Anisotropic third-harmonic generation of exfoliated As 2 S 3 thin flakes

: Van der Waals (vdW) materials have recently attracted significant interest in the context of orientation-dependent linear and nonlinear optical properties. Recently, arsenic trisulfide (As 2 S 3 ) or orpiment is identified as a new vdW layered material having anisotropic vibrational and optomechanical responses due to the reduced in-plane crystal symmetry, but its nonlinear optical response is still not well understood yet. Herein, the anisotropic third-harmonic generation (THG) response of mechanically exfoliated As 2 S 3 thin flakes is reported. The polarization-dependent evolution of THG emission from butterfly-shaped pattern to four-lobe pattern is comprehensively explored. Moreover, the third-order nonlinear susceptibility of As 2 S 3 crystal is extracted by analyzing the thickness-dependent THG emission. We anticipate that the discussed results will not only update the existing understanding on the nonlinear light-matter interaction in anisotropic vdW materials, but also promote future applications in integrated photonic circuits, on-chip nonlinear signal processing, and polarization-sensitive optical devices.


Introduction
Van der Waals (vdW) materials with strong light-matter interaction, broadband and tunable optical absorption, and high nonlinear conversion efficiency, have facilitated a versatile testbed for miniaturized nonlinear photonic devices such as ultrafast optical modulators, wavelengthdependent multiplexers, ultrafast photonic circuits, and mode-locked/Q-switched lasers [1][2][3][4][5]. A variety of vdW materials including graphene [6], vdW heterostructures [7][8][9][10], and transition metal dichalcogenides (TMDs) [11] have been explored in the context of nonlinear optical signal generation, four-wave mixing, nonlinear refraction and saturable absorption. For instance, TMDs are explored for second-harmonic generation (SHG) and four-wave mixing, while graphene nanosheets are utilized for optically or electrically driven third-harmonic generation (THG) and terahertz nonlinearity [6,12,13]. Recently, the intrinsic structural anisotropy in vdW layered materials is envisioned as an additional degree of freedom to manipulate and modulate the nonlinear optical responses, which leads to the exploration of a novel class of anisotropic layered materials such as black phosphorous (BP), ReS 2 , GeSe, GeAs, SiP, and SnSe 2 [14][15][16][17][18][19]. Moreover, there has been a recent trend in vdW materials research about the exploration of new layered materials, in order to further expand the horizon of the adaptability and versatility for utilizing these materials in the relevant applications. Following this trend, As 2 S 3 (orpiment) is recently introduced into the vdW material family [20]. The optical properties of the As 2 S 3 crystal are relatively well understood in the context of infrared material transmittivity [21], photoconductivity [22], and tunability of optical bandgap [23], which make this material attractive for photonic applications. Recently, mechanically exfoliated As 2 S 3 membranes have been explored to demonstrate anisotropic vibrational and optomechanical properties and the estimated Young's modulus [20]. It is worth noting that anisotropic nonlinear optical response of layered As 2 S 3 crystal is still unexplored so far.
Motivated with this, herein we demonstrate anisotropic THG emission in mechanically exfoliated As 2 S 3 thin flakes. The exfoliated flakes are investigated using optical microscope and atomic force microscope (AFM) to estimate the flake shape, size, thickness, and surface smoothness. Furthermore, polarization-resolved Raman spectroscopy technique is used to identify the crystal axis of the probed flakes. Then, the THG emission response with respect to the input linear polarization is investigated in the prepared As 2 S 3 flakes, where the polarizationdependent evolution of THG emission from butterfly-shaped pattern to four-lobe pattern is studied. Moreover, the third-order nonlinear susceptibility of As 2 S 3 crystal is estimated via the recorded thickness-dependent THG emission power. We envision that our findings will be relevant in advancing future applications in integrated photonic circuits, on-chip nonlinear signal processing, as well as promoting compact photonic and optoelectronic devices such as nonlinear beam converters, photodetectors, and optical switches.

