The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra

Observation of the photonic Hall effect and photonic magnetoresistance in random lasers

Modulation of scattering in random lasers (RLs) by magnetic fields has attracted much attention due to its rich physical insights. We fabricate magnetic gain polymer optical fiber to generate RLs. From macroscopic experimental phenomena, with the increase of the magnetic field strength, the magnetic transverse photocurrent exists in disordered multiple scattering of RLs and the emission intensity of RLs decreases, which is the experimental observation of photonic Hall effect (PHE) and photonic magnetoresistance (PMR) in RLs. At the microscopic level, based on the field dependence theory of magnetic disorder in scattered nanoparticles and the replica symmetry breaking theory, the magnetic-induced transverse diffusion of photons reduces the scattering disorder, and then decreases the intensity fluctuation disorder of RLs. Our work establishes a connection between the above two effects and RLs, visualizes the influence of magnetic field on RL scattering at the microscopic level, which is crucial for the design of RLs.

Random laser emission from neodymium doped alumina lead-germanate glass powder

Random lasing is reported for the first time, to our knowledge, in neodymium doped alumina lead-germanate (GPA) glass powder. The samples were fabricated by a conventional melt-quenching technique at room temperature, and x-ray diffraction was used to confirm the amorphous structure of the glass. Powders with average grain size of about 2 µm were prepared by grinding the glass samples and using sedimentation in isopropyl alcohol to remove the coarsest particles. The sample was excited using an optical parametric oscillator tuned to 808 nm, in resonance with the neodymium ion (N d ³⁺) transition ⁴ I _9/2→{⁴ F _5/2,² H _9/2}. Random laser (RL) emission at 1060 nm (N d ³⁺ transition: ⁴ F _3/2→⁴ I _11/2) was observed for an energy fluence excitation threshold (E F E _{r m t h} ) of about 0.3m J/m m ². Above the E F E _{t h} , a short RL pulse in the nanosecond range is observed, corroborating the lasing process. Contrary to what one might suppose, the use of large quantities of neodymium oxide (10% wt. of N d ₂ O ₃) in the GPA glass, which leads to luminescence concentration quenching (LCQ), is not a disadvantage, once stimulated emissions (RL emission) occur faster than the nonradiative energy-transfer time among N d ³⁺ ions responsible for the LCQ.

Random lasing and replica symmetry breaking in GeO2-PbO-MgO glass–ceramics doped with neodymium

We investigated the random lasing process and Replica Symmetry Breaking (RSB) phenomenon in neodymium ions (Nd³⁺) doped lead-germanate glass–ceramics (GCs) containing MgO. Glass samples were fabricated by conventional melt-quenching technique and the GCs were obtained by carefully devitrifying the parent glasses at 830 °C for different time intervals. The partial crystallization of the parent glasses was verified by X-ray diffraction. Photoluminescence (PL) enhancement of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx$$\end{document}≈ 500% relative to the parent glasses was observed for samples with a higher crystallinity degree (annealed during 5 h). Powders with grains having average size of 2 µm were prepared by griding the GCs samples. The Random Laser (RL) was excited at 808 nm, in resonance with the Nd³⁺ transition ⁴I_9/2 → {⁴F_5/2, ²H_9/2}, and emitted at 1068 nm (transition ⁴F_3/2 → ⁴I_11/2). The RL performance was clearly enhanced for the sample with the highest crystallinity degree whose energy fluence excitation threshold (EFE_th) was 0.25 mJ/mm². The enhanced performance is attributed to the residence-time growth of photons inside the sample and the higher quantum efficiency of Nd³⁺ incorporated within the microcrystals, where radiative losses are reduced. Moreover, the phenomenon of Replica Symmetry Breaking (RSB), characteristic of a photonic-phase-transition, was detected by measuring the intensity fluctuations of the RL emission. The Parisi overlap parameter was determined for all samples, for excitation below and above the EFE_th. This is the first time, for the best of the authors knowledge, that RL emission and RSB are reported for a glass–ceramic system.

