,
\vec{r} , \vec{r'}) B^i(\vec{r},t) \vec{Y}_\omega ^j(\vec{r'} ,t)\end{aligned}$$ The contributions $L_{e}$ and $L_m$ in the Lagrangian $L_{res}$ are equivalent to the consequences of diagonalization processes of the matter fields in the Huttner-Barnet model \[8\]. That is, $L_{e}$ ( $L_{m}$ ) is equivalent to the diagonalization of the contributions of related to three parts in the Huttner-Barnet model: the dynamical variable describing the electric polarization (magnetic polarization)of the medium , a heat-bath $B$ ( $B'$) interacting with the electric polarization (magnetic polarization ) and the interaction term between the heat-bath $B$ ( $B'$) and the electric polarization (magnetic polarization). In the present approach modeling the medium , in a phenomenological way, with two independent set of oscillators the lengthy diagonalization processes have been eliminated in the start of this quantization scheme. Particularly the diagonalization processes may be more tremendous for an anisotropic medium.\
In equations (\[c3\]) and (\[c4\]) $\vec{E}=-
\frac{\partial\vec{A}}{\partial t}-\vec{\nabla\varphi}$ and $\vec{B}=\nabla\times\vec{A}$ are electric and magnetic fields respectively, where $\vec{A}$ and $\varphi $ are the vector and the scalar potentials. The tensors $ f $ and $g$ in (\[c4\]) are called the coupling tensors of the medium with electromagnetic field and for an inhomogeneous medium are dependent on the both 