Dielectric function of layered Ga4Se3+δTe1-δ and emergent all van der Waals optical elements

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Margaryan, Maksim L. Sargsyan, Irina I. Piyanzina, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8681290/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Mar, 2026 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract Van der Waals (vdW) crystals provide an expanding platform for designing compact and reconfigurable functional optical devices mostly owing to their wide range of refractive indices, strong optical anisotropy and heterostructure compatibility. Among them, group III monochalcogenides form a prominent family of layered semiconductors exhibiting diverse crystalline phases and showing great potential for nanoscale optoelectronic applications. Despite this promise, a quantitative knowledge of their dielectric functions is yet unrevealed for many representatives of vdW family, not to mention their mixed composition ternary compounds. Here, we address this gap by presenting the complex anisotropic dielectric function of layered Ga 4 Se 3+δ Te 1−δ in visible (Vis) to near-infrared (NIR) spectral region. It exhibits a response typical for uniaxial crystals enabling simultaneous access to the high refractive indices and low optical losses within a broad spectral region. We also suggest that the optical dispersion of vdW Ga 4 Se 3+δ Te 1−δ can be adjusted by varying its ternary composition implying a tunability within a window defined by the dispersion limits of the parent binary compounds. Furthermore, we display an approach towards designing an ultrathin all-vdW optical elements exemplified by unpolarized plate-type beam splitters built on a few multilayer heterostructures of Ga 4 Se 3+δ Te 1−δ / h BN. Physical sciences/Materials science Physical sciences/Optics and photonics Physical sciences/Physics group-III monochalcogenides ternary compounds uniaxial vdW crystals complex dielectric function high-refractive index and its tunability all-vdW optical elements Figures Figure 1 Figure 2 Figure 3 Introduction Following the isolation of graphene 1 , 2 and the subsequent rise of 2D transition-metal dichalcogenides 3 , a wide variety of other 2D crystalline material families emerged 4 , 5 , 6 , 7 , 8 . These diverse families offer a broad spectrum of tunable electronic, optical, and mechanical properties distinct from their bulk vdW counterparts. GaSe, GaTe, InSe and InTe are a few prominent representatives of the group III monochalcogenide 2D family semiconductors with general formula of M III X VI , where M is a group III element and X is a group VI chalcogen atom 9 . Those, along with their vdW counterparts, hold great promise for a wide variety of next-generation nanoscale applications covering electronics, optoelectronics (including ultraviolet sensing), photonics and photocatalysis 10 , 11 , 12 , 13 , 14 . The scientific interest towards their vdW counterparts reintensified 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 once some of the family representatives were cleaved down to 23,24 or synthesized 25 in a monolayer form. Notably, these vdW crystals exhibit a variety of polymorphic hexagonal, monoclinic and other phases 26 , 27 , 28 , 29 each offering a unique set of properties. One may feature those of non-centrosymmetric symmetry allowing a strong non-linear optical effects, such as, for example, a second harmonic generation 30 , 31 and imaging 32 or sliding ferroelectric states 33 , 34 . Recent first-principles approaches propose that an oxygen functionalization of group III monochalcogenides may further affect their properties giving rise to the emergence of topological states 35 . On the other hand, a mixed ternary Janus phase with group III (or VI ) elements comprising two identical (non-identical) atoms, such as, for example, Ga 2 SSe or Al 2 SSe may lead to an appearance of anisotropic mechanical features 36 and strain-induced bandgap modifications 37 . Another sub-class of a ternary group III monochalcogenide solids comprises a mix of a sole group VI chalcogen atoms, where the two representatives, such as, for example, Selenium (Se) and Tellurium (Te) are positioned in the unit-cell of a crystal with varying, one may call an alloy-like compounds: GaSe x Te 1−x (or GaSe x S 1−x ) 38,39,40,41,42,43,44,45,46 . A structural phase diagram of the former vdW crystals 38 , 39 , 47 shows a stabilization of Se-rich compositions in a uniaxial hexagonal phase, whereas Te-rich compositions favor a biaxial monoclinic phase. Here, the uniaxial vdW crystals display an eminent decrease of a bandgap with an introduction of Te atoms into the hexagonal lattice of a pristine GaSe. In contrast, an introduction of Se atoms into a monoclinic GaTe lattice exhibiting in-plane anisotropic optical characteristics leads not only to a nominal increase of a bandgap but further spotlights a hexagonal to monoclinic phase instability crossover emerging in a narrow range of intermediate Se-Te compositions, where both phases coexist. In this manuscript, we introduce the complex dielectric function of a group III ternary monochalcogenide - vdW GaSe x Te 1−x with the composition of x = 0.78 that is farther represented by its closest rational hexagonal super-cell of Ga 4 Se 3+δ Te 1−δ exhibiting a small variation of δ (see Results). Our studies cover the 360–1000 nm spectral region positioning vdW Ga 4 Se 3+δ Te 1−δ as an emergent low-loss high-refractive index vdW crystal in Vis- to -NIR spectral region. We show that it exhibits an in-plane refractive index of ~ 3 at red-light wavelengths of Vis spectral region and a sheer optical transparency in the deep red-light and NIR spectral region. We also propose that the tuning of a ternary composition within vdW GaSe x Te 1−x may strongly influence its optical dispersion indicating a tunability within a window subject to the inherent dispersions of their pristine binary compounds. Furthermore, we demonstrate a design of a variety of sub-micron all-vdW beam splitters based on a few multilayers of h BN-Ga 4 Se 3+δ Te 1−δ operating in NIR spectral region. Our results not only place uniaxial vdW Ga 4 Se 3+δ Te 1−δ amongst the promising high refractive index materials for an assembly of compact all-vdW optical elements but also suggest a novel route for a creation of materials with prescribed optical properties. Results Identifying the crystal structure and Se:Te composition in vdW Ga 4 Se 3+δ Te 1−δ micro-crystals Figure 1 (a) presents an optical micrograph of a representative micro-mechanically cleaved 237 nm thick vdW Ga 4 Se 3+δ Te 1−δ sample (see Fig. S1 for AFM data) selected to demonstrate a swift identification of Selenium: Tellurium (Se:Te) composition in our micro-crystals. Here, by employing photoluminescence (PL) and Raman spectroscopies (see Methods), we first probe the optoelectronic and vibrational responses of our samples (see Fig. 1 (b, c)). The polarization free PL spectra measured at 633 nm and 532 nm laser excitations (see Fig. 1 (b)) show a pronounced emission at 1.85 eV. Notably, for 633 nm excitation, the emission appears at 671 nm limiting the resolution of Raman modes in 100–400 cm⁻¹ spectral region (see the shaded area in Fig. 1 (b)) and resulting in visualization of two A 1g modes, Fig. 1 (c). Nevertheless, switching to 532 nm excitations allows clear observation of high-symmetry E 2 mode at 205 cm⁻¹. Following the approach presented in 38,39,47 , we then compare the systematic shifts of PL and Raman A 1 1g mode peak positions inferring a 0.78:0.22 ratio of Se:Te, and therefore, a uniaxial hexagonal phase. To represent the inferred composition with crystal structure of well-defined parameters, we select the closest rational approximation of uniaxial vdW Ga 4 Se 3 Te (Ga 4 Se 3+δ Te 1−δ considering the exact δ = 0.125 discrepancy) constructing 4:2:1 super-cell with lattice parameters of a = 15.416 Å, b = 7.708 Å and c = 17.457 Å, as it is shown in Fig. 1 (d). Here, the first-principles calculations (see Fig. 1 (e)) yield a direct electronic bandgap of 1.69 eV emerging at Γ point of the first Brillouin zone. Assuming a linear interpolation between the calculated bandgaps for 0.75 and 0.875 Se-rich compositions, we then estimate a bandgap of 1.76 eV for our 0.78 Se-rich case (see red hexagon in Fig. 1 (f)). Notably, the obtained values are reasonably close to the experimentally observed bandgaps showing small offset within Se content vs bandgap dependence when compared with literature data 40 . The anisotropic dielectric function of uniaxial vdW GaSeTe A spectroscopic micro-ellipsometry approach was applied to study the dielectric permittivity function, and thus, optical constants of uniaxial vdW Ga 4 Se 3+δ Te 1−δ samples in 360–1000 nm spectral region, Fig. 2 . Here, for the case of typical hexagonal crystals, a conventional Ψ and Δ parameter studies are sufficient as the latter is isotropic within the ab plane. The polarization state of the incident beam is defined by a polarizer and modulated by a rotating λ /4 retarder, while an analyzer projects the reflected light to enable extraction of ellipsometric parameters Ψ and Δ (see Methods, the inset of Fig. 2 (b), and Fig. S3-Fig. S5 for further details). The in-plane (or ordinary) dielectric permittivity component, ε ₒ ≡ ε ab , and the out-of-plane (or extraordinary) component, ε ₑ ≡ ε c , were extracted by modeling ellipsometric data using Tauc-Lorentz oscillators, Fig. 2 (a, b). The ordinary component was described accounting for an in-plane interband optical response, while the extraordinary component was modeled likewise to account for another set of interband transitions extending into ultraviolet spectral region (see Table S1 – Table S3 for details of optical model and tabulated dielectric and optical constants). The optical constants, i. e. , refractive indices and extinction coefficients