Introduction

Van der Waals (vdW) crystals have received considerable interest since their first appearance1. Their captivating optical properties2,3,4,5 provided the groundwork for modern photonic applications, such as extreme skin-depth guiding2,6, topological phase singularities7,8, Mie nanoresonators9,10, exciton-polaritons11,12, to name a few. Moreover, recent studies13,14,15 demonstrated that low-symmetry vdW crystals, such as As2S313, α-MoO314, and black phosphorus15, exhibit strong in-plane optical and mechanical anisotropy, which enables novel photonic effects and devices, including ultrathin waveplates13,16, twisted nanooptics17,18,19, polarization-sensitive photodetectors20,21, and wandering principal optical axes22,23. The core parameter in all these applications is the refractive index and its unique dependence on wavelength and direction, where all records of absolute values belong to vdW materials3. As a result, several groups3,24,25 view vdW crystals as a perfect material platform for the next-generation nanophotonics. However, a smooth transition from conventional high refractive index materials, such as Si26, GaP27, and TiO228, to vdW materials is hindered by the absence of high refractive index vdW crystal transparent in the entire visible spectrum.

One promising crystals is germanium disulfide (GeS2), which stands out with low-symmetry crystallography29 and a large bandgap of 3.4–3.7 eV, which lies at the boundary between visible and ultraviolet (UV) spectral intervals30,31,32. Amorphous GeS2 has already proven its utility in versatile photonic applications, such as chalcogenides glasses in optical fibers33, photodoping34, and gradient refractive index Fresnel lenses35. With a plethora of distinguished properties, layered GeS2 also emerged as a focal point for fundamental and applied research36,37,38,39. However, the anisotropic optical properties of GeS2 have not yet been investigated thoroughly, making it a crucial area for further exploration.

This work introduces GeS2 as a new wide-bandgap vdW material with a large in-plane anisotropy. We present a comprehensive examination of its anisotropic structural, vibrational, and optical properties. First, we performed a detailed study of GeS2 crystal structure and vibrational modes, establishing the relationship between those. Then we probed the full dielectric tensor of GeS2 from ultraviolet (UV) to near-infrared (NIR) range by spectroscopic ellipsometry and underpinned our findings by first-principle calculations of dielectric function and vibrational modes. Finally, we independently verified the acquired optical constants through the characterization of waveguide modes propagating in GeS2 using s-SNOM technique. Our work shows that GeS2 demonstrates high optical anisotropy and the highest refractive index among transparent vdW materials in the visible-UV range down to 360 nm, making it, thus far, the only highly refractive anisotropic vdW material without optical losses across the entire visible spectrum.

Results

Anisotropic crystal structure of van der Waals GeS2

Germanium disulfide is a gray semiconducting layered crystal from group IV–VI metal dichalcogenides. Figure 1a shows a schematic illustration of the monoclinic GeS2 crystal structure. GeS2 unit cell consists of two layers weakly bonded by van der Waals forces29. At the same time, each layer is formed by combining visually distinctive structural units. The first block is a chain of tetrahedra GeS4 connected by a common corner. Shared sulfur atoms are referred to as “corner S-atoms”40 (marked by red rectangle). The second block is formed by two edge-shared tetrahedral units of GeS4 (marked by a blue quadrilateral). These units form Ge–S–Ge–S rings whose S atoms we will call the “edge” S-atoms. The S-atoms connecting these two blocks are called the “bridges” S-atoms and are marked by green circles. Considering all these three patterns together (see colored dashed lines in Fig. 1a), it becomes apparent that the neighboring adjacent set (inside a given sublayer) is a copy of the initial set inverted relative to the b-axis. This means that the b-axis is a screw axis of 21/с. As shown in Fig. 1a, the resulting complex structure of the individual monolayer is riddled with infinite-shape hollows. These facts make GeS2 one of the most interesting materials from the crystallographic point of view.

