We present a detailed, microscopic transport theory for light in strongly scattering disordered systems whose constituent materials exhibit linear absorption or gain. Starting from Maxwell's equations, we derive general expressions for transport quantities such as energy transport velocity, transport mean free path, diffusion coefficient, and absorption/gain length. The approach is based on a fully vectorial treatment of the generalized kinetic equation and utilizes an exact Ward identity (WI). While for loss-and gainless media the WI reflects local energy conservation, the effects of absorption or coherent gain are implemented exactly by novel, additional terms in the WI. As a result of resonant (Mie) scattering from the individual scatterers, all transport quantities acquire strong, frequency-dependent renormalizations, which are, in addition, characteristically modified by absorption or gain. We illustrate the influence of various experimentally accessible parameters on these quanitities for dilute systems. The transport theory presented here may set the stage for a theory of Random Lasing in three-dimensional disordered media.PACS numbers:
We present a detailed discussion of scalar wave propagation and light intensity transport in three-dimensional random dielectric media with optical gain. The intrinsic length and time scales of such amplifying systems are studied and comprehensively discussed as well as the threshold characteristics of single-and two-particle propagators. Our semianalytical theory is based on a self-consistent Cooperon resummation, representing the repeated self-interference, and incorporates as well optical gain and absorption, modeled in a semianalytical way by a finite imaginary part of the dielectric function. Energy conservation in terms of a generalized Ward identity is taken into account.
We present a systematical theory for the interplay of strong localization effects and absorption or gain of classical waves in 3-dimensional, disordered dielectrics. The theory is based on the selfconsistent Cooperon resummation, implementing the effects of energy conservation and its absorptive or emissive corrections by an exact, generalized Ward identity. Substantial renormalizations are found, depending on whether the absorption/gain occurs in the scatterers or in the background medium. We find a finite, gain-induced correlation volume which may be significantly smaller than the scale set by the scattering mean free path, even if there are no truly localized modes. Possible consequences for coherent feedback in random lasers as well as the possibility of oscillatory in time behavior induced by sufficiently strong gain are discussed.
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