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Emission fluctuations at the threshold.: (a) Fluctuation coefficient (f) for DCM dye solution, DCM dye doped DNA-CTMA film and pump. (b) Statistical distribution of FWHM for dye solution. (c) Statistical distribution of intensity. Both distributions expressed as relative frequency so as to insure the integral equals unity.
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Intensity fluctuations in lasers are commonly studied above threshold in some special configurations (especially when emission is fed back into the cavity or when two lasers are coupled) and related with their chaotic behaviour. Similar fluctuating instabilities are usually observed in random lasers, which are open systems with plenty of quasi-mode...
Citations
... However, the phenomenon is analyzed as an inaccurate result due to the instability of the system brought on by the precipitation of TiO 2 nanoparticles, which is confirmed by the observation of RSB in an anti-precipitation modified TiO 2 colloidal-based RL [7]. Furthermore, Basak et al. report that RSB can be observed in both dye-doped solid and liquid RL and explain it based on the intrinsic properties of dyes, which seems to indicate that RSB is robust in a dye-doped RL [8]. Meanwhile, Tommasi et al. reported the robustness of RSB in RL as well and proposed that RSB can be recognized as a marker of threshold [9]. ...
Replica symmetry breaking (RSB) has been introduced in a random laser to investigate the interactions between disorder and fluctuations. In this work, the dynamic difference between four non-energy transfer and Förster resonance energy transfer (FRET)-assisted random laser systems is investigated based on RSB. It is found that FRET is one of the key factors influencing RSB, and it is demonstrated that RSB in a random laser is not robust. This dynamic difference can be attributed to the different disorders induced by the gain mechanism in different random laser systems. This provides experimental evidence and theoretical support for the classification feasibility of RL with different emission mechanisms employing RSB.
... The typical RL configuration consists of a disordered distribution of scattering centers in a gain medium under pulsed pumping. This open configuration is inherently prone to spectral and spatial fluctuations and, in fact, under certain conditions, these fluctuations have been described in terms of the Parisi overlap function (non-trivial equilibrium properties of disordered systems) [14,15]. Such kinds of fluctuations are associated with the intrinsic disorder of RLs that triggers frustration and should not be mistaken for chaotic behavior where equal response is always elicited by equal stimuli. ...
Random lasers represent a relatively undemanding technology for generating laser radiation that displays unique characteristics of interest in sensing and imaging. Furthermore, they combine the classical laser’s nonlinear response with a naturally occurring multimode character and easy fabrication, explaining why they have been recently proposed as ideal elements for complex networks. The typical configuration of a random laser consists of a disordered distribution of scattering centers spatially mixed into the gain medium. When optically pumped, these devices exhibit spectral fluctuations from pulse to pulse or constant spectra, depending on the pumping conditions and sample properties. Here, we show clear experimental evidence of the transition from fluctuating (uncorrelated) to persistent random laser spectra, in devices in which the gain material is spatially separated from the scattering centers. We interpret these two regimes of operation in terms of the number of cavity round trips fitting in the pulse duration. Only if the cavity round-trip time is much smaller than the pulse duration are modes allowed to interact, compete for gain, and build a persisting spectrum. Surprisingly this persistence is achieved if the pumping pulse is long enough for radiation in the cavity to perform some 10 round trips. Coupled-mode theory simulations support the hypothesis. These results suggest an easy yet robust way to control mode stability in random lasers and open the pathway for miniaturized systems, as, for example, signal processing in complex random laser networks.
... Moreover, the pump power of the RL would also play an important role in the evolution of the statistics of the order parameter q. The continuous increase of pump power above the laser threshold leads to the profile broadening of the probability distribution function (PDF) of the order parameter q [25,26]. Apart from the pump power, different feedback mechanisms have been demonstrated to enable the occurrence of RSB with distinct photonic spin glass behaviors in Brillouin random fiber laser (BRFL) [21], which shows that the presence or absence of RSB caused by different feedback mechanisms is related to the stability and couple of the lasing modes in RFLs. ...
