The optical response of mono-layer transition metal dichalcogenides in a Kerr-type non-linear dielectric environment

Abstract

We study the optical behaviour of an arrangement in which the interface between a linear and non-linear dielectric media is covered by an embedded mono-layer of transition metal dichalcogenides (TMDC). The optical behaviour is qualitatively obtained through transmission and reflection coefficients which are a function of the third order non-linear susceptibility of the Kerr-type dielectric and the inter-band optical conductivity of the TMDC mono-layer. The inter-band optical conductivity of the TMCD mono-layer is calculated using the Kubo formalism from linear response theory. In particular, we theoretically demonstrate that the optical response of this arrangement can be switched between total internal reflection and a normal transmission regime by controlling the intensity of the incident radiation. The reflection and transmission functions, additionally, are shown to be amenable to further control by altering the inter-band optical conductivity of the embedded TMDC mono-layer. The optical conductivity is an outcome of its energy dispersion; we specifically choose two TMDC mono-layers, MoS$_{2}$ and WSe$_{2}$, which have nearly identical dispersion parameters apart from a much stronger spin-orbit coupling in the latter. The stronger spin-orbit coupling in WSe$_{2}$ does not significantly alter the inter-band optical conductivity to manifest in an enhanced reflection spectrum. However, we find that application of an external perturbation such as strain could be effectively used to modulate the overall optical response. We conclude by offering a brief overview of the applicability of our proposed scheme in devices that employ an all-optical switching mechanism through optical bistability which is the hallmark of a non-linear dielectric.