less than 0.07, less than 0.06, less than 0.05, less than 0.04, less than 0.03, less than 0.02, less than 0.01) in the visible and / or UV-C region (e.g., from 250 nm to 3200 nm).

[0110] In some aspects, RnBa3(B3O6)3 can have an absorption coefficient α (1 / mm) of less than 0.3 in a wavelength range of 250 nm or more (e.g., 300 nm or more, 350 nm or more, 400 nm or more, 500 nm or more, 600 nm or more, 800 nm or more, 1000 nm or more, 1200 nm or more, 1400 nm or more, 1600 nm or more, 1800 nm or more, 2000 nm or more, 2200 nm or more, 2400 nm or more, 2600 nm or more, 2800 nm or more, 3000 nm or more, 3200 nm or more). In some aspects, RnBa3(B3O6)3 can have an absorption coefficient α (1 / mm) of less than 0.3 in a wavelength range of 3200 nm or less (e.g., 3000 nm or less, 2800 nm or less, 2600 nm or less, 2400 nm or less, 2200 nm or less, 2000 nm or less, 1800 nm or less, 1600 nm or less, 1400 nm or less, 1200 nm or less, 1000 nm or less, 800 nm or less, 600 nm or less, 500 nm or less, 400 nm or less, 350 nm or less, 300 nm or less, 250 nm or less).

[0111] RnBa3(B3O6)3 can have an absorption coefficient α (1 / mm) of less than 0.3 in a wavelength range of from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, RnBa3(B3O6)3 can have an absorption coefficient α (1 / mm) of less than 0.3 in a wavelength range of from 250 nm to 3200 nm (e.g., from 300 nm to 3000 nm, from 350 nm to 2800 nm, from 400 nm to 2600 nm, from 500 nm to 2400 nm, from 600 nm to 2200 nm, from 800 nm to 2000 nm, from 1000 nm to 1800 nm, from 1200 nm to 1600 nm, from 250 nm to 1400 nm, from 300 nm to 1200 nm, from 350 nm to 1000 nm, from 400 nm to 800 nm, from 500 nm to 600 nm, from 1400 nm to 3200 nm, from 1600 nm to 3000 nm, from 1800 nm to 2800 nm, from 2000 nm to 2600 nm, from 2200 nm to 2400 nm).

[0112] In some aspects, the crystal can exhibit a transparency of greater than 60% (e.g., 65% or more, 70% or more, 75% or more, 80% or more, 85% or more, 90% or more, 95% or more, 100% or more) in a wavelength range of from 225 nm to 3200Attorney Docket No.11196-117WO1 nm. In some aspects, the crystal can exhibit a transparency of 100% or less (e.g., 95% or less, 90% or less, 85% or less, 80% or less, 75% or less, 70% or less, 65% or less) in a wavelength range of from 225 nm to 3200 nm.

[0113] The crystal can exhibit a transparency ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the crystal can exhibit a transparency of greater than 60% to 100% (e.g., from 65% to 95%, from 70% to 90%, from 75% to 85%, greater than 60% to 80%, from 65% to 75%, from 80% to 100%, from 85% to 95%) in a wavelength range of from 225 nm to 3200 nm.

[0114] In some aspects, the crystal can exhibit a transparency of greater than 60% to 100% in a wavelength range of 225 nm or more (e.g., 250 nm or more, 300 nm or more, 350 nm or more, 400 nm or more, 500 nm or more, 600 nm or more, 800 nm or more, 1000 nm or more, 1200 nm or more, 1400 nm or more, 1600 nm or more, 1800 nm or more, 2000 nm or more, 2200 nm or more, 2400 nm or more, 2600 nm or more, 2800 nm or more, 3000 nm or more, 3200 nm or more). In some aspects, the crystal can exhibit a transparency of greater than 60% to 100% in a wavelength range of 3200 nm or less (e.g., 3000 nm or less, 2800 nm or less, 2600 nm or less, 2400 nm or less, 2200 nm or less, 2000 nm or less, 1800 nm or less, 1600 nm or less, 1400 nm or less, 1200 nm or less, 1000 nm or less, 800 nm or less, 600 nm or less, 500 nm or less, 400 nm or less, 350 nm or less, 300 nm or less, 250 nm or less, 225 nm or less).

[0115] The crystal can exhibit a transparency of greater than 60% to 100% in a wavelength range of from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the crystal can exhibit a transparency of greater than 60% to 100% in a wavelength range of from 225 nm to 3200 nm (e.g., from 250 nm to 3000 nm, from 300 nm to 2800 nm, from 350 nm to 2600 nm, from 400 nm to 2400 nm, from 500 nm to 2200 nm, from 600 nm to 2000 nm, from 800 nm to 1800 nm, from 1000 nm to 1600 nm, from 1200 nm to 1400 nm, from 225 nm to 1400 nm, from 250 nm to 1200 nm, from 300 nm to 1000 nm, from 350 nm to 800 nm, from 400 nm to 600 nm, from 1200 nm to 3200 nm, from 1400 nm to 3000 nm, from 1600 nm to 2800 nm, from 1800 nm to 2600 nm, from 2000 nm to 2400 nm).

[0116] In some aspects, at least a portion of RnBa3(B3O6)3 can exhibit a hexagonal (H) phase. In some aspects, at least a portion of RnBa3(B3O6)3 (e.g., a different portion than the portion exhibiting the H phase) can exhibit a metastable low symmetry (M)Attorney Docket No.11196-117WO1 phase. As used herein, the term “metastable low symmetry phase” or “M phase” refers to a low symmetry borate phase which is created through thermal or laser excitations. Once created, the phase is stable at room temperature for at least 1 year (e.g., at least 2 years, at least 3 years, at least 4 years, at least 5 years, at least 6 years, at least 7 years, at least 8 years, at least 9 years, at least 10 years). In some aspects, the M phase can be erased by heating above about 300°C. In some aspects, at least a portion of the M phase can be at or near the surface of the crystal.

[0117] In some aspects, the M phase can be macroscopic. As used herein, the term “macroscopic” refers to the M phase having one or more dimensions on the order of tens of μm or more. For example, in some aspects, the M phase can have a length of 10 μm or more (e.g., 20 μm or more, 30 μm or more, 40 μm or more, 50 μm or more, 75 μm or more, 100 μm or more, 125 μm or more, 150 μm or more, 175 μm or more, 200 μm or more, 250 μm or more, 300 μm or more, 350 μm or more, 400 μm or more, 450 μm or more, 500 μm or more). In some aspects, the M phase can have a length of 500 μm or less (e.g., 450 μm or less, 400 μm or less, 350 μm or less, 300 μm or less, 250 μm or less, 200 μm or less, 175 μm or less, 150 μm or less, 125 μm or less, 100 μm or less, 75 μm or less, 50 μm or less, 40 μm or less, 30 μm or less, 20 μm or less, 10 μm or less)

[0118] The M phase can have a length ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the M phase can have a length of from 10 μm to 500 μm (e.g., from 20 μm to 450 μm, from 30 μm to 400 μm, from 40 μm to 350 μm, from 50 μm to 300 μm, from 75 μm to 250 μm, from 100 μm to 200 μm, from 125 μm to 175 μm, from 10 μm to 150 μm, from 20 μm to 125 μm, from 30 μm to 100 μm, from 40 μm to 75 μm, from 150 μm to 500 μm, from 175 μm to 450 μm, from 200 μm to 400 μm, from 250 μm to 350 μm).

[0119] In some aspects, the M phase can be formed by shrinking a crystallographic c-axis of RnBa3(B3O6)3. This is described in further detail in the “METHODS” section below.

[0120] In some aspects, the crystallographic c-axis can shrink by 0.05% or more (e.g., 0.1% or more, 0.15% or more, 0.2% or more, 0.25% or more, 0.3% or more, 0.35% or more, 0.4% or more, 0.45% or more, 0.5% or more). In some aspects, the crystallographic c-axis can shrink by 0.5% or less (e.g., 0.45% or less, 0.4% or less,Attorney Docket No.11196-117WO1 0.35% or less, 0.3% or less, 0.25% or less, 0.2% or less, 0.15% or less, 0.1% or less, 0.05% or less).

[0121] The crystallographic c-axis can shrink by any amount ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the crystallographic c-axis can shrink by from 0.05% to 0.5% (e.g., from 0.1% to 0.45%, from 0.15% to 0.4%, from 0.2% to 0.35%, from 0.25% to 0.3%, from 0.05% to 0.3%, from 0.1% to 0.25%, from 0.15% to 0.2%, from 0.25% to 0.5%, from 0.3% to 0.45%, from 0.35% to 0.4%).

[0122] In some aspects, after shrinking, the lattice parameter c can have a length of 17 Å or more (e.g., 17.05 Å or more, 17.1 Å or more, 17.15 Å or more, 17.2 Å or more, 17.25 Å or more, 17.3 Å or more, 17.35 Å or more, 17.4 Å or more, 17.45 Å or more, 17.5 Å or more). In some aspects, after shrinking, the lattice parameter c can have a length of 17.5 Å or less (e.g., 17.45 Å or less, 17.4 Å or less, 17.35 Å or less, 17.3 Å or less, 17.25 Å or less, 17.2 Å or less, 17.15 Å or less, 17.1 Å or less, 17.05 Å or less, 17 Å or less).

[0123] After shrinking, the lattice parameter c can have a length ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the lattice parameter c can have a length of from 17 Å to 17.5 Å (e.g., from 17.05 Å to 17.45 Å, from 17.1 Å to 17.4 Å, from 17.15 Å to 17.35 Å, from 17.2 Å to 17.3 Å, from 17 Å to 17.25 Å, from 17.05 Å to 17.2 Å, from 17.1 Å to 17.15 Å, from 17.25 Å to 17.5 Å, from 17.3 Å to 17.45 Å, from 17.35 Å to 17.4 Å).

[0124] In some aspects, the compressive strain can lower the symmetry of the crystal and induce large polarization observed by enhancement of the SHG response. In some aspects, the M phase can exhibit compressive strain (Δc / c) of 0.0005 or more along the crystallographic c-axis (e.g., 0.001 or more, 0.0015 or more, 0.002 or more, 0.0025 or more, 0.003 or more, 0.0035 or more, 0.004 or more, 0.0045 or more, 0.005 or more). In some aspects, the M phase can exhibit compressive strain (Δc / c) of 0.005 or less along the crystallographic c-axis (e.g., 0.0045 or less, 0.004 or less, 0.0035 or less, 0.003 or less, 0.0025 or less, 0.002 or less, 0.0015 or less, 0.001 or less, 0.0005 or less).

[0125] The M phase can exhibit compressive strain (Δc / c) along the crystallographic c-axis ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the MAttorney Docket No.11196-117WO1 phase can exhibit compressive strain (Δc / c) of from 0.0005 to 0.005 along the crystallographic c-axis (e.g., from 0.001 to 0.0045, from 0.0015 to 0.004, from 0.002 to 0.0035, from 0.0025 to 0.003, from 0.0005 to 0.003, from 0.001 to 0.0025, from 0.0015 to 0.002, from 0.0025 to 0.005, from 0.003 to 0.0045, from 0.0035 to 0.004).

[0126] In some aspects, the crystal can exhibit a multimodal luminescence in a wavelength range of 250 nm or more (e.g., 300 nm or more, 350 nm or more, 400 nm or more, 500 nm or more, 600 nm or more, 800 nm or more, 1000 nm or more, 1200 nm or more, 1400 nm or more, 1600 nm or more, 1800 nm or more, 2000 nm or more, 2200 nm or more, 2400 nm or more). In some aspects, the crystal can exhibit a multimodal luminescence in a wavelength range of 2400 nm or less (e.g., 2200 nm or less, 2000 nm or less, 1800 nm or less, 1600 nm or less, 1400 nm or less, 1200 nm or less, 1000 nm or less, 800 nm or less, 600 nm or less, 500 nm or less, 400 nm or less, 350 nm or less, 300 nm or less, 250 nm or less).

[0127] The crystal can exhibit a multimodal luminescence in a wavelength range of from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the crystal can exhibit a multimodal luminescence in a wavelength range of from 250 nm to 2400 nm (e.g., from 300 nm to 2200 nm, from 350 nm to 2000 nm, from 400 nm to 1800 nm, from 500 nm to 1600 nm, from 600 nm to 1400 nm, from 800 nm to 1200 nm, from 250 nm to 1000 nm, from 300 nm to 800 nm, from 350 nm to 600 nm, from 400 nm to 500 nm, from 1000 nm to 2400 nm, from 1200 nm to 2200 nm, from 1400 nm to 2000 nm, from 1600 nm to 1800 nm).

[0128] In some aspects, the crystal can exhibit a high thermal expansion coefficient of 20×10-6K-1or more (e.g., 21×10-6K-1or more, 22×10-6K-1or more, 23×10-6K-1or more, 24×10-6K-1or more, 25×10-6K-1or more, 26×10-6K-1or more, 27×10-6K-1or more, 28×10-6K-1or more, 29×10-6K-1or more, 30×10-6K-1or more, 31×10-6K-1or more, 32×10-6K-1or more, 33×10-6K-1or more, 34×10-6K-1or more, 35×10-6K-1or more). In some aspects, the crystal can exhibit a high thermal expansion coefficient of 35×10-6K-1or less (e.g., 34×10-6K-1or less, 33×10-6K-1or less, 32×10-6K-1or less, 31×10-6K-1or less, 30×10-6K-1or less, 29×10-6K-1or less, 28×10-6K-1or less, 27×10-6K-1or less, 26×10-6K-1or less, 25×10-6K-1or less, 24×10-6K-1or less, 23×10-6K-1or less, 22×10-6K-1or less, 21×10-6K-1or less, 20×10-6K-1or less).

[0129] The crystal can exhibit a high thermal expansion coefficient ranging from any of the minimum values described above to any of the maximum values describedAttorney Docket No.11196-117WO1 above. For example, in some aspects, the crystal can exhibit a high thermal expansion coefficient of 20×10-6K-1to 35×10-6K-1(e.g., from 21×10-6K-1to 34×10-6K-1, from 22×10-6K-1to 33×10-6K-1, from 23×10-6K-1to 32×10-6K-1, from 24×10-6K-1to 31×10-6K-1, from 25×10-6K-1to 30×10-6K-1, from 26×10-6K-1to 29×10-6K-1, from 27×10-6K-1to 28×10-6K-1, from 20×10-6K-1to 28×10-6K-1, from 21×10-6K-1to 27×10-6K-1, from 22×10-6K-1to 26×10-6K-1, from 23×10-6K-1to 25×10-6K-1, from 27×10-6K-1to 35×10-6K-1, from 28×10-6K-1to 34×10-6K-1, from 29×10-6K-1to 33×10-6K-1, from 30×10-6K-1to 32×10-6K-1).

[0130] In some aspects, the crystal can exhibit a decrease in positional disorder at a Ba site as compared to a substantially identical reference crystal with an absence of M phase. Positional disorder in a crystal can occur due to the coordination geometry, structural degree of freedom on a Wyckoff position leading to domain formation, or local inhomogeneity. If positional disorder is decreased or not present – particularly if the displacement of Ba with respect to O is rendered and in the same direction in a majority of unit cells – this can induce a large nonlinear polarization in the crystal, resulting in an enhancement of functional properties such as SHG.

[0131] In some aspects, the crystal can exhibit a decrease of 10% or more (e.g., 20% or more, 30% or more, 40% or more, 50% or more, 60% or more, 70% or more, 80% or more, 90% or more, 100% or more, 110% or more, 120% or more, 130% or more, 140% or more, 150% or more) in positional disorder at a Ba site as compared to a substantially identical reference crystal with an absence of M phase. In some aspects, the crystal can exhibit a decrease of 150% or less (e.g., 140% or less, 130% or less, 120% or less, 110% or less, 100% or less, 90% or less, 80% or less, 70% or less, 60% or less, 50% or less, 40% or less, 30% or less, 20% or less, 10% or less) in positional disorder at a Ba site as compared to a substantially identical reference crystal with an absence of M phase.

[0132] The crystal can exhibit a decrease in positional disorder at a Ba site as compared to a substantially identical reference crystal with an absence of M phase of any amount ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the crystal can exhibit a decrease of from 10% to 150% (e.g., from 20% to 140%, from 30% to 130%, from 40% to 120%, from 50% to 110%, from 60% to 100%, from 70% to 90%, from 10% to 80%, from 20% to 70%, from 30% to 60%, from 40% to 50%, from 80% to 150%, from 90% to 140%, from 100% to 130%, from 110% to 120%) in positionalAttorney Docket No.11196-117WO1 disorder at a Ba site as compared to a substantially identical reference crystal with an absence of M phase. In some aspects, the crystal can exhibit substantially no positional disorder at a Ba site, particularly in portions of the crystal exhibiting the M phase.

[0133] In some aspects, the crystal can be substantially stable in ambient conditions, alcohol, acetone, or any combination thereof (i.e., the crystal retains both bulk and M phase).

[0134] In some aspects, the crystal can be stable for at least 1 year (e.g., at least 2 years, at least 3 years, at least 4 years, at least 5 years, at least 6 years, at least 7 years, at least 8 years, at least 9 years, at least 10 years, at least 15 years, at least 20 years) under ambient conditions at room temperature.

[0135] In some aspects, also disclosed herein is a laser including any of the disclosed single nonlinear optical crystals. In some aspects, the laser can be an infrared laser, a visible light laser, or an ultraviolet laser. In some aspects, the laser can be a monochromatic laser, a tunable laser, or a broadband laser. In some aspects, the laser can generate multiple laser lines simultaneously. In some aspects, the laser can be a solid-state laser, a fiber laser, a gas laser, a diode laser, an excimer laser, or a dye laser.

[0136] In some aspects, the crystal can be used for frequency conversion. In some aspects, the crystal can serve as the gain medium of the laser.

[0137] In some aspects, the crystal can replace a conventional crystal in a laser which uses a BBO crystal, for example, a Nd:YAG laser, a Nd:YVO4 Q-switched laser, or a Ti:sapphire laser. In some aspects, the crystal can increase frequency conversion and / or output power of the laser.

[0138] In some aspects, disclosed herein is a quantum light emitter including any of the disclosed nonlinear optical single crystals. In some aspects, the quantum light emitter can be capable of generating single photons, entangled photons, correlated photons, or any combination thereof.

[0139] In some aspects, also disclosed herein is a device including any of the disclosed single nonlinear optical crystals, any of the disclosed lasers, or any of the disclosed quantum light emitters. For example, in some aspects, the device can be a laser cutter, a laser scanner, a laser welder, a medical laser, a fiber optic device, a laser microdissection tool, a laser engraving machine, a LiDAR device, a spectrometer, a laser micromachining system, a laser-induced breakdownAttorney Docket No.11196-117WO1 spectroscopy (LIBS) system, a laser ablation system, a photolithography system, a microscope, a photodynamic therapy (PDT) device, an optical coherence tomography (OCT) system, an optical parametric oscillator (OPO), an optical parametric amplifier (OPA), an optical switch, or any combination thereof. METHODS

[0140] In some aspects, disclosed herein is a method of forming any of the disclosed single nonlinear optical crystals, the method including growing the single crystal from a polycrystalline material having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; and wherein n is 1 to 14.

[0141] In some aspects, also disclosed herein is a method of any of the disclosed single nonlinear optical crystals, the method comprising shrinking a crystallographic c- axis of a single crystal having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from any combination of La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu; and wherein n is 1 to 14. In some aspects, the single crystal can be formed from a polycrystalline material having the chemical formula of RnBa3(B3O6)3.

[0142] In some aspects, when n is greater than 1, the single crystal or polycrystalline material can be formed by combining n compounds each having a chemical formula of R1Ba3(B3O6)3, wherein each R is different. In some aspects, the n compounds can be combined stoichiometrically to form the single crystal or polycrystalline material.

[0143] In some aspects, the polycrystalline material can be formed by a solid-state synthesis.

[0144] In some aspects, the single crystal can be formed by a floating-zone technique, Bridgman, Czochralski, top-seeded solution growth (TSSG), flux method, or any combination thereof.

[0145] In some aspects, shrinking of the crystallographic c-axis can include: a) thermal quenching; or b) forming a thermal gradient during RnBa3(B3O6)3 growth.

[0146] In some aspects, thermal quenching can include exposure to liquid nitrogen, liquid helium, ice water, room temperature water, or any combination thereof.

[0147] In some aspects, shrinking of the crystallographic c-axis can include thermal quenching from a temperature of 900°C or less (e.g., 850°C or less, 800°C or less,Attorney Docket No.11196-117WO1 750°C or less, 700°C or less, 650°C or less, 600°C or less, 550°C or less, 500°C or less, 450°C or less, 400°C or less, 350°C or less, 300°C or less) to room temperature.

[0148] In some aspects, thermal quenching can include inserting the single crystal that is at a temperature of 900°C or less (e.g., 850°C or less, 800°C or less, 750°C or less, 700°C or less, 650°C or less, 600°C or less, 550°C or less, 500°C or less, 450°C or less, 400°C or less, 350°C or less, 300°C or less) into liquid nitrogen or liquid helium.

[0149] In some aspects, thermal quenching can include inserting the single crystal that is at a temperature of 350°C or more (e.g., 360°C or more, 370°C or more, 380°C or more, 390°C or more, 400°C or more, 410°C or more, 420°C or more, 430°C or more, 440°C or more, 450°C or more) into ice water or room temperature water. thermal quenching can include inserting the single crystal that is at a temperature of 450°C or less (e.g., 440°C or less, 430°C or less, 420°C or less, 410°C or less, 400°C or less, 390°C or less, 380°C or less, 370°C or less, 360°C or less, 350°C or less) into ice water or room temperature water.

[0150] Thermal quenching can include inserting the single crystal that is at a temperature ranging from any of the minimum values described above to any of the maximum values described above into ice water or room temperature water. For example, in some aspects, thermal quenching can include inserting the single crystal that is at a temperature of from 350°C to 450°C (e.g., from 360°C to 440°C, from 370°C to 430°C, from 380°C to 420°C, from 390°C to 410°C, from 350°C to 400°C, from 360°C to 390°C, from 370°C to 380°C, from 400°C to 450°C, from 410°C to 440°C, from 420°C to 430°C) into ice water or room temperature water.

[0151] In some aspects, the single crystal may be exposed to additional heat before thermal quenching in order to raise the temperature of the single crystal and enhance the phase formation from thermal quenching. For example, in some aspects, shrinking of the crystallographic c-axis can include exposing the single crystal to a heat source (e.g., a laser, lamp, electrical heater, or another heat source) prior to thermal quenching.

