Theory of light diffusion in disordered media with linear absorption or gain

Lubatsch, Andreas; Kroha, Johann; Busch, Kurt

doi:10.1103/physrevb.71.184201

Cited by 45 publications

(57 citation statements)

References 57 publications

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“…An equivalent law for RL is missing. Nevertheless various issues (like the statistical properties and the link with spin-glass theory [9,13,14,15,16,17]), were theoretically analysed, while the leading model (quantitatively compared with experiments) is that based on the light-diffusion approximation [18,19,20,21], which however overlooks the ondulatory character of the involved photons. Within a different perspective, RL is due to several localized electromagnetic (EM) states put into oscillations in a disordered environment (as, e.g., in [9,17,22,23]).…”

Section: Pacs Numbersmentioning

confidence: 99%

Condensation in Disordered Lasers: Theory,3D+1Simulations, and Experiments

et al. 2008

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The complex processes underlying the generation of a coherent-like emission from the multiplescattering of photons and wave-localization in the presence of structural disorder are still mostly un-explored. Here we show that a single nonlinear Schroedinger equation, playing the role of the Schawlow-Townes law for standard lasers, quantitatively reproduces experimental results and threedimensional time-domain parallel simulations of a colloidal laser system. PACS numbers:Random lasers (RL) are a rapidly growing field of research, with implications in soft-matter physics, light localization and photonic devices [1,2]. Since the pioneering investigations [3,4], different groups reported on experimental observations, from paint pigments to human tissue [5,6,7,8,9]. In all of these cases a coherent-like narrow spectral line emerges from the fluorescence as the pump energy is increased and, in some instances, several spectral peaks have been reported [9,10]. In standard single-mode lasers, without structural disorder, the emission linewidth is linked to the electromagnetic energy stored in the cavity by the so-called Schawlow-Townes (ST) law [11,12]. An equivalent law for RL is missing. Nevertheless various issues (like the statistical properties and the link with spin-glass theory [9,13,14,15,16,17]), were theoretically analysed, while the leading model (quantitatively compared with experiments) is that based on the light-diffusion approximation [18,19,20,21], which however overlooks the ondulatory character of the involved photons. Within a different perspective, RL is due to several localized electromagnetic (EM) states put into oscillations in a disordered environment (as, e.g., in [9, 17, 22, 23]). In this framework, it is expected that the number of involved modes increases with the pump energy and, correspondingly, the spectrum widens. However, exactly the opposite happens and this is also accompanied by the shortening of the emitted pulse [24,25,26]. In addition, the fact that strong (or Anderson) localization of light sustains the RL action is still debated. Ab-initio computational studies were limited to 1D and 2D geometries [27,28], not accounting for the critical character of three-dimensional (3D) localization [29]. Monte-Carlo simulations neglect interference effects [30,31,32]. Here we report on an original theoretical formulation; we quantitatively compare its predictions with experiments and with the first ever reported 3D+1 ab-initio MaxwellBloch simulations. We show that the RL linewidth is ruled by a nonlinear differential-equation, which is the equivalent of the ST-law, and is formally identical to the nonlinear Schroedinger, or Gross-Pitaevskii (GP), equation governing ultra-cold atoms [33]. There is hence a strict connection between photons in RL and ultra-cold bosons; the spectral narrowing observed in RL is thus ascribed to a condensation process [34] of the involved electromagnetic resonances. Simulations -We consider a vectorial formulation of the Maxwell-Bloch (MB) equations [35,36]. 21 nonl...

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Section: Pacs Numbersmentioning

confidence: 99%

Condensation in Disordered Lasers: Theory,3D+1Simulations, and Experiments

et al. 2008

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“…66 We briefly sketch the main results here. The electric field amplitude E ω (r) of an electromagnetic wave of frequency ω in a medium with random dielectric constant ǫ(r; ω) = ǫ(ω) + ∆ǫ(r; ω), obeys the wave equation 62) where ∆ǫ(r; ω) = 0.…”

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“…(1.41): 73) and a 1 and A are defined in Ref. 66 The quantity κ describes scattering caused by a mismatch of absorption/gain between the scattering objects and the medium.…”

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Self-Consistent Theory of Anderson Localization: General Formalism and Applications

Wölfle

Vollhardt

2010

Int. J. Mod. Phys. B

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The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered solids, the regimes of weak and strong localization are discussed. Then the scaling theory of the Anderson localization transition is reviewed. The renormalization group theory is introduced and results and consequences are presented. It is shown how scale-dependent terms in the renormalized perturbation theory of the inverse diffusion coefficient lead in a natural way to a self-consistent equation for the diffusion coefficient. The latter accounts quantitatively for the static and dynamic transport properties except for a region near the critical point. Several recent applications and extensions of the self-consistent theory, in particular for classical waves, are discussed.

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“…The treatment of light propagation starting from the wave equation has been mainly conducted via the self-consistent diagrammatic theory [20,21]. Interesting results, such as corrections to the bare diffusion coefficient due to the additional terms in the Ward identity [22,23] and dynamics of Anderson localization in quasi-one-dimensional geometry [24] and open threedimensional media [25] have been obtained by these * Corresponding author; ozaitsev@khu.ac.kr…”

Section: Introductionmentioning

confidence: 99%

Nonlinearσmodel for optical media with linear absorption or gain

Lai

Zaitsev

2012

Phys. Rev. A

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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.

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Theory of light diffusion in disordered media with linear absorption or gain

Cited by 45 publications

References 57 publications

Condensation in Disordered Lasers: Theory,3D+1Simulations, and Experiments

Condensation in Disordered Lasers: Theory,3D+1Simulations, and Experiments

Self-Consistent Theory of Anderson Localization: General Formalism and Applications

Nonlinearσmodel for optical media with linear absorption or gain

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