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Abstract
Materials based on group IV chalcogenides exhibit extensive technologically important properties. Its unusual chemical bonding and off-centering of in-layer sublattices could cause chemical polarity and weakly broken symmetry, making optical field controlling feasible. Here, we fabricated large-area SnS multilayer films and observed unexpected strong SHG response at 1030 nm. The appreciable SHG intensities were obtained with an independence on layer, which is opposite to the generation principle of overall nonzero dipole moment only in odd-layer material. Taking GaAs for reference, the second-order susceptibility was estimated to be 7.25 pm/V enhanced by mixed-chemical bonding polarity. Further polarization-dependent SHG intensity confirmed the crystalline orientation of SnS films. The results imply surface inversion symmetry broken and nonzero polarization field modified by metavalent bonding should be the origin of SHG responses. Our observations establish multilayer SnS as a promising nonlinear material, and will guide in design of IV chalcogenides with improved optics and photonics properties for the potential applications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Two-dimensional (2D) atomic layered materials such as graphene, black phosphorus and transitional metal dichalcogenides, have drawn a lot of attention in field of scientific and technology communities since their unique optoelectronic properties [1–3]. In the last decade, the studies on 2D layered materials with strong light-matter interactions have been widely investigated and show large nonlinear optical (NLO) responses, such as optical saturated absorption [4], third-order nonlinear refraction [5,6], light wave mixing [7] and THz emission [8]. NLO effect, which refers to the phenomenon that polarization intensity of materials changes nonlinearly with the electric field intensity under intense optical excitation, depends on the intrinsic crystalline symmetry, microscopic transition dipole matrix, and specific frequency and orientation of optical field applied. Since that both electric field and electric polarization are polar vectors with odd parity, even-order NLO responses generally only generated by non-centrosymmetric materials with non-zero electric susceptibility tensors, and all even-order electric susceptibility tensors vanish in centrosymmetric materials. However, the ultra-thin interlayer-stacking configuration in 2D layered materials results in the intriguing structural symmetry and interlayer coupling, motivating the possibility of even-order or continuous higher-order harmonic nonlinear optics response [9–11]. For example, graphene shows large high-order harmonics excited by mid-infrared laser at room temperature, accelerating the investigation of strong-field and ultrafast dynamics and nonlinear behavior of massless Dirac fermions [12]. It was also predicted and discovered other odd layer 2D materials display effective second harmonic generation (SHG) due to its structural inversion symmetry breaking and large residual of two opposite intraband contributions [2].The study on second harmonic generation in monolayer MoS2, WSe2 shows that the effective second-order nonlinear susceptibility reduces by a factor of seven in trilayers, and by about two orders of magnitude in even layers, proving the lack of inversion symmetry in allows strong optical second harmonic generation [13]. It has a typical second-order susceptibility χ(2) of ∼10 nm/V at ∼800 nm excitation, which is three orders of magnitude larger than other nonlinear bulk crystals, such as β-barium borate crystal [14,9]. The SHG signal from mono- and few-layered GaSe is around 1-2 orders of magnitude larger than that from monolayer MoS2 [15].
It is commonly believed that the nonlinear optical effects are determined by the overall dipole moment, so that the NLO research on 2D materials usually focuses on the construction of polar structural units with large dipole moments. However, the observations of SHG in atomically thin ReS2 exhibit an unexpected layer-dependence with even (odd) numbers of ReS2 layers having strong (negligible) SHG, which is opposite to that of group VI transition metal dichalcogenides [16]. This result implies the inversion symmetry broken in odd-layer 2D materials is not the only origin of second harmonic polarizations generation, but also due to the interlayer coupling, surface electric field and so on [17]. In fact, the first principles calculations have been revealed the size of NLO effects is determined by the compliance with the dipole moment in response to external perturbation rather than the intrinsic dipole moment of the structure, making it potential for even-order nonlinear optics response in non-polar structural materials [18]. There has been reported the strong SHG from multilayer SnSe2 at fundamental excitation closing to the indirect band-edge in the absence of excitonic resonances [19].
