Electromagnetic field quantization in an anisotropic magnetodielectric medium with spatial-temporal dispersion

By modeling a linear, anisotropic and inhomogeneous magnetodielectric medium with two independent sets of harmonic oscillators, the electromagnetic field is quantized in such a medium. The electric and magnetic polarizations of the medium are expressed as linear combinations of the ladder operators of the harmonic oscillators modeling the magnetodielectric medium. Maxwell and the constitutive equations of the medium are obtained as the Heisenberg equations of the total system. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the tensors coupling the medium with the electromagnetic field. The explicit forms of the electromagnetic field operators are obtained for a translationally invariant medium.