Stabilizing Brillouin random laser with photon localization by feedback of distributed random fiber grating array

Strong scattering random media can localize light and extend photon lifetime through multiple scattering, which offers opportunities for stabilizing random lasers. Here, we demonstrate a frequency stabilized Brillouin random laser with high coherence enabled by photon localization in random fiber grating array (RFGA). Photon trapping is realized due to wave interference in multi-scattering Fabry-Pérot (FP) cavities between random fiber gratings enabling light localization to prolong photon lifetime. The formation of the high finesse peaks of RFGA suppresses multi-longitudinal modes, which offers single-mode operation at high pump power. The RFGA distributed feedback-based Brillouin random fiber laser (BRFL) maintains a small frequency drift with the pump laser (a phase-locked laser with a linewidth of 100 Hz) at 51 kHz/s for a total change of 620 kHz over 12 s. Note there is no locking between the two lasers, and the beat frequency is measured by the optical heterodyne method. The correlation coefficient change of the measured optical beat frequency is maintained at 4.5%. This indicates that the BRFL is capable of maintaining a small optical frequency difference with the phase-locked pump laser over 12 s thanks to the RFGA capable of trapping photons in the same path, which is a remarkable feature for a random fiber laser. Furthermore, we confirm the single-mode lasing with a long lifetime in the stabilizing BRFL by the replica symmetry behavior and ultralow intensity noise at high pump power. Our findings explore a new approach to stabilize the frequency of Brillouin random lasers passively without commonly used active phase locking laser themes, which makes a simple and cost-effective system.

Direct Measurement of the Reduced Scattering Coefficient by a Calibrated Random Laser Sensor

The research in optical sensors has been largely encouraged by the demand for low-cost and less or non-invasive new detection strategies. The invention of the random laser has opened a new frontier in optics, providing also the opportunity to explore new possibilities in the field of sensing, besides several different and peculiar phenomena. The main advantage in exploiting the physical principle of the random laser in optical sensors is due to the presence of the stimulated emission mechanism, which allows amplification and spectral modification of the signal. Here, we present a step forward in the exploitation of this optical phenomenon by a revisitation of a previous experimental setup, as well as the measurement method, in particular to mitigate the instability of the results due to shot-to-shot pump energy fluctuations. In particular, the main novelties of the setup are the use of optical fibers, a reference sensor, and a peristaltic pump. These improvements are devoted to: eliminating optical beam alignment issues; improving portability; mitigating the variation in pump energy and gain medium performances over time; realizing an easy and rapid change of the sensed medium. The results showed that such a setup can be considered a prototype for a portable device for directly measuring the scattering of liquid samples, without resorting to complicated numerical or analytic inversion procedures of the measured data, once the suitable calibration of the system is performed.

High efficiency Brillouin random fiber laser with replica symmetry breaking enabled by random fiber grating

We report a high efficiency Brillouin random fiber laser (BRFL) enabled by a random fiber grating (RFG) with demonstration of replica symmetry breaking (RSB). The RFG was characterized by optical coherence tomography (OCT) method, which measured the spatially resolved reflectivity of RFG by a tunable delay line. Multiple narrow linewidth peaks appeared in reflection spectrum of RFG, created by frozen scattering centers acting as narrow linewidth filters to select random modes in random fiber lasers based on Brillouin gain. With the scattering from RFG as disordered feedback, a BRFL with slope efficiency of 29.3% and lasing threshold of 10.2 mW was demonstrated with 1 kHz linewidth. Intensity dynamics show that RFG can reduce the noise of BRFL with a symmetric phase portrait, indicating the increased mean path length and coherence time of the Stokes photons. The probability distribution of the Parisi overlap parameter of intensity fluctuation spectra from trace to trace reveal a photonic spin-glass phase with RSB in the RFG enabled BRFL, providing a photonic platform to study the photon glassy behavior of random fiber lasers.