[0152] The temperature of the single crystal may be raised rapidly or slowly depending on the heat source used. For example, in some aspects, the temperature of the single crystal can be raised at a rate of 1°C / min or more (e.g., 2°C / min or more, 3°C / min or more, 4°C / min or more, 5°C / min or more, 10°C / min or more, 15°C / min or more, 20°C / min or more, 25°C / min or more, 30°C / min or more, 40°C / min or more, 50°C / min or more, 1°C / sec or more, 2°C / sec or more, 3°C / sec or more, 4°C / sec orAttorney Docket No.11196-117WO1 more, 5°C / sec or more, 10°C / sec or more, 15°C / sec or more, 20°C / sec or more). In some aspects, the temperature of the single crystal can be raised at a rate of 20°C / sec or less (e.g., 15°C / sec or less, 10°C / sec or less, 5°C / sec or less, 4°C / sec or less, 3°C / sec or less, 2°C / sec or less, 1°C / sec or less, 50°C / min or less, 40°C / min or less, 30°C / min or less, 25°C / min or less, 20°C / min or less, 15°C / min or less, 10°C / min or less, 5°C / min or less, 4°C / min or less, 3°C / min or less, 2°C / min or less, 1°C / min or less).

[0153] The temperature of the single crystal can be raised at a rate ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the temperature of the single crystal can be raised at a rate of from 1°C / min to 20°C / sec (e.g., from 2°C / min to 15°C / sec, from 3°C / min to 10°C / sec, from 4°C / min to 5°C / sec, from 5°C / min to 4°C / sec, from 10°C / min to 3°C / sec, from 15°C / min to 2°C / sec, from 20°C / min to 1°C / sec, from 25°C / min to 50°C / min, from 30°C / min to 40°C / min, from 1°C / min to 40°C / min, from 2°C / min to 30°C / min, from 3°C / min to 25°C / min, from 4°C / min to 20°C / min, from 5°C / min to 15°C / min, from 30°C / min to 20°C / sec, from 40°C / min to 15°C / sec, from 50°C / min to 10°C / sec, from 1°C / sec to 5°C / sec, from 2°C / sec to 4°C / sec).

[0154] In some aspects, the heat source can be a laser, and the single crystal can be mounted on a metal plate or a light-absorbing substrate (e.g., which can absorb the light from the laser and become heated). In some aspects, the laser can have a wavelength range of 300 nm or more (e.g., 400 nm or more, 500 nm or more, 600 nm or more, 700 nm or more, 800 nm or more, 900 nm or more, 1 µm or more, 1.5 µm or more, 2 µm or more, 2.5 µm or more, 3 µm or more, 3.5 µm or more, 4 µm or more, 4.5 µm or more). In some aspects, the laser can have a wavelength range of 4.5 µm or less (e.g., 4 µm or less, 3.5 µm or less, 3 µm or less, 2.5 µm or less, 2 µm or less, 1.5 µm or less, 1 µm or less, 900 nm or less, 800 nm or less, 700 nm or less, 600 nm or less, 500 nm or less, 400 nm or less, 300 nm or less).

[0155] The laser can have a wavelength range of from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the laser can have a wavelength range of from 300 nm to 4.5 µm (e.g., from 400 nm to 4 µm, from 500 nm to 3.5 µm, from 600 nm to 3 µm, from 700 nm to 2.5 µm, from 800 nm to 2 µm, from 900 nm to 1.5 µm, from 300 nm to 1 µm, from 400 nm to 900 nm, from 500 nm to 800 nm, from 600 nm to 700 nm, from 1 µm to 4.5 µm, from 1.5 µm to 4 µm, from 2 µm to 3.5 µm, from 2.5 µm to 3 µm).Attorney Docket No.11196-117WO1

[0156] In some aspects, the thermal quenching can have a rate of 25°C / sec or more (e.g., 30°C / sec or more, 35°C / sec or more, 40°C / sec or more, 45°C / sec or more, 50°C / sec or more, 60°C / sec or more, 70°C / sec or more, 80°C / sec or more, 90°C / sec or more, 100°C / sec or more, 110°C / sec or more, 120°C / sec or more, 130°C / sec or more, 140°C / sec or more, 150°C / sec or more). In some aspects, the thermal quenching can have a rate of 150°C / sec or less (e.g., 140°C / sec or less, 130°C / sec or less, 120°C / sec or less, 110°C / sec or less, 100°C / sec or less, 90°C / sec or less, 80°C / sec or less, 70°C / sec or less, 60°C / sec or less, 50°C / sec or less, 45°C / sec or less, 40°C / sec or less, 35°C / sec or less, 30°C / sec or less, 25°C / sec or less).

[0157] The thermal quenching can have a rate ranging from any of the minimum values described above to any of the maximum values described above. For example, in some aspects, the thermal quenching can have a rate of from 25°C / sec to 150°C / sec (e.g., from 30°C / sec to 140°C / sec, from 35°C / sec to 130°C / sec, from 40°C / sec to 120°C / sec, from 45°C / sec to 110°C / sec, from 50°C / sec to 100°C / sec, from 60°C / sec to 90°C / sec, from 70°C / sec to 80°C / sec, from 25°C / sec to 80°C / sec, from 30°C / sec to 70°C / sec, from 35°C / sec to 60°C / sec, from 40°C / sec to 50°C / sec, from 70°C / sec to 150°C / sec, from 80°C / sec to 140°C / sec, from 90°C / sec to 130°C / sec, from 100°C / sec to 120°C / sec).

[0158] In some aspects, when flux growth can be used to form the single crystal, shrinking of the crystallographic c-axis can include forming a thermal gradient during crystallization. EXAMPLES Example 1

[0159] Nonlinear optical (NLO) crystals with superior properties are significant for advancing laser technologies and applications. Introducing rare earth metals to borates is a promising and effective way to modify the electronic structure of a crystal for improving its optical properties in the visible and ultraviolet range. In this work, inversion symmetry breaking in EuBa3(B3O6)3 was computationally discovered, which was previously identified as centric, and demonstrated the noncentrosymmetry via synthesizing the single crystal for the first time by the floating zone method. It was determined the correct space group to be P6^. In addition, single crystal synthesis is reported for the first time using the floating zone method. The material has a large bandgap of 5.56 eV and is transparent down to 250 nm. The complete anisotropicAttorney Docket No.11196-117WO1 linear and nonlinear optical properties were also investigated with a d11 of ~0.52 pm / V for optical second harmonic generation. Further, it is Type I and Type II phase matchable. This work suggests that rare earth metal borates are an excellent crystal family for exploring future DUV NLO crystals. It also highlights how first principle computations combined with experiments can be used to identify noncentrosymmetric materials that have been wrongly assigned to be centrosymmetric. Introduction

[0160] Nonlinear optical (NLO) crystals are the essential components of high- power lasers for generating ultraviolet (UV) light, especially the UV-C range, defined as 200-280 nm. It has a variety of technological applications such as lithography, micromachining, and spectroscopy. The wavelengths of interest are obtained using frequency conversion through nonlinear optical phenomena such as second harmonic generation (SHG) and sum frequency generation (SFG). Generally, a good UV NLO crystal should satisfy the following requirements: large second-order nonlinearity (large SHG tensor coefficients), broad UV transparency window, phase matchability, high laser damage threshold (LDT) values, and easy synthesis. It is well-known that bandgaps and nonlinear susceptibility generally scale inversely; hence, crystals with large bandgaps (and therefore DUV transparency) usually have low nonlinear susceptibility. As a result, ultraviolet NLO crystals typically have lower SHG coefficients as compared to visible and infrared NLO crystals. Since it is difficult to find a material that satisfies all the requirements, researchers are actively looking for new UV crystals and many borate-based NLO materials such as β-BaB2O4 (BBO), LiB3O5 (LBO), CsB3O5 (CBO) and KBe2BO3F2 (KBBF) have been discovered and utilized in UV NLO applications. Among these materials, KBBF is the only crystal with efficient frequency conversion below the DUV barrier of 200nm. The rapid development of UV laser applications demands the continuous exploration of UV NLO crystals that are comparable to or even better than the currently available ones.

[0161] Borate is considered to be one of the best crystal systems for exploring good UV NLO crystals. Because of the significant electronegativity difference in boron and oxygen, the B-O bonds have strong ionic characteristics, giving rise to large bandgaps and low short-cutoff wavelengths. The typical groups formed are planar [BO3] triangles and [BO4] tetrahedra. In particular, the planar [BO3] units contain π-conjugated bonds in which the electrons are delocalized and easily polarized when an electric field is applied, thus giving gives rise to the strong SHG response. In addition, its planarAttorney Docket No.11196-117WO1 nature increases the anisotropy and leads to more significant birefringence; thus, they are more likely to be phase-matchable. In particular, rare earth borates are a promising crystal system to explore for new UV NLO crystals. Incorporating rare earth metals has several advantages. They have closed-shell or half-filled 4f orbitals; therefore, the d-d and f-f electronic transitions are impeded, which is beneficial for broadening the transparency window. Also, because of the complex electronic configuration and the large ionic radius, the rare earth elements will bond with the oxygen ions to form distorted polyhedra, enhancing the overall SHG performance.

[0162] EuBa3(B3O6)3 (EBBO) is an example of rare earth borate-based crystals with planar [BO3] triangles, which can be a new UV NLO crystal. In EBBO, three [BO3] triangles form a planar [B3O6] ring. This compound was previously synthesized in the polycrystalline form and reported to crystallize in the non-polar space group P63 / m. First principles phonon computations identified that this family of materials of formula XBa3(B3O6)3 (with X = In, Sc, … X = Ba, Eu, … which includes EBBO) present dynamic instabilities and that they should form in a noncentrosymmetric space group. It was shown that EBBO forms indeed in an acentric space group and exhibits an SHG response. EBBO was further explored as a candidate for UV nonlinear photonic applications. The first synthesis was reported as well as the linear and nonlinear optical properties of single crystal EBBO and find that EBBO is both Type I and Type II phase-matchable. These findings further confirm that rare earth borate-based crystals are promising for NLO applications and that first principles phonon databases can be used to identify noncentrosymmetric materials with applications in NLO. Experiment

[0163] Polycrystalline Crystal Synthesis: The polycrystalline EBBO powder was prepared using a solid-state reaction method. BaCO3 (Alfa Asar, 99.5%), Eu2O3(Alfa Asar, 99.9%) and H3BO3 (EMD chemicals, 99.4%) were used as source materials for polycrystalline synthesis. Powders of BaCO3, Eu2O3 and H3BO3 were mixed in a stoichiometric ratio and thoroughly ground in an agate mortar to ensure homogenous mixing. The mixed source material was placed in an Al2O3 crucible, heated to 400°C, and held at this temperature for 1 hour to decompose BaCO3 and H3BO3. Then the furnace was further heated to 850°C at the rate of 200°C / hour and held at this temperature for 72 hours, followed by turning off the furnace to cool down the material. Powder X-ray diffraction (XRD) analyses showed that the polycrystalline powder synthesized following the above procedures contains a pure EBBO phase.Attorney Docket No.11196-117WO1

[0164] Single Crystal Synthesis: The EBBO single crystals were grown using a floating-zone technique using a commercial image furnace equipped with double- elliptical mirrors (Quantum Design Model: IRF01-001-05). This method includes melting the bottom end of a feed rod suspended from above and connecting the molten zone to a seed material held from below. The single crystal is continuously grown from the molten solution by lowering both the seed and feed rods.

[0165] Polycrystalline EBBO powder was used to make feed and seed rods for growing single crystals. It was first ground into a fine powder in an agate mortar for 30 minutes. An appropriate amount of the powder (10 g) was placed into a clean cylinder- shaped rubber balloon. The balloon loaded with powder was inserted into a quartz tube with a diameter of 11 mm and a length of about 110 mm and compressed in water under a pressure of 60 MPa. After compression, the rubber balloon was carefully cut with scissors. The rod was then sintered at 800°C for 48 hours in air and cooled to room temperature in the furnace. The seed rod (3 cm in length) was prepared with a similar procedure. In the preparation of the feed and seed rods, a layer of EBBO powder was placed between the EBBO rod and the Al2O3 boat to prevent Al contamination.

[0166] To perform the floating-zone crystal growth, the feed rod was suspended from the upper shaft, and the seed rod was mounted on the bottom shaft. Both rods were well aligned along the central axis of the growth chamber (i.e., along the shaft direction). After completing the alignment, the growth chamber was closed, and the bottom end of the feed rod and the top end of the seed rod were moved to the melting zone with a small gap (~ 1.5mm) left between them. Then, the growth chamber was flushed by flowing oxygen for 15 minutes, and the oxygen pressure in the growth chamber was up to 4 atm. After the pressure reached 4 atm, the voltage of the halogen lamps was ramped up, and the upper and lower shafts were to rotate at 14 rpm (The rotation direction is opposite between the upper and lower shafts). The bottom end of the feed rod started to melt at 49 V. When the voltage was increased to 50 V, the bottom end of the feed rod had sufficiently melted. Then the feed rod was connected with the seed rod by slightly moving the bottom shaft upward. After the seed and feed rods were connected, the growth process was started, with the growth speed set at 7 mm / h and the feed speed at 30 mm / h. As the growth continued, the voltage was adjusted in the 49-55 V range in terms of the shape of the melt in the melting zone. The best shape is “T”-like for growth. The “T”-shape melting zone was mostly at 50 V.Attorney Docket No.11196-117WO1 The growth lasted 5 hours; the crystal rod was about 30 mm and contained multiple domains. Single domains were obtained by cleaving the crystal rod using a razor blade. FIG.1C shows an optical image of several cleaved crystals.

[0167] Linear Optical Properties: The short-cutoff wavelength was determined by ultraviolet-visible (UV-Vis) spectroscopy (Perkin-Elmer Lambda 950 UV-Vis-NIR Spectrophotometer) and spectroscopic ellipsometry (Woollam M-2000F) at room temperature. The UV-Vis transmittance spectrum was collected on a single crystal EBBO of thickness~500 μm sample in the range of 250-850nm with unpolarized light. The ellipsometry data was collected on a polycrystalline pallet from 0.200μm to 1μm.

[0168] The complex linear optical constants ^^ = ^ + ^^ were determined usingspectroscopic ellipsometry (Woollam M-2000F). The ellipsometry spectra werecollected from 0.200μm to 1μm and fitted to the Cauchy equation ^ = ^ + ^ ^^^ + ^^. Theextinction coefficient (describing the absorption) isabsorption ^ = ^ (^^^^^ ^) / ^^ , where k0 and E0 are the characteristicparameters of theUrbach energy related to the temperature. The absorption coefficient α can be found from k to extract the bandgap of the crystalby the Tauc analysis (^ℎ^)^ / ^ = ^(ℎ^ − ^^). Here, ν is the frequency of the photonsand n is 0.5 and 2 respectively. By plotting (^ℎ^)^ / ^vs. E, one can identify the correct transition and the bandgap by ^ / ^curve to (^ℎ^) = 0.

[0169] Generation (SHG) Measurement: The SHGin reflection geometry at normal incidence (i.e., incident laser beam along the surface normal). The 800nm fundamental laser beam was generated by Spectra-Physics Ti:sapphire (80fs, 80Mhz), and its polarization was rotated by an angle of Ψ using a halfwave plate. Then after passing through an analyzer, the p-polarized (∥) and s-polarized (⊥) SHG light was detected by a photomultiplier tube. The typical peak power used was around 700W (pulse energy ~ 0.056nJ). The beam diameter was roughly 600nm. A wedged z-cut LiNbO3 crystal (MTI Corporation) was used as a reference.

[0170] First Principle (FP) Calculations: The structural optimizations and subsequent self-consistent field calculations were carried out using the Vienna ab initio simulation package (VASP). The Perdew-Burke-Ernzerhof generalized-gradient approximation (GGA-PBE) was employed to model the exchange-correlation energy.Attorney Docket No.11196-117WO1 The projector augmented wave (PAW) method was used, and the wavefunctions were expanded on a plane-wave basis set with a kinetic energy cutoff of 520 eV. Preliminary results showed that explicitly considering the 4-f electrons in the valence leads to a metal. Indeed, these electrons were located around the Fermi level, although a wide bandgap should be present. To address this issue, the Eu_3 VASP pseudopotential with 9 valence electrons (5p65d16s2) was tested , resulting in an indirect and direct gap around 5 eV and 5.3 eV, respectively. This pseudopotential was therefore adopted. A 3×3×1 Monkhorst-Pack k-point mesh was initially employed to sample the Brillouin zone, and the electronic self-consistent loops were converged to 1 × 10−6eV of the total energy. The ionic relaxation was considered converging when the force on each atom was below 2 meV / Å. Further calculations with k-points grid of 5×5×1, energy and forces convergence thresholds of 1 × 10−9eV and 0.5 meV / Å, respectively, were subsequently performed to obtain a better estimation of the energy differences between the competing phases. Phonons were computed using the density functional perturbation theory (DFPT) as implemented in ABINIT and following the procedure used by Petretto, G., Dwaraknath, S., P.C. Miranda, H. et al. High- throughput density-functional perturbation theory phonons for inorganic materials. Sci Data 5, 180065 (2018). The calculations were performed with GGA-PBE functional (considering the f electrons as frozen for the Eu) and a q-point grid of 2×2×2. Results and Discussion

[0171] Material discovery: Starting from a phonon database of materials present in the Materials Project and previously synthesized as reported in the Inorganic Crystal Structure Database (ICSD), a family of compounds with general chemical formula MBa3B9O18 (M = Sc, In,Y, Lu) and with the centrosymmetric crystal structure (P63 / m) was identified as presenting polar imaginary phonon modes. This is a signature of polar structural instability, which has been used, for instance, to identify a new class of ferroelectric materials. Further computations with higher accuracy parameters and using phonons obtained with DFPT confirmed the dynamical instabilities. Among this family, the focus was on EBBO and report its phonon band structure in FIG.1A. The centrosymmetric structure is shown in FIG.1B (superposed to a distortion). Dynamical instabilities across the Brillouin zone are present in the phonon band structure, indicating a series of competing distortions, some belonging to polar point groups (FIG. 1A). The structure was distorted following all unstable phonons (limiting distortions to a 2×2×2 supercell) and subsequently relaxed. TABLE 1 reports all the distortedAttorney Docket No.11196-117WO1 structures following this procedure and their energy compared to the centrosymmetric phase. The preliminary conclusion from theory was that the structural ground state of EBBO is either P3 or P63 (see FIGS. 1C-1D). Both structures exhibit very similar patterns of atomic displacements and very close energy. Further calculations with more accurate relaxation criteria were performed to distinguish the true ground-state but they led to even smaller energy differences. In the P3 or P63, the atomic displacement breaking centrosymmetry is due to barium moving in an oxygen environment along the c axis (FIGS.1C-1D). Interestingly, in the P1^structure, which is only marginally higher in energy than the P3 and P63 phase, the barium displacement pattern is antipolar (FIG.1E). The presence of several phases very close in energy is the signature of a flat potential energy landscape. In all phases, the Eu and the metaborate B3O6 group do not move significantly. The noncentrosymmetric stable ground state indicates that this material could present a second harmonic generation response and potentially ferroelectric. TABLE 1. Energy difference (meV / at) between the centrosymmetric structure (P63 / m) and the different distorted structures obtained from the phonon band structure of EuBa3B9O18. P63 P-1 Pm P21 / c P21 / m P3lts, the polycrystalline EBBO with high purity using the solid-state reaction was synthesized. The phase and phase purity were confirmed by the PXRD patterns shown in FIG.2A. Then the pure polycrystalline EBBO was used to synthesize the single crystals shown in FIG. 2B using the floating zone technique. The as-grown EBBO single crystals are transparent and stable in an ambient atmosphere for at least six months. It is also stable in various solvents such as water, alcohol, and acetone.

[0173] EBBO includes planar metaborate [B3O6] rings with π-conjugated bonds, aligning parallel to each other along the

[0001] direction. It also includes EuO6 octahedra and irregular BaO6 and BaO9 polyhedra, similar to the reported YBa3B9O18 structure. Because of its planar nature, single crystal EBBO can be easily cleaved along the (0001) plane, verified by XRD (FIG.2C).Attorney Docket No.11196-117WO1

[0174] As shown later, the SHG response from the EBBO crystal was observed, suggesting the symmetry lowering from the centric P63 / m structure. To identify the detailed atomic structure experimentally, single-crystal XRD measurements were performed for the grown EBBO crystals on a Rigaku MicroMax 007 rotating anode (Cu) x-ray generator equipped with Osmic Varimax VHF monochromator, a universal four-circle kappa goniometer and a HyPix-Arc150 area detector. The collected diffraction dataset was refined using a structural model with P63, P3, and P6^, which are noncentrosymmetric subgroups of P63 / m. The P63 / m, P63, and P6^have the same unit-cell size, whereas the unit cell of the P3 structure is doubled along the c axis, i.e., a × b × 2c cell metric, where a, b, and c are the lattice vectors of the P63 / m structure. The reflection conditions of the four space groups are listed in TABLE 2. TABLE 2. Reflection conditions of the space groups P63 / m, P63, P3, and P6^. hhil hh#0l hh^2^^h^l 000l

[0005] rs, supera ce re ec ons represen ng an enarged un ce w respect to the a × b × c cell metric were investigated. No superlattice reflections were, however, observed, indicating the low possibility of the P3 structure with the doubled unit cell. Indeed, the P3 model resulted in a bad fit to the collected dataset (Rint = 38.95%), and thus the space group P3 was excluded. The dataset was then fitted with the structural model with P63 and P6^symmetries. Although the P63 model led to the best fit (R1 = 8.81%), this value is very similar to that obtained through the refinement with the P6^model (R1 = 8.85%). With the help of nonlinear optical measurements, the P6^structure was assigned to EBBO (see FIG.1B); the P6^is the only one consistent with the SHG results (shown later), where a significant SHG signal was observed at normal incident geometry. Note that no SHG signal is expected from the P63 structure at this optical geometry. The structural parameters of the P6^phase obtained from the refinement are summarized in TABLE 3. The refined crystal structure is depicted in FIG.1D.Attorney Docket No.11196-117WO1 TABLE 3. Experimental structural Parameters of EBBO determined from single crystal x-ray diffraction at 300 K obtained from refinements with a P6^model. Space group;P6^ (No. 174). *Refined anisotropically. Cell parameters; a = b = 7.2118(3) Å, c =17.3256(8) Å. Ui or U yed, and this treatment improved the fitting significantly. This is consistent with the symmetry-breaking shift of Ba atoms revealed by the FP calculations. Such displacive- type static disorder may cause the discrepancy in the space group symmetry between the computation and experiment. If the displacive disorder is ignored, as is often the case in FP calculations, the Ba atoms have no degree of freedom to shift under theP6^ symmetry, and thus the stability of the P6^ phase is probably underestimated.Despite such difficulties, analyzing unstable phonons is an effective means to search for hidden noncentrosymmetric materials as displayed in this research.Attorney Docket No.11196-117WO1

[0177] Linear Optical Properties: To understand the lower limit of the spectral range in which EBBO is applicable, its short-cutoff wavelength was investigated using both UV-Vis spectroscopy and ellipsometry. UV-Vis transmittance was collected on the (0001) plane of a single crystal EBBO with a thickness of ~500 μm (FIG.3A). In addition, the absorption coefficient α was extracted from ellipsometry data measured on a polycrystalline pellet as shown in the inset of FIG. 3B. Both the UV-Vis transmittance and ellipsometry data yielded the same short-cutoff wavelength of ~250nm.

