Birefringence is a key property of optical functional crystals, underpinning their vital applications in angle phase‐matching, polarization control, and various advanced photonic technologies. Currently, TiO 2 exhibits a large birefringence in the visible region, serving as a benchmark material. With the advancement of science and industry, the exploration of new birefringent materials in this wavelength band has become increasingly important. In this work, we proposed a mixed anion strategy to enhance the optical anisotropy, using the Hf‐O‐N system as a case study. Structures with Hf‐O‐N were screened from the NOEMD database for further first‐principles calculations. Six structures with ( E hull ≤ 0.05 eV/atom) possess large bandgaps (1.67–5.02 eV) and significant birefringence (0.17–0.403 @1064 nm). Four structures exhibit potential birefringence in the visible region, I 4/ mmm ‐Hf 2 N 2 O (0.37 @1064 nm), Cm ‐Hf 5 N 6 O (0.219 @1064 nm), C 2/ m ‐Hf 7 N 8 O 2 (0.333 @1064 nm), and Cm ‐Hf 7 N 8 O 2 (0.403 @1064 nm). The birefringence of three of these structures exceeds that of TiO 2 (0.256 @1064 nm). Through structural analysis, we identified that the [Hf 4 NO 2 ], [Hf 4 NO], and [Hf 2 NO 4 ] polyhedra are outstanding optical functional units, which tend to offer significant optical anisotropy. This result offers novel potentialities for the application of birefringent materials and guideline for novel uses of Hafnium oxynitride materials.

Fluorooxoborates are promising candidates for deep-ultraviolet (DUV) nonlinear optical (NLO) materials, with the [BO3] : [BO3F] ratio critically regulating the band gap, birefringence, and second-harmonic generation (SHG) effects. However, DUV NLO fluorooxoborate with a [BO3] : [BO3F] ratio of 2 : 1 has not yet been reported. In this work, with the [BO3] : [BO3F] ratio of 2 : 1, we conducted a targeted structural search while fixing the dimensionality of the anionic framework as [B3O5F] chains and [B6O9F2] layers and applied to the calcium fluorooxoborate system. We successfully predicted three new dynamically stable non-centrosymmetric phases of CaB3O5F and CaB6O9F2 that exhibit DUV phase-matching (PM) ability. The pronounced electron density difference along the optical principal axis within the flattened [B6O9F2] layer in CaB6O9F2-I results in the largest birefringence (0.101 at 1064 nm), making CaB6O9F2-I exhibit a full-wavelength PM down to 162 nm. The aligned arrangement of functional units in the [B3O5F] chain leads to considerable SHG response of CaB3O5F-IV (1.124 pm V-1), which is comparable to that of fluorooxoborates with higher [BO3] : [BO3F] ratios. This work fills the gap in the field of DUV NLO fluorooxoborates with a [BO3] : [BO3F] ratio of 2 : 1 and provides guidance for the design of DUV NLO materials.

Deep-ultraviolet (deep-UV) nonlinear optical (NLO) crystals are crucial for generating deep-UV lasers, and their performance is determined by the type, ratio, and arrangement of microscopic NLO functional units. Currently, there are no suitable materials capable of achieving deep-UV phase-matching (PM) laser output via direct second harmonic generation (SHG) at around 148.3 nm - a key requirement for the 2 2 9Th nuclear clock. Here, we proposed a functional-units-ratio design principle to address this bottleneck. Applying this strategy to the Li-B-O-F system, we designed two novel compositions, LiB3O4F2 and Li2B4O5F4. Subsequent crystal structure prediction identified C2-LiB3O4F2 as an exceptional candidate, exhibiting a record-short PM wavelength of 145.2 nm and a strong SHG response of 3.4 & times; KH2PO4. The prediction also revealed several other metastable phases with outstanding performance, including Cc-LiB3O4F2 (149.7 nm), P21-Li(2)B(4)O5F4 (151.6 nm), P21-LiB3O4F2-5 (156.1 nm), P21-LiB3O4F2-9 (156.8 nm), and Cm-LiB(3)O(4)F2-7 (158.2 nm), all of which surpass the previous record and have a high synthesis probability. Crucially, the combination of [BO3] and [BO2F2] functional units enables deep-UV PM with a moderate birefringence (similar to 0.05 @1064 nm), effectively circumventing the traditional performance trade-off. This work provides a generalizable design strategy for next-generation deep-UV NLO materials and paves the way for the practical development of the 229Th nuclear clock.