Preparation and characterization of mechanically exfoliated As 2 S 3 flakes
Arsenic trisulfide occurs as orpiment mineral in nature, consisting of arsenic (As) and sulfur (S). It has a monoclinic crystal structure belonging to P2 1 /n space group, which consists of 20 atoms in a unit cell [24] with the lattice parameters of a = 11.46 Å, b = 9.57 Å, c = 4.22 Å, and β = 90.5° [25]. The schematic illustration of the atomic arrangement in a typical As 2 S 3 crystal from three side views is depicted in Fig. 1(a). The structure is made of the corrugated layers of heart-shaped six-membered rings of the corner sharing As 2 S 3 pyramids. The individual layers are regarded as a macromolecular layer of As 2 S 3 composition stacked via weak vdW dipole-induced nondirectional intermolecular forces [26], which makes mechanical exfoliation feasible from the bulk crystal. Figure 1(b) shows the picture of a bulk As 2 S 3 crystal (2D Semiconductors), which is used to attain thin flakes with different thicknesses ranging from 8 nm to 52 nm via mechanical exfoliation process using Nitto tape (SPV 224) and scotch tape. The exfoliated flakes are then transferred onto the cleaned glass substrates.  nm and 21 nm thick As 2 S 3 flakes. Also, the optical microscope images of 32 nm and 52 nm thick As 2 S 3 flakes in reflection and transmission mode are shown in Figs. 1(e), 1(f) and 1(h), 1(I). The corresponding captured AFM images are shown in Figs. 1(g) and 1(j), which signify the flake thickness and surface smoothness.

Anisotropic Raman scattering and identification of crystal axis
Next, the prepared flakes are characterized using polarization-resolved Raman spectroscopy technique to get an insight on intrinsic structural anisotropy of the probed crystal and determination of the crystal's axes [16][17][18]27,28], which will be further used to investigate the anisotropic nonlinear THG emission in As 2 S 3 crystals. Figure 2(a) shows the collected Raman spectrum from the 52 nm-thick As 2 S 3 flake at the linear polarization angle of 150°with respect to the x-axis of the probed flake using a 632.8 nm He-Ne laser excitation source. The He-Ne laser beam is focused using a 40× objective lens (NA = 0.65) to illuminate the flake and the back reflected light is collected with the same objective lens. The signal is then filtered by an edge filter (Semrock, LP02-633RE-25) and routed to a spectrometer (Horiba, iHR 550) for recording the Raman scattering spectrum. The recorded Raman spectrum exhibits several distinct Raman peaks in the range of 75-400 cm −1 , located at 134, 157, 181, 205, 252, 289, 311, 329, and 355 cm −1 . It is noted that the majority of the identified Raman modes shows an excellent match with the previously reported Raman spectrum for As 2 S 3 crystal [20]. Subsequently, we investigate the polarization dependence of Raman intensity under parallel polarization configuration, where a linear polarizer analyzer in the collection path is set in the parallel direction with respect to the input linear polarization in order to resolve the parallel component of the Raman signal. Figure 2(b) shows the color map of polarization-resolved Raman spectra for the 52 nm-thick As 2 S 3 crystal. To get further insight on the anisotropic evolution of different Raman modes, the measured angular plots of individual Raman modes are corroborated with the theoretical model. For As 2 S 3 crystal belonging to the monoclinic crystal family with P2 1 /n space group, the corresponding Raman tensors for A g and B g Raman modes can be expressed as [27] where a, b, c, d, e, and f are the amplitudes of Raman tensor elements, and ∅ a , ∅ b , ∅ c , ∅ d , ∅ e , and ∅ f indicate the corresponding phases. Considering the polarization states of incident and scattering beams, the resultant expressions of the parallel polarization components for Raman A g and B g modes are where ∅ ba = ∅ b -∅ a shows the phase difference between a and b components of Raman tensor. is observed that the identified Raman modes are anisotropic in nature, which endorse the presence of the reduced in-plane structural symmetry in the probed crystal. The recorded A g modes exhibit four-lobe patterns with two unequal Raman intensity maxima along two perpendicular directions. The Raman modes at 134, 181 and 311 cm −1 show the primary maxima along 0°and 180°, whereas the Raman modes at 205 and 355 cm −1 give the primary maxima residing along around 90°and 270°. In contrast to Raman A g modes, the recorded B g mode at 289 cm −1 shows the typical four-lobe pattern of equal maxima along 45°, 135°, 225°and 315°. In addition, the retrieved relative magnitudes of Raman tensor elements |a|, |b|, and |e| for different A g and B g modes are listed in Table 1. It is clear that |a| is larger than |b| for the A g modes at 134, 181 and 311 cm −1 , while |a| is smaller than |b| for the A g modes at 205 and 355 cm −1 . Based on the previous literatures [7][8][9][10][16][17][18][27][28][29], anisotropic Raman A g modes are used to identify the crystal's axes. Hence, 0°and 90°directions are labelled as the a-axis and c-axis of the probed flake, which are further used in performing the polarization-dependent anisotropic THG study.

