Localization in a disordered multimode waveguide with absorption or amplification
Abstract
An analytical and numerical study of transmission of radiation through a multimode waveguide containing a random medium with a complex dielectric constant ɛ = ɛ‧ + iɛ″ is presented. Depending on the sign of ɛ″, the medium is absorbing or amplifying. The transmitted intensity decays exponentially ∝ exp( L/ ξ) as the waveguide length L → ∞, regardless of the sign of ɛ″. 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 FokkerPlanck approach of Dorokhov, Mello, Pereyra and Kumar to nonunitary scattering matrices. Asymptotically exact results are obtained for N≫1 and  σ≫1/ N^{2}l. An approximate interpolation formula for all σ agrees reasonably well either numerical simulations.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 February 1997
 DOI:
 10.1016/S03784371(96)003871
 arXiv:
 arXiv:condmat/9607118
 Bibcode:
 1997PhyA..236..189M
 Keywords:

 Condensed Matter
 EPrint:
 13 pages, RevTeX, 1 postscript figure