Abstract Discovering deep-ultraviolet (deep-UV) nonlinear optical (NLO) crystals is hampered by the vast structural search space and the cost of first-principles screening. Here, we establish an integrated framework coupling machine learning interatomic potential (MLIP) construction, MLIP-assisted crystal structure prediction (CSP), and first-principles property calculations and apply it to the LiB2O3F system. A total of 40 low-energy candidate structures with formation energies above the thermodynamic convex hull (Ehull) ≤ 50 meV/atom were identified. Notably, seven of these structures are thermodynamically competitive with zero/near-zero Ehull values, namely, LiB2O3F-1 (P3, Z = 6), LiB2O3F-2 (R3c, Z = 6), LiB2O3F-3 (R3, Z = 3), LiB2O3F-4 (P3, Z = 3), LiB2O3F-5 (P31c, Z = 2), LiB2O3F-6 (P3, Z = 6), and LiB2O3F-7 (P63, Z = 2). First-principles calculations further reveal that these thermodynamically competitive phases exhibit wide band gaps ranging from 7.737 to 8.133 eV at the HSE06 level, suitable second harmonic generation (SHG) coefficient magnitudes ranging from 0.367 to 0.711 pm/V, and shortest phase-matching wavelengths ranging from 162.4 to 164.7 nm, highlighting the potential of LiB2O3F as a deep-UV NLO material. These results demonstrate that MLIP-assisted CSP is an effective strategy for discovering new deep-UV NLO materials.

Two novel KTiOPO4 (KTP) derivative crystals, KTeOPO4 and NH4SnClSO4, were successfully synthesized and characterized for the first time. Both compounds exhibit significantly enhanced optical anisotropy, with birefringence values of 0.1713 and 0.1845@1064 nm for KTeOPO4 and NH4SnClSO4, respectively, surpassing that of the parent KTP material. Structural analyses reveal that the large birefringence originates from the highly distorted [TeO5] and [SnO3Cl3] polyhedra, which feature stereochemically active lone-pair electrons. Experimental and computational results confirm that KTeOPO4 and NH4SnClSO4 possess a wide band gap, indicating potential applications in the ultraviolet region. This work demonstrates the effectiveness of incorporating lone-pair cations into KTP-type frameworks to engineer crystals with superior birefringence.

Crystals with layered features, by virtue of their intrinsic structural asymmetry, exhibit pronounced optical anisotropy, positioning them as leading candidates for high-performance birefringent materials. Although numerous crystals with layered features exhibiting giant birefringence (Delta n) have been experimentally reported, a comprehensive understanding of their theoretical limits, modulation mechanisms, and structure-property relationships remains lacking. Herein, we integrate high-throughput screening with first-principles calculations to investigate 131 experimentally stable candidates, constructing an empirical band gap-birefringence Pareto frontier. Our analysis reveals that giant birefringence originates from synergistic macroscopic and microscopic mechanisms. Macroscopically, a universal "volcano-type" dependence on the packing factor (eta) identifies an optimal geometric dilution at eta approximate to 0.5. Microscopically, "covalent locking" enforces strict electron confinement within the two-dimensional plane, thereby maximizing the polarization difference. This work establishes universal design principles, transitioning the exploration of birefringent crystals from trial-and-error to rational geometric and electronic engineering.

A fluorination modulation theory embeds nonmetalfluorine covalent bonds into tetrahedral units, breaking local symmetry and stabilizing electronic structures to enable rational design of high-performance vacuum ultraviolet nonlinear optical crystals.

