Statistical Properties of the Reflectance and Transmittance of an Amplifying Random Media

Details Statistical Properties of the Reflectance and Transmittance of an Amplifying Random Media Statistical Properties of the Reflectance and Transmittance of an Amplifying Random Media

1996-05-15

arxiv.org/abs/cond-mat/9605090v1

Physics

Condensed Matter

5 pages (RevTeX)

Scientific paper

10.1103/PhysRevB.56.5974

Statistical properties of the transmittance ($T$) and reflectance ($R$) of an amplifying layer with one-dimensional disorder are investigated analytically. Whereas the transmittance at typical realizations decreases exponentially with the layer thickness $L$ just as it does in absorbing media, the average $\left\langle T\right\rangle $ and $\left\langle R\right\rangle $\ are shown to be infinite even for finite $L$ due to the contribution of low-probable resonant realizations corresponding to the non-Gaussian tail of the distribution of $\ln T$. This tail differs drastically from that in the case of absorption. The physical meaning of typical and resonant realizations is discussed.

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