Theory of radiation pressure on magneto–dielectric materials

Stephen M Barnett and Rodney Loudon

We present a classical linear response theory for a magneto–dielectric material and determine the polariton dispersion relations. The electromagnetic field fluctuation spectra are obtained and polariton sum rules for their optical parameters are presented. The electromagnetic field for systems with multiple polariton branches is quantized in three dimensions and field operators are converted to 1–dimensional forms appropriate for parallel light beams. We show that the field–operator commutation relations agree with previous calculations that ignored polariton effects. The Abraham (kinetic) and Minkowski (canonical) momentum operators are introduced and their corresponding single–photon momenta are identified. The commutation relations of these and of their angular analogues support the identification, in particular, of the Minkowski momentum with the canonical momentum of the light. We exploit the Heaviside–Larmor symmetry of Maxwell's equations to obtain, very directly, the Einsetin–Laub force density for action on a magneto–dielectric. The surface and bulk contributions to the radiation pressure are calculated for the passage of an optical pulse into a semi–infinite sample.

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