Hidden nonlinear optical susceptibilities in linear polaritonic spectra

The linear spectra of molecular polaritons are usually well described by classical optical methods, like transfer matrix, raising the issue of the missing nonlinearities expected in these strongly coupled systems. We show that the absence of these signatures stems from using low-Q cavities, which suppress nonlinearities due to a timescale hierarchy in the polariton dynamics. We derive a more general expression for the linear spectra containing signatures of nonlinear molecular susceptibilities. These show up in single-mode cavities where the photon loss is comparable to the single-molecule light-matter coupling.