Abstract
Starting from Maxwell’s equations for a linear, nonconducting, absorptive, and dispersive medium, characterized by the constitutive equations and , a unitary time evolution and canonical formalism is obtained. Given the complex, coordinate, and frequency-dependent, electric permeability , no further assumptions are made. The procedure leads to a proper definition of band gaps in the periodic case and a new continuity equation for energy flow. An -matrix formalism for scattering from lossy objects is presented in full detail. A quantized version of the formalism is derived and applied to the generation of Čerenkov and transition radiation as well as atomic decay. The last case suggests a useful generalization of the density of states to the absorptive situation.
- Received 22 December 1997
DOI:https://doi.org/10.1103/PhysRevA.57.4818
©1998 American Physical Society