Anisotropic THG and determination of third-order nonlinear susceptibility
The anisotropic THG emission in As 2 S 3 crystal is investigated using a 1560 nm pulse laser source (pulse width 90 fs, repetition rate 80 MHz), with the 1.5 µm beam spot size and the average pump power of 1.17 mW, which is equivalent to the 9.20 GW/cm 2 peak irradiance. The incident laser beam is focused on the flake using a 40× objective lens (NA = 0.65). The transmitted THG emission from the flake is collected using a 100× objective lens (NA = 0.7) from the other side of the glass substrate. A shortpass filter is engaged in the collection path to reject the laser contribution, then the filtered signal is routed to a spectrometer (Horiba, iHR 550) for recording the THG spectrum. Figure 3(a) shows the collected THG emission spectrum from the 52 nm-thick As 2 S 3 flake, showing the peak intensity at 520 nm which is exactly one third of the pump wavelength at 1560 nm. To further ensure the THG emission process, the emission power is recorded as a function of input pump power and fitted with a cubic power law, as shown in the double-scale log plot of Fig. 3(b). The measured power values are indicated with black squares, while the cubic power fit is shown with brown solid line. The retrieved slope of 2.92 ± 0.08 ensures the THG emission process. Next, the in-plane anisotropic THG emission is probed in As 2 S 3 flakes by collecting the THG intensity as a function of the input linear polarization angle of the pump beam. The input linear polarization is controlled by introducing a linear polarizer and a half-wave plate in the excitation path, while the recorded THG intensity components of I (3ω) x and I (3ω) y are further resolved in the direction along two crystal's axes of the a-axis (θ = 0°) and c-axis (θ = 90°), respectively, by engaging a linear polarizer analyzer in the collection path along each axis. The identification of the crystal's axes is performed for all the flakes using the polarization-resolved Raman spectroscopy measurements in accordance with the Raman A g modes. Figures 3(c)-3(h) display the recorded angular plots of THG emission for several exfoliated As 2 S 3 flakes with the thicknesses of 13, 21, 32, 44, 52, and 102 nm. It can be observed that the measured THG emission is highly anisotropic in nature for all the flakes. However, the resultant total THG emission resembles as a butterfly-shaped pattern for the flakes of 13, 21, 32, and 52 nm, which is substantially different from the four-lobe pattern for the flakes of 44 and 102 nm. It is inferred that the anisotropic nature of THG emission is consistent in all the investigated As 2 S 3 flakes, but the resultant total THG emission varies from butterfly-shape pattern to four-lobe pattern. The measured values along the x-axis (a-axis) and y-axis (c-axis), and the total values are represented with red squares, blue dots, and upper black triangles, respectively. Noticeably, the shape of THG emission pattern is highly sensitive to the values of nonlinear susceptibility χ (3) tensor elements. In addition, the contribution of the off-axis tensor elements also plays a crucial role in determining the shape of THG emission pattern. In case of the butterfly-shaped THG emission pattern, the contribution of the off-axis tensor elements is relatively high. Nevertheless, such contribution continuously varies from flake to flake, as shown in the THG emission measurements. It is worthwhile noting that the butterfly-shaped THG emission pattern exhibits variation as per the investigated flake. Hence, the mechanical exfoliation process can also be regarded as one of the key factors. Moreover, since the flake preparation involves several rounds of exfoliation, there is the significant probability of introducing the exfoliation led deformation in the crystal, so that the contribution of the off-axis tensor elements may vary significantly for different flakes. Such phenomena have been observed in several