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

Abstract

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 $⟨T⟩$ and $⟨R⟩$\ 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.

5 pages (RevTeX)

References in corpus (4)

• Supersymmetry and Quantum Mechanics
• Probability of Reflection by a Random Laser
• Localization of Light: Dual Symmetry between Absorption and Amplification
• Phase randomness in a one-dimensional disordered absorbing medium

Cited by in corpus (8)

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• Light scattering from an amplifying medium bounded by a randomly rough surface: A numerical study
• Minimum reflection channel in amplifying random media
• Density of reflection resonances in one-dimensional disordered Schrödinger operators