1996/07/17 by T. Sh. Misirpashaev, J. C. J. Paasschens, C. W. J. Beenakker
Physics and Astronomy · #cond-mat
paper · pdf · doi:10.1016/s0378-4371(96)00387-1
published as Physica A 236, 189-201 (1997) · 13 pages, RevTeX, 1 postscript figure
arxiv created 1996/07/17 · arxiv updated 2009/11/30
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 ∝exp(-L/ξ) as the waveguide length L→∞, 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≫1 and |σ|≫1/N2l. An approximate interpolation formula for all σ agrees reasonably well with numerical simulations.