Wave kinetics of random fibre lasers

Linewidth reduced cascaded Raman fiber lasers and their harmonic conversion for visible laser sources

Cascaded Raman Fiber Lasers (CRFLs) are wavelength versatile sources that can provide power at any wavelength in the Near-Infrared (NIR) region. Conventional CRFLs with broadband feedback are widely wavelength tunable but have broad line widths. A feedback mechanism must be used to reduce the broadening of the linewidth without compromising the wavelength tunability. Here, we propose to use a dual feedback mechanism that combines broadband feedback at all wavelengths, using a flat cleave, with filtered feedback at a desired wavelength due to a grating filter. This allows substantial linewidth reduction of CRFLs up to the 6th Raman shifts, from 1100 nm to 1500 nm, and can be extended further. Significantly reduced linewidth with multi-watt in-band output power is achieved with fine wavelength tuning within each Raman Stokes band using a fixed wavelength pump. As an application of linewidth narrowed output, we performed frequency doubling of CRFL output to generate over 100 mW of wavelength tunable yellow-green and yellow output with enhanced efficiency.

Interplay of Thermalization and Strong Disorder: Wave Turbulence Theory, Numerical Simulations, and Experiments in Multimode Optical Fibers

We address the problem of thermalization in the presence of a time-dependent disorder in the framework of the nonlinear Schrödinger (or Gross-Pitaevskii) equation with a random potential. The thermalization to the Rayleigh-Jeans distribution is driven by the nonlinearity. On the other hand, the structural disorder is responsible for a relaxation toward the homogeneous equilibrium distribution (particle equipartition), which thus inhibits thermalization (energy equipartition). On the basis of the wave turbulence theory, we derive a kinetic equation that accounts for the presence of strong disorder. The theory unveils the interplay of disorder and nonlinearity. It unexpectedly reveals that a nonequilibrium process of condensation and thermalization can take place in the regime where disorder effects dominate over nonlinear effects. We validate the theory by numerical simulations of the nonlinear Schrödinger equation and the derived kinetic equation, which are found in quantitative agreement without using any adjustable parameter. Experiments realized in multimode optical fibers with an applied external stress evidence the process of thermalization in the presence of strong disorder.

Kilowatt random Raman fiber laser with full-open cavity

Random Raman fiber laser (RRFL) has been widely studied in high-power laser generation due to its special lasing characteristics. However, all previous high-power results are based on the half-open cavity. In this letter, we demonstrate an applicable high-power RRFL with the simplest structure, that is, a full-open cavity. The lasing dynamic and output characteristics are theoretically and experimentally studied. Laser source with multi-longitudinal modes can result in the random laser output from one side even in the full-open cavity. The ratio of the backward output power is mainly determined by the reflectivity of fiber ends. The experimental results show that such a simple structure can easily generate kilowatts of random laser power and is a promising setup to achieve higher output power, which is also an important platform to study the laser dynamic in high-power full-open cavity without any point-action or regular distributed reflectors.

Spectral pedestal during the kilowatt-level amplification of a random fiber laser operating near the lasing threshold

The amplification of random fiber lasers (RFLs) attracts much attention due to their unique characteristics such as wavelength flexibility and low coherence. We present that, in the kilowatt-level amplification of RFL operating near its lasing threshold, a broad and flat spectral pedestal can co-exist with the narrow spectral peak of RFL. This phenomenon is different from the case in the amplification of fixed-cavity laser seeds. Time-domain measurements show that the broad and flat spectral pedestal, which extends to long wavelengths, is composed of temporal pulses, while few temporal pulses exist in the narrow spectral peak. We attribute the spectral pedestal to intensity fluctuations from the random seed laser and modulation instability in the amplification stage. Control experiments reveal that the working status of the random seed laser and the effective length of the amplifier can influence the spectral bandwidth. By taking advantage of this phenomenon, we propose a novel approach to achieve a high-power broadband light source through the amplification of RFLs operating near the lasing threshold.

Incoherent localized structures and hidden coherent solitons from the gravitational instability of the Schrödinger-Poisson equation

The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) equation accounting for the gravitational interaction. By increasing the amount of nonlinearity, the system self-organizes into a large-scale incoherent localized structure that contains "hidden" coherent soliton states: The solitons can hardly be identified in the usual spatial or spectral domains, but their existence can be unveiled in the phase-space representation (spectrogram). We develop a theoretical approach that provides the coupled description of the coherent soliton component [governed by the Schrödinger-Poisson equation (SPE)] and of the incoherent structure [governed by a wave turbulence Vlasov-Poisson equation (WT-VPE)]. We demonstrate theoretically and numerically that the incoherent structure introduces an effective trapping potential that stabilizes the hidden coherent soliton and we show that the incoherent structure belongs to a family of stationary solutions of the WT-VPE. The analysis reveals that the incoherent structure evolves in the strongly nonlinear regime and that it is characterized by a compactly supported spectral shape. By relating the analytical properties of the hidden soliton to those of the stationary incoherent structure, we clarify the quantum-to-classical (i.e., SPE-to-VPE) correspondence in the limit ℏ/m→0: The hidden soliton appears as the latest residual quantum correction preceding the classical limit described by the VPE. This study is of potential interest for self-gravitating Boson models of fuzzy dark matter. Although we focus our paper on the Schrödinger-Poisson equation, we show that the regime of hidden solitons stabilized by an incoherent structure is general for long-range wave systems featured by an algebraic decay of the interacting potential. This work should stimulate nonlinear optics experiments in highly nonlocal nonlinear (thermal) media that mimic the long-range nature of gravitational interactions.

