  The quantization of the electromagnetic field in a three-dimensional
inhomogeneous dielectric medium with losses is carried out in the framework of
a damped-polariton model with an arbitrary spatial dependence of its
parameters. The equations of motion for the canonical variables are solved
explicitly by means of Laplace transformations for both positive and negative
time. The dielectric susceptibility and the quantum noise-current density are
identified in terms of the dynamical variables and parameters of the model. The
operators that diagonalize the Hamiltonian are found as linear combinations of
the canonical variables, with coefficients depending on the electric
susceptibility and the dielectric Green function. The complete time dependence
of the electromagnetic field and of the dielectric polarization is determined.
Our results provide a microscopic justification of the phenomenological
quantization scheme for the electromagnetic field in inhomogeneous dielectrics.
