  We consider the so-called Hopfield model for the electromagnetic field in a
dielectric dispersive medium in a framework in which one allows a space-time
dependence of microscopic parameters, aimed to a phenomenological description
of a space-time varying dielectric perturbation induced by means of the Kerr
effect. We discuss the analogue Hawking effect, by first analyzing the
geometrical optics for the Hopfield model, and then by introducing a simplified
model which has the bonus to avoid many difficulties which are involved in the
full Hopfield model, still keeping the same dispersion relation. Amplitude
calculations are indicated, and generalized Manley-Rowe identities are derived
in a quantum scattering theory framework. Our main result is an analytical
calculation of the spontaneous thermal emission in the single-branch case,
which is provided non perturbatively for the first time in the framework of
dielectric black holes. An universal mechanism for thermality between optical
black holes and acoustic black holes is also pointed out.