Intracavity incoherent supercontinuum dynamics and rogue waves in a broadband dissipative soliton laser

Understanding dynamical complexity is one of the most important challenges in science. Significant progress has recently been made in optics through the study of dissipative soliton laser systems, where dynamics are governed by a complex balance between nonlinearity, dispersion, and energy exchange. A particularly complex regime of such systems is associated with noise-like pulse multiscale instabilities, where sub-picosecond pulses with random characteristics evolve chaotically underneath a much longer envelope. However, although observed for decades in experiments, the physics of this regime remains poorly understood, especially for highly-nonlinear cavities generating broadband spectra. Here, we address this question directly with a combined numerical and experimental study that reveals the physical origin of instability as nonlinear soliton dynamics and supercontinuum turbulence. Real-time characterisation reveals intracavity extreme events satisfying statistical rogue wave criteria, and both real-time and time-averaged measurements are in quantitative agreement with modelling.

In this work the authors perform a combined numerical and experimental study of noise-like pulse multiscale instabilities in dissipative laser systems. They reveal an underlying multiscale dynamics and report the observation of rogue wave events.

Tunable narrowband cascaded random Raman fiber laser

Random Raman fiber lasers (RRFLs) with half-opened cavity have been used as a new platform for designing high performance, wavelength-agile laser sources in the infrared region due to their intrinsic modeless property and structural simplicity. To provide the point feedbacks for cascaded random Raman lasing at different wavelengths, wavelength-insensitive broadband reflectors are commonly used in cascaded RRFLs, resulting in the rather broad high-order random Raman lasing with several nanometers of typical spectral width. Here, we experimentally demonstrate a tunable narrowband cascaded RRFL with an air-spaced etalon assisted point reflector. To realize narrowband, single- or dual-wavelength emission for each order of random lasing, the etalon is specially designed to have broad operation wavelength range, narrowband transmission lines and large free spectral range (FSR) associated with the Raman frequency shift. As a result, 1st- to 3rd-order random Raman lasing with single-wavelength emission in 1.1-1.27 μm region are generated in a 15 km single mode fiber (SMF) with -3 dB bandwidths below 0.4 nm, which are approximately four times less than those of cascaded RRFL without etalon. The maximum output power of the 3rd-order random Raman lasing is 615 mW, with 10% of optical conversion efficiency. Moreover, a tunable cascaded RRFL is performed by tuning the wavelength of pump laser or tilting the etalon. Dual-wavelength emission for each order of random lasing can also be realized at specific pump wavelengths. We also verified, by employing shorter fiber (10 km), more than 1.5 W output power of high-order RRFL can be achieved with -3 dB bandwidths less than 0.6 nm. To the best of our knowledge, this is the first demonstration of tunable sub-1 nm narrowband cascaded RRFL with single- or dual-wavelength emission for each order of random lasing.

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.

Brightness enhancement in random Raman fiber laser based on a graded-index fiber with high-power multimode pumping

A brightness-enhanced random Raman fiber laser (RRFL) with maximum power of 306 W at 1120 nm is demonstrated. A half-open cavity is built based on a graded-index (GRIN) passive fiber and single high-reflective fiber Bragg grating written in it directly. Due to the beam cleanup effect in the GRIN fiber enhanced in the half-open RRFL cavity, the output beam quality factor M² is improved from 9.15 (pump) to 1.76-2.35 (Stokes) depending on power, while the pump-Stokes brightness enhancement (BE) factor increases proportionally to output power reaching 6.1 at maximum. To the best of our knowledge, this is the highest power GRIN RRFL with BE.

Classical Rayleigh-Jeans Condensation of Light Waves: Observation and Thermodynamic Characterization

Theoretical studies on wave turbulence predict that a purely classical system of random waves can exhibit a process of condensation, which originates in the singularity of the Rayleigh-Jeans equilibrium distribution. We report the experimental observation of the transition to condensation of classical optical waves propagating in a multimode fiber, i.e., in a conservative Hamiltonian system without thermal heat bath. In contrast to conventional self-organization processes featured by the nonequilibrium formation of nonlinear coherent structures (solitons, vortices,…), here the self-organization originates in the equilibrium Rayleigh-Jeans statistics of classical waves. The experimental results show that the chemical potential reaches the lowest energy level at the transition to condensation, which leads to the macroscopic population of the fundamental mode of the optical fiber. The near-field and far-field measurements of the condensate fraction across the transition to condensation are in quantitative agreement with the Rayleigh-Jeans theory. The thermodynamics of classical wave condensation reveals that the heat capacity takes a constant value in the condensed state and tends to vanish above the transition in the normal state. Our experiments provide the first demonstration of a coherent phenomenon of self-organization that is exclusively driven by optical thermalization toward the Rayleigh-Jeans equilibrium.

