Maxwell’s equations [@BornWolf] $$\begin{aligned}
{\frac{\partial}{\partial t}}\,\bH & = & -\frac{1}{\mu} \nabla \times \bE\,,
\label{max1}\\[0.1cm]
{\frac{\partial}{\partial t}}\,{\bE} & = & \;\;\;\frac{1}{{\varepsilon}} \nabla \times {\bH}\,,
\label{max2}\\[0.3cm]
{\rm div}\,{\varepsilon}\bE & = & 0\,,
\label{max3}\\[0.3cm]
{\rm div}\,\bH & = & 0\,,
\label{max4}\end{aligned}$$ where $\bH=(H_x(\br,t),H_y(\br,t),H_z(\br,t))^T$ and $\bE=(E_x(\br,t),E_y(\br,t),E_z(\br,t))^T$ denote the magnetic and electric field vector respectively. The permeability and the permittivity are given by $\mu=\mu(\br)$ and ${\varepsilon}={\varepsilon}(\br)$. For simplicity of notation, we will omit the spatial dependence on $\br=(x,y,z)^T$ unless this leads to ambiguities. On the surface of the perfectly conducting box the EM fields satisfy the boundary conditions [@BornWolf] $$\begin{aligned}
\mathbf{n} \times \bE = 0 \quad ,\quad \mathbf{n} \cdot
\bH = 0, \label{boundcond}\end{aligned}$$ with $\mathbf{n}$ denoting the vector normal to a boundary of the surface. The conditions Eq. (\[boundcond\]) assure that the normal component of the magnetic field and the tangential components of the electric field vanish at the boundary [@BornWolf]. Some important symmetries of the Maxwell equations (\[max1\])-(\[max4\]) can be made explicit by introducing the fields $$\begin{aligned}
\bX(t)=\sqrt{\mu}\bH(t)\quad , \quad
\bY(t)=\sqrt{\varepsilon}\bE(t). \label{EY}\end{aligned}$$ In terms of the fields $\bX(t)$ and $\bY(t)$, the TDME (Eqs.(\[max1\]) and (\[max2\])) read $${\frac{\partial}{\partial t}} \left(\begin{array}{c} \bX(t) \\
\bY(t) \end{array} \right) =
 \left( \begin{array}{cc} 0 &
  -\frac{1}{\sqrt{\mu}}\mathbf{\nabla}\times\frac{1}
  {\sqrt{\varepsilon}} \\
   \frac{1}{\sqrt{\varepsilon}}\mathbf{\nabla}
   \times\frac{1}{\sqrt{\mu}} 