[@8; @9] is a canonical quantization in which the electric polarization field of the medium applies in the Lagrangian of the total system as a part of the degrees of freedom of the medium. The other parts of the degrees of freedom of the absorbing medium are related to the dynamical variables of a heat bath describing the absorptivity feature of the medium. In this method the dielectric function of the medium is found in terms of the coupling function of the heat bath and the polarization field, so that it satisfies the Kramers-Kronig relations [@18.1]. This quantization method has been generalized to an inhomogeneous medium[@19].\
In the present work we generalize our previous model[@20; @21] to an anisotropic dispersive magnetodielectric medium using a canonical approach. In this formalism the medium is modeled with two independent collections of vector fields. These collections solely constitute the degrees of freedom of the medium and it is not needed the electric and magnetic polarization fields to be included in the Lagrangian of the total system as a part of the degrees of freedom of the medium as in the Huttner-Barnett model [@8]. In fact the dynamical fields modeling the dispersive medium are able 