Fiber Raman Amplifiers and Fiber Raman Lasers

Stimulated Raman scattering (SRS) is a nonlinear optical effect, observed for the first time in 1962, which lies at the heart of fiber Raman amplifiers and fiber Raman lasers [...].

Advances in Random Fiber Lasers and Their Sensing Application

Compared with conventional laser, random laser (RL) has no resonant cavity, reducing the requirement of cavity design. In recent years, the random fiber laser (RFL), a novel kind of RL, has made great progress in theories and experiments. The RFL has a simpler structure, a more flexible design, and higher reliability. It has valuable applications for earth sciences, biological life sciences, and national defense security, due to these unique properties. This paper reviews the development of RFLs in the last decade, including their configurations based on various optical fibers and their output properties, especially the method of control. Moreover, we also introduce their applications in the optical fiber sensing system, which is a very important and practical orientation to study. Finally, this paper presents the prospects of RFLs.

Ultrafast convergent power-balance model for Raman random fiber laser with half-open cavity

The power-relevant features of Raman random fiber laser (RRFL), such as lasing threshold, slope efficiency, and power distribution, are among the most critical parameters to characterize its operation status. In this work, focusing on the power features of the half-open cavity RRFL, an ultrafast convergent power-balance model is proposed, which highlights the physical essence of the most common RRFL type and sharply reduces the computation workload. By transforming the time-consuming serial calculation to a parallel one, the calculation efficiency can be improved by more than 100 times. Particularly, for different point-mirror reflectivities and different fiber lengths, the input-output power curves and power distribution curves calculated by the present model match nicely with those of the conventional model, as well as with the experimental data. Moreover, through the present model the relationship between point-mirror reflectivity and laser threshold is analytically derived, and the way for improving RRFL's slope efficiency is also provided with a lucid theoretical explanation.

Poisson distribution of extreme events in radiation of random distributed feedback fiber laser

In the present Letter, we experimentally investigate extreme events in the time dynamics of the random distributed feedback fiber laser. We find that the probability of extreme events depends on the wavelength of the generated light. On spectrum tails, we register extreme events with intensity up to 50 times higher than the average generation power. Analysis of return times between successive rogue waves reveals their exponential distribution. Further investigation proves that the appearance of extreme waves in laser radiation obeys Poisson law. Characteristic radiation time varies from nanoseconds to tens of microseconds for most intense waves.

Statistical properties of a laser beam propagating in a turbulent medium

We examine statistical properties of a laser beam propagating in a turbulent medium. We prove that the intensity fluctuations at large propagation distances possess a Gaussian probability density function and establish quantitative criteria for realizing the Gaussian statistics depending on the laser propagation distance, laser beam waist, laser frequency, and turbulence strength. We calculate explicitly the laser envelope pair correlation function and corrections to its higher-order correlation functions breaking Gaussianity. We discuss also statistical properties of the brightest spots in the speckle pattern.

Fiber Amplifiers and Fiber Lasers Based on Stimulated Raman Scattering: A Review

Nowadays, in fiber optic communications the growing demand in terms of transmission capacity has been fulfilling the entire spectral band of the erbium-doped fiber amplifiers (EDFAs). This dramatic increase in bandwidth rules out the use of EDFAs, leaving fiber Raman amplifiers (FRAs) as the key devices for future amplification requirements. On the other hand, in the field of high-power fiber lasers, a very attractive option is provided by fiber Raman lasers (FRLs), due to their high output power, high efficiency and broad gain bandwidth, covering almost the entire near-infrared region. This paper reviews the challenges, achievements and perspectives of both fiber Raman amplifier and fiber Raman laser. They are enabling technologies for implementation of high-capacity optical communication systems and for the realization of high power fiber lasers, respectively.

Mode characteristic manipulation of random feedback interferometers in Brillouin random fiber laser

The Brillouin random fiber laser (BRFL) suffers from high intensity noise that comes mainly from longitudinal mode beating at different mode frequencies. In this Letter, we propose and demonstrate that the mode characteristic of BRFL can be manipulated by distributed random feedback, which acts as the longitudinal mode filter. A theoretical model is developed for the first time, to the best of our knowledge, to analyze the mode characteristics of BRFL with different lengths of a weak fiber Bragg grating (FBG) array. In experiment, a single FBG, weak FBG array (reflection of $ - {40}\;{\rm dB}$-40dB) at various lengths, and a Rayleigh scattering fiber are used to provide the random feedback. Both theoretical analysis and experimental results show that single longitudinal mode operation can be realized with the distributed random feedback interferometer, leading to a stable temporal intensity output of the BRFL in the time domain.

