Localization in a Disordered Multi-Mode Waveguide with Absorption or Amplification

Misirpashaev, T. Sh.; Paasschens, J. C. J.; Beenakker, C. W. J.

Localization in a Disordered Multi-Mode Waveguide with Absorption or Amplification

Authors

Misirpashaev, T. Sh.

Paasschens, J. C. J.

Beenakker, C. W. J.

Description

An analytical and numerical study is presented of transmission of radiation through a multi-mode waveguide containing a random medium with a complex dielectric constant $ε= ε'+iε''$. Depending on the sign of $ε''$, the medium is absorbing or amplifying. The transmitted intensity decays exponentially $\propto\exp(-L/ξ)$ as the waveguide length $L\to\infty$, regardless of the sign of $ε''$. The localization length $ξ$ is computed as a function of the mean free path $l$, the absorption or amplification length $|σ|^{-1}$, and the number of modes in the waveguide $N$. The method used is an extension of the Fokker-Planck approach of Dorokhov, Mello, Pereyra, and Kumar to non-unitary scattering matrices. Asymptotically exact results are obtained for $N\gg1$ and $|σ|\gg1/N^2l$. An approximate interpolation formula for all $σ$ agrees reasonably well with numerical simulations.
13 pages, RevTeX, 1 postscript figure