  The Hamiltonian of a polariton model for an inhomogeneous linear absorptive
dielectric is diagonalized by means of Fano's diagonalization method. The
creation and annihilation operators for the independent normal modes are
explicitly found as linear combinations of the canonical operators. The
coefficients in these combinations depend on the tensorial Green function that
governs the propagation of electromagnetic waves through the dielectric. The
time-dependent electromagnetic fields in the Heisenberg picture are given in
terms of the diagonalizing operators. These results justify the
phenomenological quantization of the electromagnetic field in an absorptive
dielectric.
