carrier movement is caused by $\gamma_1$, the nonlocal effect cannot be significant when $\hbar \omega \gg 2\gamma_1$.

The formulation for the transfer matrix theory based on layered conductivity is adaptable to the general case of a nonlocal response. The boundary condition is generalized from Eq. (\[eq:bc\]) to $$\begin{aligned}
 \begin{pmatrix}
  E'_1 \cr
  B'_1 \cr
  E'_2 \cr
  B'_2 \cr
  \vdots \cr
  E'_N \cr
  B'_N
 \end{pmatrix}=
 \begin{pmatrix}
  1 & 0 & 0 & 0 & \cdots & 0 & 0 \cr
  -\frac{\sigma_{1}^N}{\epsilon_0c^2} & 1 & - \frac{\sigma^N_{12}}{\epsilon_0c^2} & 0 & \cdots & - \frac{\sigma^N_{1N}}{\epsilon_0c^2} & 0 \cr
  0 & 0 & 1 & 0 & \cdots & 0 & 0 \cr
  -\frac{\sigma^N_{21}}{\epsilon_0c^2} & 0 & -\frac{\sigma_{2}^N}{\epsilon_0c^2} & 1 & \cdots & - \frac{\sigma^N_{2N}}{\epsilon_0c^2} & 0 \cr
  \vdots & \vdots & \vdots & \vdots & \ddots & 0 & 0 \cr
  0 & 0 & 0 & 0 & 0 & 1 & 0 \cr
  -\frac{\sigma^N_{N1}}{\epsilon_0c^2} & 0 & -\frac{\sigma^N_{N2}}{\epsilon_0c^2} & 0 & \cdots & -\frac{\sigma_N^N}{\epsilon_0c^2} & 1 
 \end{pmatrix}
 \begin{pmatrix}
  E_1 \cr
  B_1 \cr
  E_2 \cr
  B_2 \cr
  \vdots \cr
  E_{N} \cr
  B_{N}
 \end{pmatrix}.
 \label{eq:Apart}\end{aligned}$$ This must be solved together with Eq. (\[eq:To\]) or $$\begin{aligned}
 \begin{pmatrix}
  E_2 \cr
  B_2 \cr
  \vdots \cr
  E_{N} \cr
  