Thermal and acoustic noise insensitive Brillouin random fiber laser based on polarization-maintaining random fiber grating

Thermal and acoustic noises are crucial to the long-term stability of fiber lasers, as it introduces the fluctuation of optical path length on laser cavity, and hence imposing undesirable intensity noise and frequency drift, particularly for a random fiber laser with distributed Rayleigh scattering feedback from a long length fiber. In this Letter, we propose and demonstrate a thermal and acoustic noise insensitive Brillouin random fiber laser by utilizing the random feedback from a polarization-maintaining (PM) fiber-based random grating. A theoretical model is developed for the first time, to the best of our knowledge, to analyze environmental perturbation on the randomly induced refractive index modulation via a PM random grating. Both the theory and experiments show that the scattered optical intensity of the PM random fiber grating exhibits a weak dependence on the temperature fluctuation and the acoustic noise perturbation compared to that of the Rayleigh scattering from hundreds of meters of PM fibers, leading to the Brillouin random lasing radiation with a 20 dB relative intensity noise suppression in the frequency range from 10 Hz to 1 kHz.

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.

Dramatic Acceleration of Wave Condensation Mediated by Disorder in Multimode Fibers

Classical nonlinear waves exhibit a phenomenon of condensation that results from the natural irreversible process of thermalization, in analogy with the quantum Bose-Einstein condensation. Wave condensation originates in the divergence of the thermodynamic equilibrium Rayleigh-Jeans distribution, which is responsible for the macroscopic population of the fundamental mode of the system. However, achieving complete thermalization and condensation of incoherent waves through nonlinear optical propagation is known to require prohibitive large interaction lengths. Here, we derive a discrete kinetic equation describing the nonequilibrium evolution of the random wave in the presence of a structural disorder of the medium. Our theory reveals that a weak disorder accelerates the rate of thermalization and condensation by several order of magnitudes. Such a counterintuitive dramatic acceleration of condensation can provide a natural explanation for the recently discovered phenomenon of optical beam self-cleaning. Our experiments in multimode optical fibers report the observation of the transition from an incoherent thermal distribution to wave condensation, with a condensate fraction of up to 60% in the fundamental mode of the waveguide trapping potential.

Machine Learning Methods for Control of Fibre Lasers with Double Gain Nonlinear Loop Mirror

Many types of modern lasers feature nonlinear properties, which makes controlling their operation a challenging engineering problem. In particular, fibre lasers present both high-performance devices that are already used for diverse industrial applications, but also interesting and not yet fully understood nonlinear systems. Fibre laser systems operating at high power often have multiple equilibrium states, and this produces complications with the reproducibility and management of such devices. Self-tuning and feedback-enabled machine learning approaches might define a new era in laser science and technology. The present study is the first to demonstrate experimentally the application of machine learning algorithms for control of the pulsed regimes in an all-normal dispersion, figure-eight fibre laser with two independent amplifying fibre loops. The ability to control the laser operation state by electronically varying two drive currents makes this scheme particularly attractive for implementing machine learning approaches. The self-tuning adjustment of two independent gain levels in the laser cavity enables generation-on-demand pulses with different duration, energy, spectral characteristics and time coherence. We introduce and evaluate the application of several objective functions related to selection of the pulse duration, energy and degree of temporal coherence of the radiation. Our results open up the possibility for new designs of pulsed fibre lasers with robust electronics-managed control.

Random Raman fiber laser based on a twin-core fiber with FBGs inscribed by femtosecond radiation

Narrowband Raman lasing in a polarization-maintaining two-core fiber (TCF) is demonstrated. Femtosecond point-by-point inscription of fiber Bragg gratings (FBGs) in individual cores produces a half-open cavity with random distributed feedback. The laser linewidth in the cavity with a single FBG inscribed in one core of the TCF reduced by ∼2  times with respect to the cavity with a fiber loop mirror. It is shown that the inscription of two FBGs in different cores leads to the formation of a Michelson-type interferometer, leading to the modulation of generation spectra near threshold. This technique offers new possibilities for spectral filtering or multi-wavelength generation.

Incoherent Shock and Collapse Singularities in Non-Instantaneous Nonlinear Media

We study the dynamics of a partially incoherent optical pulse that propagates in a slowly responding nonlinear Kerr medium. We show that irrespective of the sign of the dispersion (either normal or anomalous), the incoherent pulse as a whole exhibits a global collective behavior characterized by a dramatic narrowing and amplification in the strongly non-linear regime. The theoretical analysis based on the Vlasov formalism and the method of the characteristics applied to a reduced hydrodynamic model reveal that such a strong amplitude-incoherent pulse originates in the existence of a concurrent shock-collapse singularity (CSCS): The envelope of the intensity of the random wave exhibits a collapse singularity, while the momentum exhibits a shock singularity. The dynamic behavior of the system after the shock-collapse singularity is characterized through the analysis of the phase-space dynamics.

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.