Fig. 1: Crystal structure of van der Waals GeS2 and fingerprints of its anisotropy.
Fig. 1: Crystal structure of van der Waals GeS2 and fingerprints of its anisotropy.
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a The monoclinic crystal structure of the GeS2 monolayer along the с-axis (top), and the bulk structure along the a-axis (bottom). A black dashed frame reveals the unit cell. Colored dashed lines encircle selected groups of atoms that define vibrational interaction: red – corner-sharing patterns, blue – edge-sharing patterns, green – bridge sulfur atoms b Optical image of GeS2 bulk crystal. c AFM scan of GeS2 flake, revealing the presence of GeS2 monolayer. d GeS2 in the framework of the calculated out-of-plane static dielectric constants of novel van der Waals materials vs their experimental optical bandgaps. The electronic bandstructure cuts of GeS2 along a-axis (e), b-axis (f), and c-axis (g). Orange and blue curves present conduction and valence bands, respectively

Figure 1b represents an optical image of GeS2 bulk crystal. Since precise crystallographic information is critically important for ab initio calculations, we commenced our study by applying the X-ray diffraction (XRD) technique to refine its lattice constants. Our XRD results indicate P21/с space group with lattice parameters of \(a=6.6946(14){\text{\AA}} ,b=16.037(3){\text{\AA}} ,c=11.423\left(2\right){\text{\AA}} ,\alpha =90^{\circ} ,\beta =90^{\circ} ,\gamma =90^{\circ}\) giving a remarkable accuracy with R-value of 3.6%. For further details on crystallographic data collection, see Methods and Supplementary Note 1. Additionally, we verified the crystal structure of thin GeS2 by selected area electron diffraction (see Figure S3a–c). To ensure the quality of the flake, we investigated its elemental composition by energy-dispersive X-ray spectroscopy (EDS). From EDS, we found atomic stoichiometry of Ge:S ≈ 35.9/64.1, which within the measurement accuracy corresponds to GeS2.

The bulk crystal is amenable to exfoliation into a single layer, as shown in Fig. 1c. The thickness of the monolayer is half of the unit cell along the с-axis (t ≈ 0.5 × 1.14 nm = 0.57 nm). Considering that the height step observed via AFM is less than twice this thickness, we can confirm the exfoliation of a monolayer of GeS2 (see inset in Fig. 1c). A similar discrepancy between measured (0.87 nm) and expected thicknesses in AFM studies of other 2D materials has been attributed to tip-surface interactions and surface chemistry41.

Based on these crystallographic data, we estimate dielectric properties and the bandstructure of the material via first-principles calculations (see Methods and Supplementary Note 2). Remarkably, GeS2 possesses one of the largest bandgaps within the layered semiconductor family while maintaining a relatively high out-of-plane static dielectric permittivity (see Fig. 1d). Hence, GeS2 can serve as an alternative insulating material to hBN in van der Waals nanoelectronics42. The GeS2 bandstructure cuts along crystallographic directions determined by ab initio calculations are presented in Fig. 1e–g. The differences in dispersions for different directions as well as the flat bands along the c-axis indicate a strong anisotropic dielectric response, making GeS2 a perfect candidate for optical studies.

GeS2 anisotropic vibrational response

Having refined the crystallographic properties of GeS2, we proceed with the determination of its anisotropic vibrational response. In doing so, we pursue several goals. First, polarized Raman spectra are one of the material fingerprints, that contain information regarding defects, crystallographic structure, and orientation in numerous vdW materials43,44,45,46,47,48,49,50,51,52. Although previous works have demonstrated Raman response and theoretical analysis of vibrational modes in vdW GeS232,40,53,54, the origin of the most observed Raman lines in GeS2 and their anisotropic nature remains open for further investigation. Next, ab initio calculations of vibrational response provide additional verification for other theoretical calculations, in particular, of optical properties. Considering these factors, the detailed experimental and theoretical study of anisotropic optical and vibrational properties of GeS2 is of great interest.

To explore the vibrational signature of GeS2 and identify the orientation of the crystallographic axes of the sample, we utilized the polarization-resolved Raman spectroscopy method in combination with theoretical analysis of the vibrational modes. Here, we acquired Raman spectra for different polarization angles from 0° to 360° with the step of 10° by rolling the sample between a parallel-oriented polarizer and analyzer. Then, we used a phonon-based approach to calculate the vibrational response of the whole atomic system55 (see Supplementary Note 2). A detailed discussion of vibration analysis is provided in Supplementary Note 3. Figure 2a presents the Raman spectra derived by averaging over all angles for 532 nm and 633 nm excitation wavelengths, as well as DFT vibrational mode calculations utilizing crystallographic parameters built upon our XRD measurements.