obtained from dielectric permittivity studies are presented in Fig. 2 (c). Over the Vis-NIR spectral region, vdW Ga 4 Se 3+δ Te 1−δ exhibits a consistently high in-plane refractive index allowing it to be classified as a high-index material. Specifically, the ordinary refractive index, n ₒ ≡ n ab , is about ~ 3.0 at 700 nm increasing towards shorter wavelengths and reaching 3.65 at 400 nm, while gradually decreasing to 2.83 at 1000 nm wavelengths. The in-plane extinction coefficient remains low, with k ab ≲ 0.1 ( e.g. , k ab = 0.1 at 413 nm), indicating low optical losses prior to the absorption onset. A clear onset of absorption is observed in the vicinity of 656 nm deep red wavelengths. At 633 nm, where absorption is negligible, the ordinary and extraordinary refractive indices are n ₒ ≈ 2.98 and n ₑ ≈ 2.71, yielding to a birefringence of Δn ≈ 0.27 (see Fig. S6). Our first principles (DFT) calculations of the anisotropic optical constants show good agreement with the experimental data corroborating both their magnitude and spectral dispersion (see Fig. 2 (c)). It is important to note that these results also predict an onset of a finite extinction coefficient at higher photon energies supporting the use of Tauc-Lorentz oscillators describing the out-of-plane optical response in the ellipsometric model. To verify the high accuracy of the extracted dielectric permittivity, we then performed micro-reflectance and micro-transmittance spectroscopies (see Methods) for a representative vdW Ga 4 Se 3+δ Te 1−δ samples in 420–720 nm spectral region (see Fig. 2 (d, e)). Here, we consider the ellipsometry-derived constants accurate when the calculated spectra reproduce the experimentally measured values within a deviation of less than a 3%. To calculate these spectra, the dielectric permittivity obtained from ellipsometry was interpreted within the framework of a generalized 4 × 4 transfer-matrix method as described in Methods. Figure 2 (d) and 2(e) display the transmittance, T , acquired from a uniaxial vdW Ga 4 Se 3+δ Te 1−δ sample placed onto fused-silica substrate and the differential reflectance contrast (DRC), acquired from a sample of a similar thickness placed onto a Si/SiO 2 substrate (the extended dataset is provided in Fig. S7). In the case of the former (latter), we compute the ratio of T = J S / J SUB ​ (DRC = ( J S − J SUB )/( J S + J SUB )), where J S ​ is the intensity acquired from the sample, and J SUB ​ is the intensity from a bare substrate (see Methods for more details). The observed properties of T and DRC are typical for high-refractive-index thin films. As shown in Fig. 2 (d), the former approaches unity around 720 nm, while the latter (see Fig. 2 (e)) reaches values up to 0.75 over displaying a band in 450–700 nm spectral region for the corresponding sample thicknesses. Notably, both features originate from strong Fabry-Pérot interference effects. Furthermore, to avoid correlations and ambiguities in the parameters of the optimized optical model, we also utilized another technique separately measuring the thicknesses of studied samples by an alternative means of AFM (see Supplementary Note 1 for the data from a representative sample). Designing all-vdW unpolarized beam splitters with multilayer Ga 4 Se 3+δ Te 1−δ / h BN heterostructures The advent of vdW heterostructures 48 , 49 , 50 has established a versatile platform for an engineering of artificial layered materials with tailored stacking order and composition, enabling functionalities far beyond those accessible in sole bulk crystals. The wide diversity of vdW crystals, in particular with respect to their optical constants and pronounced anisotropic properties, thus provides substantial opportunities for the realization of advanced optical elements for nanoscale optics and nanophotonics. Among these elements, unpolarized beam splitters are a particularly practical case. They enable controlled splitting of an unpolarized light into reflected and transmitted channels across a targeted spectral band providing a considerable scope for an integration into all-vdW-based nanophotonic systems. In this context, we propose a design of a plate-type unpolarized beam splitter (see Fig. 3 (a)) based on a few Ga 4 Se 3+δ Te 1−δ / h BN multilayer heterostructure placed onto a UV fused silica substrate and optimized for an operation in NIR (800–1030 nm) spectral region – a band widely used in modern nanophotonic or laser systems. The vdW h BN is selected as an optically transparent uniaxial vdW dielectric with well-defined in-plane and out-of-plane permittivity components, providing a robust low-index counterpart and an encapsulation layer. Its dielectric permittivity used in computations was separately studied by spectroscopic micro-ellipsometry and extrapolated up to 1200 nm wavelength along with vdW Ga 4 Se 3+δ Te 1−δ (see Fig. S8). In the targeted NIR band, the refractive-index contrast between vdW Ga 4 Se 3+δ Te 1−δ and vdW h BN enables a multilayer-interference, where alternating low and high index layers and their thicknesses are tailored to set the desired reflectance -to -transmittance channels. Larger refractive index contrast reduces the number of constituent layers and the total thickness of the stack. Our design targets three widely used commercial split ratio channels of R:T = 50:50, 30:70, and 10:90, Fig. 3 (c-d). Here, for each design, an individual layer thickness and number of constituent layers were optimized by minimizing the figure of merit, while corresponding reflectance and transmittance spectra were computed at each iteration using the generalized 4 × 4 transfer-matrix method (see Methods). The total thickness of a multilayer stack was kept to sub-micron for all the target designs, while achieving few amounts of constituent all-vdW multilayers with band-averaged performance comparable to commercial NIR broadband plate-type beam splitters operating at the same AoI. The full layer- by -layer thicknesses and stack sequences for all three designs are provided in Table S4 – Table S6. An analogous performance with the conventional thin-film optical materials is typically achieved with many-layer oxide/fluoride or metal-dielectric stacks 51 , 52 , 53 , whose design mainly relies on numerical optimization and optical constants that may vary with the deposition conditions, highlighting the practical advantage of achieving the required response with fewer constituent layers and smaller total thicknesses. Discussion Despite the high potential of group III monochalcogenide ternary vdW GaSe x Te 1−x compounds towards the tailoring of optical dispersion with the variation of ternary Se:Te composition, it yet received no specific attention. As a matter of fact, the dielectric function of vdW GaSe x Te 1−x was studied only in THz spectral region at best for the extreme Se-rich compositions 54 . Though the measured optical dispersions of vdW GaSe and GaTe 55 , 56 , 57 bear a resemblance of two slightly shifted spectral regions that only coincide in a narrow NIR spectral region, one may still identify practical implications. Here, the in-plane refractive index of a biaxial vdW GaTe resembles mean values of n ab ≈ 3.3 at 900 nm NIR wavelength, while for uniaxial vdW GaSe, the reports show significantly smaller values of n ab ≈ 2.8, suggesting a potential n tune ≈ 0.5 window of tunability. In the case of our uniaxial vdW Ga 4 Se 3+δ Te 1−δ , the in-plane component of the refractive index fits this window reaching values up to n ab = 2.85 at the wavelength of interest. This implies a high potential of dispersion tunability with variation of ternary composition. In this context, however, one should account the structural instability of vdW GaSe x Te 1−x ternary compounds 38 , 39 , 47 occurring within a limited range of intermediate Se:Te compositions. Furthermore, our DFT-calculations further authenticate this hypothesis. Fig. S9 demonstrates the composition variation dependent tunability of refractive indices and extinction coefficients in the ternary vdW GaSe x Te 1−x compounds offering yet limited, but practically relevant extent of adjustability (see Fig. S9). An identical interplay among the extent of a ternary composition, optical dispersion and anisotropy may also be expected for the other ternary compounds of group III monochalcogenide vdW family: GaS, InSe and InTe, that as well may crystallize in diverse polymorphic phases. This tailoring knob of the optical dispersion offers a broader platform for the achievement of controllable ViS to NIR spectral region optical properties for next-generation nanophotonic applications 58 , 59 . Methods Sample preparation. GaSe x Te 1−x crystals were purchased from 2D Semiconductors and micro-mechanically cleaved onto standard Si, Si/SiO 2 , fused silica substrates at room temperature using commercial scotch tapes from Nitto Denko Corporation. Prior to micro-mechanical cleavage, the substrates were sequentially cleaned in acetone, isopropanol, and deionized water followed by an air plasma treatment to remove residual surface contaminants and improve the adhesion. Raman/PL spectroscopies. Raman and PL spectra from vdW Ga 4 Se 3+δ Te 1−δ micro-crystals were acquired using a Horiba LabRAM HR Evolution confocal microscope equipped with a 100 X objective lens ( N.A. = 0.90) and an 1800 lines/mm diffraction grating at room temperature. The measurements were carried out with 633 nm red and 532 nm green excitation lasers and detected by SIN-EM FIUV type detector operating at -75°C temperature. Raman and PL spectra were obtained by averaging multiple accumulations to improve the signal-to-noise ratio, followed by baseline subtraction (in the case of Raman spectra) and, where applicable, Gaussian peak fitting. DFT-calculations. All DFT calculations 60 , 61 were performed using the VASP software 62 , 63 following a complex three-step procedure for an accurate