[0178] The bandgap of the crystal was extracted by the Tauc =^(ℎ^ − ^^), in which n equals 0.5 and 2 for direct and indirectthe Tauc plots for both direct and indirect bandgaps, it was found that the better fit was the direct bandgap, which was 5.56eV, as shown in FIG.3B.

[0179] To extract the complex ordinary and extraordinary refractive indices, spectroscopic ellipsometry was performed at room temperature on a single crystal in three crystal orientations:

[0001] / / lab X,

[0001] / / lab Y, and

[0001] / / lab Z. The three sets of ellipsometry spectra were fitted simultaneously to the Cauchy equation ^ = ^ +^ + ^ for the real part a (^^^^^ ^^ nd Urbach absorption equation ^ = ^^^part of the anisotropic refractive indices, 3C. Theof the Cauchy equations and Urbach are shown in TABLE 4 and TABLE 5. TABLE 4. The parameters of Cauchy equations for anisotropic refractive indices. n A B (μm2) C (μm4) no 1697 000506 16234×10-4TABLE 5. The parameters of Urbach absorption equations for imaginary refractive index. k k0 Eu (eV) E0 (eV0 ko 0.11911 2.825 4.96Attorney Docket No.11196-117WO1

[0180] Second harmonic generation: Second harmonic generation (SHG) is a process combining two photons of frequency ω into one photon of frequency 2ω through a noncentrosymmetric material. For real applications, the SHG process should take place only from the ground state to the virtual states to ensure minimal absorption and a non-resonant process. In the case of EBBO, the bandgap is 5.56eV (~220nm); therefore, fundamental wavelength needs to be longer than 440nm. The wavelength demonstrated here was 800nm, and the wavelength of the SHG was 400nm.

[0181] The SHG measurement was performed in normal reflection geometry with a nonlinear optical microscope, shown in FIG.4A. The fundamental laser beam was linearly polarized and rotated by an angle of ψ using a halfwave plate, and the SHG light was decomposed into p-polarized (∥) and s-polarized (⊥) SHG light and detected by a photomultiplier tube.

[0182] Since the crystal belongs to the hexagonal crystal system, its crystal physics coordinate (Z1, Z2, Z3) is defined as Z1 / / [21^1^0], Z2 / / [011^0], Z3 / /

[0001] . The crystal was oriented such that -Z2 and Z1 axes Y, respectively.

[0183] A significant SHG signal indicates the absence of the inversion symmetry, consistent with the FP calculations result. The observation of SHG signal in normal incidence rules out the P63space group since point group 6 should not show any SHG signal when the incidence beam is along the 6-fold axis. This fact combined with the x-ray analysis presented earlier points to the P6^as the most likely space group for this crystal. To obtain the dij coefficients ratios of EBBO, the polar plots were fitted to ananalytical model based on its point group symmetry 6^ and compared with thatmeasured on a wedged z-cut LiNbO3 reference under the same experimental conditions. The theoretical expressions for the SHG intensity at normal incidence can thus be expressed as: $%& ∝ (( sin 2- + ( c %∥ ^^ %% os 2-)%

[0184] The two both be probed usingthe chosen geometry. with respect to d22 was extracted by fitting the SHG polar plots to the second equation above, as shown in FIG.4B. The theoretical fit yielded the result of d11 / d22 = 1.47±0.04. By comparing theAttorney Docket No.11196-117WO1 SHG intensity with that of a z-cut LiNbO3 reference measured under the same experimental conditions, one can extract that |d11| = 0.52±0.03pm / V and |d22| = 0.35±0.02pm / V. In particular note that d11 and d22 share the same sign.

[0185] To ensure that the detected signal was from the second-order NLO effect, the SHG intensities were measured as a function of incident power, shown in FIG.4C. The solid red line is the quadratic fit, and the black dots are the experimental data. The SHG response demonstrates a clear quadratic dependence on the input power, confirming that the measured signal was generated by the second-order NLO effect.

[0186] Phase Matching Conditions: To obtain efficient frequency conversion, phase-matching is one of the most important criteria. The phase-matching conditions can be calculated using the Cauchy equations. From the previous section, it was found that EBBO is a negative uniaxial crystal (^1 > ^3 ). Therefore, the Type I phase-matching condition is achieved when ^1,& = ^3,%&(56) and ^& &1 + ^3 (56) =2^%&3 (56) for Type II. It was further found IIas shown in FIGS. 5A-5B. An angle φ was introduced as the azimuthal angle, as defined in FIG.5C. For fundamental light of 800nm, the effective d coefficients, deff, for both conditions can be expressed as: (377,8 = (^^ cos 56 cos 3: − (%% cos 56 sin 3:

[0187] Fromfrom FIG.5D, the maximal |deff, I| is 0.57 pm / V at φ = 108.48° and |deff, II| is 0.36 pm / V at φ = 18.6° Conclusions

[0188] EBBO was identified as a potential new noncentrosymmetric materials by analyzing unstable phonons from first principles computations in the reported centrosymmetric (P63 / m) structure. The inversion symmetry breaking was confirmed experimentally through SHG measurement, which confirms that the previous reported structure was incorrect. Combining theory and experiment, the EBBO’s space group was identified to be P6^. Moreover, the first successful single crystal synthesis of EBBO using the floating-zone method was reported. The anisotropic linear and nonlinear optical properties have been systematically characterized. It is also Type I and Type II phase-matchable in a wide range of wavelengths. FP calculations were performedAttorney Docket No.11196-117WO1 to determine the most stable structure. This work suggests that rare earth metal borates are a good material system for UV NLO crystal exploration. It also shows how crystal structure previously reported to be centrosymmetric can be identified to be in fact noncentrosymmetric in first principles high-throughput phonon databases. This approach is of interest for the identification of new materials with NLO or ferroelectric properties. The point group 6^is non-polar. Nonetheless, motivated by the theoretical calculations, attempts were made to measure the ferroelectric hysteresis loop, which were unsuccessful. Example 2

[0189] The expression of the reflected SHG intensity of the single surface for a non- absorbing material is: =% %

[0190] Thewith the following equation: %

[0191] , as ;&,||%. The Fresnel reflection coefficient, A , is defined as A = ^^U^^^T^U %&,|| %&,|| ^^UT^.d11 / d22 has been determined, then findd22 of LiNbO3 at 800 nmtoMillers’s rule and d22 = 2.1pm / V at 1064 nm. Photoluminescence measurement showed no apparent signal (FIG.5E) and confirmed the collected intensity were generated by the SHG process. Example 3

[0193] Nonlinear optical (NLO) crystals play an important role in the development of tunable laser technologies from the ultra-blue to terahertz region and are of great interest for applications such as optical rectification, modulation, remote sensing,Attorney Docket No.11196-117WO1 biological imaging, and medical surgery. The past decade has witnessed marked efforts in finding novel nonlinear optical crystals, especially in the UV-C region (100– 280 nm wavelength range). For a crystal to be a viable candidate for NLO applications, it is required to have a broad transparency window, large nonlinear coefficients, low birefringence, stability in the ambient chemical environment, low optical absorption, phase matchability, high laser damage threshold, and ease of facile growth into large single crystals. Potential material candidates investigated so far in the UV range include (Na / K / Rb)Be2B3O7, β-BaB2O4, LiB3O5, Li4Sr(BO3)2, Cs3Zn6B9O11, and KBe2BO3F2. While the transparency window of these compounds is broad, as a result of their large optical bandgaps (>6.2 eV), the non-resonant NLO coefficients, crucial for effective frequency conversion, tend to be relatively low, typically ranging from ≈ 0.3 to 0.7 pm / V, Of these, β-BaB2O4 is most commonly used due to the large phase- matched coefficient of ≈1.9 pm / V. A general trend is that crystals with large bandgap (4-7 eV) have low electronic polarizability and hence a weak second-harmonic response. Moreover, most of the aforementioned materials exhibit chemical instability at room temperature, requiring suitable surface passivation or compositional engineering for practical applications. The property tradeoffs and chemical requirements make it challenging to design nonlinear optical crystals with efficient frequency conversion in the UV and deep UV regions.

[0194] Borate crystal systems are an excellent candidate for potential NLO applications with short wavelength cutoff in the range of 200–300 nm while exhibiting relatively large second harmonic generation (SHG) coefficients as well as robustness against laser-induced damage in the UV region. One of the major contributing factors to the short wavelength cutoff is B–O bonds, which have a strong ionic character that pushes the bandgap to the deep UV region. The borate system also offers rich structural diversity; the B-O structural unit can be constructed into zero-dimensional clusters, one-dimensional chain, two dimensional layers, and also three-dimensional framework. Of these, B3O6 rings with a planar nature are of particular interest because they include both σ and π bonds. The delocalized electron cloud of the π-bonds leads to high polarizability, which allows for the coexistence of a wide band gap and a large SHG coefficient in this materials family. Recently, a rare-earth barium borate constructed with B3O6 rings, EuBa3(B3O6)3, has been reported to be noncentrosymmetric and discussed as a potential NLO crystal in the UV-C region. Another advantage of rare earth borates is the large temperature bandwidth (range ofAttorney Docket No.11196-117WO1 temperatures over which phase-matching conditions can be maintained) that provides precise temperature control in a laser system.

[0195] In this investigation, other family members of the rare-earth borates, R1Ba3(B3O6)3 (R = Nd, Sm, Tb, Dy, and Er), have been revisited as potential candidates for nonlinear optical applications in the UV-C region. Previous literature on polycrystalline synthesis reported that these rare-earth borates formed a centrosymmetric lattice and would lack second-order nonlinear optical effects. However, as reported for EuBa3(B3O6)3, the other compounds also have potential to show a structural deviation from the centrosymmetric structure to a noncentrosymmetric one with space group P6^. Employing the floating zone method, single crystals of R1Ba3(B3O6)3 with an approximate size of 5 mm were synthesized and characterized using x-ray diffraction and optical SHG measurement. The characterization identifies the crystal family as noncentrosymmetric and crystallizing in the P6^structure (similar to EuBa3(B3O6)3 crystal) as well as possessing promising nonlinear optical properties. They are also identified as Type-I and Type-II phase matchable SHG crystals. This series of materials also exhibits a strong photoluminescence response in both the visible and the infrared regions. The short wavelength electronic band-edge investigated through ellipsometry and UV-vis spectroscopy falls in the range of 250–320 nm, potentially useful in the UV-C region. Results and Discussion

[0196] Synthesis and Structure Determination: Single crystals of R1Ba3(B3O6)3 (R = Nd, Sm, Tb, Dy, and Er) have been synthesized using the optical floating zone method (see Methods section for details on the growth). The crystals are stable in open air and acetone for up to at least 3 months. It is also stable in various solvents such as water and acetone. The crystals have dimensions of about 4–6 mm (length), 2–4 mm (width), and 1–2 mm (thickness), as shown in FIG.6A. Most of the crystals are clear and transparent after polishing, except for Nd and Er compounds, which are slightly purple and pink in color, respectively.

[0197] The crystal structure of EuBa3(B3O6)3 was incorrectly assigned earlier; previous literature on polycrystalline synthesis reported that the rare-earth borates form a centrosymmetric P63 / m structure and would lack any second-order nonlinear optical responses. However, atomic displacement at the 4e Wyckoff position (occupied by Ba) causes a deviation from P63 / m to a noncentrosymmetric P6^structure, whichAttorney Docket No.11196-117WO1 has been further corroborated by the Γ-point phonon instability of the P63 / m structure. Refinements against the single-crystal x-ray datasets were performed based on the structural models under P63 / m and P6^as well as P63, P6^, and P3 symmetries; the P63 and P3 are the two lowest-energy structures predicted by past density-functional theory calculations for EuBa3(B3O6)3. The P6 structure was also included in the pool of candidates due to the same extinction condition as P6^.

[0198] As a representative example, SmBa3(B3O6)3, the Rint values are: 5.21% for P63 / m, 5.31% for P6^, 5.31% for P3, 6.13% for P63, and 5.14% for P6. The closeness of the Rintvalues, which is similarly observed for the rest of the rare-earth compositions, does not allow determination of the space-group symmetry solely by x- ray diffraction.

[0199] SHG polarimetry is a powerful tool to identify the point-group symmetry of noncentrosymmetric materials. It is employed here to unambiguously assign the P6^symmetry to R1Ba3(B3O6)3 family. A noncentrosymmetric point group would enable the dipolar SHG signal from the sample, while it will be absent in a centrosymmetric crystal. Given the candidate space groups, possible point groups of R1Ba3(B3O6)3 are6 / m, 3, 6, and 6^ , among which 6 / m is centrosymmetric, and the others arenoncentrosymmetric. Observation of strong SHG from all the R1Ba3(B3O6)3 crystals (discussed in detail later) rules out point group 6 / m (corresponding to space group P63 / m). Further, point group 6 was excluded , which should not give any SHG signal in normal incidence when the incidence beam is parallel to the c axis; however, the SHG signal in this geometry was observed.

[0200] Both point groups 6^and 3 are consistent with the SHG polarimetry result. Both of the point groups have no systematic cancellation of x-ray reflection, as they contain primitive lattices and lack both glide planes and screw axes. The determination of the point group thus depends on the structure factor relationship imposed by the symmetry groups. In this case, the structure factor relationship that should be imposed on the space group P3 is a subset of that on P6^. Thus 6^was identified to be the highest possible symmetry for the R1Ba3(B3O6)3 single crystals, with a lower symmetry of space group P3 as a possibility.

[0201] The refined crystal structure (R = Dy) based on the single-crystal x-ray data and the P6^structural model is illustrated in FIG.6E. The illustration shows that the structure contains planar [B3O6] rings aligning perpendicular to the crystallographic cAttorney Docket No.11196-117WO1 axis. Static positional disorder (or dynamic displacement) was observed for one of the Ba sites; the atoms no longer sit at the initial Wyckoff position but prefer a lower- symmetry environment at the 2g site. This is consistent with the previous computational prediction that the Ba atoms have structural instability towards polar displacement along the c direction. Some of the B and O sites also showed positional disorder, probably because of the Ba-site disorder. X-ray diffraction on powder samples in FIG.6B consistently identifies the possible reflections allowed by the P6^symmetry of the crystals.

[0202] The lattice parameters refined from the single crystal x-ray diffraction indicated a decreasing trend with increasing f orbital occupancy, i.e., in the order Nd3+(4f3), Sm3+(4f5), Tb3+(4f8), Dy3+(4f9), Er3+(4f11). (FIG.6C). This trend can also be observed in the θ-2θ scan (FIG. 6D) from a polished parallel plate of the grown crystals; for example, the 0006 and 0008 reflections shift slightly to a higher 2θ region when increasing the f-electron count, indicating a decrease in the planar spacing and a consequent contraction of the lattice parameter c. The overall change in the unit cell parameters and cell volume can be explained by lanthanide contraction, which affects the Shannon–Prewitt crystalline radius of the rare earth cation 6 as listed in FIG.6C.

[0203] Transparency, Photoluminescence and Refractive Index: The linear optical properties of R1Ba3(B3O6)3 crystals were characterized in the spectral ranges of 250–2000 nm and 2–16 µm by UV-vis and Fourier transform infrared (FTIR) spectroscopy, respectively. Their direct electronic bandgap ranges from 280 to 320 nm as shown in FIG.7A.

[0204] According to the spectrum shown in FIG. 7A, the samples have a transparency range of up to 6.5 µm in the infrared. To extract the absorption coefficient (α) considering the possible multiple reflection and absorption between the two surfaces of the parallel plate slabs, the UV-vis data was fitted using the following equations: $X % ^%YZV (1 − X) ^$ = X +W 1 − X%^^%YZAttorney Docket No.11196-117WO1 where R is the single interface reflectance, x is the thickness of the sample, Ir / Io is the total reflectance, and It / Io is the total transmittance. Phase shifts of the light when being reflected back and forth between the two surfaces is not included in the above expressions because the surfaces were not perfectly parallel, resulting in a washing out of any interference fringes. The absorption coefficient as a function of wavelength plotted in FIG.7B identifies the band edge and the f-f transitions. Among the different rare earth elements in the R1Ba3(B3O6)3 crystals, Nd exhibits the strongest absorption due to the prolific f-f electronic transitions within the electronic gap (identified in the FIG. 7A; the bands were inhomogeneously broadened and assigned to various transitions from the ground state of4I9 / 2.

[0205] The photoluminescence measurement with 532-nm pump wavelength was performed to identify the emission spectrum of the samples (FIG.8). In the case of NdBa3(B3O6)3, strong4F3 / 2 →4I11 / 2 radiative transition is observed below 1064 nm. NdBa3(B3O6)3 sample was characterized at 100 times lower incident irradiation due to its strong photoluminescence response compared to other crystals. Similarly, a strong emission spectrum was observed for both Sm- and Er-borate crystals. The strong photoluminescence response makes R1Ba3(B3O6)3 potential candidates as laser crystals.

[0206] For obtaining the real and complex parts of the refractive index, as well as the electronic bandgap, spectroscopic ellipsometry measurement were performed at room temperature in the spectral range of 200–1000 nm. Space group P6^has two distinct refractive indices, ordinary and extraordinary (no and ne). The data were taken in the reflection geometry, and the backside was wedged to minimize the multiple reflections. The measured real part of the refractive index is plotted in FIGS.9A-9B. The crystals are negative uniaxial, i.e., no > ne for all five compositions. To extract the bandgap from the imaginary part of the refractive index, Tauc analysis was conducted using the equation: (^ℎ^)^ / ^ = ^\ℎ^ − ^^]where n = 2 and 1 / 2 for the respectively (FIG.9C). Here,α is the absorption Eg is the band gap andAttorney Docket No.11196-117WO1 hν is the photon energy. The analysis reveals the direct bandgap for the crystals to be between 5.6 and 5.8 eV (FIGS.9C-9D).

[0207] Optical Second Harmonic Generation: Optical SHG is a sum frequency generation process where two photons of the same frequency, ω combine to create a photon of the double frequency, 2ω. A noncentrosymmetric point group would enable the dipolar SHG signal from the sample, while it will be absent in a centrosymmetric crystal system. As a design criterion, the SHG photon energy should be non-resonant, i.e., below the band edge energy. In the case of R1Ba3(B3O6)3 crystals, applicability range is as low as 225 nm. Building on the bandgap and emission spectrum identified by the linear optical characterization, 800-nm light has been selected for the fundamental beam of the optical SHG measurements since there are no emission bands at that wavelength, as well as no strong absorption or resonances at 400 nm. Furthermore, no photoluminescence was observed at 400 nm when a 532-nm light was used as an excitation source.

[0208] The SHG measurements were conducted in the normal transmission geometry with the polarizing half wave plate inducing a rotation of the linearly polarized light (FIG. 10A). The experimental configuration was arranged to have the crystallographic a and b orientations perpendicular and parallel to the plane of incidence, respectively. In this configuration, strong SHG signal was observed from R1Ba3(B3O6)3 crystals (FIG.10B), which can be explained by assuming the highest possible symmetry as point group symmetry 6^, as discussed above. The SHG intensity (Is and Ip) for point group 6^at normal incidence is expressed as follows: $%̂_ ∝ (( %% )%^^sin 2- + ( cos 2-%where the(B3O6)3 (FIG.10A) is assumed, and ψ is the rotation angle of the incident polarization (FIG.10A). In order to get quantitative values for the nonlinear coefficients, more precise expressions for the intensity involving the slab geometry and Fresnel coefficients were extracted from the #SHAARP.ml package.Attorney Docket No.11196-117WO1 TABLE 6. Nonlinear Optical coefficients for the R1Ba3(B3O6)3 single crystal sample. )

[0209] From the nonlinear optical fitting in FIGS.10C-10D, the relative values of the d11 and d22 were measured, and further comparison with LiNbO3 reference provided the absolute values of the coefficients. Among the R1Ba3(B3O6)3 crystals studied, DyBa3(B3O6)3 has the highest nonlinear optical coefficient d11 of 1.29 pm / V (TABLE 6). NLO coefficients of this series have been compared with the contemporary UV-C NLO crystals (FIG.10E). Laser-induced surface damage threshold (LISDT) of these crystals was measured using 800-nm, 100-fs laser light on polished crystals down to 0.05 µm diamond grid. The LISDT for these crystals are four to five times higher (650–800 GW / cm2) than the commercially available and commercially polished β-BaB2O4 crystals (FIG.10F). As most commercial utilization of these nonlinear optical materials is in frequency conversion and parametric amplification, this ensures that the crystals can withstand high power without damage. NLO coefficient ratio of ErBa3(B3O6)3 was not measured as the crystals are twinned.

[0210] Efficient conversion from fundamental optical pump to SHG requires proper phase relationship between the interacting waves, which is dictated by the phase- matching condition. Chromatic dispersion can cause phase mismatch at different wavelengths, and the choice of both the incident polarization and the crystallographic orientation is important. For the negative uniaxial crystal, the phase matching angle (θm) for Type-I and Type-II phase matching (θmIand θmII, respectively) fulfills the following conditions: ^(2n) % ^%(2n) %%( 8k ) l m 1 − ^1(n)sin 5 =^ (pqr^ − $W(n) o^1%(2n) − ^3%(2n) )Attorney Docket No.11196-117WO1

[0211] Considering an azimuthal angle of φ (defined in FIG. 6C), the effective nonlinear optical coefficient of Type-I and II phase matching conditions (deff,type-I and deff,type-II, respectively) can be calculated as:

[0212] These phase-matching angles and effective phase-matched nonlinear coefficients are plotted in FIGS.11A-11D.

[0213] This series of crystals could be explored as an environmentally stable complement to traditional β-BaB2O4 crystals. Although the phase matchable SHG coefficient of DyBa3(B3O6)3 is limited to about half of that of β-BaB2O4, the LISDT is four times higher; one can pump the DyBa3(B3O6)3 with four-times higher pump energy, yielding potentially a net SHG gain of about 2.52 ( = 6.25) times larger than the SHG from a β-BaB2O4 crystal.

