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We calculated the optical properties of an $N$-layer graphene by formulatingthe dynamical conductivity of each layer. This is the conductivity when anelectromagnetic field is localized at a particular layer and differs from thestandard conductivity calculated assuming a uniform field throughout alllayers. By combining these conductivities with a transfer matrix method, wetook into account the spatial variation of the electromagnetic field caused byinternal reflections. The results obtained from the two conductivities showthat similar peak structures originating from the interlayer electronicinteraction appear in reflectance of an $N$-layer graphene at any $N$. The peakis inherent to the AB stacking and is not seen for the AA stacking, and thepeak corresponding to a sufficiently large $N$ is considered to the oneobserved for natural graphite. We also gave physical explanations of theexisting experimental results on highly oriented pyrolytic graphite and naturalgraphite under high pressure. Although a layered conductivity underestimatesthe reflectance of graphite at photon energies below the peak, we will showthat the disagreement is attributed to a nonlocal conductivity caused byinterlayer interaction. The calculations with layered conductivity are usefulin knowing the local response to light and may be further validated by anobservation of a correction by interlayer electronic interaction to theuniversal layer number that we have discovered recently.

Layered Dynamical Conductivity for a Transfer Matrix Method -- Application to an N-layer Graphene