QED commutation relations for inhomogeneous Kramers-Kronig dielectrics

Details QED commutation relations for inhomogeneous Kramers-Kronig dielectrics QED commutation relations for inhomogeneous Kramers-Kronig dielectrics

1998-03-13

arxiv.org/abs/quant-ph/9803031v1

Physics

Quantum Physics

15 pages

Scientific paper

10.1103/PhysRevA.58.700

Recently a quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielectric medium has been developed and applied to a system consisting of two infinite half-spaces with a common planar interface (H.T. Dung, L. Knoell, and D.-G. Welsch, Phys. Rev. A 57, in press). Here we show that the scheme, which is based on the classical Green-tensor integral representation of the electromagnetic field, applies to any inhomogeneous medium. For this purpose we prove that the fundamental equal-time commutation relations of QED are preserved for an arbitrarily space-dependent, Kramers--Kronig consistent permittivity. Further, an extension of the quantization scheme to linear media with bounded regions of amplification is given, and the problem of anisotropic media is briefly addressed.

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