Propagation of electromagnetic energy and momentum through an absorbing dielectric

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Abstract
We calculate the energy and momentum densities and currents associated with electromagnetic wave propagation through an absorbing and dispersive diatomic dielectric, which is modeled by a single-resonance Lorentz oscillator. The relative and center-of-mass coordinates of the dielectric sublattices and the electromagnetic field vectors are treated as dynamical variables, while the dielectric loss is modeled by a phenomenological damping force. The characteristics of the energy propagation agree with previous work, including the form of the energy velocity. The treatment of momentum propagation extends previous work to lossy media, and it is found that the damping plays an important role in the transfer of momentum from the electromagnetic field to the center of mass of the dielectric. We discuss the significances of the momentum, the pseudomomentum, and their sum, the wave momentum. For each of these quantities we derive the density, the current density, and the appropriate conservation or continuity equation. The general expressions are illustrated by applications to a steady-state monochromatic wave and to an excitation in the form of a localized Gaussian pulse. The velocities associated with propagation of the various kinds of momentum are derived and discussed.

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