In this paper, we propose and demonstrate an all-optical control of RSB transition in a multi-wavelength Brillouin random fiber laser (MWBRFL). Multi-order Stokes light components can be subsequently generated by increasing the power of the Erbium-doped fiber amplifier (EDFA) inside the MWBRFL, providing additional disorder as well as multiple Stokes-involved interplay. It essentially allows diversified laser mode landscapes with adjustable average mode lifetime and random mode density of the 1st order Stokes, which benefits the switching between replica symmetry breaking (RSB) and replica symmetry (RS) states in an optically controlled manner. Results show that the average mode lifetime of the 1st order Stokes component gradually decreases from 250.0 ms to 1.2 ms as high orders from the 2nd to the 5th of Stokes components are activated. Meanwhile, the order parameter q of the 1st order Stokes random lasing emission presents distinct statistical distributions within the selective sub-window under various EDFA optical powers. Consequently, all-optical dynamical control of the 1st Stokes random laser mode landscapes with adjustable average mode lifetime turns out to be attainable, facilitating the RSB transition under an appropriate observation time window. These findings open a new avenue for exploring the underlying physical mechanisms behind the occurrence of the RSB phenomenon in photonic complex systems.
... By utilizing the replica method of spin-glass theory, the Parisi overlap between the pulse-to-pulse fluctuations in RLs within a framework of macroscopical observation was carried out whilst its distribution function provides evidence of a transition to a glassy light phase compatible with RSB. Subsequently, the RSB in a variety of RL systems has been discovered, including solid-state lasers [12,20], dye lasers [21], liquid-state lasers [22], liquid crystal lasers [23], semiconductor lasers [24], fiber lasers [25][26][27][28][29], etc., albeit with omission of any micro-state evolution. ...
Replica symmetry breaking (RSB), as a featured phase transition between paramagnetic and spin glass state in magnetic systems, has been predicted and validated among random laser-based complex systems, which involves numerous random modes interplayed via gain competition and exhibits disorder-induced frustration for glass behavior. However, the dynamics of RSB phase transition involving micro-state evolution of a photonic complex system have never been well investigated. Here, we report experimental evidence of transient RSB in a Brillouin random fiber laser (BRFL)-based photonic system through high-resolution unveiling of random laser mode landscape based on heterodyne technique. Thanks to prolonged lifetime of activated random modes in BRFLs, an elaborated mapping of time-dependent statistics of the Parisi overlap parameter in both time and frequency domains was timely resolved, attributing to a compelling analogy between the transient RSB dynamics and the random mode evolution. These findings highlight that BRFL-based systems with flexible harness of a customized photonic complex platform allow a superb opportunity for time-resolved transient RSB observation, opening new avenues in exploring fundamentals and application of complex systems and nonlinear phenomena.
... So, there has been a trend of searching for possible RSB in liquid phases where the system can be taken to be identical throughout the duration of observation. Although only a few reports of RSB in liquid phases have recently appeared [29][30][31][32], RSB in a plasmonic nanoparticle-based liquid RL system has not been reported yet. ...
Plasmonic random lasers have drawn significant attention recently due to their versatility, low threshold, and the possibility of achieving tunable and coherent/incoherent outputs. However, in this Letter, the phenomenon of replica symmetry breaking is reported in intensity fluctuations of a rarely used colloidal plasmonic random laser (RL) illumination. Triangular nanosilver scatter particles produced incoherent RL action when used in a dimethylformamide (DMF) environment in a Rhodamine-6G gain medium. The use of gold-coated triangular nanosilver as the scatterer in place of triangular nanosilver offered a dual contribution of scattering and lower photo-reabsorption, which caused a reduction in the lasing threshold energy of 39% compared to that obtained with the latter. Further, due to its long-term photostability and chemical properties, a phase transition from the photonic paramagnetic to the glassy phase is observed experimentally in the RL system used. Interestingly, the transition occurs at approximately the lasing threshold value, which is a consequence of stronger correlation of modal behaviors at high input pump energies.
