Theory of strong localization effects of light in disordered loss or gain media

Abstract

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.

Random nanolasing in the Anderson localized regime

“…In a conservative one-dimensional single-mode waveguide, the Anderson localization criterion requires that the average distance between random scattering events, the localization length j, is shorter than the sample length L, and their ratio universally determines the confinement of the localized modes. The presence of absorption or gain changes this simple picture, beacuse they will respectively damp or enhance the localized modes 20 , and may give rise to nonlinearities 21 . In the present experiment, for low excitation pump power, the fluorescence emitted by the excited region of the quantum wells is multiply scattered along the waveguide, but is damped due to the strong absorption of the unpumped surrounding gain material, as shown in Fig.…”

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.…”

Light transport and correlation length in a random laser

“…where the non-critical numerator N P is given explicitly in [31] and is not relevant for this discussion. The denominator, however, exhibits the typical diffusion pole structure in a non-conserving system, i. e. featuring a so-called mass term iγ a = iξ −2 a D, which may have either positive or negative sign.…”

“…The spatial arrangement of the scatterers is described through the function V ( r )= R S R ( r − R ), with S R ( r ) a localized shape function at random locations R. Linear gain (absorption) is described by a temporally constant, negative (positive) imaginary part of b and/or s . In [30][31][32] we have developed a theory for light transport in disordered media with linear gain or absorption. The result is the diffusion pole structure of the energy-density correlation function in Fourier space P ω E (Q, Ω).…”