Replica Symmetry Breaking in a Weakly Scattering Optofluidic Random Laser

We report the observation of replica symmetry breaking (RSB) in a weakly scattering optofluidic random laser (ORL). Coherent random lasing is indicated by the presence of narrow peaks rising out of the spectral background. This coherence helps to identify a random laser threshold, which is expected to be gradual with weak scattering. We find that lasing action initiated using optical pulsed pumping coincides with the onset of both RSB and Lévy flight statistics. However, the transition from the photonic paramagnetic to photonic glass phase is more subtle in that the Parisi overlap function broadens instead of completely changing shape. This subtlety is balanced by an accompanying result of identical experimental conditions giving rise to lasing or no lasing depending on the shot. Additional statistical calculations and investigations into the fundamental physical mechanisms present in the ORL support this conclusion. Using simple numerical models, we study the critical spectral properties required for RSB to occur, as indicated by the Parisi overlap function. The simplicity of the models helps demonstrate the sensitive nature of this tool and the necessity of additional verification of the physical mechanisms present in the experiment.

Theoretical investigations of power fluctuations statistics in Brillouin erbium-doped fiber lasers

We present theoretical investigations including simulations and statistical analyses on the fluctuations of the temporal output power in a Brillouin erbium-doped fiber laser. The generation of even Stokes waves up to the 5^th order is considered by solving coupled-mode equations including SBS and Kerr nonlinearities. It is demonstrated that by increasing the EDFA pump power and generating a few orders of Stokes waves in such a laser, there are strong power fluctuations and rogue events are expected. Transition from Gaussian-like to levy-like regime is described as the power is increased from threshold resulting in the initial Stokes wave generation to well beyond threshold generating 5 effective even Stokes waves. Accordingly, phase portraits confirm increasing fluctuations as a function of the power. It is also shown that at the SBS lasing threshold, the output signals have the maximum correlation over replicas in round trips, nevertheless by enhancing the power, the correlation diminishes, which results in a full symmetry breaking and the system radiates in a chaotic manner and exhibits random laser behavior.

Evidence of a Floquet Phase in a Photonic System

The ground breaking extension of the key concept of phase structure to nonequilibrium regimes was only recently achieved in Floquet systems, characterized by a time-dependent quantum Hamiltonian with a periodic driving source. However, despite the theoretical advances, only very few systems are known to display experimental Floquet phases, not one of them employing a laser emission-based mechanism. Here we report the first experimental observation of a Floquet phase in a photonic system, a disordered fiber laser with spatial eigenmode localization. We apply a periodically oscillating cw pumping source that drives the random couplings of the Floquet Hamiltonian. A photonic Floquet spin-glass phase is demonstrated in the random-lasing regime by extensive measurements of the Parisi overlap parameter and asymmetry properties of its distribution. In contrast, in the fluorescent regime below threshold, the absence of mode localization prevents the stabilization of a Floquet phase. Our results are nicely described by theoretical arguments.

Coexistence of turbulence-like and glassy behaviours in a photonic system

Coexistence of physical phenomena can occur in quite unexpected ways. Here we demonstrate the first evidence in any physical system of the coexistence in the same set of measurements of two of the most challenging phenomena in complex systems: turbulence and spin glasses. We employ a quasi-one-dimensional random fibre laser, which displays all essential ingredients underlying both behaviours, namely disorder, frustration and nonlinearity, as well as turbulent energy cascades and intermittent energy flux between fluctuation scales. Our extensive experimental results are theoretically supported by a newly defined photonic Pearson correlation coefficient that unveils the role of the intermittency and describes remarkably well both the spin-glass Parisi overlap parameter and the distribution of turbulent-like intensity increments. Our findings open the way to unravel subtle connections with other complex phenomena, such as disordered nonlinear wave propagation, Lévy statistics of intensity fluctuations, and rogue waves.

Bunimovich Stadium-Like Resonator for Randomized Fiber Laser Operation

A silica resonator was demonstrated for random laser generation. The resonator consisted of a conventional microsphere fabricated in an optical fiber tip through electric arc discharge, and modifications to its geometry were carried out to create asymmetry inside the silica structure. The resulting Bunimovich stadium-like microsphere promotes multiple reflections with the boundaries, following the stochastic properties of dynamic billiards. The interference of the multiple scattered beams generates a random signal whose intensity was increased by sputter-coating the microstadium with a gold thin film. The random signal is amplified using an erbium-doped fiber amplifier (EDFA) in a ring cavity configuration with feedback, and lasing is identified as temporal and spectral random variations of the signal between consecutive measurements.

