Quantum electromagnetic stress tensor in an inhomogeneous medium

Abstract

Continuing a program of examining the behavior of the vacuum expectation value of the stress tensor in a background which varies only in a single direction, we here study the electromagnetic stress tensor in a medium with permittivity depending on a single spatial coordinate, specifically, a planar dielectric halfspace facing a vacuum region. There are divergences occurring that are regulated by temporal and spatial point splitting, which have a universal character for both transverse electric and transverse magnetic modes. The nature of the divergences depends on the model of dispersion adopted. And there are singularities occurring at the edge between the dielectric and vacuum regions, which also have a universal character, depending on the structure of the discontinuities in the material properties there. Remarks are offered concerning renormalization of such models, and the significance of the stress tensor. The ambiguity in separating "bulk" and "scattering" parts of the stress tensor is discussed.

Casimir forces in inhomogeneous media: Renormalization and the principle of virtual work

“…One of these is the inhomogeneous medium considered in Ref. [38,44]. First, we investigate the GCC where the permittivity and permeability of the intervening medium are ε = λ/(z − c) 2 and µ = 1 with λ and c as constant parameters and b < c. The forces are given in Eq.…”

“…Although these techniques control the divergences, in general a divergent part must be removed. Typically, one will subtract a Green's function for the case where one homogeneous medium fills the whole space, which is sometimes named as the "bulk contribution" [38,43,44], from the total Green's function to obtain a subtracted Green's function, a procedure occasionally called the "Lifshitz regularization" [27,28]. However, when trying to calculate Casimir forces in the DLP configuration with the intervening medium being inhomogeneous, the authors of Ref.…”

Dispersion forces in inhomogeneous planarly layered media: A one-dimensional model for effective polarizabilities

“…Note that the reflection coefficients for a linear profile have also been determined in Refs. [20,21,22] based on methods similar to ours.…”

Casimir–Polder forces in inhomogeneous backgrounds

“…There are only a few cases where both the TE and TM equations may be solved in terms of known functions. One of them is the potential [8,13]…”

“…Efforts were made to effect a suitable renormalization [12]. We generalized these investigations to electromagnetism, and found universal behaviors for both divergences and singularities [13]. Most germane to the present investigation is the computation of energies and stresses between perfect reflectors, and between parallel planes of nonanlyticity, when the media exhibit both spatial variation (in a single perpendicular coordinate, z), and dispersion [14].…”