  Modeling a nonlinear anisotropic magnetodielectric medium with
spatial-temporal dispersion by two continuum collections of three dimensional
harmonic oscillators, a fully canonical quantization of the electromagnetic
field is demonstrated in the presence of such a medium. Some coupling tensors
of various ranks are introduced that couple the magnetodielectric medium with
the electromagnetic field. The polarization and magnetization fields of the
medium are defined in terms of the coupling tensors and the oscillators
modeling the medium. The electric and magnetic susceptibility tensors of the
medium are obtained in terms of the coupling tensors. It is shown that the
electric field satisfy an integral equation in frequency domain. The integral
equation is solved by an iteration method and the electric field is found up to
an arbitrary accuracy.