bandgap and dielectric function description. At the first step, a basic high-accuracy calculation was performed for a constructed 2 x 1 x 1 unit cell of Ga 4 Se 3 Te. That was done with PBEsol 64 exchange-correlation functional and plane-wave energy cutoff of 500 eV. The convergence criteria of electronic interaction were set to 10 − 8 for accurate description of the electronic bandstructure. Electronic smearing (Gaussian) with a small width of 0.02 was applied. A k- point grid of 7 x 9 x 3 was used. At the second step, the increased super-cell was constructed corresponding to 4 x 2 x 1 (see Fig. 1 (d)) and further distorted by performing an electron-phonon calculation using Zacharias-Giustino one-shot frozen-phonon approach 65 . The lattice parameters for a particular Ga 4 Se 3 Te stoichiometry were adjusted according to the Vegard law as in 47 . For Brillouin zone sampling, a k -point grid of 3 x 5 x 3 was used at that stage. Furthermore, at the third step, an accurate MBJLDA functional from Meta-GGA 66 , 67 was chosen, as it was specifically developed to enhance the prediction of electronic bandgaps in solids. Spectroscopic micro-ellipsometry. Spectroscopic micro-ellipsometry was performed at room temperature over 360–1000 nm spectral region using a Park Systems Accurion EP4 rotating-compensator imaging ellipsometer. All modeling was carried out using EP4Model software. Multiple vdW Ga 4 Se 3+δ Te 1−δ samples of varying thicknesses and across various substrates (Si, Si/SiO 2 and fused silica) were measured and analyzed to ensure the reliability and improve the accuracy of obtained data. To validate the uniaxial optical character of vdW Ga 4 Se 3+δ Te 1−δ , we first performed Mueller-matrix (MM) ellipsometry at a fixed wavelength, where the near-zero values of all off-diagonal MM elements confirm the absence of in-plane anisotropy (see Fig. S10 and Fig. S11). Spectra of ellipsometric parameters Ψ and Δ were acquired at angles of incidence (AOI) of 60°, 65° and 70°. Variable-angle spectroscopic ellipsometry (VASE) measurements were also performed in order to minimize the correlations among fitting parameters in the anisotropic model. An anisotropic optical model with distinct in-plane and out-of-plane components was then constructed and fitted, where each component was parameterized using Tauc-Lorentz oscillators. The dielectric function and corresponding optical constants of hexagonal vdW Ga 4 Se 3+δ Te 1−δ were obtained by minimizing the mean squared error of the model, examining the parameter correlation matrix, and accounting for depolarization effects arising from the finite source bandwidth (see Supplementary Note 4 for more details). Micro-reflectance and transmittance spectroscopies. Micro-transmittance and micro-reflectance spectra were measured under normal incidence using a Leica DM6M upright optical microscope equipped with a LED light source covering 420–720 nm spectral region. The spectra were acquired using a Thorlabs CCS100/M spectrometer coupled to an optical fiber with 105 µm core-diameter. In combination with a 20 X objective for reflectance and a 50 X objective for the transmittance measurements, this configuration enabled spectral acquisition from regions with lateral dimensions of approximately 10 µm and 4 µm 68 . Micro-transmittance measurements were also performed using an Accurion EP4 imaging spectroscopic ellipsometer operated in a transmission mode and controlled via a customized Python script. The measured micro-transmittance and micro-reflectance spectra were modeled using a generalized 4 × 4 transfer-matrix method (TMM) in which electromagnetic wave propagation and boundary conditions were explicitly defined for each interface in the optical stack (see Supplementary Note 5 for more details). All-vdW unpolarized plate beam splitter calculations. The optical responses of all-vdW Ga 4 Se 3+δ Te 1−δ / h BN multilayer plate-type beam splitters for unpolarized light were computed at an AoI of 45° using a generalized 4 × 4 transfer-matrix formalism 69 for multilayer stacks. The calculations yield the polarization-resolved reflectance and transmittance spectra, R s (λ), R p (λ), T s (λ), T p (λ), which were subsequently combined to obtain unpolarized response. The latter was quantified as R un (λ) = ( R s (λ) + R p (λ))/2, T un (λ) = ( T s (λ) + T p (λ))/2. Multilayer thicknesses were initialized from quarter-wave estimates and parameterized to ensure positivity as d = d 0 e p . For each candidate layer pair count ( N = 3) and for both starting sequences ( H - L … or L - H …; where H and L denote vdW Ga 4 Se 3+δ Te 1−δ (high-index) and vdW h BN (low-index) layers), the parameter vector p was optimized using the Nelder-Mead simplex algorithm with multiple random restarts. The objective function (figure of merit) was defined as the band-averaged squared deviation of R un (λ) and T un (λ) from the target split ratio over a discrete wavelength set within the designed spectral region, augmented by a weak energy-balance penalty enforcing R un (λ) + T un (λ) ≈ 1. A fabrication-motivated constraint of total multilayer thickness ≲ 1 µm was enforced via a large penalty for exceeding the limit, and the best solutions across all trials and configurations were selected and used to compute the dense spectra for reporting (see Supplementary Note 7 for performance characteristics). Declarations Competing interests The authors declare no competing financial or non-financial interests. Additional Information The additional information is provided in Supplementary Information. Funding This work was supported by the Higher Education and Science Committee of RA MօESCS project No. 23RL- 2A031. Accurion EP4 Ellipsometer and Leica DM6 M Microscope were acquired through scientific infrastructure renovation grants of the Higher Education and Science Committee RA MօESCS. K.S.N. acknowledges support by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-028), by the Ministry of Education, Singapore under Research Centre of Excellence award to the Institute for Functional Intelligent Materials, I-FIM (project No. EDUNC-33-18-279-V12) and by the Tier 3 program (MOE-MOET32024-0001). Author Contribution A.V.M and M.L.S. contributed equally to this work. D.A.G. initiated the project and directed it with K.S.N.. M.H.H., M.A.L. and A.V.M. prepared the samples. D.A.K. and M.L.S. performed the analytical calculations. I.I.P and H.A.Z. performed the density functional theory calculations. A.V.M., M.L.S., M.A.L. and M.H.H. performed the measurements and analyzed the data with D.A.G.. A.V.M., M.L.S. and D.A.G. drafted the initial version of the manuscript. D.A.G. and K.S.N. reviewed and amended the manuscript. All the authors contributed to the discussions. Acknowledgement This work was supported by the Higher Education and Science Committee of RA MօESCS project No. 23RL- 2A031. Accurion EP4 Ellipsometer and Leica DM6 M Microscope were acquired through scientific infrastructure renovation grants of the Higher Education and Science Committee RA MօESCS. A.V.M. thanks the Institute of Chemical Physics of NAS RA for providing access to a Raman microscope with an integrated AFM module (LabRAM HR Evolution) and A. Tsokolakyan for the assistance with the AFM measurements. The Computational resources were provided by the Armenian National Supercomputing Center (ANSCC). K.S.N. acknowledges support by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-028), by the Ministry of Education, Singapore under Research Centre of Excellence award to the Institute for Functional Intelligent Materials, I-FIM (project No. EDUNC-33-18-279-V12) and by the Tier 3 program (MOE-MOET32024-0001). Data Availability The datasets generated and/or analyzed during the current study are available within the manuscript and Supplementary Information. References Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306 , 666–669 (2004). Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438 , 197–200 (2005). Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005). Mounet, N. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat. 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Margaryan","email":"","orcid":"","institution":"Yerevan State University","correspondingAuthor":false,"prefix":"","firstName":"Artsruni","middleName":"V.","lastName":"Margaryan","suffix":""},{"id":583724128,"identity":"844aab8c-15de-4854-8e7d-13d75b6fbe02","order_by":1,"name":"Maksim L. Sargsyan","email":"","orcid":"","institution":"Yerevan State University","correspondingAuthor":false,"prefix":"","firstName":"Maksim","middleName":"L.","lastName":"Sargsyan","suffix":""},{"id":583724129,"identity":"0ed38cd8-df09-4fcb-a493-a0d814672a4e","order_by":2,"name":"Irina I. Piyanzina","email":"","orcid":"","institution":"Yerevan State University","correspondingAuthor":false,"prefix":"","firstName":"Irina","middleName":"I.","lastName":"Piyanzina","suffix":""},{"id":583724130,"identity":"879e0731-40af-4f54-a9d9-2e51ec2d3737","order_by":3,"name":"Davit A. Karakhanyan","email":"","orcid":"","institution":"Yerevan State University","correspondingAuthor":false,"prefix":"","firstName":"Davit","middleName":"A.","lastName":"Karakhanyan","suffix":""},{"id":583724131,"identity":"3b165388-fe78-412d-b341-4a097e3a573f","order_by":4,"name":"Meri H. Hayrapetryan","email":"","orcid":"","institution":"Yerevan State University","correspondingAuthor":false,"prefix":"","firstName":"Meri","middleName":"H.","lastName":"Hayrapetryan","suffix":""},{"id":583724132,"identity":"cd7734c3-87ab-44c8-b888-f5391c891ee1","order_by":5,"name":"Maria A. Levonyan","email":"","orcid":"","institution":"Yerevan State University","correspondingAuthor":false,"prefix":"","firstName":"Maria","middleName":"A.","lastName":"Levonyan","suffix":""},{"id":583724133,"identity":"d9600df0-e950-4544-93bf-800b0cff472e","order_by":6,"name":"Hayk A. 