[0214] As seen in TABLE 6, no strict trend is observed for the SHG coefficient is observed as the crystalline radius of the rare-earth cation decreases. This is because the SHG signal is arising from the positional disorder on the Ba-site (see FIG.6E). If all the Ba atoms were to move in the same direction, one would achieve the highest d coefficients for each composition. However, x-ray indicates equal probability of up versus down displacements of the Ba atom, thus effectively cancelling out most of the SHG signal. The SHG signal that was observed experimentally is thus a statistical difference between the two positions at any given location. For this reason, these numbers in TABLE 6 should be treated as lower bounds; the actual numbers may be significantly higher. It also suggests that “poling” these crystals could yield much larger SHG coefficients.Attorney Docket No.11196-117WO1

[0215] However, all other things being equal among different compositions, in TABLE 6, a general increase is observed in the SHG coefficients with a decrease in the rare-earth cation radius. The enhancement of the SHG coefficient can generally be achieved by increasing the polarizability of the system or the anharmonicity of the electronic potential wells. Since the dielectric polarizability of the rare earth cation decreases with decreasing size , the SHG coefficient enhancement in R1Ba3(B3O6)3 family with decreasing R size could possibly arise from increasing anharmonicity of the potential wells around the rare earth cations. Experimental Procedure

[0216] Crystal Synthesis: The polycrystalline synthesis was performed via the solid-state synthesis, utilizing materials sourced for their high purity: BaCO3 (99.5%, Alfa Aesar), R2O3 (99.9%, Alfa Aesar, R = Nd, Sm, Tb, Dy, and Er), H3BO3 (99.4%, EMD Chemicals). The composite material was placed in an Al2O3 crucible and initially heated to 400°C for an hour to ensure the decomposition of BaCO3 and H3BO3. The temperature was then increased to 850°C at a rate of 200°C / hour and maintained for 72 hours before allowing the crucible to cool naturally. Powder x-ray diffraction analysis confirmed the successful synthesis of polycrystalline powder in a pure R1Ba3(B3O6)3 phase. (FIG.14)

[0217] Subsequently, R1Ba3(B3O6)3 single crystals were grown using a floating- zone technique, employing a commercial image furnace equipped with double- elliptical mirrors (Model: IRF01-001-05, Quantum Design). For preparing the feed and seed rods, polycrystalline R1Ba3(B3O6)3 powder was finely ground and compressed within a cylinder-shaped rubber balloon, encased in a quartz tube, and sintered at 800°C for 48 hours. R1Ba3(B3O6)3 powder was placed at the bottom of the Al2O3 boat during the rod preparation to prevent aluminum contamination. In the floating-zone crystal growth process, the aligned feed and seed rods were positioned near the melting zone with a small gap left between them. After sealing the growth chamber and oxygenating it for 15 minutes, the oxygen pressure was increased to 2 atm. Upon reaching this pressure, the voltage to the halogen lamps was ramped up to melt the bottom end of the feed rod. The voltage was adjusted within the 35–57 V range to maintain a T-shaped melting zone, facilitating optimal crystal growth. The growth was conducted at a speed within the range of 3–20 mm / hour, resulting in a crystal rod approximately 30–50 mm in length containing multiple domains. Single-domain crystals were subsequently isolated by cleaving the rod with a razor blade.Attorney Docket No.11196-117WO1 R1Ba3(B3O6)3 single crystals contain planar [B3O6] rings in the crystallographic a-b plane, and the planar rings are separated by weak conjugated π-bonds, thereby enabling cleavage and collection of single crystal with

[0001] orientation in the thickness direction. The single crystals were mounted on a goniometer, and the crystallographic orientation was further validated using the Laue diffractometer. The goniometer stage was utilized to conduct fine adjustments and prevent misorientations of the single crystal. The R1Ba3(B3O6)3 single crystal samples were then subsequently polished to obtain parallel slabs, which were further utilized to characterize both linear and nonlinear optical properties.

[0218] Optical Second Harmonic generation: In linear optics, the polarization caused by light is proportional to its electric field, E of the incident light. In nonlinear optics, the polarization in a material may be represented as a full power series in the electric field, containing terms with higher-order dependencies on the electric field. Considering Pi0to be the spontaneous polarization and x^(^)being the n-th order non- linear susceptibility, the induced polarization Pias follows: (^) (%) (^)F = F + + x^ + + ⋯ ^

[0219] The^^%where the%in abbreviatednotation.

[0220] For thesapphire pulsed seed laser was utilized with 800-nm fundamental wavelength. Pulsed laser beam was modulated using a chopper that superimposes a frequency of 1 KHz that is detected by the lock-in amplifier. Initially, the half-wave plate was introduced to make linearly polarized light that goes through the dichroic mirror towards a numerical aperture and onto the sample. TheAttorney Docket No.11196-117WO1 dichroic mirror allows the 400-nm SHG generated light to transmit through while the reflected fundamental wavelength is being filtered through. Two bandpass filters were utilized to allow only the 400-nm light to pass through. Finally, a 50-mm convex lens was utilized to concentrate the beam onto the photomultiplier tube. The photomultiplier tube converted the photons into a photocurrent that went through a resistor, and the locking amplifier calculated the corresponding voltage.

[0221] To obtain the dij coefficients ratios of R1Ba3(B3O6)3, the polar plots were fitted to an analytical model based on its point group symmetry 6^and compared with that measured on a wedged z-cut LiNbO3 reference under the same experimental conditions.

[0222] X-Ray Crystallography: The single crystal diffraction data were collected with a diffractometer equipped with Rigaku Micromax 007 rotating anode x-ray generator (CuKα), Osmic Varimax VHF monochromator, a universal four-circle Kappa goniometer, and a HyPix-Arc150 area detector. The samples were ground up to make small flakes of about 10 µm. Then a single crystal was mounted on the goniometer to collect the diffraction data, and the collected datasets were further analyzed using direct method to extract the structural parameters such as lattice constants and atomic internal coordinates. Furthermore, θ-2θ x-ray diffraction patterns were collected with the manual z-stage (to minimize the ω shift caused by sample displacement) from the single crystals after polishing along the (0001) cleave plane. The data was collected in ω-2θ goniometer geometry. Powder x-ray characterization was also performed using Panalytical Empyrean 4 with θ-2θ goniometer geometry for the powder samples obtained by grounding the single crystals by ceramic mortar. Prior to the experiment, the systems were calibrated through powder crystalline Si.

[0223] Scanning Electron Microscope and Energy Dispersive Spectroscope: The scanning electron microscope analysis was conducted by the Apreo 5 scanning electron microscope. The samples were coated with Ir and Energy dispersive spectroscopy was conducted in low vacuum configuration.

[0224] Linear Optical Properties: Transmission and reflection at the 250–2000 nm have been characterized by UV-vis spectroscopy (Agilent UV-Vis-NIR Spectrophotometer). Fourier Transform Infrared Spectroscopy (FTIR) was utilized to measure reflection and transmission in the range of 2–16 µm using Bruker Vortex 80 instrument with HgCdTe (so-called MCD) detector. Both UV-vis and FTIRAttorney Docket No.11196-117WO1 characterization were conducted by mounting the single crystal samples facing the (0001) plane towards the beam in the integrating sphere and standard accessories configurations in both transmission and reflection geometry. The data was then fitted considering possible multiple reflection geometry of a parallel slab. To extract the absolute value of transmission and reflection, the obtained data were compared with reference spectra obtained in air (for transmission) and by reflection from gold (for reflection). Ellipsometry was utilized to extract the complex linear optical refractive index (n = n+ ik) between 200 and 1000 nm. The data was then analyzed through identifying subsequent oscillators to extract the n and k from the experimental parameters. Tauc plot was utilized with n = 2 or 1 / 2 (see the main text for the equation) for indirect and direct transitions, respectively. The final direct and indirect bandgap was calculated through extrapolating the absorption edge.

[0225] Laser-Induced Surface Damage Threshold Measurements: Laser- induced surface damage threshold (LISDT) was measured utilizing 100-fs 1-KHz Ti: Sapphire pulsed laser of 800-nm wavelength on optical grade polished (down to 0.05 µm diamond grid) sample. The laser light was focused using a 10-cm lens and consequently monitored for surface damage using an optical microscope. The beam spot size at the focus was measured using knife edge measurement. Conclusion

[0226] Single crystal growth and structural and optical characterization of rare earth borates, R1Ba3(B3O6)3 (R = Nd, Sm, Tb, Dy, and Er) are presented in this study. This is the second successful case of rare earth borate single crystal growth by the optical floating zone method. This series of borate crystals, especially DyBa3(B3O6)3, have significant SHG coefficient comparable to β-BaB2O4. Additionally, the borates are both Type-I and Type-II phase matchable and possess a large LISDT value in the range of 650–800 GW / cm2at 800-nm, 100-fs laser irradiation, which makes them an environmentally stable complement to traditional β-BaB2O4 crystal. This study also establishes a materials design approach to synthesize borates with strong SHG enhancement in the UV-C region via the tuning of potential-wells anharmonicity by chemical stress, which is in this aspect allowable by an additional degree of freedom in the chemical composition stemming from the inclusion of rare-earth cations. Example 4

[0227] X-ray Diffraction and structural analysis: Single Crystal X-ray refinement has been conducted on a diffractometer equipped with Rigaku Micromax 007 rotatingAttorney Docket No.11196-117WO1 anode Cu X-ray generator with Osmic varimax VHF monochromator, and a universal four circle kappa goniometer and a Hypix-Arc150 area detector. The samples were cut down to thin slices of 10-20 µm and analyzed through the direct X-ray method. Theconstituted unit cell upon single crystal refinement (for P6^ structure) are listed inTABLES 7-11. The measurement was conducted at room temperature (300K). TABLE 7. Single crystal X-ray refinement parameters at 300K temperature for the P6^structure of TbBa3(B3O6)3 No. Atom Number x y z Occ. SiteP6^structure of DyBa3(B3O6)3. No. Atom Number x y z Occ. Site 1 Ba Ba1 1 1 0.9823 0.5 2gAttorney Docket No.11196-117WO1TABLE 9. Single crystal X-ray refinement parameters at 300K temperature for the P6^structure of NdBa3(B3O6)3 (the photo of the single crystal rod grown according to aspects described herein is shown in FIG.26). No. Atom Number x y z Occ. Site 1 B B 1 1 1 09792 05 2Attorney Docket No.11196-117WO1TABLE 10. Single crystal X-ray refinement parameters at 300K temperature for the P6^structure of SmBa3(B3O6)3. No. Atom Number x y z Occ. Sitethe P6^structure of ErBa3(B3O6)3. No. Atom Number x y z Occ. Site 1 Ba Ba1 1 1 0.9812 0.5 2gAttorney Docket No.11196-117WO1

[0228] Single crystal refinement was conducted on Olex2 with ShelX package. To achieve proper identification of space group of this single crystal system, R-factor (measurement of agreement between the crystallographic model and the experimental x-ray pattern) was analyzed for seven different suitable crystal systems. The comparison of the Rint factor across different space groups is listed in TABLE 12. Achieving close congruence between experimental results and crystallographic modelling requires low Rint value. Notably, the X-ray selection rule provides a direct pathway to shortlist the possible candidates of space groups for this material system (in an ideal single crystal sample). The analysis indicates space group P63 / m, P6^& P1121 to be suitable for the R1Ba3(B3O6)3 single crystals. However, the centrosymmetric P63 / m space group has not been ruled out through second harmonic generation (SHG) analysis. The result from the Second harmonic generation fitting further clarified the highest possible symmetry of the point group being P6^. The fitting parameters utilizing P6^space group are listed on TABLE 13.Attorney Docket No.11196-117WO1 TABLE 12. Rint values from the Single crystal X-ray refinement parameters at 300K temperature for different point groups of R1Ba3(B3O6)3. 2 8 8 3 5 3TABLE 13. Fitting values for the single crystal X-ray refinement at 300K for point groupP6^.Sample R1(%) wR2(%) I / σ GooF Max peak Min Peak3 3 6 3 g y y g g od. The single crystals contained elements with high mass absorption coefficient (Nd, Sm, Er, Dy, Tb, Ba). Thus, samples were prepared into thin slices to mitigate this scattering and absorption issue. In a few of those thin slices (10-20 µm), a lack of long-range order has been identified. However, twinning during the single crystal x-ray analysis was not observed. Meanwhile, in the θ-2θ x-ray diffraction condition in the Empyrean 4 diffractometer and Laue diffraction experiment (FIG. 12 and FIGS. 13A-13D), ErBa3(B3O6)3 has been observed to have twinning for the large scale 2mm-3mm single crystals.

[0230] Energy-dispersive X-ray spectroscopy: Energy-dispersive X-ray spectroscopy (EDS) characterization has been conducted on the R1Ba3(B3O6)3 single crystal samples. The analysis was conducted on a low vacuum to prevent charge accumulation from the insulating samples. From the analysis, stoichiometry of the Ba / R is close to 3 for all the R1Ba3(B3O6)3 compounds but Nd Ba3(B3O6)3. TheAttorney Docket No.11196-117WO1 identification peak for the Nd is close to Ba peak and thus in the quantitative peak fitting have underestimated the Ba / Nd ratio. The proper stoichiometry has previously been confirmed using the single crystal x ray diffraction. The elemental composition for each of the single crystals are listed at TABLE 14 and the spectrum was further illustrated in FIG.15. TABLE 14. Elemental composition for the R1Ba3(B3O6)3 single crystals refined from the EDS (Energy-dispersive X-ray Spectroscopy) at low vacuum. ElementsAttorney Docket No.11196-117WO1

[0231] Homogeneity of the individual constituent element in the single crystal sample has further been analyzed using EDS at high vacuum. The single crystals samples were coated with iridium to prevent charge accumulation during mapping. The mapping indicates homogenous distribution of constituents for Nd / Sm / Tb / ErBa3(B3O6)3 samples (FIGS.16A-16E, FIGS.17A-17E, FIGS.18A-18E, FIGS.19A-19E, FIGS.20A-20E, FIGS.21A-21C, FIGS.22A-22C, FIGS.23A-23C, and FIG.24). However, Dy2O3 segregation has been observed for a specific region on the Dy Ba3(B3O6)3 samples. Otherwise, long range crystallographic ordering and elemental homogeneity can be confirmed by the single crystal X-ray and EDS analysis. The segregation behavior of the DyBa3(B3O6)3 sample has illustrated in FIGS.21A-21C. Optical microscope image of the polished DyBa3(B3O6)3 single crystal surface before (FIG.25A) and after (FIG.25B) the irradiation is shown in FIGS.25A- 25B.

[0232] Ellipsometry and linear optical characterization: The ellipsometry data has been fitted with oscillator-based modelling to define the real and complex part of the dielectric constant at optical frequency. The Lorentz oscillator is suitable to define physical phenomena response of a system under driven oscillation (fundamentally similar to the dielectric response of materials). It can be defined as: ^γ%^(^) =(^ − ^^)% +

[0233] Herem A is theE is the energy, γ is the broadening parameter and E0 is the center energy in eV. The individual oscillator parameters were listed on TABLE 15.Attorney Docket No.11196-117WO1 TABLE 15. List of amplitude, broadening parameter and center energy for the Lorentz oscillator utilized to quantify the dielectric function of the R1Ba3(B3O6)3 ,eco a o c e ea o easue e eco a onic generation measurements were conducted in the 300K temperature using fundamental 800 nm wavelength 1KHz pulsed laser. The SHG polarimetry and effective nonlinear optical coefficients are illustrated at FIGS.22A-22C and FIGS. 23A-23C. The nonlinear optical coefficients were extracted through comparing z-cut LiNbO3 at the same experimental conditions (FIG.24).Attorney Docket No.11196-117WO1 TABLE 16. List of Second harmonic generation fitting equations considering multiple reflection, phase shift utilizing #SHAARP.ml package at different sample geometries.TABLE 17. List of Second harmonic generation fitting equations considering multiple reflection, phase shift utilizing #SHAARP.ml package at different sample geometries. Samples SHG intensity as a function of incident polarization angle ]- + 2Attorney Docket No.11196-117WO1Example 5

[0235] High entropy engineering of oxide single crystals can yield enhancement of properties such as structural stability, enhanced mechanical property, and thermal stability. In this investigation, a family of high entropy oxides containing rare earth borates (R5&R6Ba3(B3O6)3 (A = Nd, Tb, Sm, Dy, Gd, Yb, and Er) with enhanced optical properties is reported. This is the first report of high entropy single crystal synthesis of rare earth borates utilizing the optical floating zone method. This series of high entropy materials is transparent and contains fewer defects than the R1Ba3(B3O6)3 single crystals.

[0236] The rare earth borates have excellent potential for both linear and nonlinear optical applications. High entropy engineering increases the configuration entropy of the solid solution phase of R1Ba3(B3O6)3 single crystals at a high temperature compared to the traditional monolithic oxides. The reduction of Gibbs free energy of the system favors the formation of a single-phase structure over the possibility of phase segregation. The blend of rare earth oxides produces unique optical properties, as due to high band degeneracy, it has interesting electronic structures with multiple states with similar energy, leading to a high number of emission spectra which can be utilized in applications such as potential laser applications. Rare earth high entropy oxide can also have complex dispersion due to the presence of multiple cations with different polarizabilities, which can be utilized in applications such as lenses and waveguides. Finally, most high symmetry structures can have a high disorder that enhances the anharmonicity of the potential well, which has the capability for large second harmonic generation enhancements.Attorney Docket No.11196-117WO1

[0237] In this investigation, the focus is on understanding structural dynamics that lead to emergent and functional properties on the rare-earth high-entropy oxide through XRD, EDS, XPS, and TEM. This will be followed by linear (UV-vis and FTIR) and nonlinear (SHG) optical characterizations. This analysis also focuses on the emission spectrum of the HEO compounds and the subsequent quantum yield for potential laser applications. Research Objectives

[0238] R1Ba3(B3O6)3 is the first reported synthesis of such high-entropy single- crystal materials. It has the potential to be utilized as an optical material. For this project, the following list of objectives was determined:

[0239] 1) Determination of crystallographic structure and subsequent comparison with the monolithic single crystals to identify the impact of disorder and high entropy in the family of materials.

[0240] 2) Characterization of linear and nonlinear optical properties to identify its potential as a functional optical material.

[0241] 3) Experimentally validate the phase-matching condition for these materials to their NLO potentials.

[0242] 4) High entropy materials are hard to synthesize in the single crystal or thin film form due to their high segregation tendency. To delineate that, systematic characterization of XPS and EPMA to validate the structure and bonding information.

[0243] 5) Identify potential functional properties such as ferroelectricity, electro- optics and piezoelectric for these single crystals. TABLE 18. Binding energy comparison between reference 4d metal and high entropy sample. Z Rare Earth 4d (metal) R6sample 60 Nd 121 121.3Attorney Docket No.11196-117WO1 Experimental Procedure

[0244] Crystal Synthesis: The single crystal synthesis is similar to the previous chapter of R1Ba3(B3O6)3 samples. Here, polycrystalline synthesis was performed by similar solid-state synthesis with sources materials BaCO3 (99.5%, Alfa Aesar), R2O3(99.9%, Alfa Aesar, R = Nd, Sm, Tb, Dy, Gd, Er and Yb), H3BO3 (99.4%, EMD Chemicals). The composite material was placed in an Al2O3 crucible and initially heated to 400°C for an hour to ensure the decomposition of BaCO3 and H3BO3. The temperature was then increased to 850°C at a rate of 200°C / hour and maintained for 72 hours before allowing the crucible to cool naturally. Powder x-ray diffraction analysis confirmed the successful synthesis of polycrystalline powder in a pure R1Ba3(B3O6)3 phase. The composite material was placed in an Al2O3 crucible, heated to 400°C for an hour to decompose BaCO3 and H3BO3, then increased to 850°C at 200°C / hour, maintained for 72 hours, and cooled naturally. Powder x-ray diffraction confirmed the synthesis of pure polycrystalline RnBa3(B3O6)3.

[0245] Single crystals of RnBa3(B3O6)3 were grown using a floating-zone technique with an image furnace. The polycrystalline powder was ground, compressed, and sintered at 800°C for 48 hours to prepare feed and seed rods. To avoid aluminum contamination, RnBa3(B3O6)3 powder was placed at the bottom of the Al2O3 boat. The growth chamber was oxygenated to 2 atm, and halogen lamps were used to melt the feed rod, maintaining the melting zone at 35-57 V. Growth was conducted at 3-20 mm / hour, producing crystal rods with multiple domains, which were isolated into single-domain crystals.

[0246] XPS measurement: XPS experiment was performed using the Physical Electronics VersaProbe III instrument with a monochromatic Al kα x-ray source (hν = 1486.6 eV) and a concentric hemispherical analyzer. Charge neutralization was performed using both low-energy electrons (<5 eV) and argon ions. The binding energy axis was calibrated using sputter-cleaned Cu (Cu 2p3 / 2 = 932.62 eV, Cu 3p3 / 2 = 75.1 eV) and Au foils (Au 4f7 / 2 = 83.96 eV). Peaks were referenced to Ba2+band in the barium 3d5 / 2 spectra at 779.6 eV. Measurements were made at a takeoff angle of 45° with respect to the sample surface plane. This resulted in a typical sampling depth of 3-6 nm (95% of the signal originated from this depth or shallower). Quantification was done using instrumental relative sensitivity factors (RSFs) that account for the x- ray cross-section and inelastic mean free path of the electrons. On homogeneousAttorney Docket No.11196-117WO1 samples, major elements (>5 atom%) tend to have standard deviations of <3%, while minor elements can be significantly higher. The analysis size was 200 in diameter. All samples were fractured in an argon glovebox and transferred to the XPS system using an inert sample transfer vessel to minimize O2 and H2O exposure.

[0247] Optical Characterization: Similar to the R1Ba3(B3O6)3 sample, a titanium sapphire pulsed laser with an 800-nm fundamental wavelength was used for nonlinear optical characterization. The pulsed laser beam was modulated using a 1 kHz chopper, detected by a lock-in amplifier. A half-wave plate produced linearly polarized light that passed through a dichroic mirror onto the sample. The dichroic mirror transmitted the 400-nm SHG light, filtering out the fundamental wavelength. Two bandpass filters allowed only 400-nm light to pass. A 50-mm convex lens focused the beam onto a photomultiplier tube, which converted photons to photocurrent. The lock- in amplifier measured the corresponding voltage.