Borates and their derivatives with nonlinear optical (NLO) effects are considered preferred materials for the generation of deep-ultraviolet (deep-UV) lasers. Despite the importance of this class of materials, only a small fraction has been explored, which greatly limits the discovery of new borate-based materials with deep-UV NLO performance. Herein, by performing crystal structure searches and first-principles properties calculations, we propose a deep-UV NLO borosilicate, RbSiB3O7, which was designed by introducing SiO2 into RbB3O5. We successfully predicted a new thermo-dynamically stable phase, RbSiB3O7-I, along with several metastable phases (RbSiB3O7-II to RbSiB3O7-XI). All of these RbSiB3O7 structures feature distinctive [SiB3O10] fundamental building blocks (FBBs), each of which consists of one [SiO4], one [BO4], and two [BO3] units. Compared with its parent compound RbB3O5, in which one [BO4] and two [BO3] units form [B3O7] rings, the introduction of the [SiO4] unit transforms the [B3O7] FBB into [SiB3O10] FBB. From structural and physical perspectives, such a modification may yield a better balance among NLO-related properties. Remarkably, RbSiB3O7-V possesses a large band gap (∼7 eV), a large second-harmonic generation coefficient (∼1.5 × KH2PO4), and suitable birefringence (∼0.07 at 1064 nm), thereby enabling deep-UV phase matching. Considering that borosilicates still contain a vast unexplored chemical space, the present study may stimulate the exploration of new deep-UV NLO borosilicates with superior properties.

At a 2 : 1 [BO 3 ] : [BO 3 F] ratio, CaB 3 O 5 F features a 1D chain (SHG d 23 =1.12 V) pm V −1 and CaB 6 O 9 F 2 forms a 2D layer (Δ n = 0.101). This fills a structural gap and advances the design of DUV NLO fluorooxoborates.

Developing new short-wavelength nonlinear optical (NLO) crystals has always been a significant and challenging area of research. Herein, guided by the cooperative optimization strategy, three new rare-earth metal borate fluorides, K2GdB3O6F2, Rb2LuB3O6F2, and Cs2LuB3O6F2, are rationally designed and fabricated by synergically assembling advantageous functional groups. Among them, a structural evolution from centrosymmetric K2GdB3O6F2 to non-centrosymmetric Rb2LuB3O6F2 and Cs2LuB3O6F2 reveals that the [B3O6] group contributes to the control of structural symmetry, owing to its sensitivity to the coordination of rare earth metal polyhedra. Notably, all the three title compounds exhibit short cutoff edges less than 200 nm, with Cs2LuB3O6F2 displaying a large experimental frequency doubling effect of 1.5 x KH2PO4. The type-I shortest phase-matching wavelengths for Rb2LuB3O6F2 and Cs2LuB3O6F2 are evaluated to be 210 and 202 nm, respectively, indicating their potential for direct output of 213 coherent lights through a fifth harmonic generation process of Nd: YAG laser. This study provides new insights into the rational design and development of short-wavelength NLO materials by exploring the sensitivity of the [B3O6] groups to the surrounding coordination environment, thereby fostering innovation in the field of NLO materials.

The indispensability of birefringent materials in advanced optical technologies stems from their pivotal role in the generation and manipulation of polarized light. Sn2+ with stereochemically active lone pairs have widespread applications in synthesizing novel birefringent materials, which are attributed to their significant enhancement of birefringence. Although the activity of lone pair electrons is influenced by different anions, there remains a lack of understanding regarding the relationship between the activity of lone pairs and birefringence in mixed halides. Herein, through an analysis of three Sn(II)-based mixed halides (SnFCl, Sn2F3I, and SnClI), we demonstrate that the activity of lone pairs is governed by the energy lever difference between cation s-states and halogen p-states, with a decreasing trend from F to I. Subsequently, we find a gradual decrease in the lone pair activity of SnFCl, Sn2F3I, and SnClI while their birefringence gradually increases. The reversal enhancement of birefringence with respect to lone pair electron activity can be ascribed to the distinct spatial orientations of stereochemically active lone pairs. These findings provide significant perspectives for comprehending birefringent materials that contain lone pair electrons.