Gain through losses in nonlinear optics

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. These instabilities are at the heart of symmetry breaking, condensate dynamics, self-organisation, pattern formation, and noise amplification across diverse disciplines, including physics, chemistry, engineering, and biology. In nonlinear optics, modulation instabilities are generally linked to the so-called parametric amplification process, which occurs when certain phase-matching or quasi-phase-matching conditions are satisfied. In the present review article, we summarise the principle results on modulation instabilities and parametric amplification in nonlinear optics, with special emphasis on optical fibres. We then review state-of-the-art research about a peculiar class of modulation instabilities (MIs) and signal amplification processes induced by dissipation in nonlinear optical systems. Losses applied to certain parts of the spectrum counterintuitively lead to the exponential growth of the damped mode themselves, causing gain through losses. We discuss the concept of imaging of losses into gain, showing how to map a given spectral loss profile into a gain spectrum. We demonstrate with concrete examples that dissipation-induced MI, apart from being of fundamental theoretical interest, may pave the way towards the design of a new class of tuneable fibre-based optical amplifiers, optical parametric oscillators, frequency comb sources, and pulsed lasers.

Mid-infrared cascaded stimulated Raman scattering up to eight orders in As-S optical fiber

Mid-infrared cascaded stimulated Raman scattering (SRS) is experimentally investigated in an As-S optical fiber which is fabricated based on As₃₈S₆₂ and As₃₆S₆₄ glasses and whose fiber loss is ∼0.08 dB/m at1545 nm. Using a nanosecond laser operated at ∼1545 nm as the pump source, mid-infrared cascaded SRS up to eight orders is obtained in a 16 m As-S fiber. To the best of our knowledge, this is the first demonstration of SRS of such high order in non-silica optical fibers, and it may contribute to developing tunable mid-infrared Raman fiber lasers using C-band pump sources.

Transition between inverse and direct energy cascades in multiscale optical turbulence

Multiscale turbulence naturally develops and plays an important role in many fluid, gas, and plasma phenomena. Statistical models of multiscale turbulence usually employ Kolmogorov hypotheses of spectral locality of interactions (meaning that interactions primarily occur between pulsations of comparable scales) and scale-invariance of turbulent pulsations. However, optical turbulence described by the nonlinear Schrodinger equation exhibits breaking of both the Kolmogorov locality and scale-invariance. A weaker form of spectral locality that holds for multi-scale optical turbulence enables a derivation of simplified evolution equations that reduce the problem to a single scale modeling. We present the derivation of these equations for Kerr media with random inhomogeneities. Then, we find the analytical solution that exhibits a transition between inverse and direct energy cascades in optical turbulence.

Intensity statistics in a long random fiber Raman laser

We study the output emission statistics of a random continuous-wave Raman fiber laser. The signal evolution is governed by a generalized nonlinear Schrödinger equation (NLSE) with inserted gain. The statistics are close to the Rayleigh one, and the deviations are caused by the Kerr nonlinearity. To characterize the deviations, we analytically find the mean of the squared output signal intensity, based on the kinetic theory. We show qualitative agreement with available experimental data and supplement the results with numerical calculations. With the limit of small gain, the kinetic theory gives a finite answer for the mean of squared intensity in the first and the second order with respect to small nonlinearity. The result is consistent with the fact that the NLSE is integrable in the case of zero gain and is applicable to any generalized NLSE if the inserted terms are effectively small.

Open-Cavity Spun Fiber Raman Lasers with Dual Polarization Output

Random distributed feedback fiber Raman lasers, where the feedback mechanism is provided by Rayleigh backscattering, have attracted a good deal of attention since they were first introduced in 2010. Their simple and flexible design, combined with good lasing efficiency and beam quality properties, comparable to those of standard cavity lasers, have led to multiple applications, particularly in the fields of fiber sensing and optical communications. In spite of these advances, the polarization properties of random fiber Raman lasers, which can strongly affect their performance in both sensing and communications, have barely been explored so far. In this article we experimentally and theoretically study the polarization properties of different open-cavity laser designs, based on either standard transmission fibers or low polarization-mode-dispersion spun fibers. By using high-power, highly-polarized pumps, we demonstrate controllable polarization-pulling and simultaneous lasing at close wavelengths with different output polarization properties in random distributed feedback fiber Raman lasers. These results advance our understanding of the polarization dynamics in ultralong lasers, and pave the way to the design of novel fiber laser sources capable of polarization-sensitive sensing and distributed amplification.

Linearly polarized cascaded Raman fiber laser with random distributed feedback operating beyond 1.5 μm

We report on, to the best of our knowledge, the first demonstration of a linearly polarized cascaded Raman fiber laser based on a simple half-open cavity with a broadband composite reflector and random distributed feedback in a polarization-maintaining phosphosilicate fiber with a zero dispersion wavelength at ∼1400  nm. Pumped by a 1080 nm Yb-doped fiber laser, the random laser delivers more than 8 W at 1262 nm and 9 W at 1515 nm with a polarization extinction ratio of 27 dB. The generation linewidths amount to about 1 and 3 nm, respectively, being almost independent of power, in correspondence with the theory of a cascaded random fiber lasing.

