Continuous Wave Sum Frequency Generation and Imaging of Monolayer and Heterobilayer Two-Dimensional Semiconductors

Abstract

We report continuous-wave second harmonic and sum frequency generation from two-dimensional transition metal dichalcogenide monolayers and their heterostructures with pump irradiances several orders of magnitude lower than those of conventional pulsed experiments. The high nonlinear efficiency originates from above-gap excitons in the band nesting regions, as revealed by wavelength-dependent second order optical susceptibilities quantified in four common monolayer transition metal dichalcogenides. Using sum frequency excitation spectroscopy and imaging, we identify and distinguish one- and two-photon resonances in both monolayers and heterobilayers. Data for heterostructures reveal responses from constituent layers accompanied by nonlinear signal correlated with interlayer transitions. We demonstrate spatial mapping of heterogeneous interlayer coupling by sum frequency and second harmonic confocal microscopy on heterobilayer MoSe2/WSe2.

Dispersion of the nonlinear susceptibility of MoS2 and WS2 from second-harmonic scattering spectroscopy

“…S5) is more problematic due to their large discrepancy, as already introduced. For MoS 2 , our data are in good agreement with pioneer works [3,4] and a very recent work [9] demonstrating susceptibility values at about several hundreds of pm/V near the main C excitonic resonance. In the 1100-1200-nm excitation range, it should be pointed out that lower values have been measured (30 pm/V near the A transition [8]), whereas susceptibilities at only a few pm/V were obtained under off-resonant conditions at 1560 nm [11,12].…”

“…In terms of TMD materials, a few studies have highlighted the effect of crystalline quality on discrepancies between the published χ (2) values between mechanically exfoliated samples and those obtained from chemical vapor deposition (CVD) [10,15]. Regarding WS 2 , less work has been performed [9,12,16,17], but similar observations have been noted.…”

“…The best approach is likely to compare signals coming from monolayers and a reference material, e.g., a quartz crystal, treating individual nanosheets as a nonlinear polarization sheet. However, a different model making use of a standard SHG reflection formalism is typically employed for the reference crystal [4,8,9], and most studies do not consider deviations that could occur under tight optical focusing conditions with high numerical-aperture (NA) objectives. On the other hand, a direct calibration using an estimated incident intensity at the beam waist was also proposed to derive the TMD susceptibility [10][11][12], but this approach appears to be delicate due to very precise identification of all beam parameters that must be integrated.…”

Twist-angle engineering of excitonic quantum interference and optical nonlinearities in stacked 2D semiconductors

“…A perfectly degenerate three-level system can therefore be fabricated. The fact that one can detect SHG under continuous-wave conditions 20,34 in the limit of monolayers indicates that the light-matter interaction is intrinsically strong. In combination with the degeneracy, it may become possible to test quantum interference in the regime of low photon numbers to probe quantum nonlinearity-strong nonlinear interactions between individual photons 35 .…”

Difference frequency generation in monolayer MoS2

“…22 Similarly, SFG in TMDs has also been reported in recent years. [23][24][25] In contrast to the SHG and SFG processes, DFG is a frequency down-conversion second-order nonlinear interaction, thus extending the application range of nonlinear processes to various fields. The exploration of such a process in nanoscale is highly important, 26 especially in 2D materials.…”