Fig. 2: Unveiling the anisotropic properties of van der Waals GeS2 with polarized Raman spectroscopy.
Fig. 2: Unveiling the anisotropic properties of van der Waals GeS2 with polarized Raman spectroscopy.
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a Raman spectra of GeS2 measured at excitation wavelengths of 532 nm and 633 nm along with the calculated spectra. b Angle-resolved polarized Raman intensity colormap of bulk GeS2 (thickness, t = 151 nm) acquired by rotating the sample in a parallel-polarized configuration. c Raman spectra along the two crystalline axes (a and b) of GeS2. d–j Polar plots of the fitted peak intensities for 7 Raman modes. Experimental data is shown by filled circles, its fitting is indicated by solid lines. DFT data is presented by hollow circles. Dashed colored lines indicate the direction of the crystallographic axes of the studied sample

Figure 2b displays the angle-dependent polarized Raman intensity colormap for 151-nm-thick GeS2 flake on Schott glass substrate. Figures 2b–j are obtained by using 532 nm excitation wavelength. The calculated angle-averaged spectrum demonstrates a high alignment with the experimentally acquired spectrum, as shown in Fig. 2a. This result is further confirmed by adequate alignment between experimentally derived and ab initio angle-resolved intensities of 22 Raman-active lines, as indicated by polar plots presented in Figure S10 (for 532 nm-excited spectra) and Figure S11 (for 633 nm-excited spectra). As suggested in40, bands in the low-wavenumber region originate from the Ge-S bending, while the high-wavenumber region is mainly attributed to the Ge-S bond stretching. Our vibrational mode analysis significantly extends this approach by elaborating on the origin of 13 lines. Among these 13 lines, the origin of 10 lines is reported for the first time. Close examination of Fig. 2b reveals that modes in the range 90–180 cm−1 are indeed assigned to various bending motions of Ge-S bonds, the 220-cm−1-centered band is attributed to the breathing mode of (GeS)2 rings, while 340–450 cm−1 peaks are mainly ascribed to the stretching oscillations of S atoms. In such high-wavenumber oscillations, Ge atoms remain relatively immobile due to their high atomic mass in comparison to S atoms (see mode visualization in Table S5 and Table S6).

Excellent corroboration between experimental and theoretical studies confirms that the suggested approach can be applied to predict Raman spectra and angle-resolved vibrational response of vdW materials. The calculated Raman spectra for incident laser polarization along two crystallographic axes, and the intensities of Raman-active modes as a function of polarization angle are shown in Figure S8. The prominent in-plane anisotropy of germanium disulfide yields notable angular intensity variation for most lines. Acknowledging the fixed patterns of polar diagrams in relation to in-plane crystallographic directions, we analyzed polar plots for five intensive modes to determine the orientation of the crystallographic axes. We fitted the experimental data and aligned the obtained curves with the calculated polar plots. The fitting model is discussed in detail in Supplementary Note 3. The resulting Raman spectra for incident laser polarization along the two crystallographic axes are shown in Fig. 2c. Figure 2d-j demonstrates an outstanding match between the experimental and calculated polar diagrams for \({A}_{{\rm{g}}}^{1}-{A}_{{\rm{g}}}^{7}\) modes. When the incident laser polarization is aligned with the b-axis of GeS2, Raman peaks at 125 \(({A}_{{\rm{g}}}^{1}),150({A}_{{\rm{g}}}^{2}),345({A}_{{\rm{g}}}^{5})\), and 430 \(({A}_{{\rm{g}}}^{7})\) cm–1 have maximum intensity. Similarly, the a-axis corresponds to the maximum of 220 \(({A}_{{\rm{g}}}^{4})\) and 360 \(({A}_{{\rm{g}}}^{6}){{\rm{cm}}}^{-1}\) (although the low aspect ratio of 360 cm–1 polar plot shape hinders its applicability in the determination of crystallographic axes). Our analysis reveals that \({A}_{{\rm{g}}}^{6}\) vibration is synphase breathing of all GeS4 tetrahedra. This explains why the mode has the highest intensity: light is scattered by simultaneously breathing tetrahedra. Hence, its Raman response is relatively isotropic, which is uncommon for anisotropic material (see Table S5). Owing to the high intensity of \({A}_{{\rm{g}}}^{1}-{A}_{{\rm{g}}}^{7}\) peaks, prominent anisotropy of their angle-resolved intensities, and their perfect match with calculated data, we propose these peaks for potential use in the determination of the crystallographic axes for layered GeS2.

