  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 cavity-less 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
three-level molecular quantum model coupled to the cavity in which saturation
reduces the Rabi splitting, thus accounting for the lower polariton band's
observed blueshift.