Recently, the group IV chalcogenides (denoted by MX with M = Ge, Sn and X = S, Se), have garnered tremendous researcher’s curiosity since its observed strong coupled ferroelectric polarization and ferroelastic lattice strain [20]. Among these, binary layered SnS material has a typical orthorhombic crystal structure, possessing a large absorption coefficient (×104), an energy gap of about 1.1 to 1.3 eV, superior carrier mobility [21]. Strong light-matter interactions and carrier dynamics of SnS caused by third-order NLO response, such as saturable absorption and nonlinear refraction, have been reported previously [22,23]. It revealed a broadband nonlinear optical absorption from 800 nm to 1550 nm with a nonlinear absorption coefficient β of 50.5 × 10−3 cm/GW [3], and the third-order nonlinearity susceptibility χ(3) was proved to be increased by the size-related quantum confinement [24,25]. As Fig. 1(a) depicted, the SnS unit cell consists of two puckered layers in which Sn and S atoms are tightly bound, leaving the lone pair electrons in the Sn atoms, which guarantee the inversion symmetry breakage and large spontaneous polarization of each monolayer SnS. The multilayer SnS are built from layers bounded by weak van der Waals force and can be easily peeled off. Based on first-principle electronic structure theory, it was expected that odd-layered SnS will exhibit enormous SHG [15]. Following that, a maximum second-order susceptibility of 1.37 pm/V was found experimentally, indicating a high conversion efficiency compared to KDP crystal [26,27]. Remarkably, the SHG signal and ferroelectric switching were also observed in the even-number SnS, thus overcoming the odd–even effect, which suggests that ultrathin SnS is grown in an unusual stacking sequence lacking centrosymmetry [28]. In addition, SnS reveals anisotropic absorption coefficients, Raman spectra, carrier mobility due to the strong interlayer interaction and distinct perspective views along with armchair and zigzag [29]. Moreover, the observations of strong in-plane ferroelectricity in SnS provides a route for exploring the structural information using the nonlinear optical effects [28,30].
Fig. 1. (a) The crystal structure of SnS (Sn atoms are dark purple and S atoms are yellow). (b) The SEM image of deposited thin film on silicon substrate. (c) The thicknesses with different sputter powers and duration. (d) The Raman spectrum of fabricated films.
Here, we investigated the NLO properties of multilayer SnS films with the dependence on wavelength and thickness prepared by magnetron sputtering deposition technology. It exhibits a strong SHG response at 1030 nm under the nonresonance condition at room temperature. The results show an independence on thickness of SnS film with a same SHG intensity, which refers surface inversion symmetry breaking should be the origin of SHG response. The laser polarization dependences of the SHG intensity were discussed as well, showing a distinct anisotropy pattern which can be used to determine the crystalline orientation of SnS film.
2. Results and discussion
2.1 Preparation and characterization
Magnetic sputtering method was used to deposit SnS thin films onto the SiO2/Si substrate and quartz glass at room temperature. The re-sputtering raw material (99.99% SnS target) was placed on the base plate, which also housed the radio-frequency (RF) power source. Considering the sputtering power has a great influence on the crystalline phase growth and composition, we prepared three kinds of SnS thin films with the sputtering power set at 30 W, 40W and 50W for 20 min. As shown in Fig. 1(b), the SEM image shows that the deposited film's surface is typically intact and consistent with no discernible convex patches. The thicknesses were determined utilizing Stylus Surface (Dektak 150, Veeco Instruments Inc.) to be 140, 180 and 230 nm respectively since the increased sputtering rate (Fig. 1(c)). Besides, a thinner film with 90 nm was prepared lasting 10 min at fixed 50 W.
Figure 1(d) shows the Raman spectroscopy at room temperature for grown thin films with different thicknesses in the range of 10-500 cm-1. A Renishaw in Via microscopic Raman spectrometer with a laser wavelength of 488 nm was carried out. For 50W-sputted SnS (230 nm, 90 nm), specific peaks were observed at 97 and 225 cm−1 in addition to bulged peaks at 68 and 178 cm−1. These peaks are well consistent with those of bulk SnS via mechanical exfoliation or PVD [31]. With a decreased sputter power and resultant thickness (140 nm, 180 nm), the Raman peaks almost vanished, while peak positions as 301 cm−1 changed to be visible clearly. It indicated the insufficient sputtering intensity may induce amount secondary phase Sn2S3 in the forming process of SnS, which possesses an orthorhombic stable structure with a predictive band gap of 0.9 eV [32,33]. However, as showing in Fig.1d, the typical Raman peaks from SnS and Sn2S3 at 97 cm−1, 225 and 301 cm−1were observed simultaneously in the 90 nm-SnS film. It reveals multiple Sn chemical states were introduced for stabilizing distorted structures during the nonequilibrium sputtering process and in turn a secondary-phase doping was realized in SnS films [34].
