Nonlinearσmodel for optical media with linear absorption or gain

Abstract

In the framework of the Keldysh technique, we formulate the nonlinear sigma model for disordered optical media with linear absorption or gain. The effective action for fluctuations of the matrix field about the saddle point acquires an extra term due to the nonconservative nature of the system. We determine the disorder-averaged Green-function correlator, which has a diffusion pole modified by a finite absorption/gain rate. The diffusion coefficient is found to be close to its value for conservative systems in the relevant range of parameters. In the medium with gain, the random-lasing threshold depends on the sample size.

Hydrodynamic and field-theoretic approaches to light localization in open media

“…The interplay between internal reflection and wave interference may lead to very rich localization behavior. The other issue, effects of (linear) absorption and gain in random media has received considerable attention [6,7,83,167,168], but these works deal with infinite media. As far as realistic optical devices or experimental environments are concerned, one often deals with open media and this will lead to intriguing phenomena (for examples, see Refs.…”

“…There have been few attempts [4][5][6][7]83] of generalizing the replica field theory [84][85][86] and the Keldysh field theory [87] to classical wave systems. However, these studies [4][5][6][7]83] focus on infinite random media. For open systems some exact solutions for Q1D strong localization have been found by using the replica field theory [38].…”

“…As mentioned above, the hyperbolic nature of the metric stems from (i) the convergence of functional integral and (ii) the analytic structure of saddle points. To build a localization theory incorporating linear gain effects [83], one must inevitably treat both (i) and (ii), since now the sign of the convergence generating factor, δ, is reversed, i.e., ω + →ω − . As such, discussions parallel to those of Ref.…”

“…However, these studies [4][5][6][7]83] focus on infinite random media. For open systems some exact solutions for Q1D strong localization have been found by using the replica field theory [38].…”

“…There have been few attempts [4][5][6][7]83] of generalizing the replica field theory [84][85][86] and the Keldysh field theory [87] to classical wave systems. However, these studies [4][5][6][7]83] focus on infinite random media.…”