[0248] To obtain the dij coefficients ratios of RnBa3(B3O6)3, polar plots were fitted to an analytical model based on its point group symmetry 6^and compared with a z-cut LiNbO3 reference under the same conditions. The linear optical property measurement and LISDT measurements were exactly the same as the RnBa3(B3O6)3 sample from the previous chapter.

[0249] Structure determination, Stoichiometry and Bonding: Structural analysis on the high entropy oxides reveals congruence with the P6^structure. The powder X-rd data in FIG.27A demonstrated similar trends among the high entropy oxides. However, direct x-ray refinement of the single crystal samples maintains a better congruence with the P3 structure. The local distortion caused by the rare earth site in the ‘2a’ Wyckoff position has significantly impacted the final unit cell in the direct X-ray refinement. Due to the complexity of the rare earth site, a successful solution has yet to be obtained from this refinement. However, from the Rint value, the bestpossible candidates are both P3, and P6^ remains the best two candidates. Highentropy oxides often have issues of segregation and clustering during the formation of the single crystal, which can lead to nonstoichiometric compounds.

[0250] To delineate the elemental composition within the single crystal, EDS measurement has been conducted and illustrated in FIG.27B. From EDS mapping, the homogeneity of the high entropy site has been validated. Furthermore, the analysis further confirms the rare earth stoichiometry for the Ra5, Rb5, and R6compounds. TheAttorney Docket No.11196-117WO1 laue diffraction experiment has been performed to judge the crystallinity and crystallographic orientation of the single crystal FIG. 27C. The sharp diffraction patterns have further validated the highly crystalline nature of the sample, and no impurity phase has been observed in both XRD and EDS experiments.

[0251] Synthesis of stable high entropy single crystal samples are challenging as most high entropy samples are highly susceptible to elemental segregation. Although XRD and EDS measurements identify that within the probing region, the stoichiometry of the rare earth elements in the high entropy site is similar, these experiments alone cannot delineate the bonding characteristics. Moreover, in rare earth-high entropy oxides, the formation of nonstoichiometric compounds can be prevalent. To validate the localized charge state and bonding characteristics of the rare earth high entropy site, XPS analysis was performed on the sample (FIGS.28A-28B). Due to the low atomic occupancy of the rare earth site in this sample, initial references were taken from the parent R1Ba3(B3O6)3 single crystals to properly identify the line shape from the rare earth 4d spectrums. The center of the line shape (binding energy) for rare earth 4d samples was compared with the reference 4d metallic spectra as well (TABLE 18). The barium and boron interference has also been accounted for in FIG. 28B. Although, due to the complexity of the peak shape for rare earth systems, the oxidation state is harder to account for, the fitting unambiguously confirms the presence of a 3+ state.

[0252] Characterization of optical properties: Linear optical characterization through UV-vis spectroscopy FIG.29A reveals high transparency of about 80-95% in the visible and IR range, which is higher than the monolithic samples. Notably, the absorption bands that were previously visible in the monolithic single-crystal sample have been quenched in the high entropy oxides. This phenomenon observed in these single crystals can have potential implications as the high entropy boasts lower optical loss than the monolithic samples.

[0253] High band degeneracy is common for rare earth samples, leading to f-f transitions that were observed in the R1BBO samples. As the high entropy sites are occupied by these rare earth elements, the concentration of individual rare earths has wholistically decreased for this series of samples, potentially leading to the quenching of these absorption bands and increasing transparency. To investigate the change of the bandgap, Tauc plot analysis has been conducted on these materials in FIG.29B that demonstrated the bandgap varies from 4.6-5.1 eV which is lower than the R1BBOAttorney Docket No.11196-117WO1 single crystals (5.5-5.7 eV). The decrease in the band gap can be associated with enhanced disorder leading to weakening of the local bond strength, a phenomenon that is well established in high entropy samples. Real and imaginary parts of the dielectric constant have been characterized by ellipsometry in FIG.29C. Similarly to monolithic samples, strong photoluminescence has been observed in both visible and infrared regions for the high-entropy oxides as shown in FIG.29D.

[0254] Nonlinear optical (NLO) characterization reveals the highest coefficient of 2.1 pm / V, which is higher than that of the monolithic single crystals. Furthermore, the measured Laser-induced surface damage threshold (LISDT) for the high-entropy single-crystal samples ranges from 685-710 GW / cm2, comparable with the monolithic samples. The high NLO coefficient coupled with large LISDT makes this series of crystals suitable for laser applications. The optical properties discussed have been listed on TABLE 19. The NLO coefficients increase as the optical bandgap decreases, which is consistent with this series of samples. Additional Research Objectives

[0255] The high entropy engineering of RnBa3(B3O6)3 single crystals elucidates its potential utilization as an optical crystal. The following list of investigations can further alleviate the complexity associated with HEOs:

[0256] 1) Refinement and analysis of the crystallographic information of the high entropy oxide, which will help discern the emergent properties.

[0257] 2) Quantification of the NLO tensor quantities and temperature-dependent SHG experiment to identify any potential ferroelectric transitions.

[0258] 3) Experimentally identify and design experimental configurations to identify the phase-matching condition, which will validate the samples as viable NLO material.

[0259] 4) Time domain photoluminescence and quantum yield measurement to quantify the emission response of the material, which have potential implications for laser application.

[0260] 5) Synthesis of other combinations of the rare earth high entropy oxides and further characterization to identify roles of individual rare earth elements towards enhancement of functional optical propertiesAttorney Docket No.11196-117WO1 TABLE 19. Optical properties of the high entropy single crystal sample (FIGS.30A- 30E). x )

[0261] Poling and SHG enhancement of the R1BBO sample: Regions of enhanced SHG response were observed in a few R1Ba3(B3O6)3 single crystals. As discussed earlier, due to the dynamic instability / static positional disorder observed in the RnBa3(B3O6)3 single crystal family, the bulk average response can be decreased. Observing regions with enhanced SHG response can be a potential pathway to engineer such properties on these single crystals. The region has been illustrated in FIG.31A. Here, the overall SHG response is 50X compared to the rest of the bulk.

[0262] PE loop measurements were conducted to determine whether the material is ferroelectric. From the PE loop measurement in FIG.31B, no saturation polarization was observed, so it was not identified as ferroelectric in the current optimization condition.

[0263] Further investigation of the local SHG-enhanced regions should be conducted via in situ X-ray microscopy. So far, the polarimetry from the SHG- enhanced region and the average bulk region indicate (FIGS. 31C-31D) different responses indicating a potential crystallographic change. The SHG-enhanced region has been fitted considering a monoclinic unit cell, and the individual coefficients were not delineated. However, the differences in response are apparent, and further investigation will be conducted to engineer SHG enhancement on this single crystal. Poling can be another potential pathway to enhance the SHG response of these materials, as discussed in detail above. Example 6

[0264] This study reports the first successful synthesis and characterization of a new family of high-entropy rare earth borate (RnBBO) single crystals with compositions R5Ba3(B3O6)3 and R6Ba3(B3O6)3 (R = Nd, Tb, Sm, Dy, Gd, Yb, Er). Using configurational entropy as a tuning knob, these systems have been grown as large,Attorney Docket No.11196-117WO1 highly crystalline boules that exhibit a bandgap of ≈5eV and significantly enhanced optical transparency (20-50%) over single component systems. The presence of multiple rare-earth elements results in broadband photoluminescence in both the visible and the near-infrared wavelengths ranges, with co-existing emission bands at 605, 705, 813, 910, and 1030 nm. Further, broken inversion symmetry enables optical second-harmonic generation (SHG) with potential for both type-I and type-II phase matching. The highest observed effective phase-matched SHG coefficient of ≈2.1 pm / V at 800 nm to 400 nm wavelength conversion is 20% better than the commercial β-BaB2O4 (BBO), while its laser-induced surface damage threshold is 5-6 × larger for 100fs 800 nm pulse, enabling potentially an order of magnitude improvement in the frequency conversion efficiency. This work illuminates the promise of high entropy synthesis strategy for designing next-generation optoelectronic materials that combine increased transparency, strong broadband luminescence, and enhanced nonlinear response in a single platform. Introduction

[0265] In the field of optoelectronics, the engineering and generation of ultraviolet (UV-C, 100-280 nm) wavelengths enable many technologies, including frequency doubling and tripling of solid state lasers, ultraviolet (UV) sources for precision spectroscopy and high resolution lithography. Direct lasing in the UV-C is difficult due to the scarcity of suitable active media with a wide bandgap and efficient population inversion. A versatile method to obtain these wavelengths is through frequency conversion processes such as optical second-harmonic generation (SHG), sum and difference frequency generation, or other optical parametric processes. The design of the new nonlinear optical system with high optical quality and nonlinear susceptibility in the UV-C ranges, therefore, remains an important frontier in photonics and optoelectronics, demanding continued development and innovation.

[0266] The historical development of UV-C nonlinear optical crystals can be traced back to the discovery of quartz in 1961; however, it has limited SHG conversion efficiency. With the further development of crystal growth methodologies and improved understanding of crystal chemistry, nonlinear optical crystals such as Li / CsB3O5 (CBO & LBO), β-BaB2O4 (BBO), CsLiB6O10 (CLBO), and KBe2BO3F2 (KBBF) have been discovered, offering large phase-matching bandwidth, laser damage threshold, nonlinear optical (NLO) susceptibility, and a large transparency window. However, these breakthroughs introduced additional constraints: narrow thermal acceptance inAttorney Docket No.11196-117WO1 LBO the need for defect-free growth over large volumes in BBO hygroscopicity in CLBO and extreme layer-cleavage tendencies in KBBF. As a result, present-day ultraviolet laser systems are still engineered around delicate trade-offs among transparency, nonlinearity, birefringence, growth feasibility, and long-term stability (FIG. 32B). As a design rule, the traditional systems should maintain a balance between large laser damage threshold and large nonlinear optical coefficient, since instability under high laser fluence can significantly influence the performance (FIG. 32C). Despite these limitations, the laser labs across the world extensively utilize the BBO, casting it as one of the most important discoveries in the field of optical technology.

[0267] Among the available material candidates, rare earth borates are therefore an excellent alternate choice for frequency conversion applications due to their wide bandgap, good laser damage threshold, and can be designed to have a reasonable nonlinear optical susceptibility. Recently, R1Ba3B9O18 (R = Nd, Sm, Tb, Dy, and Er) single crystals with one cation on the R site have been reported, exhibiting an NLO susceptibility comparable to the BBO and a large laser damage threshold that is ≈5× larger than BBO. These crystals improved upon the known limitations of BBO, demonstrating better thermal and moisture stability. Observation of such excellent properties motivated further development of this newly discovered crystal family for lasers and wide-bandgap NLO applications.

[0268] On a parallel discussion, crystals with rare-earth dopants can also be utilized as a gain medium to generate tunable sources in the near-UV, down to approximately 200 nm. The presence of lanthanide dopants offers 4f-5d and parity- forbidden 4f-4f transitions that emit stable and narrow emission lines, which are invaluable for laser seeding, optical frequency standards, and pump–probe metrology. Borates are usually a suitable host for such application since they restrict the probability of multi-phonon quenching events in the bulk, preserving the optical emission. However, most systems containing rare earth only support a limited number of transitions. A medium capable of simultaneously accommodating multiple lanthanides without decreasing transparency would enable broadband emission and quasi-continuous tunability in a single platform.

[0269] The high entropy design introduces precisely this flexibility. When several cations of comparable radius and valence randomly share a crystallographic site, the high configurational entropy can stabilize a single solid solution that would otherwiseAttorney Docket No.11196-117WO1 result in phase segregation. Local structural dynamics leading to properties such as band gap tunability and low thermal conductivity can be achieved by using configurational entropy as a tuning knob. In oxide systems, the associated disorder perturbs phonon spectra, enhances lattice anharmonicity, and broadens local electronic environments without necessarily degrading transparency. The trigonal borate framework R1Ba3(B3O6)3 (R = Nd, Sm, Tb, Dy, Er, and Yb) is particularly suited to such an approach: its rigid B3O6 backbone delivers an intrinsic bandgap exceeding 5 eV, its negative–uniaxial birefringence favors type-I and type-II phase matching (a condition where the fundamental and second harmonic wave maintains a phase correlation, thereby maximizing the energy conversion), and its eight- to nine-fold A- site coordination tolerates the full lanthanide series from Nd to Yb.

[0270] Designing a single crystal with five or more rare earth elements on the R site will yield a high entropy configuration with degenerate 4f manifolds. The crystals would therefore possess a broadband photoluminescence ranging from the visible to the infrared (IR). For nonlinear optical applications, the added anharmonicity due to the disorder could additionally enable an effective second-order susceptibility χ(2). Such a material would exhibit two unique capabilities in a single-material platform: broadband emission and efficient nonlinear conversion that are conventionally obtained from separate crystals in ultraviolet laser materials.

[0271] The present work examines the prototype composition RnBa3(B3O6)3 with n rare earth elements, R, present in nominally equal molar ratio of 1 / n each. While this design space is large, this study focuses on three nominal compositions in this work, namely, Ra5Ba3(B3O6)3 = (NdTbSmDyEr)0.2Ba3(B3O6)3, Rb5Ba3(B3O6)3 = (NdTbSmDyYb)0.2Ba3(B3O6)3 and R6Ba3(B3O6)3 = (NdGdSmDyErYb)0.167Ba3(B3O6)3; for brevity, this study will henceforth refer to them as Ra5, Rb5, and R6respectively. Experimental deviations from these target compositions are discussed in the supporting information. The rare earth elements in the R site have been interchanged among the three high-entropy compositions to observe their corresponding effects on lowering absorption, enhancing nonlinear optical susceptibility, and maximizing broadband luminescence. Few of the rare earths like Nd, Sm, and Dy are present in all the compounds as the previous experiment on the parent borates showed improved functional properties (Nd borate had the highest photoluminescence yield while Dy and Sm containing borates had the highest NLO susceptibility).Attorney Docket No.11196-117WO1

[0272] Through compositional engineering, this work provides a framework for designing next-generation materials for optoelectronic applications. Commencing with comprehensive chemical and structural characterization through atomic-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF- STEM), X-ray photoelectron spectroscopy (XPS), and hard X-ray nanoprobe, the study aims to establish the crystallographic factors responsible for property enhancement and high-symmetry phase formation. In parallel, the study tests the hypothesis that improving lattice anharmonicity can improve NLO susceptibility, while enhanced crystallinity and long-range order enhance transparency, both of which have been assessed through detailed optical metrology. This broad characterization approach has led to the development of a superior optical crystal, exhibiting large SHG, improved transparency, and broadband photoluminescence that surpasses traditional commercially used crystals. Results and Discussion

[0273] Local structure and bonding: High-entropy rare earth borates (Ra5, Rb5, and R6) were synthesized using the optical floating zone method. This work reports the first successful synthesis of high-entropy borate in the single-crystal form. In the bulk form, the crystal can be refined to have the highest possible symmetry of P6^(No. 174) with lattice constants of a ≈ 7.17 Å and c ≈ 17.2 Å, archetypal to the parent compounds. The structure contains a 6-fold rotoinversion symmetry about the crystallographic c-axis and a horizontal mirror in the a – b crystallographic plane (FIGS. 33A-33B). The rare earth compounds (Nd, Sm, Gd, Tb, Dy, Er, or Yb) are tetrahedrally coordinated with oxygen (FIG. 33C). The structural framework is built upon the barium and rare earth components bonded with planar B3O6 rings. The bonding between boron and oxygen is ionic in nature due to the large electronegativity difference between the species. However, experimentally observed bond lengths are similar (vary between 1.34 and 1.47 Å within the ring structure). This π-conjugated nature of the bond (forming B3O6 ring) gives rise to electron delocalization, similar to resonance stabilization that helps maintain the flat geometry in the a – b crystallographic plane. Additionally, the planar nature of this bonding gives rise to a rigid structure having a wider bandgap and a large damage threshold under laser excitation, ideal for most optical applications. The framework is built from layers of corner-sharing B3O6 triangles that alternate with puckered Ba / R–O polyhedral slabsAttorney Docket No.11196-117WO1 along c, giving an ABA-stacked sequence in which the 2a Wyckoff site (Ba + R mixture) and the 6 B3O6 rings define channels parallel to the three-fold axis (FIGS. 33A-33C). On the other hand, the Barium atoms occupy two different Wyckoff positions within the lattice, while the refinement suggests a static positional disorder in the ‘2i’ site. The rotoinversion 6^axis imposes a horizontal mirror that bifurcates the ‘2i’ site. This symmetry restriction is not present if the structure is refined with a lower symmetry. There are additional theoretical bases for this assumption, where in a prototype sample, the formation enthalpy was calculated to be lowest for the P3 space group. In the parent compound where the rare earth site is only occupied by a single element, the refinement for both of the options gave similar results, and thereby thehighest symmetry of P 6^ has been considered for analysis to prevent over-parametrization. In a high-entropy setting, a singular Wyckoff position can accommodate different elements; consequently, their subsequent size differences can decrease the overall symmetry. From the structural refinement using direct x-ray, a nominal improvement of the Rint (a quantitative metric describing consistency of X-ray diffraction intensity between multiple reflection; a lower value indicate a better agreement) value for P3 vs P6^space group (3.4% vs 4.5% for R6compound) is seen.

[0274] The optical floating zone growth of the high-entropy borate yields a large boule (up to 5 cm × 3 cm × 1 cm dimensions) of crystals with multiple domains. The experimental diffraction pattern shows an excellent agreement with the theoretical x- ray data (FIG.33D). As the bonding is stronger in the a – b plane compared to the crystallographic c-direction due to B3O6 planar rings, the single crystals can be cleaved easily along the (0001) plane. The cleaved crystals typically have a dimensions of 1.5 cm × 1 cm × 0.8 cm, with their crystallographic c-axis oriented along the out-of-plane direction (FIG.33K). Notably, despite lacking a 6-fold rotation axis (space group P6^), the Laue backscattering diffraction patterns measured on these crystals depict a 2D projection of the reciprocal space containing information of the Laue class 6 / m. The Laue diffraction pattern shows sharp peaks about the (000l) zone axis. The simulated Laue pattern based on the P6^structure matches well with the experimental pattern (FIG.33E). The orientation as well as good crystalline quality are further verified by the sharp specular (000l) diffraction peaks in the θ-2θ measurement geometry (FIG. 33F), consistent with similar investigations.Attorney Docket No.11196-117WO1

[0275] Rare earth lanthanides in the periodic table, from Nd to Yb, have a Shannon- Prewitt crystallographic radius that changes from 98.3 pm to 86.8 pm, a variation of ≈15%. The rare earth borates (R1Ba3B9O18, R is the rare earth site) exhibits a similar hexagonal lattice with a general trend of cell volume decreasing with the increasing f orbital occupancy mainly due to the lanthanide contraction observed in the rare earth elements (FIG.33G). The single-crystal high-entropy oxides fall within the average cell volume between the individual monolithic compounds. The broader concept of solubility and preference in substitutional alloy formation is traditionally captured by the Hume-Rothery rule. This rule, originally described for metallic systems, suggests that a successful solid solution should maintain similarity of atomic size, crystal structure, electronegativity, and valence between the soluble elements. However, in designing high entropy oxides, the general guidelines of the rule can still be relevant according to contemporary theoretical and experimental frameworks. The rare earth elements prefer a predominant 3+ state, although they are highly sensitive to oxygen partial pressure. Individually, parent R1Ba3B9O18 single crystals are isostructural, while the electronegativity difference is small (≈0.15) between the rare earths. That also reflects in the experimental observation, where the high entropy borates form larger, clearer, and less defective crystals (Rint 4-5%) as compared to the parent compounds (Rint 8-10%).

[0276] To obtain a more rigorous elucidation of the local structure, the study has employed both scanning diffraction X-ray microscopy (SDXM) on the high entropy compounds. The SDXM measurement around the (0008) reflection (FIG. 33H) revealed that the change in c-lattice parameter is smaller than 5 × 10−5for a region over 110 μm long with ≈30 nm spatial resolution (FIG.33I). This corresponds to a variation of the unit cell length of less than ≈0.017 pm. Notably, the crystallographic c- axis of NdBBO and ErBBO (two end members of Ra5compound) are 1.75 nm and 1.705 nm respectively, which is a fractional change of ≈0.026; however, in the high entropy composition, the mixture of these rare earth elements forms a stable structure with a deviation that is three orders of magnitude lower. Furthermore, considering a prototype sample, the cell volume of Ra5is close to the average of the single R cation parent compounds (R1BBO). This indicates that irrespective of the disorder of the motif, the structure is stabilized to an average periodic unit.

[0277] To delineate the elemental composition within the single crystal, EDS measurements were conducted as illustrated in FIG. 33J. From EDS mapping, theAttorney Docket No.11196-117WO1 homogeneity of the high-entropy site has been validated. It also demonstrates the stoichiometry of the Ra5, Rb5, and R6compounds. These complementary characterization methods, encompassing X-ray diffraction (capturing long-range order), transmission electron microscopy and selected area electron diffraction (capturing atomic scale resolution of lattice coherency), energy dispersive X-ray spectroscopy and electron probe microanalysis (capturing micron-scale elemental distributions), and X-ray photoelectron spectroscopy (capturing surface chemistry and bonding states), collectively reveal a homogenous structure with no strong evidence of a secondary phase across these diverse length scales.