Optical anisotropy of van der Waals GeS2

Generally, for monoclinic crystals, the dielectric tensor has a very nontrivial form22,23,56. Indeed, since the crystallographic axes are non-orthogonal - the dielectric tensor in Cartesian representation contains mixed contributions from different crystallographic axes, making extraction of underlying optical constants challenging. Fortunately, the monoclinic angle β of GeS2, with a value of 90.935(7)°, is practically indistinguishable from 90°, allowing us to treat GeS2 as an orthorhombic crystal. Hence, we can use the diagonal form of the GeS2 dielectric tensor, neglecting its off-diagonal elements.

We exfoliated GeS2 flakes onto Si and Schott glass substrates, initially determining GeS2 crystallographic axes by angle-resolved polarized Raman spectroscopy. Then, we performed spectroscopic ellipsometry measurements (see Methods and Supplementary Note 4 for more details). For enhanced accuracy, we analyzed data from multiple flakes with different thicknesses. The optical constants acquired from the ellipsometry data spectra are depicted in Fig. 3a. The inset in Fig. 3a presents the birefringence values between the in-plane refractive indexes and between the optical constants along the b- and c-axis. As a result, the measured in-plane birefringence of GeS2 reaches Δn ~ 0.12. Utilizing the crystallographic data acquired through XRD analysis, we calculated the anisotropic permittivity tensor using first-principle calculations (see Methods and Supplementary Note 2). As shown in Fig. 3a, the experimentally measured refractive index and birefringence are in precise agreement with the theoretical estimates.

Fig. 3: Optically anisotropic van der Waals GeS2 in the family of high refractive index materials.
Fig. 3: Optically anisotropic van der Waals GeS2 in the family of high refractive index materials.
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a Optical constants of GeS2 crystal, obtained via spectral ellipsometry. The inset shows the resulting in-plane (dotted line) and out-of-plane (solid line) birefringence. The shaded blue region indicates the spectral range with optical losses. b, c Experimental and calculated polarized micro-transmittance of 151-nm-thick GeS2 flake obtained in parallel-polarized configuration. The dashed lines show the position of a (red) and b (green) crystallographic axes. d The comparison of the refractive indices of van der Waals GeS2 with traditional photonic materials in their respective transparency windows. Tabulated optical constants of GeS2 are collected in Supplementary Note 7

For additional verification, we performed polarized micro-transmittance measurements of GeS2 flakes exfoliated on Schott glass substrates (see Methods and Supplementary Note 5). Then, we calculated the transmittance spectra based on the optical constants (see Supplementary Note 8). Figure 3b, c shows the exemplified experimental and calculated transmittance maps in parallel-polarized configuration for 151-nm-thick flake. Notably, strong polarization-dependent transmittance already confirms high optical anisotropy of GeS2. We note that calculated spectra perfectly match the experimental data, affirming the reliability of the measured optical constants. Remarkably, the results yield the extinction coefficient k close to zero for wavelengths above 362 nm. Hence, our quantitative study extends the list of lossless (bandgap > 3.4 eV) high-refractive-index vdW materials. Meanwhile, GeS2 possesses in-plane and natural vdW out-of-plane anisotropy, as shown in Fig. 3a, d. Both in-plane and out-of-plane birefringent properties, in combination with the transparency in the ultraviolet-visible range, distinguish GeS2 among the broad family of vdW materials.

