Extraordinary Second Harmonic Generation in Tungsten Disulfide Monolayers

Abstract

We investigate Second Harmonic Generation (SHG) in monolayer WS2 both deposited on a SiO2/Si substrate or suspended using transmission electron microscopy grids. We find unusually large second order nonlinear susceptibility, with an estimated value of deff ~ 4.5 nm/V nearly three orders of magnitude larger than other common nonlinear crystals. In order to quantitatively characterize the nonlinear susceptibility of two-dimensional (2D) materials, we have developed a formalism to model SHG based on the Green's function with a 2D nonlinear sheet source. In addition, polarized SHG is demonstrated as a useful method to probe the structural symmetry and crystal orientation of 2D materials. To understand the large second order nonlinear susceptibility of monolayer WS2, density functional theory based calculation is performed. Our analysis suggests the origin of the large nonlinear susceptibility in resonance enhancement and a large joint density of states, and yields an estimate of the nonlinear susceptibility value deff = 0.77 nm/V for monolayer WS2, which shows good order-of-magnitude agreement with the experimental result.

Second and third harmonic generation in few-layer gallium telluride characterized by multiphoton microscopy

“…v ð2Þ ¼ 4.5 nm/V has been reported for synthesized monolayer WS 2 at an excitation wavelength of 832 nm. 25 Therefore, we conclude that the second-order nonlinearity coefficient of GaTe is around two and three orders of magnitude lower than the v ð2Þ of MoS 2 and WS 2 measured at the wavelength of $800 nm, respectively. However, our measurements have been done at the wavelength of 1560 nm, and therefore, the second-harmonic wavelength is 780 nm (lower photon energy than the band-gap).…”

“…where R is the repetition rate, t i the pulse width, P avi the average power (i ¼ 1: fundamental, 2: SH), and / ¼ 3.56 from 25 We used refractive indices for SiO 2 of n 2 ¼ 1:45 and n 1 ¼ 1:44 determined at the wavelength of 780nm and 1560nm, respectively. 26 Here, the repetition rate was R¼75MHz, pulse widths t 1 ¼t 2 ¼228fs, fundamental average laser power P av1 ¼ 5 Â 10 À3 W, average 2016) laser power of the SHG signal on the 14nm thick GaTe flake P av2 ¼ 8:93 Â 10 À13 W, numerical aperture NA¼0.5, permittivity of free space e 0 ¼ 8:854Â10 À12 Fm À1 , velocity of light c ¼ 2:99Â10 8 ms À1 , and the wavelength of the SHG signal k 2 ¼ 780nm were used to calculate the sheet nonlinear susceptibility of 14-nm-thick GaTe.…”

Observation of excitonic resonances in the second harmonic spectrum ofMoS2

“…Accordingly, a great deal of attention has been devoted to the linear optical properties of these compounds [1][2][3] . Also, non-linear optical techniques have been demonstrated as particularly powerful probes for the microscopic structure of few-layered TMD crystals, revealing e.g., their crystallographic orientation 7,[14][15][16][17] , and stacking angle 18 . Moreover, second-harmonic (SH) spectroscopy allows for insights into the electronic structure of TMD flakes 14 , exposing edge-localized effects 19 , or valley-coherent excitations 7 .…”

Optical third harmonic generation in black phosphorus

“…Applications include four-wave mixing [3,4], efficient lasing [5], and harmonic generation, more specifically third harmonic generation (THG) [6,7] and second harmonic generation (SHG) in noncentrosymmetric crystals, such as transitionmetal dichalcogenides (TMDs) [8][9][10][11][12][13] and hexagonal boron nitride (hBN) [8]. Recent advances in atomically thin materials, such as graphene, TMDs, and others have sparked interest in two-dimensional (2D) optoelectronic devices.…”