Electrodynamics of nonlocal media

A method, based upon Wiener-Hopf techniques, is presented for calculating the reflectivity of an $s$- or $p$- polarized plane electromagnetic wave from a semi-infinite medium whose dielectric response is spatially nonlocal. The method is applicable to media that can be adequately described by the dielectric approximation and by two scalar dielectric response functions, ${\epsilon }_L(\overrightarrow{\mathrm{r}}, \omega )$ and ${\epsilon }_T(\overrightarrow{\mathrm{r}}, \omega )$, which are subject only to weak boundedness and asymptotic conditions. As an example of the method, the reflectivities are calculated for a medium characterized by a dielectric response appropriate to the neighborhood of an isolated exciton transition frequency.