To further understand the optical photons vibration modes in phase-doped film, Fig. 2(a) shows the fitted information of all active modes in Raman spectra. It reveals peaks at 59 cm-1, 68 cm-1, 97 cm-1, 158 cm-1, 194 cm-1, 225 cm-1, 258 cm-1 and 286 cm-1, containing both the characteristic vibration modes of SnS and Sn2S3. The peak at 97 cm-1 represents the transverse optical Ag (TO) mode, whereas the peaks at 194 cm-1 and 225 cm-1 represent the longitudinal optical Ag (LO) mode of SnS phase. The B1g and B3g mode are represented by peaks at 68 cm-1 and 158 cm-1. The detected peak at 258 cm-1 is attribute to B2g optical mode of SnS phase, which is consistent with reported findings [21,32]. The Ag and B2g modes are responsible for the mode at 59 cm−1. Besides, the peak at 286 cm-1 can be regarded as the compressive mode of SnS layer along c axis. One significant Sn2S3 mode at 301 cm-1 vibrated in its symmetric interlayer, confirms the presence of intricate phase environment in fabricated thin film.
Fig. 2. (a) The diagram of optical photons vibration modes and Raman analysis of 50W-10 min as-fabricated SnS film. (b) The XPS spectra and bonding analysis of Sn element. (c) The XPS spectra and bonding analysis of S element.
High resolution X-ray photoelectron spectroscopy (XPS) spectra were further carried out to classify the film component with Sn 3d and S 2p core levels. Utilizing Gaussian/Lorentzian mixing function with fixed separation of 8.5 eV and 1.2 eV for Sn 3d and S 2p spin orbit split and fixed branch ratio of 2:3 and 1:2 respectively, we carried out the fitting of Sn 3d and S 2p double peaks by using commercial Avantage software. The emission peaks of Sn 3d state are shown in Fig. 2(b), along with the relative locations of Sn 3d5/2 and Sn 3d3/2. With the smallest fitting standard deviation, the observed Sn 3d5/2 peaks are separated into two peaks located at 485.6 eV and 486.5 eV according to the electronegativity difference of Sn2+ and Sn4+. Similar results of S 2p3/2 are shown in Fig. 2(c) with peaks at 160.9 eV and 161.4 eV corresponding to S-Sn2+ bond and S-Sn4+ bond. Combined with Raman spectroscopy, it confirmed the presence of SnS and secondary phase Sn2S3 [23,35]. The SnS phase contributes most of the +2 valence of Sn atoms in the mixed-valence films, while the secondary phase Sn2S3 contributes the remaining +2 valence and all the +4 valence Sn atoms. Based on it, we characterized the phase ratio of SnS and Sn2S3 to be 1.94. For the sake of discription, we use SnS and SnxSy in the following discussions to represent 230 nm SnS film and 90 nm (SnS)1.94Sn2S3 film respectively.
2.2 Second harmonic generation response
The second-order NLO properties of SnS and SnxSy films were systematically characterized utilized a fs pulsed laser at 1030 nm. A sensitive microcopy probe system was constructed showing in Fig. 3 (See Section 4, Methods for details). There was no observed sample damage by the laser illumination during the measurements. Figures 4(a) and 4(b) displays a typical SHG spectrum of SnS and SnxSy films with different excitation intensities. The SHG peak locates at 516 nm, deviating slightly from the half of the excitation wavelength and beyond that, an extremely weak signal peak at 514 nm was also observed with unchanged baseline (Supplement 1, Fig. S1), which may caused by the broad excitation spectrum. For 230 nm SnS film (Fig. 4(a)), it launches a distinguishable sharp peak of which the power-independent half width is estimated to be 0.5 nm. However, for 90 nm SnxSy film, the half width of SHG signal broadened to be 1.8 nm. According to the electric dipole theory, the SHG conversion intensities as a function of excitation intensities are governed by a square power law ${I_{SHG}} = \alpha {I^2}$, where α is a proportionality constant capturing the second-order nonlinearity. As shown in Fig. 4(c) and 4(d), power dependent SHG measurements exhibit a quadratic dependence on the excitation power, which further confirms the occurrence of second-order NLO effect. Notably, the relative SHG intensity to device nosie of SnxSy film reaches 1500 at 85 mW but grudgingly 254 of SnS film, exhibiting a strong polarity enhancement on SHG response by mixed-chemical bonding and broken symmetry in a small surface domain. The comparison of SHG intensity between SnS film and blank substrate at 50 mW was shown in Supplement 1, Fig. S2a to fight off the influence of the ultrathin oxide layer adhered silicon substrate.