Turbulence hierarchy in a random fibre laser

Turbulence is a challenging feature common to a wide range of complex phenomena. Random fibre lasers are a special class of lasers in which the feedback arises from multiple scattering in a one-dimensional disordered cavity-less medium. Here we report on statistical signatures of turbulence in the distribution of intensity fluctuations in a continuous-wave-pumped erbium-based random fibre laser, with random Bragg grating scatterers. The distribution of intensity fluctuations in an extensive data set exhibits three qualitatively distinct behaviours: a Gaussian regime below threshold, a mixture of two distributions with exponentially decaying tails near the threshold and a mixture of distributions with stretched-exponential tails above threshold. All distributions are well described by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence, which includes energy cascade and the intermittence phenomenon. Our findings have implications for explaining the remarkably challenging turbulent behaviour in photonics, using a random fibre laser as the experimental platform.

Random fibre lasers constitute a class of lasers where the optical feedback is provided by multiple scattering in a disordered system. Here, González et al. theoretically and experimentally study the statistical turbulence behaviour in relation to the lasing transition in such lasers.

Spectral correlations in a random distributed feedback fibre laser

Random distributed feedback fibre lasers belong to the class of random lasers, where the feedback is provided by amplified Rayleigh scattering on sub-micron refractive index inhomogenities randomly distributed over the fibre length. Despite the elastic nature of Rayleigh scattering, the feedback mechanism has been insofar deemed incoherent, which corresponds to the commonly observed smooth generation spectra. Here, using a real-time spectral measurement technique based on a scanning Fabry-Pérot interferometer, we observe long-living narrowband components in the random fibre laser's spectrum. Statistical analysis of the ∼10⁴ single-scan spectra reveals a preferential interspacing for the components and their anticorrelation in intensities. Furthermore, using mutual information analysis, we confirm the existence of nonlinear correlations between different parts of the random fibre laser spectra. The existence of such narrowband spectral components, together with their observed correlations, establishes a long-missing parallel between the fields of random fibre lasers and conventional random lasers.

The feedback mechanism in random fibre lasers has been insofar deemed incoherent. To reveal the dynamic evolution of the random fibre laser spectra, Sugavanam et al. use a real-time spectral measurement technique and observe long-lived narrowband components in the random fibre laser's spectrum.

High-efficiency Brillouin random fiber laser using all-polarization maintaining ring cavity

We report a high-efficiency (25%) Brillouin random fiber laser (BRFL) with Brillouin gain medium of 2-km polarization maintaining fiber (PMF) as well as distributed Rayleigh scattering feedback from 500-m PMF. The characteristics of lasing efficiency and relative intensity noise (RIN) have been comprehensively studied comparing with the BRFLs with half-open ring cavity and bidirectional pumping linear open configuration. The enhanced lasing efficiency using PMF-BRFL with half-open ring cavity enables sub-kHz linewidth, lower phase fluctuation and frequency jitter comparing with phase locked pump laser, thanks to the polarization-matched efficient Brillouin gain in PMFs. The RIN and frequency instability of the proposed PMF-BRFL induced from external disturbance, e.g., mechanical and thermal noise, have been effectively suppressed with respect to conventional SMF-based BRFL.

Linearly polarized low-noise Brillouin random fiber laser

A linearly polarized Brillouin random fiber laser (LP-BRFL) with distributed feedback along 2 km polarization-maintaining fibers (PMFs) is demonstrated. The laser was built up using a bidirectional pumping mechanism in an all-PMF configuration, yielding a radiation with 8% power efficiency and more than 25 dB polarization extinction ratio. A high lasing efficiency is achieved due to the polarization-matched Brillouin amplification and distributed feedback along kilometer long PMFs. The relative intensity noise and the thermal-induced frequency noise of this random laser have also been measured and compared to that of a custom single-mode-fiber-based random laser and a conventional phase-locked laser.

Powerful linearly-polarized high-order random fiber laser pumped by broadband amplified spontaneous emission source

A great deal of attention has been drawn to Random fiber lasers (RFLs) for their typical features of modeless, cavity-less and low coherence length. However, most previously reported high power RFLs employ narrowband fiber lasers as the pump source, thus inducing the self-pulsing transferring from pump source to output Stokes. In this contribution, linearly-polarized RFL pumped by broadband amplified-spontaneous-emission (ASE) is demonstrated and continuous-wave (CW) high order Stokes can be obtained.With 30.6 W pump injected into the half-opened cavity, 23.51 W the 2^nd order Stokes centered at 1178 nm with a full width at half-maximum linewidth of 1.73 nm and polarization extinction ratio of about 25 dB can be obtained. The standard deviation and peak-vale value of the 2^nd order Stokes light at maximal output power is just 0.47% and 4.10%, which indicates the good power stability. Significantly, the corresponding quantum efficiency of the 1^st and 2^nd order Stokes light is about 87% and 85%, and almost all pump photons are converted into Stokes photons. As far as we know, it is the highest power ever reported from linearly polarized RFL, and further power scaling is available in the case of more powerful pump source and optimization of system parameters.

