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In the context of the interaction between the electromagnetic field and adielectric dispersive lossless medium, we present a non-linear version of therelativistically covariant Hopfield model, which is suitable for thedescription of a dielectric Kerr perturbation propagating in a dielectricmedium. The non-linearity is introduced in the Lagrangian through aself-interacting term proportional to the fourth power of the polarizationfield. We find an exact solution for the nonlinear equations describing apropagating perturbation in the dielectric medium. Furthermore the presence ofan analogue Hawking effect, as well as the thermal properties of the model, arediscussed, confirming and improving the results achieved in the scalar case.

The Hopfield-Kerr model and analogue black hole radiation in dielectrics