Fig. 4. (a) The SHG response of 230 nm SnS depends on excitation intensities at 1030 nm. (b) The SHG response of 90 nm SnxSy depends on excitation intensities at 1030 nm. (c) Power dependent SHG intensities corresponding to (a). (d) Power dependent SHG intensities corresponding to (b).
In order to distinguish the nonlinear effects that contribute to the response signal most, an open aperture Z-scan system was fabricated for characterizing the third-order nonlinear optical properties. Relevant details and setup were shown in Fig. 5(a) and Section 4. As the sample moved through the focus of the beam along the laser propagation direction, it experiences a different light intensity and exhibits a nonlinear variation on transmittance as a function of excitation intensity at 690 nm, 800 nm and 900 nm. We defined a peak-valley difference Δ as the difference between the transmittance of steady state and the nonlinear induced transmittance at the focal point. As discussed in Fig. 5(b), with the excitation wavelength increases to 900 nm, the Δ decreases from 8% to 2%, followed by a positive/negative conversion to -0.2%, showing the strong reverse saturable absorption behavior switches to saturable absorption. According to the optical transmittance spectrum (Fig. S3, in Supplement 1), we can observed the nonlinear response was excited by laser which was located at band edge. Through fitting the obtained Z-scan data (Fig. S4 in Supplement 1), the two-photon absorption coefficient was extracted to be 3.57 × 106 cm/GW at 690 nm and saturated absorption coefficient at 900 nm is about -8 × 104 cm/GW, as shown in Fig. 5(c). In addition, we further observe the contribution of thermal nonlinearity by calculating the thermal establishment time τc defined as τc =ω0/νs, where the waist radius ω0 can be obtained to be about 0.7 µm (800 nm) and velocity of sound wave νs in solid material is reported to be 5200 m/s [36]. Thus, τc was estimated to be 135 fs (800 nm), which is basically equal to the employed pulse width (140 fs), suggesting the thermal nonlinearity should have low-impact to nonlinear absorption efficiency due to the limited wave velocity. The nonlinear absorption coefficients β and dispersion relation at excitation wavelength was also discussed. Note that, two-photon absorption efficiency depends on excitation wavelength, leading β decreases dramatically and tends to zero for λ > 900 nm at the approximate excitation intensities. The result can be confirmed by the two-band model [10,37,38] described as $\beta (\lambda )= K\frac{{\sqrt {{E_0}} }}{{{\textrm{n}_0}^2{E_g}^3}} \cdot \frac{{{{({2x - 1} )}^{3/2}}}}{{{{({2x} )}^5}}}$, where $F(x )= \frac{{{{({2x - 1} )}^{3/2}}}}{{{{({2x} )}^5}}}$ is the β dipersion function, K and E0 are the materials-independent constants, n0 refers the refractive index, and x is the dipersion parameter expressed by hc/λEg. Therefore, it enables us to cerify the response peak located at half-of-wavelength position should root from SHG effect but not third-order nonlinear process when an infrared laser of 1030 nm was employed for excitation.
Fig. 5. (a) Third-order optical nonlinear experiments. (b) Z-scan data of normalized transmittances excited by 690 nm, 800 nm and 900 nm. (c) The transmittances and effective nonlinear absorption coefficients with different excitation wavelength.
We then calculated the absolute second-order nonlinearity of SnS film at this wavelength by normalizing the SHG intensity to the reference SHG intensity from commercial (110)-cut GaAs wafer. The SHG intensity can be expressed as [16]:
To facilitate the understanding of correlation between SHG effect and the crystal structure, the in-plane anisotropy in multilayer film was also explored by monitoring SHG signals as a function of the laser polarization in a reflection collection mode. For the sake of clarity, a surface coordinate was assigned, where y is along the preset armchair orientation structure and x axis is perpendicular to the y axis referring zigzag direction. During the measurement, the excitation laser holds a perpendicular (parallel) linearly polarized beam and parallel to the x (y) axis, and is incident from a direction perpendicular to the x-y plane. The azimuthal angle θ, the one between x (y) axis of film surface and incident laser polarization direction, was rotated by a 1/2 wave plate at 5° intervals from 0 to 90°, that is the polarization of emission light rotated from 0 to 180°. With parallel configuration to x axis, Fig. 6(a) plots the obtained SHG spectra when θ changes from 0 to 180° pumped by 1030 nm with same incident power at room temperature. A strict polarization-dependence was exhibited and the maximum SHG intensity occurs when the laser polarization is along x-axis. The polarization dependent SHG intensities could be described by polarized second-order nonlinear susceptibility tensor d which could be analyzed from the matrix calculations of P = Ed, given by:
Fig. 6. Anisotropy SHG response of 90 nm SnxSy thin film. (a) Polarization-resolved SHG response spectrum with the laser parallel to x axis, measured at 10°intervals from 0° to 180°. (b) Polarization dependent SHG intensities of SnxSy films under parallel configuration. (c) Polarization-resolved SHG response spectrum with the laser perpendicular to x axis, measured at 20°intervals from 0° to 180°. (d) Polarization dependent SHG intensities of SnxSy films under perpendicular configuration.