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Ghazaryan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+UlEQVRIiWNgGAWjYDCCAzAEATZEajmA0JJGnBYGJC2HCevgO37G8PCHX3fk5dvPPpP4ueN84vwZCYyfbuDRInkmx+DAwb5nho096WaSvWduJ264kcAsnYNHi8GBtIQDB3sOMzYzpLFJ8LYBtUgkMODXcv4ZWIt9G/8zNsm/bedADmP+jVfLjeQDBw78OJzYI5HGJs3bdiCx4UYCG15bJG88PnDgbMPh5BkSz5itZduSjTecedhmjU8L3/nE5g8Vfw7bzu9PY7z5ts1Odn578uHb+LSAAWMbmGKRABKODQyMDYQ0AMEfMMn8AUjYE6F8FIyCUTAKRhgAAIAOYIJGaeP2AAAAAElFTkSuQmCC","orcid":"","institution":"Yerevan State University","correspondingAuthor":true,"prefix":"","firstName":"Davit","middleName":"A.","lastName":"Ghazaryan","suffix":""}],"badges":[],"createdAt":"2026-01-23 16:53:49","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8681290/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8681290/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-026-42182-y","type":"published","date":"2026-03-08T15:57:50+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":101648884,"identity":"37d8c27a-665a-4f98-b4ad-f5107bc97688","added_by":"auto","created_at":"2026-02-02 09:01:56","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":8773024,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe hexagonal crystal structure and initial characterization of uniaxial vdW Ga\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eSe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e3+δ\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eTe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1-δ\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e. (a) \u003c/strong\u003e20 X optical micrograph of a representative vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1-δ\u003c/sub\u003e sample with highlighted shaded region used to map the thickness by an AFM (see Supplementary Note 1), and a spot (red marker) used for Raman and PL spectra acquisition. \u003cstrong\u003e(b)\u003c/strong\u003e PL spectra acquired from a sample shown in (a) under 532 nm and 633 nm laser excitations. \u003cstrong\u003e(c)\u003c/strong\u003e Similar to (b) but presenting Raman spectra. \u003cstrong\u003e(d)\u003c/strong\u003e The hexagonal crystal structure for the constructed closest rational composition of vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eTe with a uniaxial super-cell of 4:2:1. \u003cstrong\u003e(e) \u003c/strong\u003eFirst-principles electronic bandstructure of uniaxial vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eTe. The red line depicts the direct bandgap transition at \u003cem\u003eΓ\u003c/em\u003e point. \u003cstrong\u003e(f) \u003c/strong\u003eFirst-principles\u003cstrong\u003e \u003c/strong\u003eternary composition dependent electronic bandgaps of uniaxial vdW GaSe\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003e1-x\u003c/sub\u003e (see Fig. S2 for more details), where \u003cem\u003ex\u003c/em\u003e = 0.5, 0.625, 0.75 and 0.875 correspond to the rational compositions of vdW Ga\u003csub\u003e2\u003c/sub\u003eSeTe, Ga\u003csub\u003e8\u003c/sub\u003eSe\u003csub\u003e5\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e, Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eTe\u003csub\u003e \u003c/sub\u003eand Ga\u003csub\u003e8\u003c/sub\u003eSe\u003csub\u003e7\u003c/sub\u003eTe.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-8681290/v1/94718d1db84386561d6cb9a7.png"},{"id":101753396,"identity":"057fcd3d-e6b2-4acb-a1eb-f439962afb49","added_by":"auto","created_at":"2026-02-03 10:39:57","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":3113810,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe dielectric function and optical constants of uniaxial vdW Ga\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eSe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e3+δ\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eTe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1-δ\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e. (a) \u003c/strong\u003eReal (Re[\u003cem\u003eε\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e] and Re[\u003cem\u003eε\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e]), and \u003cstrong\u003e(b)\u003c/strong\u003e Imaginary (Im[\u003cem\u003eε\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e], Im[\u003cem\u003eε\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e]) parts of dielectric permittivity of uniaxial vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1-δ \u003c/sub\u003eas function of wavelength in 360-1000 nm spectral region. The inset displays the spectroscopic micro-ellipsometry setup operating in a conventional \u003cem\u003eΨ\u003c/em\u003e, \u003cem\u003eΔ\u003c/em\u003e acquisition mode. \u003cstrong\u003e(c)\u003c/strong\u003e The extracted anisotropic refractive indices (\u003cem\u003en\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e, \u003cem\u003en\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e) and extinction coefficients (\u003cem\u003ek\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e, \u003cem\u003ek\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e) along \u003cem\u003eab\u003c/em\u003e plane and \u003cem\u003ec\u003c/em\u003e-axis. The inset displays the ellipsometric micrograph of a representative vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1-δ\u003c/sub\u003e sample with the highlighted region of interest (RoI) selected to ensure reliable signal collection from a homogeneous area. \u003cstrong\u003e(d)\u003c/strong\u003e Same as (c) but obtained from first-principles calculations for the closest rational composition of vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eTe. \u003cstrong\u003e(e)\u003c/strong\u003e Transmittance, \u003cem\u003eT\u003c/em\u003e, spectrum of vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1-δ\u003c/sub\u003e acquired from a sample with thickness of 130 nm placed onto fused silica substrate. \u003cstrong\u003e(f)\u003c/strong\u003e Differential reflectance contrast (DRC) spectrum of vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1-δ\u003c/sub\u003e acquired from a sample with thickness of 135 nm placed onto Si/SiO\u003csub\u003e2\u003c/sub\u003e substrate.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-8681290/v1/378605c2673be50a7eda4069.png"},{"id":101648883,"identity":"d93b08d4-a1c2-4e55-8299-420fe23aeaa1","added_by":"auto","created_at":"2026-02-02 09:01:56","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2184350,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMultilayer Ga\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eSe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e3+δ\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eTe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1-δ\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e/\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eh\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003eBN heterostructures for unpolarized plate-type beam splitters. (a) \u003c/strong\u003eSchematic illustration of a plate-type beam splitter built on a few multilayer Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1-δ\u003c/sub\u003e/hBN heterostructure placed onto a fused silica substrate. Reflectance-\u003cem\u003eto\u003c/em\u003e-transmittance (R:T) channels of sub-micron thick beam splitters designed for an operation at an angle of incidence (AoI) of 45° in the targeted NIR spectral 800-1030 nm band. R:T channel splitting ratios of \u003cstrong\u003e(b)\u003c/strong\u003e 50:50 \u003cstrong\u003e(c) \u003c/strong\u003e30:70 and \u003cstrong\u003e(d)\u003c/strong\u003e 10:90.\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-8681290/v1/c341eece1c7af0255989189f.png"},{"id":104250853,"identity":"2ebc49f7-0b53-449f-b677-d967ef78fc90","added_by":"auto","created_at":"2026-03-09 16:10:16","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":21818989,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8681290/v1/15731fae-0e2a-4e8c-84c6-ef683d27d25b.pdf"},{"id":101648882,"identity":"08135044-d61a-4023-9417-4bae0cf57622","added_by":"auto","created_at":"2026-02-02 09:01:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":2139085,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryinformationforDielectricfunctionoflayeredGa4Se3Te1andemergentallvanderWaalsopticalelements.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8681290/v1/e8ac1e5177a345bb5a09f418.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dielectric function of layered Ga4Se3+δTe1-δ and emergent all van der Waals optical elements","fulltext":[{"header":"Introduction","content":"\u003cp\u003eFollowing the isolation of graphene\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e and the subsequent rise of 2D transition-metal dichalcogenides\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, a wide variety of other 2D crystalline material families emerged\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. These diverse families offer a broad spectrum of tunable electronic, optical, and mechanical properties distinct from their bulk vdW counterparts. GaSe, GaTe, InSe and InTe are a few prominent representatives of the group \u003cem\u003eIII\u003c/em\u003e monochalcogenide 2D family semiconductors with general formula of \u003cem\u003eM\u003c/em\u003e\u003csup\u003eIII\u003c/sup\u003e\u003cem\u003eX\u003c/em\u003e\u003csup\u003eVI\u003c/sup\u003e, where \u003cem\u003eM\u003c/em\u003e is a group \u003cem\u003eIII\u003c/em\u003e element and \u003cem\u003eX\u003c/em\u003e is a group \u003cem\u003eVI\u003c/em\u003e chalcogen atom\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Those, along with their vdW counterparts, hold great promise for a wide variety of next-generation nanoscale applications covering electronics, optoelectronics (including ultraviolet sensing), photonics and photocatalysis\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. The scientific interest towards their vdW counterparts