Near-field imaging of waveguide modes in GeS2 flakes

To unambiguously verify the extracted dielectric function, we probed propagating modes in GeS2 using scattering-type Scanning Near-field Optical Microscopy (s-SNOM) in the reflection mode (see Fig. 4a). A vertically oscillating metalized atomic force microscopy (AFM) tip was illuminated with p-polarized light using a parabolic mirror while scanning the GeS2 flake. Acting as an antenna, the mirror concentrated the incident field at the very tip, forming a nano-sized focal spot for local study of material properties and excitation of polaritons. The radiation scattered by the tip and edges of the flake was recorded simultaneously with the topography, enabling near-field imaging with nanoscale resolution. At the same time, a pseudo-heterodyne interferometric module made it possible to recover both the phase and amplitude information from near-field radiation. We performed s-SNOM measurements at three representative wavelengths (700 nm, 850 nm, 1000 nm) on a freshly exfoliated 215-nm-thick GeS2 flake placed on top of the Schott glass substrate.

Fig. 4: Confirmation of optical anisotropy of van der Waals GeS2 by near-field measurements.
Fig. 4: Confirmation of optical anisotropy of van der Waals GeS2 by near-field measurements.
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a Schematics of the s-SNOM experimental configuration for GeS2 sample on top of Schott glass substrate. b AFM image of the studied GeS2 flake’s corner. The inset shows the cross-section height plot. c, d Near-field images: amplitude Amp(E) and phase Arg(E) of the electric field at the incident wavelength of λ = 1000 nm (the other wavelength images are displayed in Supplementary Note 6). e The line profiles are taken from (c) and (d). f Fourier transform amplitude of the complex near-field signal presented in (e). Transfer-matrix calculations for propagating modes GeS2 flake along the a (g) and b (h) crystallographic directions. Dashed blue lines denote TM and TE fundamental modes. The green dots indicate experimental data points obtained from s-SNOM imaging. In calculations, we used the permittivity extracted from the ellipsometric measurements as an input

Prior to the examination of the acquired results, we determined in-plane axes orientations by polarized Raman spectroscopy as discussed in previous sections. Figure 4b–d shows topography and near-field amplitude Amp(E) and phase Arg(E) signal maps recorded at the wavelength of 1000 nm. In the s-SNOM experiment, we observed multiple bright fringes parallel to all the flake edges. The observed fringes result from the interference between two signals: (1) the wave excited at the probe tip that propagates to the sample edge and scatters, and (2) the background signal, which is the result of the reflection of the evanescent field from the sample surface at the probe-sample interface (see Figure S16). This interference pattern creates alternating regions of constructive and destructive interference, manifesting as the visible fringe pattern in the experimental observations. In the frequency domain, this background signal corresponds to the zero-frequency peak in the Fast Fourier Transform (FFT) of the fringe pattern. Importantly, the strong dependence of the fringes period on the direction is not only due to the anisotropy of the material but also due to the spatial frequency shift effect arising due to the geometry of the experiment.

To derive effective indices of propagating modes in GeS2 flake, we analyzed the Fourier transform (FT) of complex near-field amplitude built upon both Amp(E) and Arg(E) line profiles extracted from experimental maps (see Fig. 4e, f). In our analysis, we utilized the established fact that modes propagating in different orientations within the flake exhibit spatial frequency shifts for s-SNOM measurements in reflection mode57,58. These shifts are intricately linked to the orientation of the flake’s edge that scatters the propagating mode and described by the following formula:

$${n}_{{\rm{eff}}}={n}_{{\rm{obs}}}+\cos ({\rm{\alpha }})\cos ({\rm{\beta }})$$
(1)

where \({n}_{{\rm{eff}}}\) is the actual effective index of the mode, \({n}_{{\rm{obs}}}\) is the observable effective mode index, α is the angle between the wavevector k of the incident light and its projection of the sample surface kII, and β is the angle between kII and the direction of propagation of the mode in the sample. Within the recorded near-field maps, we successfully identified both transverse electric (TE) and transverse magnetic (TM) fundamental modes within the GeS2 flake, alongside the presence of air modes. To validate this observation, we performed transfer-matrix calculations59 based on the previously determined dielectric function of the material. Figure 4g, h indicates calculated energy (Eph = hc/λvac with λvac being the wavelength of light in vacuum) versus in-plane momentum (qa,b = 1/λa,b with λa,b being the wavelength of a guided mode) dispersion relation for waveguide modes in a planar waveguide of thickness 215 nm placed on top of the glass. The plotted variable Im(rp + rs) allows to observe singularities in the reflection amplitudes rp and rs corresponding to the TM and TE-polarized guided modes when in-plane component of the incident wavevector is below the light cone, i.e., the “incident wave” is evanescent. The experimentally determined effective mode indices for both in-plane directions are shown in dispersion maps as green dots. The agreement between experimental and calculated values serves as a robust confirmation of the constants derived in preceding chapters.

