Extension of the Huttner-Barnett model to a magnetodielectric medium

Abstract

The Huttner$-$Barnett model is extended to a magnetodielectric medium by adding a new matter field to this model. The eigenoperators for the coupled system are calculated and electromagnetic field is written in terms of these operators. The electric and magnetic susceptibility of the medium are explicitly derived and shown to satisfy the Kramers$-$Kronig relations. It is shown that the results obtained in this model are equivalent to the results obtained from the phenomenological methods.Comment: 25 page

Casimir force in the presence of a medium

“…In this section we develop the formalism to EM field in the presence of a magnetodielectric medium [25]. The Lagrangian of EM field in the presence of a medium can be written as…”

“…after quantization of the fields, where byˆwe mean operator and the operator with positive frequency is the Hermitian conjugate of the negative one.P ± N is the noise part of the polarization field that according to the fluctuationdissipation theorem [25,28] satisfies…”

“…(1). We model the magnetodielectric medium by a continuum of harmonic oscillators (Hopfield Model) [23][24][25].…”

Quantum electrodynamics near a dispersive and absorbing dielectric

“…[10]. This model has also been extended to include spatial dispersion [15] and magnetodielectrics [16]. Practical applications of the Huttner-Barnett model, e.g., the calculation of spontaneous decay rates [17], work well for bulk dielectrics where simple forms of the relevant operators can be found, although an additional difficulty is that, in a bulk medium, local field corrections play an important role and need to be included.…”

Finite-temperature Casimir effect in the presence of nonlinear dielectrics

“…which shows that χ (1) (ω) is a linear electric susceptibility [34,37]. In this way, we can easily define the nonlinear susceptibilities of the medium via two-, three-, and n-point correlation functions between the electromagnetic field and the polarization field [39].…”