Relaxing symmetry rules for nonlinear optical interactions via strong light-matter coupling

Transition Metal Dichalcogenides (TMDCs) have been in the limelight for the past decade as a candidate for several optoelectronic devices, and as a versatile test bed for various fundamental light-matter interaction phenomena thanks to their exceptional linear optical properties arising from their large binding energy, strong spin-orbit coupling and valley physics in the monolayer (ML) limit. They also boast strong non-linear properties fortied by excitonic responses in these systems. However, the strong second order non-linear responses are mostly restricted to the ML limit owing to crystal symmetry requirements, posing several limitations in terms of smaller interaction length and lower damage threshold. Here we demonstrate a self-hybridized exciton-polariton system in bulk WSe2 that allows us to relax the crystal symmetry rules that govern second order non-linearities. The demonstrated polariton system shows intense Second Harmonic Generation (SHG) when the fundamental wavelength is resonant with the lower polariton, with an efficiency comparable to the one from a ML WS2 when excited at the same fundamental wavelength and intensity. We model this phenomenon by considering a system with alternating second- order susceptibilities under an asymmetric electric field profile determined by the polariton mode. Helicity resolved polarization experiments show very similar non-linear response as the one from a ML where the helicity of the SHG flips with respect to the fundamental harmonic. This polaritonic system offers a platform to leverage robust second order non-linear response from centrosymmetric systems, while at the same time allowing access to third-order non-linearity inherent in strongly coupled systems.