Nonlinear optical susceptibility of two-dimensional WS₂ measured by hyper Rayleigh scattering: erratum

Abstract

This erratum corrects errors in the expressions for ⟨β⟩ and fitted form of I and a consequent data point in Fig. 4 of a recent Letter [Opt. Lett.42, 5018 (2017)OPLEDP0146-959210.1364/OL.42.005018]. It also supplies data for the reference compound para-nitroaniline (pNA). The correction to ⟨β⟩ improves experimental agreement from 46% to within 21% of independent scissors-corrected density functional theory (DFT) calculations. Central findings from the original Letter remain intact.

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

“…For Absolute measurements of χ (2) are then performed at 1064 nm from the linear increase in SH intensities versus TMD (and pNA) concentrations, as described in Ref. [22]. From the measured slopes in Fig.…”

“…For spherical nanoparticles, T is calculated from the quasistatic approximation provided for a sphere, which allows us to estimate the inner field according to the refractive indices of the solvent and of the particles [36]. However, this approximation is no longer appropriate for a 2D nanosheet, and we here assume, because of the ultrathin monolayer thickness, that the incident fundamental field is not modified within the nanosheet, i.e., T = 1 [22]. Importantly, this assumption is the same as the one commonly used to describe a nonlinear polarization sheet deposited on top of a substrate.…”

“…Dividing this sheet susceptibility by the monolayer thickness (t = 0.65 nm) then allows derivation of the effective volume susceptibility χ (2) as usually reported in previous works. Comparison with the single nonzero tensor element χ (2) xxx retrieved in typical SHG microscopy experiments is then readily achieved since the orientation-averaging procedure leads to χ (2) xxx = −χ (2) xyy = −χ (2) yyx = χ (2) yxy = (21/8) 1/2 χ 2 for the D 3h point-group symmetry of TMD monolayers [22].…”

“…SHS spectroscopy is an ensemble measurement probing under low focusing conditions a very large number of sheets within TMD suspensions. This alternative approach was initially employed to derive the susceptibility of WS 2 at a single excitation wavelength of 1064 nm [22]. This work expands scope to a wide excitation range (710-1300 nm) via a femtosecond tunable laser source to assess dispersion of the orientationaveraged χ (2) and to probe impacts of the excitonic resonances of MoS 2 and WS 2 on their χ (2) dispersion magnitude.…”

Second harmonic scattering from mass characterized 2D graphene oxide sheets

“…This value reported here for GO sheets is in the same order of magnitude than that reported for 2D WS2 monolayers under 1064 nm laser irradiation using paranitroaniline as the external reference. 30,31 However, the SHG signal in 2D WS2 monolayers may find a different origin as compared to the SHG signal in GO because WS2 monolayers lack inversion symmetry and have therefore a non-vanishing first hyperpolarizability. Further analysis through DFT calculations have indicated that this large first hyperpolarizability in WS2 monolayers is due to resonance enhancement as well as the presence of a large joint density of states.…”