reintensified\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e once some of the family representatives were cleaved down to\u003csup\u003e23,24\u003c/sup\u003e or synthesized\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e in a monolayer form. Notably, these vdW crystals exhibit a variety of polymorphic hexagonal, monoclinic and other phases\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e each offering a unique set of properties. One may feature those of non-centrosymmetric symmetry allowing a strong non-linear optical effects, such as, for example, a second harmonic generation\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e and imaging\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e or sliding ferroelectric states\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e,\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eRecent first-principles approaches propose that an oxygen functionalization of group \u003cem\u003eIII\u003c/em\u003e monochalcogenides may further affect their properties giving rise to the emergence of topological states\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. On the other hand, a mixed ternary Janus phase with group \u003cem\u003eIII\u003c/em\u003e (or \u003cem\u003eVI\u003c/em\u003e) elements comprising two identical (non-identical) atoms, such as, for example, Ga\u003csub\u003e2\u003c/sub\u003eSSe or Al\u003csub\u003e2\u003c/sub\u003eSSe may lead to an appearance of anisotropic mechanical features\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e and strain-induced bandgap modifications\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. Another sub-class of a ternary group \u003cem\u003eIII\u003c/em\u003e monochalcogenide solids comprises a mix of a sole group \u003cem\u003eVI\u003c/em\u003e chalcogen atoms, where the two representatives, such as, for example, Selenium (Se) and Tellurium (Te) are positioned in the unit-cell of a crystal with varying, one may call an alloy-like compounds: GaSe\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;x\u003c/sub\u003e (or GaSe\u003csub\u003ex\u003c/sub\u003eS\u003csub\u003e1\u0026minus;x\u003c/sub\u003e)\u003csup\u003e38,39,40,41,42,43,44,45,46\u003c/sup\u003e. A structural phase diagram of the former vdW crystals\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e shows a stabilization of Se-rich compositions in a uniaxial hexagonal phase, whereas Te-rich compositions favor a biaxial monoclinic phase. Here, the uniaxial vdW crystals display an eminent decrease of a bandgap with an introduction of Te atoms into the hexagonal lattice of a pristine GaSe. In contrast, an introduction of Se atoms into a monoclinic GaTe lattice exhibiting in-plane anisotropic optical characteristics leads not only to a nominal increase of a bandgap but further spotlights a hexagonal to monoclinic phase instability crossover emerging in a narrow range of intermediate Se-Te compositions, where both phases coexist.\u003c/p\u003e \u003cp\u003eIn this manuscript, we introduce the complex dielectric function of a group \u003cem\u003eIII\u003c/em\u003e ternary monochalcogenide - vdW GaSe\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;x\u003c/sub\u003e with the composition of \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.78 that is farther represented by its closest rational hexagonal super-cell of Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e exhibiting a small variation of \u003cem\u003eδ\u003c/em\u003e (see Results). Our studies cover the 360\u0026ndash;1000 nm spectral region positioning vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e as an emergent low-loss high-refractive index vdW crystal in Vis-\u003cem\u003eto\u003c/em\u003e-NIR spectral region. We show that it exhibits an in-plane refractive index of ~\u0026thinsp;3 at red-light wavelengths of Vis spectral region and a sheer optical transparency in the deep red-light and NIR spectral region. We also propose that the tuning of a ternary composition within vdW GaSe\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;x\u003c/sub\u003e may strongly influence its optical dispersion indicating a tunability within a window subject to the inherent dispersions of their pristine binary compounds. Furthermore, we demonstrate a design of a variety of sub-micron all-vdW beam splitters based on a few multilayers of \u003cem\u003eh\u003c/em\u003eBN-Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e operating in NIR spectral region. Our results not only place uniaxial vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e amongst the promising high refractive index materials for an assembly of compact all-vdW optical elements but also suggest a novel route for a creation of materials with prescribed optical properties.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eIdentifying the crystal structure and Se:Te composition in vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e micro-crystals\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a) presents an optical micrograph of a representative micro-mechanically cleaved 237 nm thick vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e sample (see Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e for AFM data) selected to demonstrate a swift identification of Selenium: Tellurium (Se:Te) composition in our micro-crystals. Here, by employing photoluminescence (PL) and Raman spectroscopies (see Methods), we first probe the optoelectronic and vibrational responses of our samples (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b, c)). The polarization free PL spectra measured at 633 nm and 532 nm laser excitations (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b)) show a pronounced emission at 1.85 eV. Notably, for 633 nm excitation, the emission appears at 671 nm limiting the resolution of Raman modes in 100\u0026ndash;400 cm⁻\u0026sup1; spectral region (see the shaded area in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b)) and resulting in visualization of two \u003cem\u003eA\u003c/em\u003e\u003csub\u003e1g\u003c/sub\u003e modes, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c). Nevertheless, switching to 532 nm excitations allows clear observation of high-symmetry \u003cem\u003eE\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e mode at 205 cm⁻\u0026sup1;. Following the approach presented in\u003csup\u003e38,39,47\u003c/sup\u003e, we then compare the systematic shifts of PL and Raman \u003cem\u003eA\u003c/em\u003e\u003csup\u003e1\u003c/sup\u003e\u003csub\u003e1g\u003c/sub\u003e mode peak positions inferring a 0.78:0.22 ratio of Se:Te, and therefore, a uniaxial hexagonal phase. To represent the inferred composition with crystal structure of well-defined parameters, we select the closest rational approximation of uniaxial vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eTe (Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e considering the exact \u003cem\u003eδ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.125 discrepancy) constructing 4:2:1 super-cell with lattice parameters of \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15.416 \u0026Aring;, \u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;7.708 \u0026Aring; and \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;17.457 \u0026Aring;, as it is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(d). Here, the first-principles calculations (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(e)) yield a direct electronic bandgap of 1.69 eV emerging at \u003cem\u003eΓ\u003c/em\u003e point of the first Brillouin zone. Assuming a linear interpolation between the calculated bandgaps for 0.75 and 0.875 Se-rich compositions, we then estimate a bandgap of 1.76 eV for our 0.78 Se-rich case (see red hexagon in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(f)). Notably, the obtained values are reasonably close to the experimentally observed bandgaps showing small offset within Se content \u003cem\u003evs\u003c/em\u003e bandgap dependence when compared with literature data\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eThe anisotropic dielectric function of uniaxial vdW GaSeTe\u003c/h3\u003e\n\u003cp\u003eA spectroscopic micro-ellipsometry approach was applied to study the dielectric permittivity function, and thus, optical constants of uniaxial vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e samples in 360\u0026ndash;1000 nm spectral region, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Here, for the case of typical hexagonal crystals, a conventional \u003cem\u003eΨ\u003c/em\u003e and \u003cem\u003eΔ\u003c/em\u003e parameter studies are sufficient as the latter is isotropic within the \u003cem\u003eab\u003c/em\u003e plane. The polarization state of the incident beam is defined by a polarizer and modulated by a rotating \u003cem\u003eλ\u003c/em\u003e/4 retarder, while an analyzer projects the reflected light to enable extraction of ellipsometric parameters \u003cem\u003eΨ\u003c/em\u003e and \u003cem\u003eΔ\u003c/em\u003e (see Methods, the inset of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b), and Fig. S3-Fig. S5 for further details). The in-plane (or ordinary) dielectric permittivity component, \u003cem\u003eε\u003c/em\u003eₒ \u0026equiv; \u003cem\u003eε\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e, and the out-of-plane (or extraordinary) component, \u003cem\u003eε\u003c/em\u003eₑ \u0026equiv; \u003cem\u003eε\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e, were extracted by modeling ellipsometric data using Tauc-Lorentz oscillators, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a, b). The ordinary component was described accounting for an in-plane interband optical response, while the extraordinary component was modeled likewise to account for another set of interband transitions extending into ultraviolet spectral region (see Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e \u0026ndash; Table S3 for details of optical model and tabulated dielectric and optical constants).