We give a unified approach to macroscopic QED in arbitrary linearly
responding media, based on the quite general, nonlocal form of the conductivity
tensor as it can be introduced within the framework of linear response theory,
and appropriately chosen sets of bosonic variables. The formalism generalizes
the quantization schemes that have been developed previously for diverse
classes of linear media. In particular, it turns out that the scheme developed
for locally responding linear magnetodielectric media can be recovered from the
general scheme as a limiting case for weakly spatially dispersive media. With
regard to practical applications, we furthermore address the dielectric
approximation for the conductivity tensor and the surface impedance method for
the calculation of the Green tensor of the macroscopic Maxwell equations, the
two central quantities of the theory.Comment: 22 pages, no figure
Within the framework of macroscopic quantum electrodynamics, general expressions for the Casimir force acting on linearly and causally responding magnetodielectric bodies that can be embedded in another linear and causal magnetodielectric medium are derived. Consistency with microscopic harmonic-oscillator models of the matter is shown. The theory is applied to planar structures and proper generalizations of Casimir's and Lifshitz-type formulas are given.
Recently the influence of dielectric and geometrical properties on the
Casimir force between dispersing and absorbing multilayered plates in the
zero-temperature limit has been studied within a 1D quantization scheme for the
electromagnetic field in the presence of causal media [R. Esquivel-Sirvent, C.
Villarreal, and G.H. Cocoletzi, Phys. Rev. Lett. 64, 052108 (2001)]. In the
present paper a rigorous 3D analysis is given, which shows that for complex
heterostructures the 1D theory only roughly reflects the dependence of the
Casimir force on the plate separation in general. Further, an extension of the
very recently derived formula for the Casimir force at zero temperature [M.S.
Toma\v{s}, Phys. Rev. A 66, 052103 (2002)] to finite temperatures is given, and
analytical expressions for specific distance laws in the zero-temperature limit
are derived. In particular, it is shown that the Casimir force between two
single-slab plates behaves asymptotically like $d^{-6}$ in place of $d^{-4}$
($d$, plate separation).Comment: 19 pages, 17 figures -- published in Phys. Rev.
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