Field theoretic description of partially reflective surfaces

Abstract

The issue of electric charges in interaction with partially reflective surfaces is addressed by means of field theoretic methods. It is proposed an enlarged Maxwell lagrangian, describing the electromagnetic field in the presence of a semitransparent surface, and its corresponding photon propagator is computed exactly. The amended Green function reduces to the one for a perfect conductor in the appropriate limit, and leads to the interaction between charges and surfaces with varying degrees of transparency, featured by a phenomenological parameter. The interaction found via image method is recovered, in the limiting case of perfect mirrors, as a testimony to the validity of the model.

Dynamical Casimir effect withδ−δ′mirrors

“…[37]). In this way, we expect that a partially reflecting δ mirror [24] also leads to asymmetric boundary conditions for the TE and TM modes on each side of the mirror, but with the TE mode in the right side of a moving mirror associated with the same particle production of the TE mode in the left side (the same symmetry occurring for the TM mode). For the case of a partially reflecting δ − δ ′ mirror, we expect that it also leads to asymmetric boundary conditions for the TE and TM modes on each side of the mirror, but now with the TE mode in the right side associated with a different particle production if compared with the TE mode in the left side of the moving mirror (this asymmetry also occurring for the TM mode).…”

“…[24]. In this context, the perfect pure δ mirror is equivalent to a perfectly conducting plate [24] and, therefore, the transverse electric (TE) and transverse magnetic (TM) modes of the field obey the Dirichlet and Neumann boundary conditions respectively [37].…”

“…Beyond the scalar field, the consideration of partially reflecting mirrors by means of terms in the Lagrangian involving δ functions, as in Eq. (1), have been done by Barone and Barone who proposed an enlarged gauge-invariant Maxwell Lagrangian describing the field in the presence of a δ mirror, investigating the interaction between a static charge and a δ mirror [24], and also the static Casimir effect between two δ mirrors [25]. Parashar, Milton, Shajesh and Schaden [26], in a different approach, considered the electric and magnetic properties of an infinitesimally thin mirror by means of the electric permittivity and magnetic permeability described in terms of δ functions, deriving the boundary conditions for the electromagnetic field on the mirror and investigating the Casimir-Polder interaction between an atom and the mirror.…”

Field theoretic description of electromagnetic boundaries

“…In [18], the description of a single partially reflective surface was carried out by adding to the Maxwell Lagrangian a new term. Making a trivial generalization to two parallel surfaces located at positions a i = (0, 0, a i ), i = 1, 2, and ones perpendicular to the x 3 axis, the model takes the form…”

“…In a recent paper [18] we have formulated a field theoretic description of a single bidimensional dielectric surface, by adding to the Maxwell Lagrangian an appropriate electromagnetic potential. The corresponding photon propagator was computed exactly, leading to the interaction energy between electric charges and the partially reflective surface.…”