of the wave function. The possible effects outside of this approximation may be examined by introducing an appropriate dielectric constant of the space.

By multiplying the transfer matrix with the field at an infinitesimal distance above the top layer $N-1$ times, we obtain the field at an infinitesimal distance below the $N$th layer, $$\begin{aligned}
 \begin{pmatrix}
  E'_{N}(z_N) \cr B'_{N}(z_N)
 \end{pmatrix}
 =
 \begin{pmatrix}
  1 & 0 \cr
  -\frac{\sigma^N_N}{\epsilon_0 c^2} & 1 
 \end{pmatrix}
 T_{N-1}\cdots T_2 T_1
 \begin{pmatrix}
  E_{1}(z_1) \cr B_{1}(z_1)
 \end{pmatrix}.
 \label{eq:ebmatrix}\end{aligned}$$ We normalize the amplitude of the incident light to unity ($c_0^t=1$); $E_{1}(z_1)=e^{i\omega z_1/c}+c_0^r e^{-i\omega z_1/c}$ and $cB_{1}(z_1)=e^{i\omega z_1/c}-c_0^r e^{-i\omega z_1/c}$ holds for the light at the entrance. Because $c_N^r$ should vanish for the field at the exit, $E'_{N}(z_N)=c_N^t e^{i\omega z_N/c}$ and $cB'_{N}(z_N)=c_N^t e^{i\omega z_N/c}$ or $E'_{N}(z_N)=cB'_{N}(z_N)$ must hold. Thus, Eq. (\[eq:ebmatrix\]) provides two equations for determining the amplitudes $c_0^r$ and $c_N^t$, by which we obtain $R_N$ and $T_N$.

The total absorptance is given by $A^N=1-R_N-T_N$. By defining a Pointing vector, it is straightforward to show using Eq. (\[eq:bc\]) that $\epsilon_0 c^2 (E'_j)^* B'_j=\epsilon_0 c^2 E_j^* B_j - \sigma_j^N |E_j|^2$ (where $E_j^*$ is the complex conjugate of $E_j$) and that $A^N$ is equivalent to the sum of the energies absorbed by each 