Localization in a disordered multi-mode waveguide with absorption or amplification

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

Physica A: Statistical Mechanics and its Applications, 1997, vol. 236, issue 3, 189-201

Abstract: An analytical and numerical study of transmission of radiation through a multi-mode waveguide containing a random medium with a complex dielectric constant ε = ε′ + iε″ is presented. 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 either numerical simulations.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:236:y:1997:i:3:p:189-201

DOI: 10.1016/S0378-4371(96)00387-1

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