Polarizing beamsplitter based on GeS2-TiO2 interface

Obtained anisotropic optical properties of GeS2 offer numerous perspectives for photonic applications. To demonstrate this, we notice that GeS2 refractive index na along the crystallographic a-axis almost coincides with TiO2 refractive index nTiO2, as seen in Fig. 5a. At the same time, other components of GeS2 refractive indices nb and nc significantly differ from nTiO2 (Fig. 5a). Hence, one can construct a high-performance polarizing beamsplitter using an anisotropic/isotropic interface of TiO2/GeS2 (see the inset in Fig. 5a). It follows from the Fresnel equations of p- and s-polarized reflection coefficients \({r}_{{\rm{p}}}\) and \({r}_{{\rm{s}}}\), respectively:

$${r}_{p}=\frac{{n}_{c}{n}_{b}\sqrt{{n}_{{TiO}2}^{2}-{n}_{{TiO}2}^{2}{\sin }^{2}\varphi }-{n}_{{TiO}2}^{2}\sqrt{{n}_{c}^{2}-{n}_{{TiO}2}^{2}{\sin }^{2}\varphi }}{{n}_{c}{n}_{b}\sqrt{{n}_{{TiO}2}^{2}-{n}_{{TiO}2}^{2}{\sin }^{2}\varphi }+{n}_{{TiO}2}^{2}\sqrt{{n}_{c}^{2}-{n}_{{TiO}2}^{2}{\sin }^{2}\varphi }}$$
(2)
$${r}_{s}=\frac{\sqrt{{n}_{{TiO}2}^{2}-{n}_{{TiO}2}^{2}{\sin }^{2}\varphi }-\sqrt{{n}_{a}^{2}-{n}_{{TiO}2}^{2}{\sin }^{2}\varphi }}{\sqrt{{n}_{{TiO}2}^{2}-{n}_{{TiO}2}^{2}{\sin }^{2}\varphi }+\sqrt{{n}_{a}^{2}-{n}_{{TiO}2}^{2}{\sin }^{2}\varphi }}$$
(3)

where φ is the incidence angle (see the inset in Fig. 5a). From Eqs. (2) and (3), Rs = |rs | 2 ≈ 0 since na ≈ nTiO2, whereas Rp = |rp | 2 ≠ 0 because nb, nc ≠ nTiO2 for a broad spectral range and incident angles (Fig. 5b, c). As a result, the extinction reflection ratio Rp/Rs reaches high values from 102 to above 106 (Fig. 5d, e), which is a record characteristic compared to commercial solutions (Thorlabs PBSW-405 λ0 = 405 nm; EdmundOptics #21-884 λ0 = 355 nm and #48-998 λ0 = 550 nm) with only up to 105 extinction reflection ratios in the UV range (Fig. 5f). Furthermore, this result can be further improved by multilayer stacking of TiO2/GeS2. Thus, the proposed polarizing beamsplitter based on TiO2/GeS2 interface demonstrates a great promise of GeS2 optical properties for polarization optics.

Fig. 5: GeS2 anisotropic optical constants for UV polarization optics.
Fig. 5: GeS2 anisotropic optical constants for UV polarization optics.
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a Anisotropic optical constants of GeS2 in comparison with TiO2. The inset shows the interface TiO2/GeS2, which effectively acts as a polarizing beamsplitter. b Reflection coefficient of TiO2/GeS2 interface for p-polarization. c Reflection coefficient of TiO2/GeS2 interface for s-polarization. d Extinction reflection ratio map for TiO2/GeS2 interface. e Extinction reflection ratio spectra of TiO2/GeS2 interface for three incident angles. f Comparison of TiO2/GeS2 polarizing beamsplitter with commercial solutions \({\lambda }_{0}\) shows the central wavelength of polarizing beamsplitter

