  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.