[0278] To probe the local bonding and electronic state, X-ray photoelectron spectroscopy (XPS) was employed (FIGS.33L-33N). All samples were fractured in an argon glovebox and transferred to the XPS system using an inert sample transfer vessel to minimize O2 and H2O exposure. Due to the low atomic occupancy (0.6 and 0.5 atom%, respectively, for the R5and R6compositions) of the rare earth site in the investigated samples, initial reference spectra were taken from the parent R1Ba3(B3O6)3 single crystals to properly identify the line shape from the rare earth 4d spectra. This is essential, as the core levels for the rare earth elements may contain unique and convoluted line shapes due to intrinsic multiplet splitting and complex final- state effects. For the lanthanide elements, the unpaired 4f electrons can play a significant role in any core-level spectroscopy due to significant spin-orbit coupling and interaction between the electronic levels. This causes overlapping final states, forming a broad asymmetric peak. From the experimental fitting (described in detail in the supporting section), the center of the line shape (indicating the binding energy) for rare earth 4d samples was compared with the reference 4d metallic spectra and other reported oxides, indicating a better match with the rare earth elements in the 3+ oxidation state. The lanthanides usually have an electronic configuration with 4f and 6s on the outer shell ([Xe]4fn6s2). While the first two electrons (6s2) are indeed the easiest to ionize, the third electron, which is typically from the 4f or 5d subshell, is not tightly bound. In most lanthanides, the energy required to remove a third electron is not excessively high, and the resulting 4fnconfiguration in the 3+ state is usually more stable overall, especially due to favorable lattice or solvation energies in compounds. However, the local bonding environment for high-entropy oxides is highly sensitive to the growth conditions, and a potential intermixing between various oxidation states is plausible.Attorney Docket No.11196-117WO1

[0279] To enhance understanding of the local atomic-scale perturbation, the study conducted an HAADF-STEM experiment. The unit cell includes heavy atoms like barium and rare earth elements, paired with lighter atoms like boron and oxygen, which were not visible in the STEM analysis. FIGS. 34A-34M presents atomic- resolution HAADF-STEM imaging, simulations, and structural analysis of RnBa3(B3O6)3 along the [101^0] zone axis. The experimental image (FIG.34A) and its magnified region (FIG. 34B), together with the simulated image based on DyBa3(B3O6)3 (FIG.34C) and the projected atomic structure model (FIG.34D), confirm that the material adopts a HCP structure same as DyBa3(B3O6)3. FIG.34E overlays the atomic displacement vectors at the X-site on the HAADF-STEM image in FIG.34A, highlighting the local distortion introduced by high-entropy element substitution. Finally, FIGS.34F-34G show averaged HAADF-STEM images and intensity profiles of single Ba columns and Ba dumbbell columns extracted from FIG.34A, confirming the presence of Ba dumbbell configurations along the [101^0] zone axis. X-ray indicates positional disorder in one of the Ba sites in the c-direction, which, if ordered, is predicted by theory to exhibit enhanced polarity. The theoretical prediction identified a Γ-point displacement of the Ba site that should lead to a ferroelectric soft mode. Experimentally, the ferroelectricity was not observed with reasonable fields applied to the sample; instead, the average structure exhibits a nonpolar, noncentrosymmetric P6^space group from x-ray structural refinement. The STEM analysis directly reveals the presence of dynamic instability in high-entropy element sites (FIG. 34E). This Gaussian fit of intensity profile of the average barium sites from STEM image reveals an increase of the FWHM of 32.1 pm (FIG. 34G). This is on the same order as observed in the classic ferroelectrics such as LiNbO3, where the Nb displacement of ≈20-35 pm has been observed through STEM analysis. Furthermore, the displacement of the rare earth and barium is not purely along the crystallographic c- axis, since it contains a small tilt angle in the a – c plane (FIG.34E). The hexagonal symmetry restricts the atomic motion to only along the c-axis; however, an in-plane tilt could cause the formation of a lower symmetry (monoclinic or triclinic) phase.

[0280] The large perturbation along the c-axis indicates that the structure can have a large thermal expansion anisotropy, given that the movement in that direction is energetically more favorable without breaking the symmetry constraints. To further investigate this, a high-temperature x-ray experiment on the high-entropy sample wasAttorney Docket No.11196-117WO1 conducted (FIGS.34H-34M). Temperature-dependent X-ray diffraction on the powder samples of the three RnBa3(B3O6)3 crystals is shown in FIGS. 34H-34J. From the intensity of the Bragg reflection on the powder sample, the study observed a large change in the specular (000l) peaks (FIG.34K), indicating a large anisotropy between the lattice parameters. The elongation in the c direction (FIG.34K) far exceeds the elongation in-plane a, b directions (FIG.34L). The thermal expansion coefficient (ac) is ≈(30-35) × 10−6K−1, which is similar but a bit smaller than that of BBO single crystals (FIG.34M).

[0281] Enhanced optical properties in high entropy borates: To explore the potential for optical applications of the high-entropy borate, the study investigated both its linear and nonlinear optical properties. The linear optical response is characterized through measurements of transparency, refractive index, and photoluminescence. In parallel, the nonlinear behavior is examined through SHG and phase-matching capabilities, providing insights into its suitability for frequency conversion applications.

[0282] Characterization of linear optical properties: Doping with rare earth elements on the R site leads to band degeneracy, which introduces in-gap states. Generally, it is expected that this would cause multi-photon absorption and thereby decrease optical transparency; however, the study observed an increased transparency in high-entropy crystals, as discussed next. UV-visible spectrophotometry measurements reveal a transmittance of ≈80-82% in the visible and IR range, which is 15-20% higher than in crystals with a single rare earth cation (FIGS.35A-35L). Notably, some of the absorption bands that were previously visible in the monolithic single-crystal sample FIG.35A have been quenched (FIG.35A) in the high entropy oxides.

[0283] In a high configurational entropy system, using structural disorder as a tuning knob can significantly alter the electronic band structure while altering both the density of states and the bandgap. In the context of rare earth borates, parent R1Ba3(B3O6)3 single crystals exhibit a number of f-f transitions due to the band degeneracy of the rare earth elements. In practice, such an electronic landscape will give rise to multi-photon absorption, hindering its widespread utilization. However, for the high-entropy borate, it was observed that the presence of five or more lanthanides quenches the absorption bands, thus increasing the bulk optical transparency.

[0284] This phenomenon of transparency enhancement can be linked to the crystallographic factors, reduced clustering, and parasitic effect, which will beAttorney Docket No.11196-117WO1 discussed in detail. These rare-earth borates, although they crystallize in a different symmetry, have a local bonding environment similar to BBO. Both are layered crystals with an alkaline and / or rare earth metal anchoring B-O rings. The presence of rare earth is a major differentiating factor between RnBBO and BBO. The presence of rare- earth causes additional absorption in most of the parent R1BBO crystals, although surprisingly, the high entropy borate is visually transparent and colorless. The high entropy borate can manifest an identical structure as R1BBO, without having a high concentration of any single rare earth element. For individual rare earth ions, the absorption cross-sections can vary depending on their constituent f-f transitions. Additionally, the concentration of each rare earth is 5-6 times lower than that of the parent compounds, which can be phenomenologically described as the suppression of domain clustering. Decreasing molar concentration of individual rare earth elements also suppresses the parasitic absorption. The disorder may also restrict the multi- phonon relaxation pathways through the phonon bottleneck effect. To summarize, the high entropy design can provide enhancement to the optical transparency. This design also provides a larger design space since the f-f transitions are different for different rare earth elements. For example, the presence of in-gap states is less prevalent for elements such as Ce, Gd, Lu; incorporating them into high-entropy crystals in future studies can further improve the transparency of these single crystals. Notably, a similar behavior of optical transparency improvement through high-entropy engineering has been demonstrated in a previous work containing a transparent, correlated disordered oxide system, further validating this trend.

[0285] Bandgap tunability is observed in the high entropy borates (FIGS. 35B- 35C). The nature of the in-gap transitions is different for the combination of rare earths utilized in Ra5, Rb5, & R6samples. For the parent compounds with a single rare-earth cation, the optical bandgap varied from 5.6-5.8 eV, which is about ≈0.5 eV larger than the high entropy borates. The addition of structural disorder causes a change in the bandgap. In addition, these crystals are negative uniaxial with ordinary refractive index higher than the extraordinary one (FIGS.35D-35E). The refractive index varies from 1.4 to 1.8 in the visible to NIR region. The birefringence varied from 0.1 to 0.15 across the photon energies lower than the bandgap. The low refractive index can be attributed to the low polarizability, which is commonly found in most insulating wide-bandgap systems. Additionally, the result further clarifies that the electronic polarizability along the ^-axis is less than that in the a – b plane.Attorney Docket No.11196-117WO1

[0286] One of the major benefits of having a system with multiple rare earths is having multiple emission lines that can potentially be utilized for laser applications. A common example of a gain medium is Nd:YAG, where only 0.3-0.8% doping of Nd enables a strong emission at 1064 nm through stimulated emission. For the stimulated emission to be possible, the lattice needs at least three distinct energy states where nonradiative relaxation from the highest energy state to the intermediate one (that has a long lifetime) is required. For the high entropy borate, the energy landscape is highly convoluted due to the presence of so many bands allowing multitudes of possibilities for transitions (FIGS. 35F-35G). Experimentally, the study has observed strong emission lines, mainly from the f-f transitions of the Sm, Nd, and Er. Among them, the Nd emission lines are the strongest, although slightly blue shifted compared to the Nd:YAG 946 nm emission line (4F3 / 2 →4I9 / 2). Additional sharp emission lines have been observed in the 600-625, 630-664, 700-720, and 800-830 nm wavelength range, with weak emission lines across the 550-580 nm range. Through detailed optical metrology, capturing the energies of both absorption and emission events, the study was able to deconvolute the absorption cross-section of the rare earth borates, as demonstrated in FIGS.35H-35L for the Ra5example. The study additionally observed emission lines in the NIR and MIR range, although the yield is lower compared to the aforementioned wavelengths. This is unique from the materials design point of view, as the presence of different emission lines can be designed to be used as a gain medium to generate multiple laser lines simultaneously. Although the energy landscape of such a convoluted structure demands more in-depth analysis, especially through time-domain spectroscopy, the presence of these lines indicates the decay rate is within measurement capabilities. Notably, for Nd:YAG, the lifetimes are usually in the order of a few microseconds, which can be similar to the rare earth borates. The borate is also a suitable host for these applications, as it exhibits multimodal luminescence while maintaining high transparency in the visible and NIR ranges.

[0287] Characterization of nonlinear optical properties: The traditional β-BaB2O4 (BBO) single crystal remains one of the most widely studied nonlinear optical (NLO) materials due to its strong second-harmonic generation (SHG) activity. Its effectiveness originates from a combination of features: a noncentrosymmetric R3c space group that permits even-order NLO processes, a wide band gap (∼ 6.3 eV) that allows low optical absorption in the UV-visible range, and sufficient birefringence enabling efficient phase matching across a broad spectral range. These attributes leadAttorney Docket No.11196-117WO1 to a phase-matched SHG coefficient of 1.8 pm / V and a moderate laser-induced surface damage threshold (LISDT) (100 GW / cm2). However, BBO’s limitations – including two-photon absorption of the second-harmonic output and relatively low LISDT (relative to other rare-earth borate, such as KBBF, YBCO, and R1BBO) – leave room for improvement in applications requiring high laser intensities. The high entropy borates overcome most of these limitations. The crystals have a 5-6 times LISDT compared to BBO, enabling pumping of the crystal with larger fluence, thereby enhancing efficient frequency conversion. The crystals are environmentally stable compared to the BBO, which is hygroscopic and requires special optical coating.

[0288] For the two different analyzer configuration the nonlinear optical susceptibility is as follows: =(^)^ (%)^ ^ (^) ⋯ ^where the = % xF|} groupFor the two different the nonlinear optical susceptibility is asfollows:$%& ∝ (( )%^ ^^sin2- + (%%cos2-

[0289] The detailshave been included in the supporting information. Notably, the measurement was done using an 800 nm fundamental wavelength laser beam, where the study measured SHG at 400 nm. No photoluminescence has been observed at a 400 nm wavelength, which confirms that the optical response is purely of second harmonic origin.

[0290] The highest phase-matched effective nonlinear optical coefficient in the high-entropy borates was measured to be 2.1 pm / V. This surpasses the phase- matched coefficient of BBO. Earlier, it was hypothesized that the introduction of highAttorney Docket No.11196-117WO1 entropy on the borate lattice can enhance the local anharmonicity of the potential well, which can be responsible for significantly altering the NLO susceptibility. The experimental results support this hypothesis, as a significant enhancement was observed compared to the parent compound and BBO. This is also a potential chemical pathway for designing the next generation of NLO optical crystals, where controlling disorder can improve the SHG coefficients. This is the first report of this phenomenon, where lattice disorder directly contributes to enhancing the NLO susceptibility. Another key advancement over BBO & parent R1compounds is the suppression of multi-photon absorption, enhancing SHG conversion efficiency by preventing reabsorption of the generated second harmonic. The higher crystallinity and transparency have also actively contributed to the enhanced intrinsic NLO susceptibility. Similar to the parent compounds, the birefringence of these compounds is large enough for it to be phase-matchable (both type-I and type-II) over the visible and IR ranges. These findings position high-entropy borates as promising candidates for high-power laser frequency conversion applications, offering a rare combination of large NLO coefficients, wide bandgap transparency, and exceptional laser damage resistance. Conclusion and Outlook

[0291] This work showcased the high entropy borate to be an excellent candidate for optoelectronic applications. Flux growth yields optically clear boules several millimeters long; single-crystal and powder X-ray diffraction confirm phase purity and the retention of the parent trigonal symmetry. Spatially resolved energy-dispersive spectroscopy and high-resolution electron microscopy verify chemical homogeneity at the nanometer scale, while X-ray photoelectron spectroscopy establishes that all lanthanides remain predominantly trivalent. Atomic-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) imaging confirms that RnBa3(B3O6)3 adopts a DyBa3(B3O6)3-type hexagonal close-packed (HCP) structure, reveals local R-site distortions induced by high-entropy element substitution, and verifies the presence of Ba dumbbell columns along the [101^0] zone axis. Optical transmission exceeds 80-90% from 190 nm to 5 µm, and ellipsometric analysis reveals sufficient birefringence for critical phase matching. Under near-UV excitation, the crystal exhibits strong emission, and the SHG measurements show tensor coefficient rivaling those of BBO under similar pump conditions. While the largeAttorney Docket No.11196-117WO1 LISDT showcased the possibility of enhancing the conversion efficiency an order of magnitude. These observations indicate that high entropy borates offer a tangible route to single-phase single crystals that unite broadband photoluminescence, wide UV-C transparency, and strong optical nonlinearity. Such multifunctional behavior has the potential to expand upon potential ultraviolet laser systems, extend frequency- conversion limits toward the UV-C, and provide new degrees of freedom for wavelength-agile optical components used in spectroscopy, high-order harmonic generation, and gain media in laser cavities. Experimental Procedure

[0292] Crystal Synthesis: The polycrystalline synthesis was performed via the solid-state synthesis, utilizing materials sourced for their high purity: BaCO3 (99.5%, Alfa Aesar), R2O3 (99.9%, Alfa Aesar, R = Nd, Sm, Tb, Dy, Gd, Yb and Er), H3BO3 (99.4%, EMD Chemicals). The composite material was placed in an Al2O3 crucible and initially heated to 400°C for an hour to ensure the decomposition of BaCO3 and H3BO3. The temperature was then increased to 850°C at a rate of 200 C / hour and maintained for 72 hours before allowing the crucible to cool naturally. Powder x-ray diffraction analysis confirmed the successful synthesis of polycrystalline powder in a pure RnBa3(B3O6)3 phase.

[0293] Subsequently, RnBa3(B3O6)3 single crystals were grown using a floating- zone technique, employing a commercial image furnace equipped with double- elliptical mirrors (Model: IRF01-001-05, Quantum Design). For preparing the feed and seed rods, polycrystalline RnBa3(B3O6)3 powder was prepared by mixing single- component R1BBO in an equal molar ratio. The mixed powder thoroughly ground and pressed to ∼ 10 cm rods with a diameter of ∼ 4.5 mm using a cylinder-shaped rubber balloon, encased in a quartz tube, under a pressure of 50 MPa. The rods were then sintered at 800°C for 48 hours. A ∼ 4 cm long seed rod was prepared following a similar procedure. The study placed RnBa3(B3O6)3 powder at the bottom of the Al2O3 boat during the rod preparation to prevent aluminum contamination. In the floating zone crystal growth process, the aligned feed and seed rods were positioned near the melting zone with a small gap left between them. After sealing the growth chamber, it was flushed with oxygen flow for 15 minutes. The oxygen pressure was then increased to 2 atm. Upon reaching this pressure, the voltage to the halogen lamps was ramped up to melt the bottom end of the feed rod. The voltage was adjusted within the 35 − 57 V range to maintain a T-shaped melting zone, facilitating optimal crystal growth.Attorney Docket No.11196-117WO1 The growth was conducted at a speed within the range of 6 − 10 mm / hour . Through these growth procedures, the study obtained crystal rods approximately 30 − 50 mm in length containing multiple domains. Single-domain crystals were subsequently isolated by cleaving the rod with a razor blade. RnBa3(B3O6)3 single crystals contain planar [B3O6] rings in the crystallographic a-b plane, and the planar rings are separated by weak conjugated π-bonds, thereby enabling cleavage and collection of single crystal with the

[0001] orientation along the out-of-plane direction. This crystallographic orientation was verified by the Laue pattern, as discussed in the main text. The RnBa3(B3O6)3 single crystal samples were then subsequently polished to obtain slabs, which were further utilized to characterize both linear and nonlinear optical properties.

[0294] Linear optical properties: The optical transparency and reflectivity for the high-entropy borate single crystal have been measured across a broad spectral window (0.2 μm to 6 μm). Uv-vis-NIR measurement (Agilent UV-vis-NIR spectrophotometer) was utilized to measure transmission and reflection in the spectral range of 0.2 μm to 2 μm. Complementary mid-infrared (2 μm to 6 μm) measurement has been conducted by Fourier transform infrared spectroscopy (FTIR) measurements using a Vertex 80 FTIR spectrometer equipped with a liquid-nitrogen-cooled HgCdTe detector. For both measurements, the crystal was mounted with its crystallographic c- axis oriented perpendicular to the incident beam. For calibration, Spectralon was utilized in the UV-vis measurement, and a freshly evaporated gold mirror was used for the FTIR measurement. Ellipsometry measurement has been performed on the high- entropy borate to extract the real (no and imaginary (ne) parts of the refractive indices in the spectral range of 0.2 μm to 1 μm using a Wollam M2000X ellipsometer. The experiment has been done on two experimental geometries, where the plane of incidence is parallel to crystallographic [21^1^0] and

[0001] . Both of the datasets were simultaneously fitted with the Cauchy model (n(λ) = A+B / λ2+C / λ4where A, B, and C are constant depending on the material) to extract the real and imaginary part of the refractive indices. Photoluminescence measurement has been performed using a LabRAM HR Evolution Raman spectrometer upon exciting the sample with Nd:YAG (532 nm) and He-Ne (633 nm) continuous wavelength lasers, while detection was done by Synapse and Synapse II (InGaAs) detectors.Attorney Docket No.11196-117WO1

[0295] Nonlinear optical characterization: SHG measurement has been performed in normal transmission geometry using a Spectra-Physics Solstice Ace 100 fs 1KHz Ti: Sapphire pulsed laser of fundamental 800 nm wavelength. The transmitted beam has been split into two distinct components using an analyzer (X and Y, as shown in the experimental geometry). The signals were then measured using a photomultiplier tube, which converted photons to photocurrent, which was measured using a lock-in amplifier.

[0296] Electron Probe Microanalysis (EPMA): The elemental composition of the high-entropy borate has been characterized using the Cameca SXFive Electron Probe Micro-Analyzer (EPMA). This instrument utilizes a five-wavelength dispersive spectrometer and a LaB6 source, and the measurement has been done at 15 keV with a beam current of 30 nA. For rare earth element reference, standard Nd, Sm, Dy, Tb, Er, and Gd glass has been utilized (composition and initial spectrometer conditions are listed in the supporting information).

[0297] Scanning Electron Microscope and Energy Dispersive Spectroscopy: The scanning electron microscope analysis was conducted by the Apreo 5 scanning electron microscope. The samples were coated with Ir and Energy dispersive spectroscopy was conducted in low vacuum configuration.

[0298] X-Ray Crystallography: The single crystal diffraction data were collected with a diffractometer equipped with Rigaku Micromax 007 rotating anode x-ray generator (CuKα), Osmic Varimax VHF monochromator, a universal four-circle Kappa goniometer, and a HyPix-Arc150 area detector. The samples were ground up to make small flakes of about 10 μm. Then a single crystal was mounted on the goniometer to collect the diffraction data, and the collected datasets were further analyzed using direct method to extract the structural parameters such as lattice constants and atomic internal coordinates. Furthermore, θ-2θ x-ray diffraction patterns were collected with the manual z-stage (to minimize the ω shift caused by sample displacement) from the single crystals after polishing along the (0001) cleave plane. The data was collected in ω-2θ goniometer geometry. Powder x-ray characterization was also performed using Panalytical Empyrean 4 with θ-2θ goniometer geometry for the powder samples obtained by grounding the single crystals by ceramic mortar. Prior to the experiment, the systems were calibrated through powder crystalline Si.

[0299] Laser-Induced Surface Damage Threshold Measurements: Laser- induced surface damage threshold (LISDT) was measured utilizing 100-fs 1-KHz Ti:Attorney Docket No.11196-117WO1Sapphire pulsed laser of 800-nm wavelength on optical grade polished (down to 0.05^m diamond grid) sample. The laser light was focused using a 10-cm lens andconsequently monitored for surface damage using an optical microscope. The beam spot size at the focus was measured using knife edge measurement.

[0300] Transmission Electron Microscopy (TEM):

[0301] TEM sample preparation: A thin TEM specimen as shown in FIGS.34A- 34M was prepared in a Thermo Fisher Scientific (TFS) Helios 660 focused ion beam (FIB)-scanning electron microscopy (SEM) system. Initially the sample was sputter- coating the region of interest with approximately 200 nm of platinum (Pt) to improve surface conductivity. A 2 μm layer of amorphous Pt was then deposited using a 30 kV, 0.23 nA Ga ion beam to protect the sample during the future milling and thinning. From this protected region, a 1.5 μm-thick lamella was extracted and transferred in situ on a copper half grid. Final thinning to electron transparency was achieved by progressively reducing the Ga ion beam voltage from 30 kV down to 2 kV, thereby minimizing ion-beam-induced damage.

[0302] TEM characterization: The atomic-scale HAADF-STEM image depicted in FIGS. 34A-34M was acquired on an aberration-corrected TFS Titan3 G2 60-300 TEM / STEM operating at 300 kV. Prior to imaging, the sample was tilted to align its hexagonal close-packed lattice as closely as possible to the [101^0] zone axis. The microscope was configured with 70 μm C2 aperture, spot size 8, 115 mm camera length, and 25.2 mrad convergent angle. The HAADF detector collected electrons between 52–253mrad, and the image was recorded with a beam current of 0.03 nA. To improve signal to noise ratio, HAADF-STEM image was processed via inverse FFT, LASSO-based filtering, and background removal.

[0303] STEM simulation: STEM simulation was performed using the abTEM multislice simulation package. The study employed the frozen-phonon approximation by generating an ensemble of eight frozen-phonon snapshots with displacement standard deviation of 0.1Å to model thermal scattering. A supercell measuring 34.23108Å (x), 24.93425Å (y), and 503.853Å (z) was built, and its electrostatic potential was sampled at 0.05Å in reciprocal space. The potential was sliced along the beam-propagation direction into 1Å thick layers using the infinite potential projection method. A 300 kV probe wave function was formed with 10 ^m spherical aberration and Scherzer defocus. HAADF-STEM intensities were integrated over scatteringAttorney Docket No.11196-117WO1 angles from 65 mrad to 196 mrad, and the resulting measurement was interpolated to a 0.05Å per pixel sampling rate. Partial spatial coherence was modeled by Gaussian convolution (σ = 0.3Å), and a finite electron dose of 107 e−Å−2was imposed via Poisson-distributed noise.

