Scalar wave propagation in random amplifying media: Influence of localization effects on length and time scales and threshold behavior

Abstract

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.

Coherent transport and symmetry breaking—laser dynamics of constrained granular matter

“…We use a diagrammatic field theory ansatz for light in a diffusive system including interferences, the Vollhardt-Wölfle theory of photons [18,19], which has proven to be rigorous for signatures of Anderson localization in non-linear random media [20]. Vollhardt-Wölfle ansatz precisely means that the modes we derive here are in their information value not restricted to the coherence of the wave, but that they additionally describe the coherence of transported light intensity and itʼs decay.…”

“…A B J here given in terms of the momenta: Φ ϵϵ equals the energy density and Φ ϵ J equals the energy current, while A and B are pre-factor terms derived in [18]. Starting with the renormalized scattering mean free path l s , the framework yields all relevant transport lengths and includes all interference effects.…”

“…Ω is the center of mass frequency and D is the self-consistently derived diffusion constant. c 1 , c 2 are coefficients explained in [18].…”

“…This is in contrast to previous work where the results were derived solely in momentum space for infinite sized systems. Here we follow methodologically the systematically outlined transport scheme in [18] but we additionally take into account the spatial dependence as denoted in equation (3) and displayed in figure 1: the sample shall be homogeneously pumped from above. Diffusive transport, especially interferences, occur preferentially on long paths in-plane of the large scaled random laser sample.…”

Optical properties of periodic, quasi-periodic, and disordered one-dimensional photonic structures

“…Myriads' of' possible' applications' arise' for' the' three' different' structures,' such' ,' as' photonic' crystal'lasers' [22,23]'and'quasicrystal'lasers' [24,25],'optical'fibers' [26,27],'and'sensors' [28][29][30],' when' concerning' photonic' crystals' and' quasicrystals.' Instead,' focussing' on' disordered' photonic'structures,'a'variety'of'interesting'features'have'been'discovered'in'different'fields,' as'random'lasing' [31][32][33][34][35][36][37],'diffuse'optical'imaging' [38],'and'light'harvesting'for'solar'devices' [39][40][41][42].' Many' physical' effects' have' been' observed' in' oneJdimensional' disordered' photonic' structures,' as' the' Anderson' localization' of' light' [43,44],' the' optical' Bloch' oscillations' and' necklace'states' [45][46][47][48],'and'an'interesting'oscillation'of'the'average'light'transmission'as'a' function'of'the'sample'length' [49].…”