Based on this model, we theoretically simulate the polarization dependent SHG intensities and utilize it to fit our results. As shown in Fig. 6(b), it exhibits highly polarized SHG response with its maximum value located on the parallel component at θ=0. The first-principle theoretical calculations reported reveals that the SHG polarization anisotropy and crystallographic orientation has one-to-one corresponding relations and can be utilized to assign the armchair and zigzag directions of the multilayer SnS [40]. Therefore, the zigzag directions can be obtained along the parallel component and its vertical direction along the negligible four-petal structures stands for the armchair direction. With perpendicular configuration to the x axis, the anisotropic degree of SHG response was apparently going down accompanied by a blue shift of dominant SHG frequency as shown in Fig. 5(c). It is may be due to the structure distortion induced by doped phase and the nonresonant response of substrate. Fitting by SHG expression, it shows a four-petal patterns with the maximum value of SHG intensity locating at four inclined components in the direction of 66° and its accumulated vertical components. The armchair direction was assigned along the center of obtuse angle in the anisotropic SHG pattern and is orthogonal to the zigzag direction. The obtained zigzag direction of 16° slightly varies from that obtained with parallel configuration (0°) which may be caused by imprecise control of rotation angle and the fitting error. These results suggest the feasibility for the determining of crystallographic orientation of 2D film utilizing SHG anisotropy.
3. Conclusion
In summary, large-area uniform SnS multilayer films were fabricated utilizing magnetron sputtering deposition method. As sputter power and sputter time changes, the varition of thickness and phase component were system characterized through XPS and Raman sprctra. Upon the excitation laser at 1030 nm, we experimentally observed layer-independent, strong and anistropic SHGs in multilayer SnS films, indicating it likely rooted from surface symmetry breaking. The possible confusion genarated by third-order nonlinear response was also explained through Z-Scan technique. It shows extraordinary reverse absorption coefficients of 1.79 × 106 cm/GW at 690 nm, while cutoff frequency response at 1030 nm. Taking GaAs for reference, the maximum χS(2) was estimated to be 7.25 pm/V at room temperature. The results indicate the disorted lattice structure of SnS film induced by mixed-chemical bonding could enhance the surface polarized electric field and thus posecsses more unequal and nonzero second-order susceptibility elements. Further more, polarization dependent SHG study reveals the typical anisotropy pattern which can be used to determine the crystalline orientation of SnS film. From the point of view of innately nontoxic, versatile and semiconducting feature, our work not only experimentally provides an in-depth understanding to unusual nonlinear properties of SnS through mixed-chemical bonding, but suggests its potential application in the control of optical field on the nanoscale.
4. Methods
Z-scan measurement: The fundamental pulses with a width of 140 ps were produced from an optical parametric oscillator, centered at a modulated wavelength in the range of 680 nm∼1080 nm. The repetition rate of the laser was 80 MHz. The homochromatic directional laser at 690 nm, 800 nm and 900 nm were employed of which the spots were totally collected by a large-diameter lens and focalized to a radius-size of 16 µm. The fundamental laser was divided in half by means of a beam splitter into reference beam and transmitted which were monitored by two powermeters modules in succession. The Z-scan technique and the analysis of the Z-scan traces are based on the assumption that the excitation laser has a Gaussian beam profile.
