Microscopic calculation of the wave-vector dependence of the third-order nonlinearity due to excitonic polaritons in CuCl

The wave-vector dependence of the third-order nonlinearity due to the excitonic polaritons in CuCl is microscopically calculated using the Bloch functions at finite wave vectors obtained from the $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ perturbation method. It is found that in the spatially dispersive region the magnitude of the nonlinearity is not so strongly dependent on the wave vector over the range from less than ${10}^6$ ${\mathrm{cm}}^{-1\mathrm{}}$ (upper-branch polariton) up to ${10}^7$ ${\mathrm{cm}}^{-1\mathrm{}}$ (lower-branch polariton).