Discussion

In summary, we present a detailed analysis of the structural and optical properties of exfoliated GeS2 flakes. Using a phonon-based approach, we calculated the vibrational response of the whole structure involving the simultaneous vibration of several structural units and their interactions. Combining polarized non-resonant Raman spectroscopy with ab initio calculations we revealed the vibrational origin of 13 lines and identified 5 well-resolved lines whose polar plot maxima and minima are aligned with crystallographic axes. Furthermore, we found that GeS2 demonstrates the highest refractive index among transparent van der Waals materials in the visible and near-ultraviolet regions. It exhibits a remarkably large in-plane and out-of-plane birefringence up to 0.12 and 0.63, respectively. As a result, GeS2 is a rare example of a highly refractive material with a transparency band spanning over the whole visible spectral range. Such materials are very promising for use in integrated photonic nanostructures for light manipulation, e.g., waveguide networks and metasurfaces, and for macroscopic-scale structures, such as waveguide combiners for AR/VR headsets, for example. The former benefits from improved field confinement due to the high refractive index and optical anisotropy3,25. In the case of waveguide combiners, the wave nature of light limits the optical resolution to \(R < \pi {nd}\cos (\alpha )/(90\lambda )\) pixels per degree, where d is the thickness of the waveguide, n is the refractive index of waveguide material, λ is free space wavelength of light, and α is the angle between the waveguide surface and the ray. Hence, waveguides based on high-n-materials can be made thinner, lighter, and easier to wear. Also, higher n extends the range of possible propagation angles α, which leads to a greater field of view60. More advantages, such as higher diffraction efficiency and suppressed rainbow effect, are gained from the use of highly refractive material in waveguide in- and out-couplers60,61. Still, the question of large-scale manufacturing of GeS2 poses a challenge to its industrial implementation. To date, the best van der Waals crystals in terms of optical properties are produced by exfoliation62. While having the etalon properties, they are limited in lateral size to a few hundreds of micrometers and require manual handling, which is convenient in laboratory conditions, but is incompatible with mass production. In microelectronics and photonics, high-quality atomically smooth layers of semiconductors are grown by molecular beam epitaxy. The development of epitaxial growth methods for van der Waals materials is at the initial stage, but rapidly advances towards single-crystal quality, which preserves high-performance properties of the exfoliated counterpart63. Although epitaxial technology is mostly focused on the synthesis of MoS2 because of its promising properties, we hope our work ignites a substantial interest in epitaxial growth of GeS2 and other van der Waals materials. As a result, our findings of GeS2 promising optical properties expand the engineering capabilities for van der Waals materials-based photonics.

Materials and methods

Sample preparation

Bulk synthetic GeS2 crystals were purchased from SixCarbon Technology (Shenzhen, China) and exfoliated on top of Si, Si/SiO2, and Schott glass substrates at room temperature using commercial scotch tapes from Nitto Denko Corporation (Osaka, Japan). Prior to exfoliation, the corresponding substrates were subsequently cleaned in acetone, isopropanol alcohol, and deionized water, and then subjected to air plasma to remove the ambient adsorbates. To perform TEM analysis, GeS2 flakes were transferred onto TEM membranes (EMS non-porous Si TEM grid) using a polymer-assisted dry-transfer technique performed with polydimethylsiloxane (PDMS) films.

Raman measurements

Raman spectra were acquired with a Horiba LabRAM HR Evolution (HORIBA Ltd., Kyoto, Japan) confocal Raman microscope. 100× (N.A. = 0.90) microscope objective and 1800 lines/mm diffraction grating were used. The studies were carried out at 532 nm and 633 nm excitation wavelengths. For 532 nm, excitation power density was 60 kW cm−2, and integration time was 120 s for each point. For 633 nm, excitation power density was 11 kW cm−2, integration time was 200 s for each point. In both cases, the spot area was 1.8 μm2. The processing of the spectra was carried out as follows: first, the spectra background was subtracted. Afterward, background-subtracted spectra were fitted by Lorentzian lines. Finally, the results of the fitting were used to fit the data and construct the polar graphs. MagicPlot was used to fit the spectra, while OriginPro was used for background subtraction, polar plot fitting, and figure construction. Throughout the studies, angle-resolved Raman spectra were excited by various laser powers and acquired from multiple flakes to ensure the consistency and repeatability of obtained results.

