Mechanisms for nonlinear refractive index in organic cavity polaritons

The nonlinear optical response of organic polaritonic matter has received increasing attention due to their enhanced and controllable nonlinear response and their potential for novel optical devices such as compact photon sources and optical and quantum information devices. Using $z$ scans at different wavelengths and incident powers we have studied the nonlinear optical dispersion of ultrastrongly coupled organic cavity polaritons near the lower polariton band. We show that the up to 150-fold enhancement of the nonlinear response compared to a cavityless organic film arises from an intensity-dependent polaritonic resonant frequency shift (``blueshift''). Consequently, we find that these $z$-scan data can only be described by several terms of a power series expansion in intensity whose respective contributions depend on power broadening and detuning from the lower polariton band. We further show that the nonlinear response can be quantitatively described by a semiclassical three-level molecular model coupled to the cavity in which saturation reduces the Rabi splitting, thus accounting for the lower polariton band's observed blueshift.