SHG measurement: A fs pulsed laser with a repetition rate of 200 KHz and a pulse width of 250 ps at 1030 nm was employed as fundamental pump radiation for the investigation of second order nonlinear optical effects. A sensitive microcopy probe system was constructed to monitored the SHG signal of prepared mixed valence thin film and the integrated setup was sketched in Fig. 3(a). Pump laser is focused by a 50× objective lens with a NA = 0.5 (focal length F = 200 mm, aperture radius a = 100 mm, numerical aperture NA = a/F) into a spot size of about ϕ20 µm on the sample. Under the excitation, the SHG signal scattered from the mixed Sn-S sample is collected by the same objective lens, which is then examined by a spectrometer mounted with a cooled silicon CCD. We can obtain linearly polarized light with different polarization directions through modulating the polarization vector of the fundamental frequency light by rotating the half wave-plate. Notably, an extinction ratio of 1/100000 Gran prism was mounted behind the half wave-plate to ensure the linear polarization of the fundamental frequency light and confirm its polarization direction.
Funding
Natural Science Foundation of Zhejiang Province (LY23E020005); Special fund for Talents Project (2021A-048-C); Natural Science Foundation of Ningbo (2021J078); National Natural Science Foundation of China (62105169).
Acknowledgments
Ying Xie and Haohai Yu thank the National Natural Science Foundation of China, Science Technology Department of Zhejiang Province, and Ningbo Natural Science Foundation for supporting the implementation of this work. Thanks to Prof. Feifei Chen and Prof. Guoxiang Wang for the assistance on the Z-scan experiments and sample fabrication.
Disclosures
The authors declare that there are no conflicts of interest related to this article. The authors declare no competing financial interest.
Data availability
No data were generated or analyzed in the presented research.
Supplemental document
See Supplement 1 for supporting content.
References
1. C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elias, N. Perea-Lopez, M. Terrones, V. Crespi, and Z. Liu, “Extraordinary Second Harmonic Generation in tungsten disulfide monolayers,” Sci. Rep. 4(1), 5530 (2014). [CrossRef]
2. K. Q. Lin, S. Bange, and J. M. Lupton, “Quantum interference in second-harmonic generation from monolayer WSe2,” Nat. Phys. 15(3), 242–246 (2019). [CrossRef]
3. H. Liu, Z. Li, Y. Yu, J. Lin, S. Liu, F. Pang, and T. Wang, “Nonlinear optical properties of anisotropic two-dimensional layered materials for ultrafast photonics,” Nanophotonics 9(7), 1651–1673 (2020). [CrossRef]
4. G. Wang, X. Marie, I. Gerber, T. Amand, D. Lagarde, L. Bouet, M. Vidal, A. Balocchi, and B. Urbaszek, “Giant enhancement of the optical second-harmonic emission of WSe2 monolayers by laser excitation at exciton resonances,” Phys. Rev. Lett. 114(9), 097403 (2015). [CrossRef]
5. R. Biswas, S. Menon, K. K. Jha, M. Dandu, K. Majumdar, and V. Raghunathan, “Third-harmonic generation in multilayer Tin Diselenide under the influence of Fabry-Perot interference effects,” Opt. Express 27(5), 20 (2019). [CrossRef]
6. S. Y. Hong, J. I. Dadap, N. Petrone, P. C. Yeh, J. Hone, and R. O. Jr, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3(2), 021014 (2013). [CrossRef]
7. Y. Ye, Z. J. Wong, X. Lu, X. Ni, H. Zhu, X. Chen, Y. Wang, and X. Zhang, “Monolayer excitonic laser,” Nat. Photonics 9(11), 733–737 (2015). [CrossRef]
8. Y. Huang, L. Zhu, Q. Zhao, Y. Guo, Z. Ren, J. Bai, and X. Xu, “Surface optical rectification from layered MoS2 crystal by THZ time-domain surface emission spectroscopy,” ACS Appl. Mater. Interfaces 9(5), 4956–4965 (2017). [CrossRef]
9. J. Ribeiro-Soares, C. Janisch, Z. Liu, A. L. Elías, M. S. Dresselhaus, M. Terrones, L. G. Cançado, and A. Jorio, “Second Harmonic Generation in WSe2,” 2D Mater. 2(4), 045015 (2015). [CrossRef]