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe optical constants, \u003cem\u003ei. e.\u003c/em\u003e, refractive indices and extinction coefficients obtained from dielectric permittivity studies are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(c). Over the Vis-NIR spectral region, vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e exhibits a consistently high in-plane refractive index allowing it to be classified as a high-index material. Specifically, the ordinary refractive index, \u003cem\u003en\u003c/em\u003eₒ \u0026equiv; \u003cem\u003en\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e, is about\u0026thinsp;~\u0026thinsp;3.0 at 700 nm increasing towards shorter wavelengths and reaching 3.65 at 400 nm, while gradually decreasing to 2.83 at 1000 nm wavelengths. The in-plane extinction coefficient remains low, with \u003cem\u003ek\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e ≲ 0.1 (\u003cem\u003ee.g.\u003c/em\u003e, \u003cem\u003ek\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e = 0.1 at 413 nm), indicating low optical losses prior to the absorption onset. A clear onset of absorption is observed in the vicinity of 656 nm deep red wavelengths. At 633 nm, where absorption is negligible, the ordinary and extraordinary refractive indices are \u003cem\u003en\u003c/em\u003eₒ \u0026asymp; 2.98 and \u003cem\u003en\u003c/em\u003eₑ \u0026asymp; 2.71, yielding to a birefringence of \u003cem\u003eΔn\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;0.27 (see Fig. S6). Our first principles (DFT) calculations of the anisotropic optical constants show good agreement with the experimental data corroborating both their magnitude and spectral dispersion (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(c)). It is important to note that these results also predict an onset of a finite extinction coefficient at higher photon energies supporting the use of Tauc-Lorentz oscillators describing the out-of-plane optical response in the ellipsometric model.\u003c/p\u003e \u003cp\u003eTo verify the high accuracy of the extracted dielectric permittivity, we then performed micro-reflectance and micro-transmittance spectroscopies (see Methods) for a representative vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e samples in 420\u0026ndash;720 nm spectral region (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(d, e)). Here, we consider the ellipsometry-derived constants accurate when the calculated spectra reproduce the experimentally measured values within a deviation of less than a 3%. To calculate these spectra, the dielectric permittivity obtained from ellipsometry was interpreted within the framework of a generalized 4 \u0026times; 4 transfer-matrix method as described in Methods. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(d) and 2(e) display the transmittance, \u003cem\u003eT\u003c/em\u003e, acquired from a uniaxial vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e sample placed onto fused-silica substrate and the differential reflectance contrast (DRC), acquired from a sample of a similar thickness placed onto a Si/SiO\u003csub\u003e2\u003c/sub\u003e substrate (the extended dataset is provided in Fig. S7). In the case of the former (latter), we compute the ratio of \u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eJ\u003c/em\u003e\u003csub\u003eS\u003c/sub\u003e/\u003cem\u003eJ\u003c/em\u003e\u003csub\u003eSUB\u003c/sub\u003e​ (DRC = (\u003cem\u003eJ\u003c/em\u003e\u003csub\u003eS\u003c/sub\u003e \u0026minus; \u003cem\u003eJ\u003c/em\u003e\u003csub\u003eSUB\u003c/sub\u003e)/(\u003cem\u003eJ\u003c/em\u003e\u003csub\u003eS\u003c/sub\u003e + \u003cem\u003eJ\u003c/em\u003e\u003csub\u003eSUB\u003c/sub\u003e)), where \u003cem\u003eJ\u003c/em\u003e\u003csub\u003eS\u003c/sub\u003e​ is the intensity acquired from the sample, and \u003cem\u003eJ\u003c/em\u003e\u003csub\u003eSUB\u003c/sub\u003e​ is the intensity from a bare substrate (see Methods for more details). The observed properties of \u003cem\u003eT\u003c/em\u003e and DRC are typical for high-refractive-index thin films. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(d), the former approaches unity around 720 nm, while the latter (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(e)) reaches values up to 0.75 over displaying a band in 450\u0026ndash;700 nm spectral region for the corresponding sample thicknesses. Notably, both features originate from strong Fabry-P\u0026eacute;rot interference effects. Furthermore, to avoid correlations and ambiguities in the parameters of the optimized optical model, we also utilized another technique separately measuring the thicknesses of studied samples by an alternative means of AFM (see Supplementary Note 1 for the data from a representative sample).\u003c/p\u003e \u003cp\u003e \u003cb\u003eDesigning all-vdW unpolarized beam splitters with multilayer Ga\u003c/b\u003e \u003csub\u003e \u003cb\u003e4\u003c/b\u003e \u003c/sub\u003e \u003cb\u003eSe\u003c/b\u003e \u003csub\u003e \u003cb\u003e3+δ\u003c/b\u003e \u003c/sub\u003e \u003cb\u003eTe\u003c/b\u003e \u003csub\u003e \u003cb\u003e1\u0026minus;δ\u003c/b\u003e \u003c/sub\u003e \u003cb\u003e/\u003c/b\u003e \u003cb\u003eh\u003c/b\u003e \u003cb\u003eBN heterostructures\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe advent of vdW heterostructures\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e,\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e,\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e has established a versatile platform for an engineering of artificial layered materials with tailored stacking order and composition, enabling functionalities far beyond those accessible in sole bulk crystals. The wide diversity of vdW crystals, in particular with respect to their optical constants and pronounced anisotropic properties, thus provides substantial opportunities for the realization of advanced optical elements for nanoscale optics and nanophotonics. Among these elements, unpolarized beam splitters are a particularly practical case. They enable controlled splitting of an unpolarized light into reflected and transmitted channels across a targeted spectral band providing a considerable scope for an integration into all-vdW-based nanophotonic systems. In this context, we propose a design of a plate-type unpolarized beam splitter (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a)) based on a few Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e/\u003cem\u003eh\u003c/em\u003eBN multilayer heterostructure placed onto a UV fused silica substrate and optimized for an operation in NIR (800\u0026ndash;1030 nm) spectral region \u0026ndash; a band widely used in modern nanophotonic or laser systems. The vdW \u003cem\u003eh\u003c/em\u003eBN is selected as an optically transparent uniaxial vdW dielectric with well-defined in-plane and out-of-plane permittivity components, providing a robust low-index counterpart and an encapsulation layer. Its dielectric permittivity used in computations was separately studied by spectroscopic micro-ellipsometry and extrapolated up to 1200 nm wavelength along with vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e (see Fig. S8). In the targeted NIR band, the refractive-index contrast between vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e and vdW \u003cem\u003eh\u003c/em\u003eBN enables a multilayer-interference, where alternating low and high index layers and their thicknesses are tailored to set the desired reflectance\u003cem\u003e-to\u003c/em\u003e-transmittance channels. Larger refractive index contrast reduces the number of constituent layers and the total thickness of the stack.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOur design targets three widely used commercial split ratio channels of R:T\u0026thinsp;=\u0026thinsp;50:50, 30:70, and 10:90, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(c-d). Here, for each design, an individual layer thickness and number of constituent layers were optimized by minimizing the figure of merit, while corresponding reflectance and transmittance spectra were computed at each iteration using the generalized 4 \u0026times; 4 transfer-matrix method (see Methods). The total thickness of a multilayer stack was kept to sub-micron for all the target designs, while achieving few amounts of constituent all-vdW multilayers with band-averaged performance comparable to commercial NIR broadband plate-type beam splitters operating at the same AoI. The full layer-\u003cem\u003eby\u003c/em\u003e-layer thicknesses and stack sequences for all three designs are provided in Table S4 \u0026ndash; Table S6. An analogous performance with the conventional thin-film optical materials is typically achieved with many-layer oxide/fluoride or metal-dielectric stacks\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e,\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e,\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e, whose design mainly relies on numerical optimization and optical constants that may vary with the deposition conditions, highlighting the practical advantage of achieving the required response with fewer constituent layers and smaller total thicknesses.