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

Abstract

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...

The mode-locking transition of random lasers

“…The simultaneous presence of structural disorder and nonlinearity makes these devices a fertile ground to connect photonics with advanced theoretical paradigms[2] like chaos [3], non Gaussian statistics[4], complexity [5] and also the physics of Bose Einstein condensation [6]. Historically there has been a bridge in the RL interpretation.…”

Non-locality and collective emission in disordered lasing resonators

“…We stress that recently, the problem of light condensation has been discussed by several authors, either with reference to dissipative systems (as lasers) 17,34 or Hamiltonian dynamics; [36][37][38] ; the validity of a GP-like (or purely real Ginzburg-Landau) equation to describe the spatial distribution of energy in experiments casts new light on the investigation of these effects, for which further theoretical work is needed and will be reported elsewhere.…”

“…25 Here, we will demonstrate that the change in the mode shape with H for a fixed disorder is due to a novel form of non-locality mediated by the mode-coupling between the open cavities constituting the set of involved resonators. 17,28 To date, spatial non-locality has been largely investigated in Hamiltonian nonlinear optical systems, but here we report the first evidence in a dissipative disordered medium.…”

“…11 RLs are among the most complex systems in photonics, encompassing structural disorder, nonlinearity, 12 strong nonlinear interaction 13 and different photon statistics 14 in systems ranging from micron-sized optical cavities 15 to kilometer-long fibers. 16 First-principles timedomain simulations show that the modes of a RL arise from localized electromagnetic states, [17][18][19] which may appear in a localized or an extended fashion. Several experiments have been reported on the nature of these modes, 15,[20][21][22] and these studies attempted to address the correlation between the structure and the degree of localization.…”

Triggering extreme events at the nanoscale in photonic seas

“…These range from extremely sensitive spectrometers based on speckles [36], to new sensing apparatus based on random light patterns randomly displaced in two dimensions [37], to low-threshold lasers sustained by randomly localized electromagnetic modes [38], and new energy harvesting devices relying on chaotic light motion [32].…”