10. F. O. Saouma, C. C. Stoumpos, J. Wong, M. G. Kanatzidis, and J. I. Jang, “Selective enhancement of optical nonlinearity in two-dimensional organic-inorganic lead iodide perovskites,” Nat. Commun. 8(1), 742 (2017). [CrossRef]
11. J. Zhang, W. Zhao, P. Yu, G. Yang, and Z. Liu, “Second harmonic generation in 2D layered materials,” 2D Mater. 7(4), 042002 (2020). [CrossRef]
12. N. Yoshikawa, T. Tamaya, and K. Tanaka, “High-harmonic generation in graphene enhanced by elliptically polarized light excitation,” Science 356(6339), 736–738 (2017). [CrossRef]
13. N. Kumar, S. Najmaei, Q. N. Cui, F. Ceballos, P. M. Ajayan, J. Lou, and H. Zhao, “Second harmonic microscopy of monolayer MoS2,” Phys. Rev. B 87(16), 161403 (2013). [CrossRef]
14. H. Hong, C. Wu, Z. Zhao, Y. Zuo, J. Wang, C. Liu, J. Zhang, F. Wang, J. Feng, and H. Shen, “Giant enhancement of optical nonlinearity in two-dimensional materials by multiphoton-excitation resonance energy transfer from quantum dots,” Nat. Photonics 15(7), 510–515 (2021). [CrossRef]
15. X. Zhou, J. Cheng, Y. Zhou, T. Cao, H. Hong, Z. Liao, S. Wu, H. Peng, K. Liu, and D. Yu, “Strong Second-Harmonic Generation in Atomic Layered GaSe,” J. Am. Chem. Soc. 137(25), 7994–7997 (2015). [CrossRef]
16. Y. Song, S. Q. Hu, M. L. Lin, X. T. Gan, P. H. Tan, and J. L. Zhao, “Extraordinary Second Harmonic Generation in ReS2 Atomic Crystals,” ACS Photonics 5(9), 3485–3491 (2018). [CrossRef]
17. Z. Lei, Y. Huang, W. Du, Z. Fan, J. Chang, H. Wang, Y. Jin, and X. Xu, “Nonlinear optical response on the surface of semiconductor SnS2 probed by terahertz emission spectroscopy,” J. Phys. Chem. C 124(39), 21559–21567 (2020). [CrossRef]
18. X. X. Jiang, S. G. Zhao, Z. S. Lin, J. H. Luo, P. D. Bristowe, X. G. Guand, and C. T. Chena, “The role of dipole moment in determining the nonlinear optical behavior of materials: ab initio studies on quaternary molybdenum tellurite crystals,” J. Mater. Chem. C 2(3), 530–537 (2014). [CrossRef]
19. R. Biswas, M. Dandu, A. Prosad, S. Das, S. Menon, J. Deka, K. Majumdar, and V. Raghunathan, “Strong near band-edge excited second-harmonic generation from multilayer 2 H Tin diselenide,” Sci. Rep. 11(1), 15017 (2021). [CrossRef]
20. H. R. Jussila, Y. Y. Dai, Y. D. Wang, H. Lipsanen, and Z. P. Sun, “Nonlinear Optics with 2D Layered Materials Anton Autere,” Adv. Mater. 30, 1705963 (2018). [CrossRef]
21. X. Wang, Z. Liu, X. G. Zhao, J. Lv, K. Biswas, and L. Zhang, “Computational design of mixed-valence tin sulfides as solar absorbers,” ACS Appl. Mater. Interfaces 11(28), 24867–24875 (2019). [CrossRef]
22. I. M. Catalano, A. Cingolani, A. Minafra, and C. J. Paorici, “Second harmonic generation in layered compounds,” Opt. Commun. 24(1), 105–108 (1978). [CrossRef]
23. L. Wu, Z. Xie, L. Lu, J. Zhao, Y. Wang, X. Jiang, Y. Ge, F. Zhang, S. Lu, and Z. Guo, “Few-layer tin sulfide: A promising black-phosphorus-analogue 2D material with exceptionally large nonlinear optical response, high stability, and applications in all-optical switching and wavelength conversion,” Adv. Opt. Mater. 6(2), 1700985 (2018). [CrossRef]
24. Z. Xie, F. Zhang, Z. Liang, T. Fan, Z. Li, X. Jiang, H. Chen, J. Li, and H. Zhang, “Revealing of the ultrafast third-order nonlinear optical response and enabled photonic application in two-dimensional tin sulfide,” Photonics Res. 7(5), 9 (2019). [CrossRef]
25. F. Zhang, N. Xu, J. Zhao, Y. Wang, X. Jiang, Y. Zhang, W. Huang, L. Hu, Y. Tang, and S. Xu, “Quantum confinement-induced enhanced nonlinearity and carrier lifetime modulation in two-dimensional tin sulfide,” Nanophotonics 9(7), 1963–1972 (2020). [CrossRef]
26. M. Zhu, M. Zhong, X. Guo, Y. Wang, Z. Chen, H. Huang, J. He, C. Su, and K. P. Loh, “Efficient and anisotropic second harmonic generation in few-layer SnS film,” Adv. Opt. Mater. 9(22), 2101200 (2021). [CrossRef]
27. D. Nithyaprakash and J. Chandrasekaran, “NLO properties of tin sulfide nanoparticle by precipitation method,” Optoelectronics Adv. Mater. - Rapid Communications 4(10), 1445–1447 (2010).
