  Recently reported large values of exciton-polariton nonlinearity of
transition metal dichalcogenide (TMD) monolayers coupled to optically resonant
structures approach the values characteristic for GaAs-based systems in the
regime of strong light-matter coupling. Contrary to the latter, TMD-based
polaritonic devices remain operational at ambient conditions and therefore have
greater potential for practical nanophotonic applications. Here we present the
study of the nonlinear properties of Ta$_2$O$_5$ slab waveguide coupled to a
WSe$_2$ monolayer. We first confirm that the hybridization between waveguide
photon mode and a 2D semiconductor exciton resonance gives rise to the
formation of exciton-polaritons with Rabi splitting of 36 meV. By measuring
transmission of ultrashort optical pulses through this TMD-based polaritonic
waveguide, we demonstrate for the first time the strong nonlinear dependence of
the output spectrum on the input pulse energy. Our theoretical model provides
semi-quantitative agreement with experiment and gives insights into the
dominating microscopic processes which determine the nonlinear pulse
self-action: Coulomb inter-particle interaction and scattering to incoherent
excitonic reservoir. We also confirm that at intermediate pump energies the
system supports quasi-stationary solitonic regime of pulse propagation. Our
results are essential for the development of nonlinear on-chip polaritonic
devices based of 2D semiconductors.
