  Third order anharmonic scattering in light-matter systems can drive a wide
variety of practical and physically interesting processes from lasing to
polariton condensation. Motivated by recent experimental results in the
nonlinear optics of localised phonon polaritons, in this Letter we develop a
quantum theory capable of describing four-wave mixing in arbitrarily
inhomogeneous photonic environments. Using it we investigate Kerr
self-interaction and parametric scattering of surface and localised phonon
polaritons, showing both processes to be within experimental reach.