我们提出了一种双功能基团驱动极化增强策略: 通过两种不同 双折射活性基团, 线性拟卤素和具有立体化学活性孤对电子的Sn2+ 的共同作用实现大光学各向异性. 结果表明, SnCN2 、Sn2OCN2 、 Sn(SCN)2 和Sn(SCN)F表现出大的双折射率(Δn = 0.44–0.73, 1064 nm). Sn(SCN)2 显示出宽带隙及高双折射率(Δn = 0.64, 1064 nm)是典型双折 射材料CaCO3 (Δn = 0.16, 1064 nm)的4倍. 第一性原理计算阐明了线性 拟卤素基团([NCN]/[SCN])与具有立体化学活性孤对电子的Sn2+ 引起 的电子密度分布各向异性在光学性质中的关键作用. 这种双功能基团 策略为探索高性能双折射光学晶体建立了范例.

Two-dimensional (2D) materials with large band gaps and strong and tunable second-harmonic generation (SHG) coefficients play an important role in the miniaturization of deep-ultraviolet (DUV) nonlinear optical (NLO) devices. Despite the existence of numerous experimentally synthesized 2D materials, none of them have been reported to meet DUV NLO requirements. Herein, to the first time, an experimentally available graphene-like BeO monolayer only formed by NLO-active [BeO3] unit is suggested as a promising 2D DUV NLO material due to its ultrawide band gap (6.86 eV) and a strong SHG effect (\{chi}_"22" ^((2))(2D) = 6.81 {\AA}\times pm/V) based on the first-principles calculations. By applying stacking, strain, and twist engineering methods, several 2D BeO sheets have been predicted, and the flexible structural characteristics endow them with tunable NLO properties. Remarkably, the extremely stress-sensitive out-of-plane \{chi}_"15" ^((2))(2D) and \{chi}_"33" ^((2))(2D) (exceptional 30% change) and the robust in-plane \{chi}_"22" ^((2))(2D) against large strains can be achieved together in AC-, AAC-, AAE, and ACE-stacking BeO sheets under in-plane biaxial strain, exhibiting emergent phenomena uniquely not yet seen in other known 2D NLO materials. Our present results reveal that 2D BeO systems should be a new option for 2D DUV NLO materials.

Deep ultraviolet (DUV) fluorooxoborates with a large second harmonic generation (SHG) response and suitable birefringence are preferred materials for new DUV nonlinear optical (NLO) crystals, which are urgently needed in modern laser technology. While most reported fluorooxoborates with DUV phase matching abilities feature anionic frameworks combining pi-conjugated functional units [BO3] with non-pi-conjugated units [BO3F], systems incorporating [BO3] and [BO2F2] remain notably less explored. By performing crystal structure prediction and first-principles calculations, we predicted two new DUV NLO fluorooxoborates, namely, CaB4O5F4 and CaB6O8F4, whose anionic architectures uniquely integrate [BO3] and [BO2F2] units. CaB4O5F4 demonstrates a 1 : 1 [BO3]/[BO2F2] stoichiometric ratio, a structural configuration previously unreported for DUV NLO materials, exhibiting the shortest phase-matching wavelength of 157 nm. For CaB6O8F4, when the [BO3]/[BO2F2] ratio is 2, the shortest phase-matching wavelength is 163 nm. We note here that CaB6O8F4 not only maintains a large bandgap (7.66 eV) but also exhibits a large birefringence (0.106 at 1064 nm) and SHG response (3.5 x KDP). Further analysis indicates that a well-designed combination of [BO3] and [BO2F2] units can effectively modulate the bandgap, birefringence, and SHG response. This study offers a promising hybridization tailoring strategy for the exploration of novel fluorooxoborate crystals through rational anion engineering.