Extended Propagation of Powerful Laser Pulses in Focusing Kerr Media

Powerful incoherent laser pulses can propagate in focusing Kerr media much longer distances than can coherent pulses, due to the fast phase mixing that prevents transverse filamentation. This distance is limited by 4-wave scattering, which accumulates waves at small transverse wave numbers, where phase mixing is too slow to retain the incoherence and thus prevent the filamentation. However, we identify how this theoretical limit can be overcome by countering this accumulation through transverse heating of the pulse by random fluctuations of the refractive index. Thus, the laser pulse propagation distances are significantly extended, making feasible, in particular, the generation of unprecedentedly intense and powerful short laser pulses in a plasma by means of backward Raman amplification in new random laser regimes.

Decoupled polarization dynamics of incoherent waves and bimodal spectral incoherent solitons

We consider the propagation of strongly incoherent waves in optical fibers in the framework of the vector nonlinear Schrödinger equation (VNLSE) accounting for the Raman effect. On the basis of the wave turbulence theory, we derive a kinetic equation that greatly simplifies the VNLSE and provides deep physical insight into incoherent wave dynamics. When applied to the study of polarization effects, the theory unexpectedly reveals that the linear polarization components of the incoherent wave evolve independently from each other, even in the presence of weak fiber birefringence. When applied to light propagation in bimodal fibers, the theory reveals that the incoherent modal components can be strongly coupled. After a complex transient, the modal components self-organize into a vector spectral incoherent soliton: The two solitons self-trap and propagate with a common velocity in frequency space.

Statistical properties of radiation of multiwavelength random DFB fiber laser

In the presented paper, the temporal and statistical properties of a Lyot filter based multiwavelength random DFB fiber laser with a wide flat spectrum, consisting of individual lines, were investigated. It was shown that separate spectral lines forming the laser spectrum have mostly Gaussian statistics and so represent stochastic radiation, but at the same time the entire radiation is not fully stochastic. A simple model, taking into account phenomenological correlations of the lines' initial phases was established. Radiation structure in the experiment and simulation proved to be different, demanding interactions between different lines to be described via a NLSE-based model.

Narrowband random lasing in a Bismuth-doped active fiber

Random fiber lasers operating via the Rayleigh scattering (RS) feedback attract now a great deal of attention as they generate a high-quality unidirectional laser beam with the efficiency and performance comparable and even exceeding those of fiber lasers with conventional cavities. Similar to other random lasers, both amplification and random scattering are distributed here along the laser medium being usually represented by a kilometers-long passive fiber with Raman gain. However, it is hardly possible to utilize normal gain in conventional active fibers as they are usually short and RS is negligible. Here we report on the first demonstration of the RS-based random lasing in an active fiber. This became possible due to the implementation of a new Bi-doped fiber with an increased amplification length and RS coefficient. The realized Bi-fiber random laser generates in a specific spectral region (1.42 μm) exhibiting unique features, in particular, a much narrower linewidth than that in conventional cavity of the same length, in agreement with the developed theory. Lasers of this type have a great potential for applications as Bi-doped fibers with different host compositions enable laser operation in an extremely broad range of wavelengths, 1.15–1.78 μm.

Frequency doubling of Raman fiber lasers with random distributed feedback

This Letter presents what we believe is the first experimental study of frequency doubling of a Raman fiber laser (RFL) with random distributed feedback (RDFB) in an MgO:PPLN crystal. We compared two laser configurations, each with a half-open cavity. The cavity contained either a broadband Sagnac mirror or a narrowband fiber Bragg grating (FBG). We found that spectral broadening in the studied configurations of the RDFB RFLs differed from that found in a conventional RFL with a linear cavity, as well as from each other. We also compared the second harmonic generation (SHG) efficiency for these three types of lasers. The highest SHG efficiency was obtained for the RDFB RFL with the FBG delivering >100  mW power at 654 nm.

High-order random Raman lasing in a PM fiber with ultimate efficiency and narrow bandwidth

Random Raman lasers attract now a great deal of attention as they operate in non-active turbid or transparent scattering media. In the last case, single mode fibers with feedback via Rayleigh backscattering generate a high-quality unidirectional laser beam. However, such fiber lasers have rather poor spectral and polarization properties, worsening with increasing power and Stokes order. Here we demonstrate a linearly-polarized cascaded random Raman lasing in a polarization-maintaining fiber. The quantum efficiency of converting the pump (1.05 μm) into the output radiation is almost independent of the Stokes order, amounting to 79%, 83%, and 77% for the 1(st) (1.11 μm), 2(nd) (1.17 μm) and 3(rd) (1.23 μm) order, respectively, at the polarization extinction ratio >22 dB for all orders. The laser bandwidth grows with increasing order, but it is almost independent of power in the 1-10 W range, amounting to ~1, ~2 and ~3 nm for orders 1-3, respectively. So, the random Raman laser exhibits no degradation of output characteristics with increasing Stokes order. A theory adequately describing the unique laser features has been developed. Thus, a full picture of the cascaded random Raman lasing in fibers is shown.