previous studies, where the observed dissimilarities between the values of the χ (3) tensor elements in the two scenarios of emission pattern are attributed to the mechanical exfoliation induced deformation in the crystal [30][31][32]. To get further insight about the observed THG emission patterns, the measured values are corroborated with a theoretical model of the third-order nonlinear susceptibility. Since As 2 S 3 crystal belongs to monoclinic crystal family, the third-order nonlinear susceptibility in the contracted form can be expressed as [27,28] where the first subscript of 1, 2, and 3 denotes x, y, and z respectively, and the second subscript refers to the combination of three components as xxx yyy zzz Taking into account the incident pump beam with frequency ω and linear polarization angle θ with respect to the a-axis (x-axis) of the crystal, the linearly polarized pump beam can be expressed as ⃗ E (ω) =x(|E 0 |cosθ) +ŷ(|E 0 |sinθ). In accordance with the experimental configuration, the incident beam resides in the x-y plane, thus the z-containing tensor elements are neglected and only four nonzero terms of χ 11 , χ 18 , χ 22 and χ 29 contribute to the in-plane THG emission. The resultant expression for THG emission along the x-axis and y-axis can be written as Equations (6) and (7) are used to fit the measured THG emission patterns and the theoretical fits are shown in Figs. 3(c)-3(h) with solid lines in the corresponding colors. It is clear that the theoretical fits give a good agreement with the experimental data. It is worth noting that the x-component THG emission I (3ω) x remains a dipolar two-lobe pattern for all the flakes, whereas the y-component I (3ω) y exhibits the change from a conventional two-lobe pattern to a four-lobe pattern, leading to the variation in the resultant total THG emission I (3ω) from a four-lobe pattern into a butterfly-shaped pattern. This interesting feature can be explained in terms of the relative contributions of nonlinear susceptibility tensor elements. Figure 4(a) shows the plot of the extracted average relative magnitudes of χ (3) elements as a function of the flake thickness, which underlines the significant variations in the relative magnitudes of χ (3) elements. Based on the extracted χ (3) values, it is inferred that the relative contributions of the off-axis tensor elements χ 18 and χ 29 compared to the on-axis elements χ 11 and χ 22 play a crucial role in determining the shape of total THG emission pattern. According to the expression for I (3ω) x in Eq. (6), since the value of χ 11 is much higher compared to χ 18 for all the flakes, no significant off-axis contribution is involved in determining the THG emission pattern of I (3ω) x , which results in a dipolar two-lobe pattern. In contrast, the difference between the values of χ 22 and χ 29 is not large enough for the flakes of 13, 21, 32 and 52 nm, hence the contribution of the off-axis tensor element χ 29 will be significant, which leads to the four-lobe pattern signature for the THG emission I (3ω) y . Consequently, the total THG emission pattern emerges as a butterfly-shaped pattern. On the other hand, for the 44 nm and 102 nm-thick flakes, the difference between χ 22 and χ 29 is high, which leads to a dipolar two-lobe pattern for the THG emission I (3ω) y . Thereby, the resultant total THG emission pattern evolves as a typical four-lobe pattern. The distinct changes in the values of the off-axis tensor elements χ 18 and χ 29 in the two cases may arise from the crystal lattice deformation induced in the mechanical exfoliation process, which has also been observed in the exfoliated GeSe flakes [18]. Nevertheless, the average relative magnitudes of χ (3) elements are extracted as χ 11 : χ 18 : χ 22 : χ 29 = 1 : 0.29 : 0.60 : 0.29, which also endorses the intrinsic nonlinear optical anisotropy in As 2 S 3 crystals. Furthermore, the average THG anisotropy ratio (| χ 11 | 2 /| χ 22 | 2 ) is calculated as 2.78.