[0304] Scanning Diffraction X-ray Microscopy: SDXM measurement was performed on the Hard X-ray Nanoprobe (HXN) beamline at the Advanced Photon Source (APS). The X-ray energy was 8.5 keV. The X-ray was focused by a Fresnel Zone Plate with 160 μm diameter and 30 nm outermost zone width. Diffraction patterns were collected on a Eiger 2 X 1M detector with 75 μm pixel size, positioned at 0.9 m from the sample. SDXM tilt series was performed by repeating the same 1D spatial scan at 51 sample angles distributed evenly around the (0008) reflection with a step size of 0.02°. The resulted 4D data was analyzed using a python script, which extracted information such as d-spacing variation and lattice distortion by analyzing the shift of the diffraction vector in reciprocal space. Example 7

[0305] EDS and XRF: The composition of the high-entropy borates has been delineated using the EDS and XRF measurements. The results (TABLES 20-21 shows consistency between the two techniques within reasonable accuracy. From the measurement, it can be identified that the compositions present in the high-entropy borates are close to equimolar. The study observed smaller systematic variations with slight Nd deficiency and Yb excess. The Shannon-Prewitt radius of the rare earths decreases with f orbital occupancy because of the contraction of lanthanide. For the high entropy compound, the smaller radius of Yb is nominally favored from the measurement. Although it is difficult to deconvolute the exact composition as the rare earth site is only present in smaller concentrations and the f orbital elements usually have convoluted peak shapes with interference (FIGS.36A-36B). However, the study suggests an equimolar composition close to that of these rare earths.Attorney Docket No.11196-117WO1 TABLE 20. Composition of the individual rare earth elements in the R site of the high- entropy borate single crystals measured from EDS and XRF technique. The expected stoichiometric compositions of each rare earth element for the Ra5, Rb5, and R6compounds are 20 and 16.67 atom %, respectively. Method Sam le Nd (%) Sm (%) Gd (%) D (%)TABLE 21. Composition of the individual rare earth elements in the R site of the high- entropy borate single crystals measured from EDS and XRF technique. The expected stoichiometric compositions of each rare earth element for the Ra5, Rb5, and R6compounds are 20 and 16.67 atom %, respectively. Method Sample Er (%) Yb (%) Tb (%)are earth elements, Electron probe microanalyzer (EPMA) mapping experiment has been conducted. For the rare earth elements, the characteristic emission peaks have a convoluted shape, and improving energy resolution can help delineate the stoichiometry. The study conducted a mapping experiment to identify the elemental homogeneity of the sample with higher energy resolution. The results for the high entropy oxides show excellent homogeneity in the micron resolution with no visible segregation (FIGS.37A-37H, FIGS.38A-38H, and FIGS.39A-39I).Attorney Docket No.11196-117WO1

[0307] Linear Optical Properties: Real and imaginary parts of the refractive index for the high-entropy borate single crystals have been characterized through ellipsometry measurements. It was parameterized using a Cauchy model, and the parameters are listed in TABLE 22. TABLE 22. The parameters of Cauchy equations for fitting the anisotropic refractive indices of the Ra5, Rb5, and R6compounds. n Sample A B (μm2) C (μm4) k Amplitude Exponent

[0308] Spin coating and drop casting: High-entropy borate single crystals have been ground and mixed in an acetone, alcohol, and water solution. The material exhibits no miscibility with any of these compounds. Using a glass substrate, the study performed spin coating and drop casting that form dispersed powder films (FIGS.40A- 40B) that retained the same crystallinity with the bulk phase.

[0309] Comment on entropy stabilization: A dominant factor in high entropyoxides is the stabilization through increasing of the configurational entropy (Δ^config =−X∑GF^^  ^Fln^F), where R is the molar gas constant, and xi are the molar fractions of theithelement. In a random distribution of multiple elements across equivalent(relevant for the high entropy borate since the rare earth elements occupy a single Wyckoff position), the configuration entropy for R5and R6compounds is 1.609R and 1.792R. In contrast, for a binary compound having 0.5 mole fraction each, the configurational entropy is 0.693 R. Considering a traditional oxide system, the molar enthalpy ΔH varies between 200-1000 J / mol.k (although for formation or fusion, it can be an order of magnitude higher). The prototype BBO, for example, has an enthalpy of formation of -2020.3 kJ / mol. Having an increase of configuration entropy of 1.79R decreases the free energy at 300 K (ΔG = ΔH – TΔS) by 4.462 kJ / mol. This can impact the phase stability substantially. Considering the coexistence of twoAttorney Docket No.11196-117WO1 phases A and B, described by a Boltzmann factor, PA / PB=eΔG / RTwhere ΔG = GB – GA is the free energy change between the two phases, and PA and PB are the probability of formation of the coexisting phases. For ΔG = 4.462 kJ / mol, the probability of formation of A increases by about 38% of any existing secondary phase. Notably, for an non-ideal mixing case, the enthalpy change due to the addition of individual elements on the lattice can also be substantial. Only in the case of ideal mixing, the enthalpy change is zero.

[0310] XPS: XPS experiment was performed using the Physical Electronics VersaProbe III instrument with a monochromatic Al kα x-ray source (hν = 1486.6 eV) and a concentric hemispherical analyzer. Charge neutralization was performed using both low-energy electrons (<5 eV) and argon ions. The binding energy axis was calibrated using sputter-cleaned Cu (Cu2p3 / 2 = 932.62 eV,Cu3p3 / 2 = 75.1 eV) and Au foils (Au4f7 / 2 = 83.96 eV). Peaks were charge referenced to Ba2+band in the barium 3d5 / 2 spectra at 779.6 eV. Measurements were made at a takeoff angle of 45° with respect to the sample surface plane. This resulted in a typical sampling depth of 3-6 nm (95% of the signal originated from this depth or shallower). Quantification was done using instrumental relative sensitivity factors (RSFs) that account for the x-ray cross- section and inelastic mean free path of the electrons. On homogeneous samples, major elements (>5 atom %) tend to have standard deviations of <3%, while minor elements can be significantly higher. The analysis size was 200 in diameter. All samples were fractured in an argon glovebox and transferred to the XPS system using an inert sample transfer vessel to minimize O2 and H2O exposure. Binary R1Ba3(B3O6)3 (R = Nd, Sm, Dy, Gd, Yb, Er, Tb) has been utilized to obtain the reference rare earth peaks. The information from the binary phase measurement has been utilized to analyze the high-entropy oxide. In addition, the starting compounds for the synthesis of these rare earth borates involve individual rare earth oxides in the 3 + (R2O3) configuration. In the absence of a significant reducing potential, it is likely that they retain a similar oxidation state in the single crystal, which is also nominally consistent with the experimental result.

[0311] Shannon-Prewitt radii for the rare-earth elements: See TABLE 23.Attorney Docket No.11196-117WO1 TABLE 23. The Shannon-Prewitt ionic radius for the rare earth in tetrahedral coordination geometry.

[0312] Transmission Electron Microscopy (TEM): To better visualize the atomic distortion of the R-site atomic columns of RnBa3(B3O6)3, the study has defined a workflow to plot the displacement map.

[0313] First, the study analyzed the multislice-simulated HAADF-STEM image along the [101^0] zone axis, based on the DyBa3(B3O6)3 atomic model. The white dashed line in FIG.41A highlights a unit cell, where black circles indicate the 2 single Ba atomic column locations at the top of the unit cell. Similarly, the study labeled the 2 single Ba atomic column locations of the unit cell below. The center of these four black circles are highlighted by a red star.

[0314] The red circles in FIG.41A indicate the positions of the Dy atomic columns in the unit cell. The blue circles show the detected A-site positions in the HAADF- STEM image of R6Ba3(B3O6)3. The displacement vector (⃗ is calculated based on: (⃗ =^A^^%⃗ − ^ A^^^⃗ , where ^ A^^^⃗ and ^ A^^%⃗ are the vector from the red star to the red circle, and the vectorfrom the red star to the blue circle, respectively (FIGS. 41A-41B). Finally, as theto see clearly, the study plotted ^ (^^^⃗ = 10 × (⃗ and overlaid thecenter of the vector on the A-site columns in the STEM images, as shown in FIG.41C.

[0315] Second harmonic generation (SHG) characterization: For the P6^space group, the relationship between polarization (Pi) and incident electric field (Ei) can be written as:Attorney Docket No.11196-117WO1 ö ÷÷÷øwhere the SHG ^ for point group 6^ is given in abbreviated notation.For the two differentthe nonlinear optical susceptibility is as follows: ∝2- %^ + 2-

[0316] Efficient conversion from fundamental optical pump to SHG requires proper phase relationship between the interacting waves, which is dictated by the phase- matching condition. Chromatic dispersion can cause phase mismatch at different wavelengths, and the choice of both the incident polarization and the crystallographic orientation is important. For the negative uniaxial crystal, the phase matching angle (θm) for Type-I and Type-II phase matching (θmIand θmII, respectively) fulfills the following conditions: %( 8 ) ^m(2n) % ^%W(2n) − ^%W(n)sin 5k = l o^ − (Type-I))

[0317] opticalcoefficient of Type-I and II phase matching conditions (deff,type-I and deff,type-II, respectively) can be calculated as: (= ( cos 58 cos 3w − 8m^^,[^^m^  ^^ k (%%cos 5k sin 3wAttorney Docket No.11196-117WO1

[0318] Structural Refinement: Single crystal refinement was conducted on Olex2 with the ShelX package. To achieve proper identification of the space group of this single-crystal system, the R-factor (measurement of agreement between the crystallographic model and the experimental X-ray pattern) was analyzed for multiple different suitable crystal systems. The comparison of the Rint factor across differentspace groups suggest two potential candidates (P 6^ and P3). Achieving closecongruence between experimental results and crystallographic modeling requires a low Rintvalue. Notably, the X-ray selection rule provides a direct pathway to shortlist the possible candidates of space groups for this material system (in an ideal single crystal sample). Additionally guided by the SHG investigation, the study identified the highest possible symmetry space group to be P6^with P3 as a possibility. Example 8

[0319] The above examples have described the successful synthesis and characterization of a new family of high-entropy rare earth borate single crystals with compositions RnBa3(B3O6)3 (R = Nd, Tb, Sm, Dy, Gd, Yb, Er; one of these present), R5Ba3(B3O6)3 (R5= Nd, Tb, Sm, Dy, Er; all five present) and R6Ba3(B3O6)3 (R6= Nd, Sm, Dy, Gd, Yb, Er; all six present). Compared to their monolithic counterparts, these multicomponent systems exhibit significantly enhanced infrared transparency, improved crystallinity and enhanced nonlinear optical property. In addition to this improved property in the bulk high-entropy phase, an emergent phenomenon has been observed in these samples where applying chemical stress through quenching can induce a giant enhancement of nonlinear optical susceptibility. Previous investigations on the borate single crystal systems have indicated the presence of soft modes that can give rise to potential ferroelectricity. The leading hypothesis is that thermal quenching locks in a low symmetry non-centrosymmetric phase.

[0320] Executive Summary: New rare earth borate crystals crystal compositions have been prepared, namely compositions RnBa3(B3O6)3 (A = Nd, Tb, Sm, Dy, Gd, Yb, Er; one of these present), R5Ba3(B3O6)3 (R5= Nd, Tb, Sm, Dy, Er; all five present in equal mole fractions) and R6Ba3(B3O6)3 (R6= Nd, Sm, Dy, Gd, Yb, Er; all six present in equal mole fractions). The R5Ba3(B3O6)3 and R6Ba3(B3O6)3 are termed high entropy borates, the first such crystal growth. Many such compounds are possible. They haveAttorney Docket No.11196-117WO1 large bandgaps of ~5.5eV, leading to a transparency from 225nm (ultraviolet) to 3200nm (infrared) wavelengths.

[0321] The high entropy R5borate crystals show enhanced transparency over the R1crystal compositions. The photoluminescence peaks due to rare earths is quenched in the high entropy versions. A large anisotropic thermal expansion of ~0.75% is observed in the c-axis orientation of these nominally hexagonal (H) symmetry crystals relative to the a-axis which barely changes from 23-650°C. This anisotropic thermal expansion becomes the key to stabilizing a new low symmetry phase with outstanding nonlinear properties. The crystals are Optical second harmonic generation (SHG) active, meaning that they can double the frequency of light incident upon them. This can for example take a near infrared photon (800nm) and convert it to blue photon (400nm) or say convert a visible photon (500nm) and convert it to ultraviolet photon (250nm).

[0322] Impressively, when thermally quenched from high temperature to room or low temperature, there is a large sudden thermal compression leading to a metastable low symmetry phase, M which is likely a monoclinic phase. This thermal treatment induced hexagonal to monoclinic phase transition is labeled as H→M. This M phase has exceptional 67X the SHG coefficient of the original H phase. To put this in context, the commercial “king of wide bandgap nonlinear optical crystals” is β-BaB2O4 (beta- barium borate)” which has an SHG coefficient of ~1.8pm / V. The H phase has a similar SHG coefficient. In contrast, the M phase has an SHG coefficient of 120pm / V. Since the efficiency of conversion of light depends on the square of the SHG coefficient, the efficiency could potentially be ~672=4489× that of the commercial β-BaB2O4.

[0323] Laser damage threshold, the highest laser power that a crystal could still withstand and generate new colors is 4-5 times higher than for the commercial β- BaB2O4. This again means that 42to 52, i.e., 16-25× improvement in the output laser power after frequency conversion. The combination of high laser damage threshold and the large coefficient means that up to 1.1 million × improvement in laser performance as compared to any other wide-bandgap laser crystal demonstrated.

[0324] Compositional analysis: Energy-dispersive X-ray Spectroscopy (EDS) and Electron Probe Microanalysis (EPMA) measurements have been conducted on the high-entropy borate to delineate the elemental composition within the single crystal. The elemental compositions measured from these techniques are listed in TABLES 24-25. The rare earth elements are stoichiometric based on EDS analysis.Attorney Docket No.11196-117WO1 TABLE 24. Composition of the individual rare earth elements in the R site of the high- entropy borate single crystals measured from EDS and XRF technique. The expected stoichiometric compositions of each rare earth element for the Ra5, Rb5, and R6compounds are 20 and 16.67 atom %, respectively. Method Sample Nd (%) Sm (%) Gd (%) Dy (%)TABLE 25. Composition of the individual rare earth elements in the R site of the high- entropy borate single crystals measured from EDS and XRF technique. The expected stoichiometric compositions of each rare earth element for the Ra5, Rb5, and R6compounds are 20 and 16.67 atom %, respectively. Method Sample Er (%) Yb (%) Tb (%)to overlapping peaks, especially among L-lines. These overlaps can lead to inaccurate elemental identification and quantification. Matrix effects and detector resolution further complicate the analysis. The EPMA analysis has been conducted to mitigate this issue, as having higher spectral resolution helps resolve the individual peaks from the rare earth. It shows that some rare earth elements in the high entropy compounds are off stoichiometric and may have local area variation. EDS analysis in the FocusedAttorney Docket No.11196-117WO1 Ion Beam (FIB) cut sample can also be used to resolve further the local area variation and the proper stoichiometry of the compounds.

[0326] Anomalous Thermal Expansion: The high-entropy borate single crystals have strongly bonded planar [B3O6] rings. This contains a large anisotropy of the thermal expansion in the crystallographic c direction. Due to the anisotropy of the bond strength, the crystals are more expandable in the c direction in comparison to the in- plane direction. To delineate this property, a temperature-dependent X-ray diffraction experiment has been conducted on the powder R6Ba3(B3O6)3 sample.

[0327] The intensity of the individual Bragg peaks as a function of temperature has been demonstrated on FIG. 42A. The diffraction peaks containing the specular reflection from the (00l) planes showcase a large change as a function of temperature. From the powder diffraction data, the lattice parameters have been calculated as a function of temperature (FIG.42B). There, the study has additionally observed the large anisotropy of the thermal expansion, reaffirming the previous analysis.

[0328] One conclusion from this data is that upon thermal quench form a high temperature, the c-axis of the crystal will shrink dramatically, which could be stabilizing the new emergent phase with superior properties described below.

[0329] Linear Optical Properties: Crystallographic structural change can also be observed through linear optical property measurement. For the bulk phase, the space group P6^should have an isotropic refractive index in the crystallographic a-b plane. Considering this scenario, the refractive index for the M phase increases in the visible and IR regime (FIG.43A). However, having ellipsometry measurements at different angles of incidence at the a-b plane shows a change in the refractive index. This is a clear indication of the symmetrical breaking, which causes the breaking of the in-plane isotropy.

[0330] Transmission Electron Microscope analysis: To delineate local crystallographic structure, transmission electron microscope analysis has been conducted on the bulk and the M phase. Structural analysis on both the parent and the M phase (FIGS.44A-44D and FIGS.45A-45D) through HRTEM analysis reveals the following key details. The M phase has a distortion in the crystallographic a-c plane, indicating a potential lowering of the symmetry. Atomic-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) on both phases reveals a more pronounced distortion in the barium and rare earth site for theAttorney Docket No.11196-117WO1 M phase. The static positional disorder or dynamic instability at the barium site is absent in the M phase, suggesting that the polar order may not be suppressed for up and down domains as it is in the bulk phase.

[0331] Optical Second Harmonic Generation: The study has also measured the optical second harmonic generation (SHG) as a function of temperature for both the high-entropy and binary compounds. This technique detects non-centrosymmetry (which is broken inversion symmetry) in the material when an SHG signal is present. Notably, the high-entropy oxide exhibits anomalously large SHG signal as compared to the binary compounds. While the SHG intensity of the binary compound changes monotonically with temperature, the high-entropy compound displays two distinct peaks.

[0332] Creation of the new emergent M phase: A new phase, called M phase, can be induced in bulk high-entropy borate through thermal quenching via rapid heating and cooling cycles. Experimentally, one effective method for forming this new phase involves heating the sample to 600°C at 10°C / min, followed by rapid quenching in liquid nitrogen. This process successfully generates the new phase uniformly through the crystal characterized by enhanced nonlinear optical properties. The lowest temperature at which the formation of this phase has been achieved is by heating up to 350°C, followed by quenching in liquid room temperature water. Many other variations are possible, for example, by heating to higher temperatures and then quenching. Quenching could be done in many ways, e.g., with ice water, or liquid nitrogen (77K) or even liquid helium (4K). If quenched in such a manner, one might be able to heat to temperatures even less than 350°C and achieve the M phase.

[0333] Alternatively, similar phase formation was observed using an 800^nm, 100^fs, 1KHz focused laser while the sample was mounted on a copper or any metal plate. In this setup, M domains form near the crystal surface closest to the metal plate. To achieve this, the laser has been irradiated on the sample for 10-15 seconds with an incidence power of 1.8-2.1 mW. This is likely due to the influence of laser heating of the copper plate that in turn heats the crystal adjacent to it and rapidly cools, resulting in the new phase. A possible thermal treatment, therefore, would be to laser heat the crystal using a laser of wavelength greater than 4.5μm beyond which the crystal absorbs due to phonons. This would result in a much more uniform heating through the crystal thickness through its entire thickness followed by thermal quench when it is cooled. One way to do this would be to mount the crystal on a cooling block,Attorney Docket No.11196-117WO1 such as a piece of metal cooled by liquid nitrogen or ice water, and then scan a laser beam with wavelength greater than 4.5μm (e.g., CO2 laser has a wavelength of 10.6 μm) which can be absorbed by the crystal, leading to rapid heating. When the laser is turned off, the irradiated region can cool and result in the formation of the new phase. A range of wavelengths from ultraviolet to visible to infrared could work, and a range of pulses from femtosecond to picosecond, nanosecond and even continuous wave lasers could work. Heat lamps could also work.

[0334] For a few of the bulk single crystal as grown samples, the new phase can also be observed as discontinuous independent nuclei without the action of any thermal quenching. These natural formations can be caused by the thermal gradient formed during the crystallization during the flux growth process. This phase has been reproduced over multiple samples of the high-entropy oxide. Interestingly, even for the binary compound (e.g. SmBa3(B3O6)3 and DyBa3(B3O6)3) a similar thermal quenching experiment can form a domain of enhanced SHG, but the M phase forms sporadically in only a few regions, unlike in high-entropy oxides where it forms uniformly over the whole crystal.

[0335] Quantification of the emergent M phase: The bulk high-entropy oxide, like the binary phase, has a static positional disorder / dynamic instability of the Barium site. This can potentially decrease the average SHG response from the bulk single crystals. Interestingly, it has been observed that the material forms distinct domain like features while being quenched through thermal or laser excitation. This new region of M phase has a giant enhancement of the nonlinear optical coefficient, which was two orders of magnitude higher than any other crystals with similar bandgap.

[0336] To characterize and delineate the newly formed phase, the study conducted second harmonic generation (SHG) microscopy on the local domains of the high- entropy sample. The experimental configuration for SHG microscopy is illustrated in FIG.46A. As shown in the SHG intensity mapping (FIG.43B), two distinct regions are clearly identifiable: a darker region corresponding to the bulk phase previously characterized, and a brighter region corresponding to the newly written phase. The contrast in SHG intensity between these two domains highlights a substantial enhancement in the nonlinear optical response in the written region (FIG.43C).

[0337] To further investigate the origin of this M phase, SHG polarimetry was employed, revealing a distinct change in polarization dependence between the bulk and written phases. This change in SHG anisotropy is indicative of a local structuralAttorney Docket No.11196-117WO1 transformation, most likely induced by thermally driven quenching during the phase- writing process. The emergence of this structurally distinct phase and its associated nonlinear enhancement has been reproducibly observed across multiple high-entropy oxide samples, underscoring the robustness and repeatability of the effect.

[0338] For the polarimetry analysis in the earlier panel b, the bulk phase has beenfitted with the previously reported P6^ space group. However, in that experimentalconfiguration, the fitting with that space group is not able to explain the change of the polarimetry in the enhanced region. The highest possible symmetry for which this polarimetry can be fitted is monoclinic m with a vertical mirror parallel to the lab Y direction (parallel to the (21^1^0) planes of the bulk coordinate).

[0339] The SHG tensor for the monoclinic point group m is: (^^ (^% (^^ 0 (^¡ 0K

[0340] Based on the polarimetry analysis, the study has identified the following ratio of the coefficients d11:d12:d13=5.58:2.38:1.