Observation of replica symmetry breaking in disordered nonlinear wave propagation

A landmark of statistical mechanics, spin-glass theory describes critical phenomena in disordered systems that range from condensed matter to biophysics and social dynamics. The most fascinating concept is the breaking of replica symmetry: identical copies of the randomly interacting system that manifest completely different dynamics. Replica symmetry breaking has been predicted in nonlinear wave propagation, including Bose-Einstein condensates and optics, but it has never been observed. Here, we report the experimental evidence of replica symmetry breaking in optical wave propagation, a phenomenon that emerges from the interplay of disorder and nonlinearity. When mode interaction dominates light dynamics in a disordered optical waveguide, different experimental realizations are found to have an anomalous overlap intensity distribution that signals a transition to an optical glassy phase. The findings demonstrate that nonlinear propagation can manifest features typical of spin-glasses and provide a novel platform for testing so-far unexplored fundamental physical theories for complex systems.

Replica Symmetry Breaking in the Photonic Ferromagneticlike Spontaneous Mode-Locking Phase of a Multimode Nd:YAG Laser

We demonstrate the replica symmetry breaking (RSB) phenomenon in the spontaneous mode-locking regime of a multimode Q-switched Nd:YAG laser. The underlying mechanism is quite distinct from that of the RSB recently observed in random lasers. Here, there is no random medium and the phase is not glassy with incoherently oscillating modes as in random lasers. Instead, in each pulse a specific subset of longitudinal modes are activated in a nondeterministic way, whose coherent oscillation dominates and frustrates the others. The emergence of RSB coincides with the onset of ultrashort pulse generation typical of the spontaneous mode-locking regime, both occurring at the laser threshold. On the other hand, when high losses are introduced, RSB is inhibited and only the amplified stimulated emission with replica symmetry is observed. Our results disclose the only theoretically predicted photonic phase with RSB that remained unobserved so far.

Temporal profiles for measuring threshold of random lasers pumped by ns pulses

The working threshold is an important parameter to assess the performance of cavity-free random lasers. Here, the temporal profile measurement is proposed as an alternative method to determine the thresholds of the surface plasmon based random lasers pumped by ns pulses based on analyzing the delay time (t Delay) and rising time (t R) of the emission signal. The obvious and slight inflection points of the curves of t Delay and t R varying with the pump power density are observed as indicators for the thresholds of random lasing and for the transition of lasing mode, respectively. The proposed method supplies consistent values to those supplied by traditional methods in frequency-domain for the random systems with different gain length. The demonstrated temporal profile approaches are free from the spectrometers and may be as a candidate for measuring the threshold of random lasers in ultrafast optics, nonlinear optics and bio-compatible optoelectronic probes.

Inverse problem for multi-body interaction of nonlinear waves

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable temperature-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems. The high versatility of the exposed techniques also concerns the number of expected interactions: results are presented for different graph topologies, ranging from sparse to dense graphs.

Robustness of replica symmetry breaking phenomenology in random laser

Random lasers are optical sources where light is amplified by stimulated emission along random paths through an amplifying scattering medium. Connections between their physics and the one of quenched disordered nonlinear systems, notably spin glasses, have been recently suggested. Here we report a first experimental study of correlations of spectral fluctuations intensity in a random laser medium where the scatterers displacement significantly changes among consecutive shots. Remarkably, our results reveal that the replica symmetry breaking (RSB) phenomenology is robust with respect to an averaging over different realizations of the disorder. Moreover, besides opening new intriguing questions about the understanding of such a phenomenon, this work aims to clarify the connection between the RSB with the onset of the Lévy regime, i.e. the fluctuations regime that is a peculiar feature of the random lasing under critical conditions. Our results suggest that the former occurs independently of the latter and then the RSB phenomenology is a generic feature linked to the random laser threshold.