Spectroscopic ellipsometry

To analyze the anisotropic optical response of GeS2, we used a commercial imaging spectroscopic ellipsometer Accurion nanofilm_ep4 in the nulling mode. Ellipsometry spectra were recorded for three samples with various thicknesses of t = 66 nm, 87 nm, and 128 nm in the spectral range from ultraviolet (250 nm) to near-infrared (1650 nm). For ellipsometry analysis, we followed an algorithm similar to the procedure described in our recent work2. However, for a biaxial material, such as GeS2, the key difference was the alignment of the sample in such a way that one of its in-plane optical axes was perpendicular to the plane of incidence. This was crucial for the separation of s- and p-polarized light, and therefore, Mueller-matrix measurement and analysis were not necessary for measuring the in-plane anisotropy of GeS2.

Micro-transmittance

Spectroscopic transmittance was measured using a Zeiss Axio Lab.A1 optical microscope equipped with a halogen light source. Coupling to an Ocean Optics QE65000 grating spectrometer was achieved through a Thorlabs M92L02 optical fiber with a 200 µm core diameter. Transmitted light was collected from a spot smaller than 15 µm, utilizing the “N-Achroplan” 50× Pol M27 objective with a numerical aperture of 0.8. For a more detailed description of this micro-transmittance setup see ref. 64.

Atomic force microscopy

The thickness of GeS2 flakes was accurately characterized by an atomic force microscope (NT-MDT Ntegra II) operated in contact mode at ambient conditions. AFM measurements were obtained employing silicon tips (ETALON, HA_NC ScanSens) with a spring constant of 3.5 N/m and a resonant frequency of 140 kHz. Image processing and quantitative analysis were performed in Gwyddion software.

Scanning Near-Field Optical Microscopy

Near-field measurements were performed using a scanning near-field optical microscope (“NeaSNOM” from company Neaspec GmbH). Ti:Sapphire continuous wave tuning laser (TiC, AVESTA Lasers, and Optical Systems) with fiber coupling output was used, working at a wavelength range of λ = 700–1000 nm. We used Pt-coated silicon tip oscillating at a resonance frequency of Ω ≈ 280 kHz with an amplitude of \(\sim\)80 nm (ARROW-NCPt-50). The microscope was used in the reflection mode, meaning the same parabolic mirror was used to excite and collect near-field signals. To enhance the quality of the near-field image, we reduced the optical background by demodulating the received signal at a high-order harmonic frequency nΩ (where n can be 2, 3, or 4), and using an interferometric pseudoheterodyne approach with a reference beam modulated by an oscillating mirror. For this study, the signal demodulated at the third harmonic (3Ω) proved adequate for analysis free from background interference.

X-ray diffraction analysis

X-ray diffraction analysis of GeS2 single crystal was performed on a Bruker D8 QUEST diffractometer with a Photon III CMOS area detector using Mo Kα radiation (λ = 0.71073 Å) focused by a multilayer Montel mirror. The full data set was collected at 300 K within two ω-scans applying a sample-to-detector distance of 60 mm. Raw data were indexed with cell_now and integrated using Bruker APEX4 and SAINT V8.40B programs. Absorption correction was performed using a numerical method based on crystal shape as implemented in SADABS65. Crystal structure was solved by direct methods using SHELXS and refined anisotropically with the full-matrix F2 least-squares technique by SHELXL66,67. CSD reference number 2363955 contains supplementary crystallographic data for this paper. These data can be obtained free of charge from the Cambridge Crystallographic Data Centre via https://www.ccdc.cam.ac.uk/data_request/cif.

First-principle calculations

Ab initio calculations were performed using Vienna ab initio simulation package (VASP) code68. The core electrons were described with projector augmented wave (PAW) pseudopotentials treating the Ge 3 d, 4 s, and 4p and the S 3 s and 3p electrons as valence electrons. A kinetic energy cutoff for the plane-wave basis was set to 450 eV. For all of the computations, the lattice parameters, as well as atomic positions, were taken from our XRD measurements. Raman spectra and polar diagrams were computed based on the Phonopy-Spectroscopy package with our modifications. Optical properties of GeS2 were calculated within GW approximation on top of wavefunctions calculated using PBE functional using the VASP code. For this, we used Г-centered k-points mesh sampling the Brillouin zone with a resolution of 2π ∙ 0.05 Å−1.