Extension of the Huttner-Barnett model to a magnetodielectric medium

The Huttner-Barnett model is extended to a magnetodielectric medium by adding a matter field to this model. The eigenoperators for the coupled system are calculated and electromagnetic field is written in terms of these operators. The electric and magnetic susceptibilities of the medium are explicitly derived and shown to satisfy the Kramers-Kronig relations. It is shown that the results obtained in this extended model are equivalent to their counterparts obtained in the phenomenological methods.