hold (because of broken selection rule) for the layered conductivity, the persistence of the peak structure at $\hbar \omega = 2\gamma_1$ suggests that the two factors are approximately valid.

![(Color Online) Layered (left) and bunched (right) conductivities of an $N$-layer graphene as a function of photon energy $\hbar \omega$. The layered and bunched conductivities are scaled by $\sigma^1_1$ or $\sigma_1 d$, respectively. The error bars denote the standard deviation. []{data-label="fig:sigma"}](69750Fig2.eps)

It is also seen that the layered conductivity is suppressed (monotonically for a large $N$) below the peak by decreasing $\hbar \omega$. Meanwhile, the bunched conductivity $\sigma_{N}(\omega)$ is suppressed at low photon energies below the peak, however, returns to unity at zero energy limit. The difference between these features suggests that a lateral polarization (within a layer) weakens due to the electron hopping between layers, especially in the $\omega=0$ limit, and that an out of plane polarization exists. The latter makes a net in-plane polarization comparable to the monolayer case of $N=1$, when it is projected in the lateral direction.

Reflectance
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We plot the calculated reflectance as a function of photon energy in Fig. \[fig:Ref\]. The reflectance was calculated by using the transfer matrix method as explained in Sec. 