... On the other hand, RLs have been employed as photonic * Corresponding author: palaciosg226@gmail.com platforms to advance the understanding of a number of complex systems behaviors, including Lévy statistics and extreme value events [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], turbulence [53][54][55], and the replica symmetry breaking (RSB) phenomenon [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73]. In particular, the use of RLs as actual systems to probe theoretical predictions from Parisi's RSB analysis [74][75][76][77] of disordered complex systems (such as magnetic spin glasses) can be regarded as an outstanding scientific achievement [78,79]. ...
... On the experimental side, the RSB phenomenon had its first demonstration in the glassy phase of a two-dimensional amorphous solid-state RL material [64]. Subsequently, the RSB behavior was reported as well in diverse photonic systems [65][66][67][68][69][70][71][72][73]. ...
... where g (2) k 1 ,k 2 and g (4) k 1 ,k 2 ,k 3 ,k 4 denote complex quadratic and quartic couplings, respectively, among overlapping slowamplitude modes {a k }, with the latter related to the nonlinear optical χ (3) susceptibility (see, e.g., [56,91]). The semiclassical approximation is related to the regime with a high density of photons, which represents the case of interest in the present work and also corresponds to the experimental situation considered, e.g., in [64][65][66][67][68][69][70][71][72][73]. We also comment that the interactions between modes in a nonlinear optical system can generally give rise to phenomena such as energy transfer between modes and excitation of new modes due to nonlinear interactions. ...
We investigate the replica symmetry breaking (RSB) phenomenon in random lasers (RLs) through Monte Carlo simulations employing photonic random walkers that diffuse and get randomly scattered in the active medium. The walkers interact not only with the population of excited atoms, but also among themselves, in a mean-field-type approach based on the Langevin equation for the stochastic dynamics of RL modes. We obtain the proper profile of the distribution P(q) of the Parisi overlap parameter in the RSB glassy phase, with two pronounced side maxima at q=±1 above the RL threshold, in contrast with some recent numerical studies. Remarkably, when the interactions among photonic walkers are not included, a replica-symmetric profile with a single maximum of P(q) at q=0 is found for any excitation energy. We further study the Gaussian and Lévy emission regimes and statistical correlations of intensity fluctuations in distinct modes of the same spectrum, using a Pearson correlation coefficient recently applied to RLs. Our findings are consistent with experimental results for the intensity statistics and P(q) distributions in RL materials.
... In the last years experiments on a certain class of random lasers provided evidence of particularly non-trivial correlations between the shot-to-shot fluctuations of the emission spectra. We will refer to those as glassy random lasers [13,[28][29][30][31][32]. These special correlations are predicted by a theory based on statistical mechanics of complex disordered systems [33][34][35]. ...
... From the point of view of statistical mechanics of complex disordered systems, random lasers represent, so far, the only physical system where the relevant degrees of freedom, namely the complex amplitudes of the light modes, naturally form a dense interaction network of the kind for which replica symmetry breaking mean-field theory [42] is proved to work, as in high dimension spin-glasses or structural glasses made of hard spheres [43]. It is not by chance that random lasers are, so far, the only complex disordered system providing experimental evidence of a continuous replica symmetry-breaking pattern [13,[28][29][30][31][32]. Actually, mean-field theory for an infinite number of replica symmetry breakings has rigorously been derived [44,45] only for fully connected systems, including the random laser model in the narrow-band approximation [33,38]. ...
By means of enhanced Monte Carlo numerical simulations parallelized on GPUs we study the critical properties of the spin-glass-like model for the mode-locked glassy random laser, a 4 4 -spin model with complex spins with a global spherical constraint and quenched random interactions. Implementing two different boundary conditions for the mode frequencies we identify the critical points and the critical indices of the random lasing phase transition with finite size scaling techniques. The outcome of the scaling analysis is that the mode-locked random laser universality class is compatible with a mean-field one, though different from the mean-field class of the Random Energy Model and of the glassy random laser in the narrow band approximation, that is, the fully connected version of the present model. The low temperature (high pumping) phase is finally characterized by means of the overlap distribution and evidence for the onset of replica symmetry breaking in the lasing regime is provided.