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eDespite the high potential of group \u003cem\u003eIII\u003c/em\u003e monochalcogenide ternary vdW GaSe\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;x\u003c/sub\u003e compounds towards the tailoring of optical dispersion with the variation of ternary Se:Te composition, it yet received no specific attention. As a matter of fact, the dielectric function of vdW GaSe\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;x\u003c/sub\u003e was studied only in THz spectral region at best for the extreme Se-rich compositions\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e. Though the measured optical dispersions of vdW GaSe and GaTe\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e,\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e,\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e bear a resemblance of two slightly shifted spectral regions that only coincide in a narrow NIR spectral region, one may still identify practical implications. Here, the in-plane refractive index of a biaxial vdW GaTe resembles mean values of \u003cem\u003en\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e \u0026asymp; 3.3 at 900 nm NIR wavelength, while for uniaxial vdW GaSe, the reports show significantly smaller values of \u003cem\u003en\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e \u0026asymp; 2.8, suggesting a potential \u003cem\u003en\u003c/em\u003e\u003csub\u003etune\u003c/sub\u003e \u0026asymp; 0.5 window of tunability. In the case of our uniaxial vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e, the in-plane component of the refractive index fits this window reaching values up to \u003cem\u003en\u003c/em\u003e\u003csub\u003eab\u003c/sub\u003e = 2.85 at the wavelength of interest. This implies a high potential of dispersion tunability with variation of ternary composition. In this context, however, one should account the structural instability of vdW GaSe\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;x\u003c/sub\u003e ternary compounds\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e occurring within a limited range of intermediate Se:Te compositions. Furthermore, our DFT-calculations further authenticate this hypothesis. Fig. S9 demonstrates the composition variation dependent tunability of refractive indices and extinction coefficients in the ternary vdW GaSe\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;x\u003c/sub\u003e compounds offering yet limited, but practically relevant extent of adjustability (see Fig. S9). An identical interplay among the extent of a ternary composition, optical dispersion and anisotropy may also be expected for the other ternary compounds of group \u003cem\u003eIII\u003c/em\u003e monochalcogenide vdW family: GaS, InSe and InTe, that as well may crystallize in diverse polymorphic phases. This tailoring knob of the optical dispersion offers a broader platform for the achievement of controllable ViS to NIR spectral region optical properties for next-generation nanophotonic applications\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e,\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e \u003cb\u003eSample preparation.\u003c/b\u003e GaSe\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;x\u003c/sub\u003e crystals were purchased from 2D Semiconductors and micro-mechanically cleaved onto standard Si, Si/SiO\u003csub\u003e2\u003c/sub\u003e, fused silica substrates at room temperature using commercial scotch tapes from Nitto Denko Corporation. Prior to micro-mechanical cleavage, the substrates were sequentially cleaned in acetone, isopropanol, and deionized water followed by an air plasma treatment to remove residual surface contaminants and improve the adhesion.\u003c/p\u003e \u003cp\u003e \u003cb\u003eRaman/PL spectroscopies.\u003c/b\u003e Raman and PL spectra from vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e micro-crystals were acquired using a Horiba LabRAM HR Evolution confocal microscope equipped with a 100 X objective lens (\u003cem\u003eN.A.\u003c/em\u003e = 0.90) and an 1800 lines/mm diffraction grating at room temperature. The measurements were carried out with 633 nm red and 532 nm green excitation lasers and detected by SIN-EM FIUV type detector operating at -75\u0026deg;C temperature. Raman and PL spectra were obtained by averaging multiple accumulations to improve the signal-to-noise ratio, followed by baseline subtraction (in the case of Raman spectra) and, where applicable, Gaussian peak fitting.\u003c/p\u003e \u003cp\u003e \u003cb\u003eDFT-calculations.\u003c/b\u003e All DFT calculations\u003csup\u003e\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e,\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e\u003c/sup\u003e were performed using the VASP software\u003csup\u003e\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e,\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e\u003c/sup\u003e following a complex three-step procedure for an accurate bandgap and dielectric function description. At the first step, a basic high-accuracy calculation was performed for a constructed 2 x 1 x 1 unit cell of Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eTe. That was done with PBEsol\u003csup\u003e\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e\u003c/sup\u003e exchange-correlation functional and plane-wave energy cutoff of 500 eV. The convergence criteria of electronic interaction were set to 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e for accurate description of the electronic bandstructure. Electronic smearing (Gaussian) with a small width of 0.02 was applied. A \u003cem\u003ek-\u003c/em\u003epoint grid of 7 x 9 x 3 was used. At the second step, the increased super-cell was constructed corresponding to 4 x 2 x 1 (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(d)) and further distorted by performing an electron-phonon calculation using Zacharias-Giustino one-shot frozen-phonon approach\u003csup\u003e\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e\u003c/sup\u003e. The lattice parameters for a particular Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eTe stoichiometry were adjusted according to the Vegard law as in\u003csup\u003e47\u003c/sup\u003e. For Brillouin zone sampling, a \u003cem\u003ek\u003c/em\u003e-point grid of 3 x 5 x 3 was used at that stage. Furthermore, at the third step, an accurate MBJLDA functional from Meta-GGA\u003csup\u003e\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e,\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e\u003c/sup\u003e was chosen, as it was specifically developed to enhance the prediction of electronic bandgaps in solids.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSpectroscopic micro-ellipsometry.\u003c/b\u003e Spectroscopic micro-ellipsometry was performed at room temperature over 360\u0026ndash;1000 nm spectral region using a Park Systems Accurion EP4 rotating-compensator imaging ellipsometer. All modeling was carried out using EP4Model software. Multiple vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e samples of varying thicknesses and across various substrates (Si, Si/SiO\u003csub\u003e2\u003c/sub\u003e and fused silica) were measured and analyzed to ensure the reliability and improve the accuracy of obtained data. To validate the uniaxial optical character of vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e, we first performed Mueller-matrix (MM) ellipsometry at a fixed wavelength, where the near-zero values of all off-diagonal MM elements confirm the absence of in-plane anisotropy (see Fig. S10 and Fig. S11). Spectra of ellipsometric parameters \u003cem\u003eΨ\u003c/em\u003e and \u003cem\u003eΔ\u003c/em\u003e were acquired at angles of incidence (AOI) of 60\u0026deg;, 65\u0026deg; and 70\u0026deg;. Variable-angle spectroscopic ellipsometry (VASE) measurements were also performed in order to minimize the correlations among fitting parameters in the anisotropic model. An anisotropic optical model with distinct in-plane and out-of-plane components was then constructed and fitted, where each component was parameterized using Tauc-Lorentz oscillators. The dielectric function and corresponding optical constants of hexagonal vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e were obtained by minimizing the mean squared error of the model, examining the parameter correlation matrix, and accounting for depolarization effects arising from the finite source bandwidth (see Supplementary Note 4 for more details).\u003c/p\u003e \u003cp\u003e \u003cb\u003eMicro-reflectance and transmittance spectroscopies.\u003c/b\u003e Micro-transmittance and micro-reflectance spectra were measured under normal incidence using a Leica DM6M upright optical microscope equipped with a LED light source covering 420\u0026ndash;720 nm spectral region. The spectra were acquired using a Thorlabs CCS100/M spectrometer coupled to an optical fiber with 105 \u0026micro;m core-diameter. In combination with a 20 X objective for reflectance and a 50 X objective for the transmittance measurements, this configuration enabled spectral acquisition from regions with lateral dimensions of approximately 10 \u0026micro;m and 4 \u0026micro;m\u003csup\u003e68\u003c/sup\u003e. Micro-transmittance measurements were also performed using an Accurion EP4 imaging spectroscopic ellipsometer operated in a transmission mode and controlled \u003cem\u003evia\u003c/em\u003e a customized Python script. The measured micro-transmittance and micro-reflectance spectra were modeled using a generalized 4 \u0026times; 4 transfer-matrix method (TMM) in which electromagnetic wave propagation and boundary conditions were explicitly defined for each interface in the optical stack (see Supplementary Note 5 for more details).\u003c/p\u003e \u003cp\u003e \u003cb\u003eAll-vdW unpolarized plate beam splitter calculations.