Large fluctuations at the lasing threshold of solid- and liquid-state dye lasers

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-modes whose non orthogonality enables them to exchange energy and provides the sort of loss mechanism whose interplay with pumping leads to replica symmetry breaking. The latter however, had never been observed in plain cavity lasers where disorder is absent or not intentionally added. Here we show a fluctuating lasing behaviour at the lasing threshold both in solid and liquid dye lasers. Above and below a narrow range around the threshold the spectral line-shape is well correlated with the pump energy. At the threshold such correlation disappears, and the system enters a regime where emitted laser fluctuates between narrow, intense and broad, weak peaks. The immense number of modes and the reduced resonator quality favour the coupling of modes and prepares the system so that replica symmetry breaking occurs without added disorder.

Observation of photonic paramagnetic to spin-glass transition in a specially designed TiO2 particle-based dye-colloidal random laser

Colloidal-based random lasers (RLs) are highly efficient and have been exploited in a wide range of geometries. However, in the particular case of ethanol solutions of rhodamines and TiO₂ particles, the RL behavior is quite unstable due to the fast precipitation of the particles. In this Letter, specially designed amorphous TiO₂ particles were synthesized by a sol-gel method, preventing the degradation of the RL for long operating lifetimes of over 10⁵ shots. As a consequence, this modified colloidal RL allowed the observation of a clear replica-symmetry-breaking phase transition from the paramagnetic fluorescent to spin-glass RL behavior, which has not been observed in the system with nonfunctionalized TiO₂ particles.

Observation of Lévy distribution and replica symmetry breaking in random lasers from a single set of measurements

Random lasers have been recently exploited as a photonic platform for studies of complex systems. This cross-disciplinary approach opened up new important avenues for the understanding of random-laser behavior, including Lévy-type distributions of strong intensity fluctuations and phase transitions to a photonic spin-glass phase. In this work, we employ the Nd:YBO random laser system to unveil, from a single set of measurements, the physical origin of the complex correspondence between the Lévy fluctuation regime and the replica-symmetry-breaking transition to the spin-glass phase. A novel unexpected finding is also reported: the trend to suppress the spin-glass behavior for high excitation pulse energies. The present description from first principles of this correspondence unfolds new possibilities to characterize other random lasers, such as random fiber lasers, nanolasers and small lasers, which include plasmonic-based, photonic-crystal and bio-derived nanodevices. The statistical nature of the emission provided by random lasers can also impact on their prominent use as sources for speckle-free laser imaging, which nowadays represents one of the most promising applications of random lasers, with expected progress even in cancer research.

Observation of Lévy distribution and replica symmetry breaking in random lasers from a single set of measurements

Random lasers have been recently exploited as a photonic platform for studies of complex systems. This cross-disciplinary approach opened up new important avenues for the understanding of random-laser behavior, including Lévy-type distributions of strong intensity fluctuations and phase transitions to a photonic spin-glass phase. In this work, we employ the Nd:YBO random laser system to unveil, from a single set of measurements, the physical origin of the complex correspondence between the Lévy fluctuation regime and the replica-symmetry-breaking transition to the spin-glass phase. A novel unexpected finding is also reported: the trend to suppress the spin-glass behavior for high excitation pulse energies. The present description from first principles of this correspondence unfolds new possibilities to characterize other random lasers, such as random fiber lasers, nanolasers and small lasers, which include plasmonic-based, photonic-crystal and bio-derived nanodevices. The statistical nature of the emission provided by random lasers can also impact on their prominent use as sources for speckle-free laser imaging, which nowadays represents one of the most promising applications of random lasers, with expected progress even in cancer research.

Fiber-Type Random Laser Based on a Cylindrical Waveguide with a Disordered Cladding Layer

This letter reports a fiber-type random laser (RL) which is made from a capillary coated with a disordered layer at its internal surface and filled with a gain (laser dye) solution in the core region. This fiber-type optical structure, with the disordered layer providing randomly scattered light into the gain region and the cylindrical waveguide providing confinement of light, assists the formation of random lasing modes and enables a flexible and efficient way of making random lasers. We found that the RL is sensitive to laser dye concentration in the core region and there exists a fine exponential relationship between the lasing intensity and particle concentration in the gain solution. The proposed structure could be a fine platform of realizing random lasing and random lasing based sensing.