... A careful investigation of how magnitude localization coexists with RSB in disordered systems is therefore a gap that needs to be filled. Some signatures of strong breaking of intensity equipartition have been already highlighted in [25] as features of the emission spectra of glassy random lasers at high pumping [26][27][28][29][30][31][32]. By means of numerical simulations on a slightly different model for random lasers with respect to the one of [25], we will now deepen the study of such phenomenology and we will connect it with the most recent literature on intensity localization in systems with locally unbounded variables and global constraints [17,18,[33][34][35]. ...
Evidence of an emergent pseudo-localized phase characterizing the low-temperature replica symmetry breaking phase of the complex disordered models for glassy light is provided in the mode-locked random laser model. A pseudo-localized phase corresponds to a state in which the intensity of light modes is neither equipartited among all modes nor strictly condensed on few of them. Such a hybrid phase, recently characterized as a finite size effect in other models, such as the discrete non-linear Schrödinger equation, in the low temperature phase of the glassy random laser appears to be robust in the limit of large size.
... It reveals the nonlinear interactions between RL quasimodes frustrated by disorder [7]. In 2016 [11], S. Basak et al. showed that the RL system can enters the RSB regime at a narrow range around the threshold, where the phase state in the system will transfer to spin-glass phase from paramagnetic phase. In the same year [12], a phase transition from the paramagnetic phase to the spin-glass phase was observed in the modified colloidal RL by P. I. Pincheira et al., who recognized the RSB as a sign of colloidal-based RL threshold. ...
Replica symmetry breaking (RSB) has been widely recognized as a statistical analysis approach to understand the disorder and nonlinear interactions in complex systems ranging from atoms to the cosmic scale. However, it is challenging to analyze the nonlinear optical characteristics of random laser (RL) in disordered gain medium via RSB due to the lack of a general RSB-based statistical analysis framework. In this work, we report the tunable RSB in polymer fiber RL, where the effects of temperature and different structures on RSB are investigated experimentally and theoretically. It experimentally proves that RSB in RL is not robust, and disorder and temperature are responsible for tunable RSB in RL, which contributes to the improvement of the statistical analysis framework for investigating the optical principles of RL using RSB. And the finding of the tunable RSB allows to investigate the dynamical differences for various RL systems, which broadens the directions for the use of spin-glass theory to explore the physical mechanism of RL.
... RLs and RFLs, described as open complex photonic systems, have been recently employed as successful platforms to access nontrivial complex phases, such as equilibrium spin glasses [29][30][31][32][33][34][35][36] and turbulent regimes [37][38][39][40], as theoretically justified in [38][39][40][41][42] (for more details, we refer the reader to Chapters 5-7 of this book). In the erbium-doped RFL studied in the present work, disorder was introduced by inscribing a remarkable amount (∼10 3 ) of specially designed stationary (i.e., quenched) random Bragg gratings [43] in the fiber core. ...
... On the experimental side, the equilibrium photonic spin glass phase with RSB properties was first demonstrated in an amorphous solid-state RL [29] (see, also, Refs. [30][31][32][33][34][35][36] for more photonic experimental examples of such phase). Actually, the work by Ghofraniha and collaborators [29] constituted the first direct empirical evidence of the RSB phenomenon in any actual physical system (see, also, Chapter 6). ...
... Therefore, the photonic RSB spin-glass transition is established when the parameter q max , corresponding to the position of the maximum of P (|q|), shifts from zero to ≈1 as the pump intensity increases, a value that generally saturates for excitation powers P well above the threshold power P th . In addition to the first experimental demonstration of photonic RSB spin-glass phase in a RL system, more recently other experimental evidences of equilibrium photonic RSB spin glass phase have been also reported in several disordered materials [30][31][32][33], including the erbium-based RFL [34][35][36]. ...