\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe optical responses of all-vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e/\u003cem\u003eh\u003c/em\u003eBN multilayer plate-type beam splitters for unpolarized light were computed at an AoI of 45\u0026deg; using a generalized 4 \u0026times; 4 transfer-matrix formalism\u003csup\u003e\u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e\u003c/sup\u003e for multilayer stacks. The calculations yield the polarization-resolved reflectance and transmittance spectra, \u003cem\u003eR\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e (λ), \u003cem\u003eR\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e (λ), \u003cem\u003eT\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e (λ), \u003cem\u003eT\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e (λ), which were subsequently combined to obtain unpolarized response. The latter was quantified as \u003cem\u003eR\u003c/em\u003e\u003csub\u003eun\u003c/sub\u003e (λ) = (\u003cem\u003eR\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e (λ) + \u003cem\u003eR\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e (λ))/2, \u003cem\u003eT\u003c/em\u003e\u003csub\u003eun\u003c/sub\u003e (λ) = (\u003cem\u003eT\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e (λ) + \u003cem\u003eT\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e (λ))/2. Multilayer thicknesses were initialized from quarter-wave estimates and parameterized to ensure positivity as \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ed\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u003cem\u003ee\u003c/em\u003e\u003csup\u003ep\u003c/sup\u003e. For each candidate layer pair count (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3) and for both starting sequences (\u003cem\u003eH\u003c/em\u003e-\u003cem\u003eL\u003c/em\u003e\u0026hellip; or \u003cem\u003eL\u003c/em\u003e-\u003cem\u003eH\u003c/em\u003e\u0026hellip;; where \u003cem\u003eH\u003c/em\u003e and \u003cem\u003eL\u003c/em\u003e denote vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e (high-index) and vdW \u003cem\u003eh\u003c/em\u003eBN (low-index) layers), the parameter vector \u003cem\u003ep\u003c/em\u003e was optimized using the Nelder-Mead simplex algorithm with multiple random restarts. The objective function (figure of merit) was defined as the band-averaged squared deviation of \u003cem\u003eR\u003c/em\u003e\u003csub\u003eun\u003c/sub\u003e (λ) and \u003cem\u003eT\u003c/em\u003e\u003csub\u003eun\u003c/sub\u003e (λ) from the target split ratio over a discrete wavelength set within the designed spectral region, augmented by a weak energy-balance penalty enforcing \u003cem\u003eR\u003c/em\u003e\u003csub\u003eun\u003c/sub\u003e (λ) + \u003cem\u003eT\u003c/em\u003e\u003csub\u003eun\u003c/sub\u003e (λ)\u0026thinsp;\u0026asymp;\u0026thinsp;1. A fabrication-motivated constraint of total multilayer thickness\u0026thinsp;≲\u0026thinsp;1 \u0026micro;m was enforced \u003cem\u003evia\u003c/em\u003e a large penalty for exceeding the limit, and the best solutions across all trials and configurations were selected and used to compute the dense spectra for reporting (see Supplementary Note 7 for performance characteristics).\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing financial or non-financial interests.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eAdditional Information\u003c/h2\u003e \u003cp\u003eThe additional information is provided in Supplementary Information.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis work was supported by the Higher Education and Science Committee of RA MօESCS project No. 23RL- 2A031. Accurion EP4 Ellipsometer and Leica DM6 M Microscope were acquired through scientific infrastructure renovation grants of the Higher Education and Science Committee RA MօESCS. K.S.N. acknowledges support by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-028), by the Ministry of Education, Singapore under Research Centre of Excellence award to the Institute for Functional Intelligent Materials, I-FIM (project No. EDUNC-33-18-279-V12) and by the Tier 3 program (MOE-MOET32024-0001).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eA.V.M and M.L.S. contributed equally to this work. D.A.G. initiated the project and directed it with K.S.N.. M.H.H., M.A.L. and A.V.M. prepared the samples. D.A.K. and M.L.S. performed the analytical calculations. I.I.P and H.A.Z. performed the density functional theory calculations. A.V.M., M.L.S., M.A.L. and M.H.H. performed the measurements and analyzed the data with D.A.G.. A.V.M., M.L.S. and D.A.G. drafted the initial version of the manuscript. D.A.G. and K.S.N. reviewed and amended the manuscript. All the authors contributed to the discussions.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis work was supported by the Higher Education and Science Committee of RA MօESCS project No. 23RL- 2A031. Accurion EP4 Ellipsometer and Leica DM6 M Microscope were acquired through scientific infrastructure renovation grants of the Higher Education and Science Committee RA MօESCS. A.V.M. thanks the Institute of Chemical Physics of NAS RA for providing access to a Raman microscope with an integrated AFM module (LabRAM HR Evolution) and A. Tsokolakyan for the assistance with the AFM measurements. The Computational resources were provided by the Armenian National Supercomputing Center (ANSCC). K.S.N. acknowledges support by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-028), by the Ministry of Education, Singapore under Research Centre of Excellence award to the Institute for Functional Intelligent Materials, I-FIM (project No. EDUNC-33-18-279-V12) and by the Tier 3 program (MOE-MOET32024-0001).\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated and/or analyzed during the current study are available within the manuscript and Supplementary Information.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eNovoselov, K. S. et al. Electric field effect in atomically thin carbon films. \u003cem\u003eScience\u003c/em\u003e \u003cb\u003e306\u003c/b\u003e, 666\u0026ndash;669 (2004).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNovoselov, K. S. et al. 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Generalized 4 \u0026times; 4 matrix formalism for light propagation in anisotropic stratified media: study of surface phonon polaritons in polar dielectric heterostructures. \u003cem\u003eJ. Opt. Soc. Am. B\u003c/em\u003e. \u003cb\u003e34\u003c/b\u003e, 2128\u0026ndash;2139 (2017).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"group-III monochalcogenides, ternary compounds, uniaxial vdW crystals, complex dielectric function, high-refractive index and its tunability, all-vdW optical elements","lastPublishedDoi":"10.21203/rs.3.rs-8681290/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8681290/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eVan der Waals (vdW) crystals provide an expanding platform for designing compact and reconfigurable functional optical devices mostly owing to their wide range of refractive indices, strong optical anisotropy and heterostructure compatibility. Among them, group \u003cem\u003eIII\u003c/em\u003e monochalcogenides form a prominent family of layered semiconductors exhibiting diverse crystalline phases and showing great potential for nanoscale optoelectronic applications. Despite this promise, a quantitative knowledge of their dielectric functions is yet unrevealed for many representatives of vdW family, not to mention their mixed composition ternary compounds. Here, we address this gap by presenting the complex anisotropic dielectric function of layered Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e in visible (Vis) to near-infrared (NIR) spectral region. It exhibits a response typical for uniaxial crystals enabling simultaneous access to the high refractive indices and low optical losses within a broad spectral region. We also suggest that the optical dispersion of vdW Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e can be adjusted by varying its ternary composition implying a tunability within a window defined by the dispersion limits of the parent binary compounds. Furthermore, we display an approach towards designing an ultrathin all-vdW optical elements exemplified by unpolarized plate-type beam splitters built on a few multilayer heterostructures of Ga\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e3+δ\u003c/sub\u003eTe\u003csub\u003e1\u0026minus;δ\u003c/sub\u003e/\u003cem\u003eh\u003c/em\u003eBN.\u003c/p\u003e","manuscriptTitle":"Dielectric function of layered Ga4Se3+δTe1-δ and emergent all van der Waals optical elements","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-02 09:01:51","doi":"10.21203/rs.3.rs-8681290/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-04T09:48:50+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-03T01:36:53+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-01T08:17:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"159596218409728250284263153245728838458","date":"2026-02-01T06:47:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"151041310741937009576063828915423219301","date":"2026-01-30T00:30:56+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-29T08:43:32+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-01-28T17:12:43+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-27T10:23:31+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-27T10:20:39+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-01-23T16:32:10+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7ea0d577-9678-4c69-b14d-fd6e3449ba4a","owner":[],"postedDate":"February 2nd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":62102228,"name":"Physical sciences/Materials science"},{"id":62102229,"name":"Physical sciences/Optics and photonics"},{"id":62102230,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-03-09T16:05:25+00:00","versionOfRecord":{"articleIdentity":"rs-8681290","link":"https://doi.org/10.1038/s41598-026-42182-y","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-03-08 15:57:50","publishedOnDateReadable":"March 8th, 2026"},"versionCreatedAt":"2026-02-02 09:01:51","video":"","vorDoi":"10.1038/s41598-026-42182-y","vorDoiUrl":"https://doi.org/10.1038/s41598-026-42182-y","workflowStages":[]},"version":"v1","identity":"rs-8681290","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8681290","identity":"rs-8681290","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}