$T_N$ and reflectance $R_N$, respectively.

We define electromagnetic fields at an infinitesimal distance ($\epsilon$) above and below the $j$th layer as $$\begin{aligned}
 \begin{pmatrix}
  E_{j} \cr B_{j}
 \end{pmatrix}
 \ {\rm and} \
 \begin{pmatrix}
  E'_{j} \cr B'_{j}
 \end{pmatrix},\end{aligned}$$ respectively. These are related by the boundary condition of the fields as $$\begin{aligned}
 \begin{pmatrix}
  E'_{j} \cr B'_{j}
 \end{pmatrix}
 =
 \begin{pmatrix}
  1 & 0 \cr
  -\frac{\sigma^N_j}{\epsilon_0 c^2} & 1 
 \end{pmatrix}
 \begin{pmatrix}
  E_{j} \cr B_{j}
 \end{pmatrix}.
 \label{eq:bc}\end{aligned}$$ The boundary condition is given by an integral of Maxwell’s equations (in differential form) over an infinitesimal interval $[z_j-\epsilon,z_j +\epsilon]$ containing the $j$th graphene. The electric field is continuous ($E'_{j}=E_{j}$) according to Faraday’s law, while the magnetic field is discontinuous ($B'_{j}=B_{j}-J^N_j/\epsilon_0 c^2$) according to Ampère’s circuital law. Since the discontinuity is given by the current of $j$th layer in an $N$-layer graphene which is $J^N_j= \sigma^N_j E_j$, the layered dynamical conductivity $\sigma^N_j$ appears in the off-diagonal term of Eq. (\[eq:bc\]).

By assuming that electromagnetic fields with angular frequency of $\omega$ propagate freely in the interlayer vacuum space of distance $d$ by speed of light $c$, the electromagnetic fields between $j$ and $j+1$th layer ($z_{j} \le z \le z_{j+1}$) \[or at the $j$th interlayer space\], are written in terms of 