Finally, we estimate the third-order nonlinear susceptibility of As 2 S 3 crystal via collecting the THG emission power as a function of the flake thickness. The thickness-dependent THG emission measurement is conducted while the incident linear polarization is along the x-axis. The total THG emission is collected as no analyzer is engaged in the collection path. Figure 4(b) shows the recorded THG emission power for As 2 S 3 flakes with the thicknesses ranging from 8 to 152 nm. The THG emission power is recorded at the pump power of 1.17 mW (9.20 GW/cm 2 peak irradiance) with the 1.5 µm beam spot size. Noticeably, the THG emission power first exhibits an continuous increase up to 102 nm and afterwards an exponentially decay for larger thickness. This phenomenon of thickness-dependent THG emission can be explained in the context of two simultaneous competitive processes of optical gain and loss. For flake thicknesses lower than 102 nm, the THG emission is proportional to the square of the flake thickness. It is worth noting that the absorption loss is not strong at low flake thickness, so there is a systematic increase in THG emission power up to 102 nm. In contrast, at higher thicknesses, the presence of strong optical absorption plays a crucial role in attenuating the THG signal propagation through the flakes. Consequently, the exponential decay of THG signal is observed for the flake thickness larger than 102 nm. Importantly, the exponential decay trend offers an opportunity to extract the imaginary part of the refractive index (k 3 ) at λ 3 = 520 nm for As 2 S 3 crystal, by fitting the THG emission power with the expression P (3ω) (l) = Al 2 exp where A is a constant, l is the flake thickness. The retrieved value of k 3 is found to be 0.76. In addition, the third-order nonlinear susceptibility of As 2 S 3 crystal can be further extracted by the following expression [29], by considering other experimental parameters related to the laser excitation source and the As 2 S 3 crystal, including repetition rate f rep = 80 MHz, beam spot size W = 1.5 µm, pulse width τ = 90 fs, and the refractive indices of the As 2 S 3 crystal at the fundamental wavelength n 1 and the THG wavelength n 3 . Based on the previous literature [33], the refractive index values of As 2 S 3 are considered as n 1 = 2.44 and n 3 = 2.73. ∆k = 6π λ 1 (n 1 − n 3 ) represents the phase mismatch between the pump beam and the forward propagating THG beam in transmission configuration. Thus, the χ (3) value of As 2 S 3 crystal can be estimated as 1.20 × 10 −20 m 2 /V 2 , which has the similar order of magnitude as other recently explored vdW materials [16][17][18][27][28][29]. Moreover, since the estimated χ (3) value of As 2 S 3 crystal from Eq. (8) is based on the measured THG emission power under the incident linear polarization along the x-axis, it represents the χ 11 element. According to the average relative magnitudes of χ (3) elements, the actual estimated values of the four independent coefficients of χ 11 , χ 18 , χ 22 and χ 29 are 1.20 × 10 −20 , 0.348 × 10 −20 , 0.72 × 10 −20 , and 0.348 × 10 −20 m 2 /V 2 , respectively.

Conclusion
In summary, we have demonstrated the in-plane anisotropic THG emission from mechanically exfoliated As 2 S 3 thin flakes. First, the crystal's axes of As 2 S 3 flakes are determined by performing polarization-resolved Raman spectroscopy. The anisotropic nature of Raman scattering for different Raman modes are studied by corroborating the experimental observation with the theoretical expression of Raman intensity under parallel polarization configuration. It is shown that the anisotropic nature of As 2 S 3 crystal is facilitated by the reduced in-plane crystal symmetry. Then, the anisotropic nature of THG emission is investigated, showing that the As 2 S 3 crystal exhibits two different types of the resultant total THG emission patterns as four-lobe pattern and butterfly-shaped pattern. This unique feature is further explained in the context of the relative contributions of the off-axis nonlinear susceptibility tensor elements compared to the on-axis elements. Finally, the third-order nonlinear susceptibility of As 2 S 3 crystal is extracted from the thickness-dependent THG emission. With this hindsight, we envisage that these findings will not only provide a comprehensive understanding of anisotropic nonlinear light-matter interactions in vdW materials especially in the context of the polarization-dependent evolution of THG emission patterns, but also further pave a way to the advancement in future applications in optical communication, secured data processing, integrated photonic circuits, and compact nonlinear optical devices.