[0341] To quantify the nonlinear optical response more accurately, the study employed a tabletop SHG measurement setup (FIG.47A). The previous microscopy configuration involved a high numerical aperture (NA) objective, which introduced complexities in intensity calibration and made quantification challenging. In the tabletop measurement, using a fundamental excitation wavelength of 800 nm— nonresonant for these crystals—the study determined an effective second-order nonlinear optical coefficient of approximately deff,~120 pm / V. This is a remarkably high value, significantly exceeding that of conventional UV-C nonlinear optical materials. For instance, a widely used benchmark material like β-BaB2O4 (BBO) exhibits a phase-matched SHG coefficient of only ~1.8 pm / V under similar conditions.

[0342] The written domains exhibiting this enhanced SHG response are also macroscopic in size, as demonstrated in the representative plots shown in FIGS.48A- 48B. This large-area formation is particularly promising for practical applications in frequency conversion and integrated nonlinear optics, where domain size and uniformity are critical.Attorney Docket No.11196-117WO1

[0343] The substantial increase in nonlinear susceptibility observed here opens new possibilities in the design of functional optical materials. It suggests that high- entropy oxides, beyond their configurational complexity, can host metastable polar phases with exceptional optical nonlinearity, offering an exciting platform for next- generation photonic devices.

[0344] Enhancement of transparency for high entropy compound: Compared to the binary phase, the high-entropy compounds exhibit enhanced optical properties, including increased transparency and photoluminescence. Previous reports lacked quantitative and comparative analyses of these characteristics. To address this gap, the study performed UV-Vis spectroscopy on both the binary and high-entropy compounds, ensuring identical sample thicknesses to allow for an accurate comparison (FIG.49A). The results clearly show that the high-entropy compounds possess significantly higher transparency across the measured spectral range than their binary counterparts.

[0345] Furthermore, the transparency window illustrated in FIG. 49B reveals a reduced number of f–f transitions in the high-entropy sample, suggesting suppressed localized electronic transitions typically associated with rare-earth elements. This finding is particularly significant, as it highlights the potential of high-entropy oxide design to minimize the extinction coefficient, especially by quenching interband transitions that usually lead to optical losses.

[0346] In conventional systems, doping a single-phase crystal with multiple elements often introduces in-gap states due to lattice distortions or localized electronic interactions. These states can contribute to parasitic absorption and unwanted radiative recombination, both of which degrade optical transparency. In contrast, high- entropy compounds appear to mitigate these effects through their configurational entropy-driven structural stabilization, which quenches the emission of these defect states and improved transmission. The higher entropy crystals also grow as higher quality crystals, which may also contribute to better optical transparency with lower scattering.

[0347] This insight underscores the potential of high-entropy design strategies in developing next-generation optical materials with superior transparency and reduced optical losses, suitable for applications in photonics, transparent electronics, and laser systems.Attorney Docket No.11196-117WO1

[0348] Diffraction reveals a new phase: In order to elucidate the local structural features that give rise to the enhanced second-harmonic generation (SHG), the study employed a hard x-ray nanoprobe at Argonne National Laboratory, operating at an incident energy of 8.5^keV and focused to a spot size of 20^nm via a Fresnel zone plate. This configuration yields a donut-shaped beam, enabling high spatial resolution for mapping lattice distortions across the sample. Two representative Bragg reflections, (0008) were selected to investigate both out-of-plane (c-axis) and in-plane structural parameters.

[0349] Summary: Collectively, these findings indicate that high-entropy doping and subsequent thermal / laser treatment stabilize a non-centrosymmetric, low- symmetry phase with measurable compressive strain. The high-entropy compositions improve optical transparency. An exceptional optical second harmonic generation coefficient that is two orders of magnitude higher than commercial beta-barium borate crystals is observed for such a large electronic bandgap. The emergence of such a phase in a nominally commensurate crystal is particularly striking as it implies that the configurational freedom introduced by multiple atomic species can unlock structural states that are otherwise inaccessible in simpler, chemically homogeneous compounds. Future metrology efforts will focus on detailed reciprocal space mapping, local diffraction tomography, and complementary techniques to fully characterize the structural, electronic, and vibrational signatures of this phase. Through this comprehensive approach, the study aims to understand how such strains and distortions correlate with the observed SHG enhancement and to establish a broader framework for designing next-generation optoelectronic materials through high- entropy engineering. EXAMPLE ASPECTS

[0350] Example 1: A single nonlinear optical crystal having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; wherein n is 1 to 14; and wherein the crystal exhibits a second harmonic generation (SHG) coefficient of from 0.2 pm / V to 200 pm / V.

[0351] Example 2: The single nonlinear optical crystal of any examples herein, particularly Example 1, wherein the crystal has a non-centrosymmetric crystal structure.Attorney Docket No.11196-117WO1

[0352] Example 3: The single nonlinear optical crystal of any examples herein, particularly Examples 1-2, wherein n is 1.

[0353] Example 4: The single nonlinear optical crystal of any examples herein, particularly Example 3, wherein R is Eu, Nd, Sm, Tb, or Dy.

[0354] Example 5: The single nonlinear optical crystal of any examples herein, particularly Examples 1-2, wherein n is greater than 1 and R is any combination of Nd, Sm, Tb, Dy, Er, Gd, and Yb.

[0355] Example 6: The single nonlinear optical crystal of any examples herein, particularly Example 5, wherein n is 5 and R is: a) Nd, Tb, Sm, Dy, and Er; or b) Nd, Tb, Sm, Dy, and Yb.

[0356] Example 7: The single nonlinear optical crystal of any examples herein, particularly Example 5, wherein n is 6 and R is Nd, Sm, Dy, Gd, Yb, and Er.

[0357] Example 8: The single nonlinear optical crystal of any examples herein, particularly Examples 5-7, wherein each rare earth element in R is present in a substantially equal mole fraction.

[0358] Example 9: The single nonlinear optical crystal of any examples herein, particularly Examples 1-8, wherein RnBa3(B3O6)3 has a bandgap of from 4 eV to 6.5 eV.

[0359] Example 10: The single nonlinear optical crystal of any examples herein, particularly Examples 1-9, wherein RnBa3(B3O6)3 exhibits a laser-induced surface damage threshold (LISDT) of from 400 GW / cm2to 1000 GW / cm2for laser pulses of from 100 fs to 300 fs wide in a wavelength range of from 300 nm to 3000 nm.

[0360] Example 11: The single nonlinear optical crystal of any examples herein, particularly Examples 1-10, wherein RnBa3(B3O6)3 has an absorption coefficient α (1 / mm) of less than 0.3 in the visible and / or UV-C region (from 250 nm to 3200 nm).

[0361] Example 12: The single nonlinear optical crystal of any examples herein, particularly Examples 1-11, wherein RnBa3(B3O6)3 has an absorption coefficient α (1 / mm) of less than 0.15 in the visible and / or UV-C region (from 250 nm to 3200 nm).

[0362] Example 13: The single nonlinear optical crystal of any examples herein, particularly Examples 1-12, wherein the crystal exhibits a transparency of greater than 60% to 100% in a wavelength range of from 225 nm to 3200 nm.

[0363] Example 14: The single nonlinear optical crystal of any examples herein, particularly Examples 5-13, wherein at least a portion of RnBa3(B3O6)3 exhibits a hexagonal (H) phase.Attorney Docket No.11196-117WO1

[0364] Example 15: The single nonlinear optical crystal of any examples herein, particularly Examples 5-14, wherein at least a portion of RnBa3(B3O6)3 exhibits a metastable low symmetry (M) phase.

[0365] Example 16: The single nonlinear optical crystal of any examples herein, particularly Example 15, wherein the M phase is macroscopic.

[0366] Example 17: The single nonlinear optical crystal of any examples herein, particularly Examples 15 or 16, wherein the SHG coefficient of the crystal is from 10 to 100 times greater than an SHG coefficient of a commercially available BaB2O4 crystal.

[0367] Example 18: The single nonlinear optical crystal of any examples herein, particularly Examples 15-17, wherein the M phase is formed by shrinking a crystallographic c-axis of RnBa3(B3O6)3.

[0368] Example 19: The single nonlinear optical crystal of any examples herein, particularly Example 18, wherein shrinking of the crystallographic c-axis comprises: a) thermal quenching from a temperature of 900°C or less to room temperature, wherein the thermal quenching has a rate of from 25°C / sec to 150°C / sec; or b) forming a thermal gradient during RnBa3(B3O6)3 growth.

[0369] Example 20: The single nonlinear optical crystal of any examples herein, particularly Examples 1-19, wherein the crystal is substantially stable in ambient conditions, alcohol, acetone, or any combination thereof.

[0370] Example 21: A single nonlinear optical crystal having a formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; wherein n is 1 to 14; and wherein at least a portion of RnBa3(B3O6)3 exhibits a metastable low symmetry (M) phase.

[0371] Example 22: The single nonlinear optical crystal of any examples herein, particularly Example 21, wherein the M phase is macroscopic.

[0372] Example 23: The single nonlinear optical crystal of any examples herein, particularly Examples 21 or 22, wherein the SHG coefficient of the single nonlinear optical crystal is from 10 to 100 times greater than an SHG coefficient of a commercially available BaB2O4 crystal.

[0373] Example 24: The single nonlinear optical crystal of any examples herein, particularly Examples 21-23, wherein the M phase exhibits compressive strain (Δc / c) of from 0.0005 to 0.005 along the crystallographic c-axis.Attorney Docket No.11196-117WO1

[0374] Example 25: The single nonlinear optical crystal of any examples herein, particularly Examples 21-24, wherein RnBa3(B3O6)3 exhibits a laser-induced surface damage threshold (LISDT) that is from 2 to 6 times higher than a LISDT of a commercially available BaB2O4 crystal.

[0375] Example 26: The single nonlinear optical crystal of any examples herein, particularly Examples 21-25, wherein the crystal exhibits a transparency of from 80% to 100% in a wavelength range of from 225 nm to 3200 nm.

[0376] Example 27: The single nonlinear optical crystal of any examples herein, particularly Examples 21-26, wherein the crystal is substantially stable in ambient conditions, alcohol, acetone, or any combination thereof.

[0377] Example 28: The single nonlinear optical crystal of any examples herein, particularly Examples 21-27, wherein the crystal exhibits a multimodal luminescence in a wavelength range of from 250 nm to2400 nm.

[0378] Example 29: The single nonlinear optical crystal of any examples herein, particularly Examples 21-28, wherein the crystal exhibits a high thermal expansion coefficient of 20×10-6K-1to 35×10-6K-1.

[0379] Example 30: The single nonlinear optical crystal of any examples herein, particularly Examples 21-29, wherein the crystal exhibits a decrease of from 10% to 150% in positional disorder at a Ba site as compared to a substantially identical reference crystal with an absence of M phase.

[0380] Example 31: The single nonlinear optical crystal of any examples herein, particularly Examples 21-30, wherein the crystal is stable for at least 1 year under ambient conditions at room temperature.

[0381] Example 32: A laser comprising a single nonlinear optical crystal of any examples herein, particularly Examples 1-31.

[0382] Example 33: A quantum light emitter comprising the single nonlinear optical crystal of any examples herein, particularly Examples 1-31.

[0383] Example 34: A device comprising the single nonlinear optical crystal of any examples herein, particularly Examples 1-31, the laser of any examples herein, particularly Example 32, or the quantum light emitter of any examples herein, particularly Example 33.

[0384] Example 35: A method of forming the single nonlinear optical crystal of any examples herein, particularly Examples 1-20, the method comprising growing the single crystal from a polycrystalline material having a chemical formula ofAttorney Docket No.11196-117WO1 RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; and wherein n is 1 to 14.

[0385] Example 36: The method of any examples herein, particularly Example 35, wherein the polycrystalline material is formed by a solid-state synthesis.

[0386] Example 37: The method of any examples herein, particularly Examples 35 or 36, wherein growing the single crystal comprises a floating-zone technique, Bridgman, Czochralski, top-seeded solution growth (TSSG), flux method, or any combination thereof.

[0387] Example 38: A method of forming the single nonlinear optical crystal of any examples herein, particularly Examples 21-31, the method comprising shrinking a crystallographic c-axis of a single crystal having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from any combination of La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu; and wherein n is 1 to 14.

[0388] Example 39: The method of any examples herein, particularly Example 38, wherein the single crystal is formed from a polycrystalline material having the chemical formula of RnBa3(B3O6)3.

[0389] Example 40: The method of any examples herein, particularly Example 39, wherein the polycrystalline material is formed by a solid-state synthesis.

[0390] Example 41: The method of any examples herein, particularly Examples 38-40, wherein the single crystal is formed by a floating-zone technique, Bridgman, Czochralski, top-seeded solution growth (TSSG), flux method, or any combination thereof.

[0391] Example 42: The method of any examples herein, particularly Examples 38-41, wherein shrinking of the crystallographic c-axis comprises: a) thermal quenching from a temperature of 900°C or less to room temperature, wherein the thermal quenching has a rate of 25°C / sec to 150°C / sec; or b) forming a thermal gradient during RnBa3(B3O6)3 growth.

[0392] Example 43: The method of any examples herein, particularly Example 42, wherein thermal quenching comprises inserting the single crystal that is at a temperature of 900°C or less into liquid nitrogen or liquid helium.

[0393] Example 44: The method of any examples herein, particularly Example 42, wherein thermal quenching comprises inserting the single crystal that is at a temperature of from 350°C to 450°C into ice water or room temperature water.Attorney Docket No.11196-117WO1

[0394] Example 45: The method of any examples herein, particularly Examples 38-41, wherein shrinking of the crystallographic c-axis comprises exposing the single crystal to a laser prior to thermal quenching.

[0395] Example 46: The method of any examples herein, particularly Example 45, wherein the laser has a wavelength range of from 300 nm to 4.5 µm; and wherein the single crystal is mounted on a metal plate or a light-absorbing substrate.

[0396] Example 47: The method of any examples herein, particularly Examples 45-46, wherein thermal quenching comprises exposure to liquid nitrogen, liquid helium, ice water, room temperature water, or any combination thereof.

[0397] Example 48: The method of any examples herein, particularly Example 41, wherein, when flux growth is used to form the single crystal, shrinking of the crystallographic c-axis comprises forming a thermal gradient during crystallization.

[0398] Any patents, applications and publications as listed throughout this document are hereby incorporated by reference in their entirety herein.

Claims

Attorney Docket No.11196-117WO1 CLAIMS 1. A single nonlinear optical crystal having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; wherein n is 1 to 14; and wherein the crystal exhibits a second harmonic generation (SHG) coefficient of from 0.2 pm / V to 200 pm / V.

2. The single nonlinear optical crystal of claim 1, wherein the crystal has a non- centrosymmetric crystal structure.

3. The single nonlinear optical crystal of any one of claims 1-2, wherein n is 1.

4. The single nonlinear optical crystal of claim 3, wherein R is Eu, Nd, Sm, Tb, or Dy.

5. The single nonlinear optical crystal of any one of claims 1-2, wherein n is greater than 1 and R is any combination of Nd, Sm, Tb, Dy, Er, Gd, and Yb.

6. The single nonlinear optical crystal of claim 5, wherein n is 5 and R is: a) Nd, Tb, Sm, Dy, and Er; or b) Nd, Tb, Sm, Dy, and Yb.

7. The single nonlinear optical crystal of claim 5, wherein n is 6 and R is Nd, Sm, Dy, Gd, Yb, and Er.

8. The single nonlinear optical crystal of any one of claims 5-7, wherein each rare earth element in R is present in a substantially equal mole fraction.

9. The single nonlinear optical crystal of any one of claims 1-8, wherein RnBa3(B3O6)3 has a bandgap of from 4 eV to 6.5 eV.Attorney Docket No.11196-117WO1 10. The single nonlinear optical crystal of any one of claims 1-9, wherein RnBa3(B3O6)3 exhibits a laser-induced surface damage threshold (LISDT) of from 400 GW / cm2to 1000 GW / cm2for laser pulses of from 100 fs to 300 fs wide in a wavelength range of from 300 nm to 3000 nm.

11. The single nonlinear optical crystal of any one of claims 1-10, wherein RnBa3(B3O6)3 has an absorption coefficient α (1 / mm) of less than 0.3 in the visible and / or UV-C region (from 250 nm to 3200 nm).

12. The single nonlinear optical crystal of any one of claims 1-11, wherein RnBa3(B3O6)3 has an absorption coefficient α (1 / mm) of less than 0.15 in the visible and / or UV-C region (from 250 nm to 3200 nm).

13. The single nonlinear optical crystal of any one of claims 1-12, wherein the crystal exhibits a transparency of greater than 60% to 100% in a wavelength range of from 225 nm to 3200 nm.

14. The single nonlinear optical crystal of any one of claims 5-13, wherein at least a portion of RnBa3(B3O6)3 exhibits a hexagonal (H) phase.

15. The single nonlinear optical crystal of any one of claims 5-14, wherein at least a portion of RnBa3(B3O6)3 exhibits a metastable low symmetry (M) phase.

16. The single nonlinear optical crystal of claim 15, wherein the M phase is macroscopic.

17. The single nonlinear optical crystal of claim 15 or 16, wherein the SHG coefficient of the crystal is from 10 to 100 times greater than an SHG coefficient of a commercially available BaB2O4 crystal.

18. The single nonlinear optical crystal of any one of claims 15-17, wherein the M phase is formed by shrinking a crystallographic c-axis of RnBa3(B3O6)3.Attorney Docket No.11196-117WO1 19. The single nonlinear optical crystal of claim 18, wherein shrinking of the crystallographic c-axis comprises: a) thermal quenching from a temperature of 900°C or less to room temperature, wherein the thermal quenching has a rate of from 25°C / sec to 150°C / sec; or b) forming a thermal gradient during RnBa3(B3O6)3 growth.

20. The single nonlinear optical crystal of any one of claims 1-19, wherein the crystal is substantially stable in ambient conditions, alcohol, acetone, or any combination thereof.

21. A single nonlinear optical crystal having a formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; wherein n is 1 to 14; and wherein at least a portion of RnBa3(B3O6)3 exhibits a metastable low symmetry (M) phase.

22. The single nonlinear optical crystal of claim 21, wherein the M phase is macroscopic.

23. The single nonlinear optical crystal of claim 21 or 22, wherein the SHG coefficient of the single nonlinear optical crystal is from 10 to 100 times greater than an SHG coefficient of a commercially available BaB2O4 crystal.

24. The single nonlinear optical crystal of any one of claims 21-23, wherein the M phase exhibits compressive strain (Δc / c) of from 0.0005 to 0.005 along the crystallographic c-axis.

25. The single nonlinear optical crystal of any one of claims 21-24, wherein RnBa3(B3O6)3 exhibits a laser-induced surface damage threshold (LISDT) that is from 2 to 6 times higher than a LISDT of a commercially available BaB2O4 crystal.Attorney Docket No.11196-117WO1 26. The single nonlinear optical crystal of any one of claims 21-25, wherein the crystal exhibits a transparency of from 80% to 100% in a wavelength range of from 225 nm to 3200 nm.

27. The single nonlinear optical crystal of any one of claims 21-26, wherein the crystal is substantially stable in ambient conditions, alcohol, acetone, or any combination thereof.

28. The single nonlinear optical crystal of any one of claims 21-27, wherein the crystal exhibits a multimodal luminescence in a wavelength range of from 250 nm to2400 nm.

29. The single nonlinear optical crystal of any one of claims 21-28, wherein the crystal exhibits a high thermal expansion coefficient of 20×10-6K-1to 35×10-6K-1.

30. The single nonlinear optical crystal of any one of claims 21-29, wherein the crystal exhibits a decrease of from 10% to 150% in positional disorder at a Ba site as compared to a substantially identical reference crystal with an absence of M phase.

31. The single nonlinear optical crystal of any one of claims 21-30, wherein the crystal is stable for at least 1 year under ambient conditions at room temperature.

32. A laser comprising a single nonlinear optical crystal of any one of claims 1-31.

33. A quantum light emitter comprising the single nonlinear optical crystal of any one of claims 1-31.

34. A device comprising the single nonlinear optical crystal of any one of claims 1- 31, the laser of claim 32, or the quantum light emitter of claim 33.

35. A method of forming the single nonlinear optical crystal of any one of claims 1-20, the method comprising growing the single crystal from a polycrystalline material having a chemical formula of RnBa3(B3O6)3 wherein R is n different rareAttorney Docket No.11196-117WO1 earth elements selected from La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and any combination thereof; and wherein n is 1 to 14.

36. The method of claim 35, wherein the polycrystalline material is formed by a solid-state synthesis.

37. The method of claim 35 or 36, wherein growing the single crystal comprises a floating-zone technique, Bridgman, Czochralski, top-seeded solution growth (TSSG), flux method, or any combination thereof.

38. A method of forming the single nonlinear optical crystal of any one of claims 21-31, the method comprising shrinking a crystallographic c-axis of a single crystal having a chemical formula of RnBa3(B3O6)3 wherein R is n different rare earth elements selected from any combination of La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu; and wherein n is 1 to 14.

39. The method of claim 38, wherein the single crystal is formed from a polycrystalline material having the chemical formula of RnBa3(B3O6)3.

40. The method of claim 39, wherein the polycrystalline material is formed by a solid-state synthesis.

41. The method of any one of claims 38-40, wherein the single crystal is formed by a floating-zone technique, Bridgman, Czochralski, top-seeded solution growth (TSSG), flux method, or any combination thereof.

42. The method of any one of claims 38-41, wherein shrinking of the crystallographic c-axis comprises: a) thermal quenching from a temperature of 900°C or less to room temperature, wherein the thermal quenching has a rate of 25°C / sec to 150°C / sec; or b) forming a thermal gradient during RnBa3(B3O6)3 growth.Attorney Docket No.11196-117WO1 43. The method of claim 42, wherein thermal quenching comprises inserting the single crystal that is at a temperature of 900°C or less into liquid nitrogen or liquid helium.

44. The method of claim 42, wherein thermal quenching comprises inserting the single crystal that is at a temperature of from 350°C to 450°C into ice water or room temperature water.

45. The method of any one of claims 38-41, wherein shrinking of the crystallographic c-axis comprises exposing the single crystal to a laser prior to thermal quenching.

46. The method of claim 45, wherein the laser has a wavelength range of from 300 nm to 4.5 µm; and wherein the single crystal is mounted on a metal plate or a light-absorbing substrate.

47. The method of any one of claims 45-46, wherein thermal quenching comprises exposure to liquid nitrogen, liquid helium, ice water, room temperature water, or any combination thereof.

48. The method of claim 41, wherein, when flux growth is used to form the single crystal, shrinking of the crystallographic c-axis comprises forming a thermal gradient during crystallization.

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