The simultaneous achievement of wide band gap and strong nonlinear optical (NLO) effect poses a challenging task in the development of infrared (IR) NLO materials. The coupling strategy of polyhedral building blocks has been demonstrated to be one of the effective approaches for constructing superior optical materials with well-balanced performance. Here, a new family of IR NLO materials AI2Mg3Ga12S22 (AI = K, Rb) that first contain [MgS6] octahedra and T2-type supertetrahedra was designed and synthesized. K2Mg3Ga12S22 exhibits a wide band gap of 3.34 eV, and a moderate second-harmonic generation response intensity of 0.4 times that of AgGaS2 under 2 µm Q-switched laser radiation. Furthermore, the birefringence of K2Mg3Ga12S22 is calculated to be 0.028@1064 nm, resulting in favorable phase-matching behavior in IR region. These characteristics suggest that K2Mg3Ga12S22 could be a promising material for nonlinear frequency conversion applications and it provides new ideas into the design of novel compounds with outstanding IR NLO performances.

This work reviews selenoborates, categorizing them by structure, synthesis methods, and highlighting their bandgaps, nonlinear optical properties, and potential as IR functional materials.

As an emerging system, fluorooxoborate has attracted much attention due to its excellent performance. To systematically study the effects of cations on the structures and properties, a new fluorooxoborate Cs2B3O4F3 was purposefully synthesized to supplement the A2B3O4F3 (A = alkali metal) family, which was selected as a better system to discuss this problem. The fundamental building block of Cs2B3O4F3 is the annular [B3O5F3] unit, which forms the one-dimensional [B3O4F3]infinity chains. The diffuse reflection spectrum shows that it has deep-ultraviolet transparency. Meanwhile, by comparing the crystal structures and analyzing the first principle-calculation results, the influence of the size effect of cations on the crystal structure, bandgap, and birefringence was studied under the perfect system with the same basic building block. What's more, to facilitate the evaluation of the decisive factor birefringence, the regression equation between the anionic unit and birefringence was fitted. These results will promote the structure prediction and directional synthesis of fluorooxoborates.

Mixed-coordinated borophosphates containing π-conjugated [BO3] and non-π-conjugated [BO4] and [PO4] tetrahedra have been a research hot spot benefiting from their diverse structures and the presentation of pre-eminent optical performances. Through the high-temperature solution method, a new mixed-coordinated borophosphate K2PbB5P3O17 was synthesized. This compound exhibits an unprecedented [B5P3O21] fundamental building block consisting of apex-sharing [B3O7], [BO4], and [PO4] units, possessing a short ultraviolet cutoff edge of 234 nm as well as moderate birefringence (0.045@1064 nm). Compared with the tetra-coordinated borophosphate KPbBP2O8 with the same elemental composition, the birefringence of K2PbB5P3O17 achieves a great enhancement induced by the introduction of the planar [B2O5] unit.

Three new metal borates containing d10 cations, namely, Li4PbZn3B12O24, Na2Cd2B8O15, and K2Sr4ZnB10O19(CO3)2, were synthesized using the flux method. K2Sr4ZnB10O19(CO3)2 is the first Zn-containing borate carbonate and has an unprecedented fundamental building block, [B10O22]. Furthermore, experimental and first-principles theoretical studies were performed.

Two borates, K3Al2B11O21 (KABO) and K3Al2MoB9O21 (KAMBO), with edge-sharing [BO4] (ES-[BO4]) tetrahedra and different B-O configurations in one structure, were rationally designed and prepared at atmospheric pressure by introducing covalent tetrahedra. KABO is the first borate identified to have ES-[BO4] tetrahedra and two different dimensional B-O groups, namely, isolated [B6O12] groups with ES-[BO4] and one-dimensional (1)(infinity)[B5O9] infinite chains. In addition, KAMBO is a rare borate that features ES-[BO4] tetrahedra and two distinct isolated B-O groups ([B6O12] and [B3O6]). The discovery of these two compounds not only enriches the structures of borates, but also suggests a novel method for creating borates with ES-[BO4] tetrahedral structures and flexible B-O configurations at atmospheric pressure.