Active spectroscopy of polaritons (phenomenological description)

An analysis is made of the contribution of three-photon cascade processes, involving polariton states, to four-photon processes in noncentrosymmetric crystals. It is shown that in the case of a sample which is opaque to virtual polaritons this contribution is governed by the tensor $\gamma_{\text{cas}}=\beta G\beta$ [$\beta(\omega_0)$ the polarizability of the medium, which is a quadratic function of the field, and $G(\omega_0k_0$), is the spectral polariton Green's function which is related by a one-to-one correspondence to the linear polarizability $\alpha(\omega_0)$]. Thus, the dependence of the effect in question on $k_0$ is governed by the function $G(k_0)$, and it can be used to determine the dispersion law of polaritons. The dependence of the effect on $\omega_0$ is considered using a single-pole approximation of the dispersion of polarizabilities. It is shown that the cascade processes make it possible to study [with the aid of $\beta(\infty)$] matter resonances which are forbidden in the Raman scattering but which make a contribution to $\alpha$.