28. N. Higashitarumizu, H. Kawamoto, C. J. Lee, B. H. Lin, F. H. Chu, I. Yonemori, T. Nishimura, K. Wakabayashi, W. H. Chang, and K. Nagashio, “Purely in-plane ferroelectricity in monolayer SnS at room temperature,” Nat. Commun. 11(1), 2428 (2020). [CrossRef]
29. M. Patel, A. Chavda, I. Mukhopadhyay, J. Kim, and A. Ray, “Nanostructured SnS with inherent anisotropic optical properties for high photoactivity,” Nanoscale 8(4), 2293–2303 (2016). [CrossRef]
30. Y. Bao, P. Song, Y. Liu, Z. Chen, M. Zhu, I. Abdelwahab, J. Su, W. Fu, X. Chi, W. Yu, W. Liu, X. X. Zhao, Q. H. Xu, M. Yang, and K. P. Loh, “Gate-tunable in-plane ferroelectricity in few-layer SnS,” Nano Lett. 19(8), 5109–5117 (2019). [CrossRef]
31. M. L. Li, Y. M. Wu, T. S. Li, Y. L. Chen, H. Y. Ding, Y. Lin, N. Pan, and X. P. Wang, “Revealing anisotropy and thickness dependence of Raman spectra for SnS flakes,” RSC Adv. 7(77), 48759–48765 (2017). [CrossRef]
32. B. H. Baby and D. Bharathi Mohan, “The effect of in-situ and post deposition annealing towards the structural optimization studies of RF sputtered SnS and Sn2S3 thin films for solar cell application,” Sol. Energy 189, 207–218 (2019). [CrossRef]
33. D. J. Singh, “Optical and electronic properties of semiconducting Sn2S3,” Appl. Phys. Lett. 109(3), 359 (2016). [CrossRef]
34. T. F. Zhou, W. K. Pang, C. F. Zhang, J. Yang, Z. Chen, H. K. Liu, and Z. P. Guo, “Enhanced sodium-ion battery performance by structural phase transition from two-dimensional hexagonal-SnS2 to orthorhombic-SnS,” ACS Nano 8(8), 8323–8333 (2014). [CrossRef]
35. M. Cruz, J. Morales, J. P. Espinos, and J. Sanz, “XRD, XPS and Sn NMR study of tin sulfides obtained by using chemical vapor transport methods,” J. Solid State Chem. 175(2), 359–365 (2003). [CrossRef]
36. A. Gnoli, L. Razzari, and M. Righini, “Z-scan measurements using high repetition ratelasers: how to manage thermal effects,” Opt. Express 13(20), 7976–7981 (2005). [CrossRef]
37. J. I. Jang, S. Park, D. J. Clark, F. O. Saouma, D. Lombardo, C. M. Harrison, and B. Shim, “Impact of two-photon absorption on second-harmonic generation in CdTe as probed by wavelength-dependent Z-scan nonlinear spectroscopy,” J. Opt. Soc. Am. B 30(8), 2292 (2013). [CrossRef]
38. J. H. Zhang, D. J. Clark, J. A. Brant, K. A. Rosmus, P. Grima, J. W. Lekse, J. I. Jang, and J. A. Aitken, “α-Li2ZnGeS4: A wide-bandgap diamond-like semiconductor with excellent balance between laser-induced damage threshold and second harmonic generation response,” Chem. Mater. 32(20), 8947–8955 (2020). [CrossRef]
39. T. Skauli, K. L. Vodopyanov, T. J. Pinguet, A. Schober, O. Levi, L. A. Eyres, M. M. Fejer, J. S. Harris, B. Gerard, L. Becouarn, E. Lallier, and G. Arisholm, “Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation,” Opt. Lett. 27(8), 628–630 (2002). [CrossRef]
40. H. Wang and X. F. Qian, “Giant optical second harmonic generation in two-dimensional multiferroics,” Nano Lett. 17(8), 5027–5034 (2017). [CrossRef]
