  We consider a moving refractive index perturbation in an optical medium as an
optical analogue to waves under the influence of gravity. We describe the
dielectric medium by the Lagrangian of the Hopfield model. We supplement the
field theory in curved spacetime for this model to solve the scattering problem
for all modes and frequencies analytically. Because of dispersion, the
kinematic scenario of the field modes may contain optical event horizons for
some frequencies. We calculate the spectra of spontaneous emission in the frame
co-moving with the perturbation and in the laboratory frame. We also calculate
the spectrally-resolved photon number correlations in either frame. The emitted
multimode field comes in different types depending on the presence of horizons.
We show that these types are robust against changes in the system parameters
and thus are genuine features of optical and non-optical analogues. These
methods and findings pave the way to new observations of analogue gravity in
dispersive systems.
