Effects of Excitonic Resonance on Second and Third Order Nonlinear Scattering from Few-Layer MoS₂

Abstract

Nonlinear optical scattering from single- and few-layer MoS2 contains important information about the orientation, inversion symmetry, and degree of interlayer coupling between the layers. We simultaneously map second harmonic generation (SHG) and four wave mixing (FWM) signals in chemical vapor deposition (CVD) grown 2H-phase MoS2 from single to five layers. We tune the excitation wavelengths to compare cases where the nonlinear signals are on and off resonance with the A-exciton band. The SHG signal shows the expected 4-fold symmetry, however, the FWM signal depends on the incident laser polarization only, and is independent of the crystallographic orientation. We show using the symmetry of the χ(3) tensor that this results from out of plane FWM dipoles. We explore the scaling of SHG and FWM signals with layer number on and off excitonic resonance When a nonlinear scattered signal overlaps with the A excitonic band, the scaling of the signals with layer number deviates from the expected values, due to the layer dependent red shift in the exciton absorption peak due to interlayer coupling. Finally we show that circularly polarized excitation significantly enhances nonlinear scattering which overlaps with the A excitonic band and indicates the presence of spin splitting of valence bands at the energy degenerate points (K, K′) of the Brillouin zone.

Nonlinear optics of two‐dimensional transition metal dichalcogenides

“…34 Since then, both the experiments and calculations indicated that A and B exciton could also enhance SHG. 48,57,59,61,65,66,146,147 Typically, Wang et al recorded an enhancement up to three order of magnitude at A (1s) and B (1s) exciton resonance of WSe 2 at 4 K ( Figure 4A). 66 Janisch et al calculated χ (2) of WS 2 in the range of 0.5 to 2.5 eV, and the excitonic-enhanced nonlinear susceptibility was well resolved ( Figure 4B).…”

“…Malard et al observed that χ (2) was enhanced for about four times when SHG energy was in resonance with the C exciton of MoS 2 . Since then, both the experiments and calculations indicated that A and B exciton could also enhance SHG . Typically, Wang et al recorded an enhancement up to three order of magnitude at A (1 s ) and B (1 s ) exciton resonance of WSe 2 at 4 K (Figure A) .…”

“…SHG of the bulk MoS 2 is very weak and χ (2) is around 10 −14 m/V; however, three groups simultaneously reported that SHG of monolayer MoS 2 , WS 2 , and WSe 2 increased dramatically . Later, numerous SHG studies were conducted on MoS 2 , WS 2 , WSe 2 , MoSe 2 , and MoTe 2 , and χ (2) was reported on the order of magnitude of 1 nm/V, which is much higher than the most used commercial nonlinear crystals (eg, χ (2) of BBO, KTP, and LiNbO 3 are on the order of magnitude of pm/V). The large nonlinear susceptibility of monolayer compared with bulk is ascribed to the inversion symmetry breaking.…”

Second-harmonic generation enhancement in monolayer transition-metal dichalcogenides by using an epsilon-near-zero substrate

“…Several strategies have been designed to enhance the nonlinear optical SHG process in TMDCs and other 2D materials, such as excitation near excitonic resonances [25][26][27][28] , including experiments carried out at low temperature 29 and with electrostatic doping 30 . Another promising class of methods is the combination of the 2D materials with different fieldenhancement platforms, including plasmonic nanostructures for localized surface plasmon excitation [31][32][33][34][35] , hybrid dielectric structures 36,37 , metallic and dielectric metasurfaces governed by bound states in the continuum [38][39][40][41][42] , photonic crystal nanocavities 43,44 , optical microcavities 45,46 and waveguides 47 .…”

Extraordinary Temperature Dependent Second Harmonic Generation in Atomically Thin Layers of Transition‐Metal Dichalcogenides

“…[16,17] The remarkable layer dependent properties of TMDs suggest their potential to be used in nanoscale optical and electronic device fabrication. [18][19][20][21][22][23][24][25][26][27] Temperature is found to alter optoelectronic properties such as bandgap modulation, [17] variation in phonon modes, [28][29][30][31] and tuning in carrier mobility [32][33][34][35][36] in nano materials. Therefore, it is important to investigate the layer dependent thermal variation in 2D TMDs in order to better control and optimize the performance of electronic devices.…”