or $R=[(n-1)^2+\kappa^2]/[(n+1)^2+\kappa^2]$, where optical constants were determined by $\varepsilon_N = (n+i\kappa)^2$, namely, $$\begin{aligned}
 n(\omega)= \sqrt{\frac{1+\sqrt{1+ \left( \frac{\sigma_N(\omega) c}{\omega} \right)^2 }}{2} }, \ \
 \kappa(\omega)= \frac{\sigma_N(\omega) c}{2n(\omega) \omega}.\end{aligned}$$

Electronic Properties
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We review the electronic properties of an $N$-layer graphene with AB stacking order. [@Min2008] Due to the reflections of electrons taking place at the first and $N$th surface layers caused by the broken translation symmetry of the lattice, the electron standing wave is formed and the state is characterized by the wavenumber along the $c$-axis as, $$\begin{aligned}
 k_r = \frac{r\pi}{N+1}, \  \ (r =1,\cdots,N).\end{aligned}$$ For each layer, we adopt the model of massless Dirac fermions with a linear energy dispersion $\pm vp$, where $p$ is the magnitude of two dimensional (in plane or lateral) wavevector ${\bf p}$ and $v$ the Fermi velocity. Hereafter we use a unit in which $v$ is unity, because the calculated results are independent of it. Note that we neglect lateral standing waves within a layer that appear near the edge of a graphene layer by assuming that each layer is sufficiently large. [@Sasaki2011]

The effect of the hopping integral $\gamma_1$ between the nearest layers on massless Dirac fermions can be taken into account as a 