(b) The layered conductivity of a $j$th layer in an $N$-layer graphene, $\sigma^ N_j$, is calculated by assuming that the electric field exists only at the $j$th layer. (c) We apply $\sigma^ N_j$ to the transfer matrix method for light propagation in an $N$-layer graphene. The interlayer distance $d$ is 0.335 nm. []{data-label="fig:sl"}](69750Fig1.eps)

We may adopt a different approach in which the conductivity is calculated layer by layer, by assuming that an electric field localizes at only $j$th layer, as shown in Fig. \[fig:sl\](b). The dynamical conductivity $\sigma^N_j$ may vary depending on the layer position $j$ ($=1,\cdots,N$) because of interlayer electronic coupling. Since the selection rule concerning the wavenumber along the $c$-axis is broken, the matrix element of the current operator of a layer includes all the possible final states that are energetically allowed. As a result, the calculation becomes more complicated than $\sigma_N$. However, the calculation based on $\sigma^N_j$ may have a wide application range. For example, when light fields are enhanced in a specific layer by plasmon resonance or by a metal layer as in the case of graphite intercalation compounds, the fields around that layer are also enhanced. Even in such a case, the optical characteristics of 