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

Abstract

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

25 pages, 4 figures

References in corpus (4)

• Fiber-optical analogue of the event horizon
• Hawking radiation from ultrashort laser pulse filaments
• Dielectric black holes induced by a refractive index perturbation and the Hawking effect
• Quantum vacuum emission in a nonlinear optical medium illuminated by a strong laser pulse

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• Quantization and soliton-like solutions for the $\Phi \Psi$-model in a optic fiber