# Extracting Optical Conductivity From Optical Transmission Data in Graphene on SiC Wafer:

In this paper, the authors write

Matching the optical boundary conditions at the air/graphene/SiC interfaces, the optical transmission $t(\omega)$ through $N$ graphene layers on a SiC wafer (normalized to the transmission through a plain graphene wafer) can be written as $$t(\omega) = \frac{1}{1+N\sigma(\omega)\sqrt{\mu_{0}/\epsilon_{0}}/(1+n_{\rm{SiC}}) }$$ where $n_{\rm{SiC}}$ is the refractive index of SiC.

In this paper, the same authors write

Matching the optical boundary conditions at the air/graphene/SiC interfaces, the optical transmission $T(\omega)$ through $N$ graphene layers on a SiC wafer (normalized to the transmission through a plain SiC wafer) can be written in terms of the complex optical conductivity $\sigma(\omega)$ as $$T(\omega) = \left|1 + N\sigma(\omega)\sqrt{\mu_{0}/\epsilon_{0}}/(1+n_{\rm{SiC}}) \right|^{-2}$$

These two expressions do not reduce to each other in the limit $\Im(\sigma(\omega))\to 0$, or in the limit $|\sigma(\omega)| \to 0$. What have I missed that explains this discrepancy?

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The difference is only that what, $T = t^2$? This just strikes me as confusingly worded, but not inconsistent with notation from optics, where one alternately deals with transmission and reflection amplitudes such that $t^2 + r^2 = 1$ or that $T + R = 1$, where $T = t^2$ and $R = r^2$. In optics, the lowercase coefficients follow more directly from, e.g. the Fresnel equations, while the uppercase coefficients are easier to deal with conceptually. –  Muphrid Dec 31 '12 at 0:07