Short cavity-length random fiber laser with record power and ultrahigh efficiency

We report the result of achieving a random fiber laser (RFL) with record 200-W-level power output. The highest output power is realized by a simple 120 m long cavity at a working wavelength of 1173 nm while pumping at 1120 nm. The maximum observed optical-to-optical efficiency reaches ∼89%, which is believed to be the highest value ever reported for RFLs. In addition, numerical calculations on different order Raman Stokes wave thresholds based on the theoretical model are carried out for comparison with the experimental data. The presented work effectively advances the power scalability, and the numerical model well describes the lasing thresholds in such short cavity RFLs.

Radiation build-up in laminar and turbulent regimes in quasi-CW Raman fiber laser

We study the radiation build-up in laminar and turbulent generation regimes in quasi-CW Raman fiber laser. We found the resulted spectral shape and generation type is defined by the total spectral broadening/narrowing balance over laser cavity round-trip, which is substantially different in different regimes starting from first round-trips of the radiation build-up. In turbulent regime, the steady-state is reached only after a few round-trips, while in the laminar regime the laser approaches the equilibrium spectrum shape asymptotically.

Spatio-temporal generation regimes in quasi-CW Raman fiber lasers

We present experimental measurements of intensity spatio-temporal dynamics in quasi-CW Raman fiber laser. Depending on the power, the laser operates in different spatio-temporal regimes varying from partial mode-locking near the generation threshold to almost stochastic radiation and a generation of short-lived pulses at high power. The transitions between the generation regimes are evident in intensity spatio-temporal dynamics. Two-dimensional auto-correlation functions provide an additional insight into temporal and spatial properties of the observed regimes.

From coherent shocklets to giant collective incoherent shock waves in nonlocal turbulent flows

Understanding turbulent flows arising from random dispersive waves that interact strongly through nonlinearities is a challenging issue in physics. Here we report the observation of a characteristic transition: strengthening the nonlocal character of the nonlinear response drives the system from a fully turbulent regime, featuring a sea of coherent small-scale dispersive shock waves (shocklets) towards the unexpected emergence of a giant collective incoherent shock wave. The front of such global incoherent shock carries most of the stochastic fluctuations and is responsible for a peculiar folding of the local spectrum. Nonlinear optics experiments performed in a solution of graphene nano-flakes clearly highlight this remarkable transition. Our observations shed new light on the role of long-range interactions in strongly nonlinear wave systems operating far from thermodynamic equilibrium, which reveals analogies with, for example, gravitational systems, and establishes a new scenario that can be common to many turbulent flows in photonic quantum fluids, hydrodynamics and Bose–Einstein condensates.

Understanding turbulent flows arising from random dispersive waves that interact through nonlinearities is a challenging issue in physics. Here, the authors model and observe experimentally in a nonlinear optics set-up the transition between a sea of small-scale shocklets and a giant collective shock wave.

Linearly polarized random fiber laser with ultimate efficiency

Linearly polarized pumping of a random fiber laser made of a 500-m PM fiber with PM fiber-loop mirror at one fiber end results in generation of linearly polarized radiation at 1.11 μm with the polarization extinction ratio as high as 25 dB at the output power of up to 9.4 W. The absolute optical efficiency of pump-to-Stokes wave conversion reaches 87%, which is close to the quantum limit and sets a record for Raman fiber lasers with random distributed feedback and with a linear cavity as well. Herewith, the output linewidth at high powers tends to saturation at a level of 1.8 nm.

Inverse four-wave-mixing and self-parametric amplification effect in optical fibre

An important group of nonlinear processes in optical fibre involves the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect, self-parametric amplification (SPA), which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from an inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. SPA and the observed stable nonlinear spectral propagation with random temporal waveform can find applications in optical communications and high power fibre lasers with nonlinear intra-cavity dynamics.

Hundred-watt-level high power random distributed feedback Raman fiber laser at 1150 nm and its application in mid-infrared laser generation

Two kinds of hundred-watt-level random distributed feedback Raman fiber have been demonstrated. The optical efficiency can reach to as high as 84.8%. The reported power and efficiency of the random laser is the highest one as we know. We have also demonstrated that the developed random laser can be further used to pump a Ho-doped fiber laser for mid-infrared laser generation. Finally, 23 W 2050 nm laser is achieved. The presented laser can obtain high power output efficiently and conveniently and opens a new direction for high power laser sources at designed wavelength.

Intensity dynamics and statistical properties of random distributed feedback fiber laser

We present first experimental investigation of fast-intensity dynamics of random distributed feedback (DFB) fiber lasers. We found that the laser dynamics are stochastic on a short time scale and exhibit pronounced fluctuations including generation of extreme events. We also experimentally characterize statistical properties of radiation of random DFB fiber lasers. We found that statistical properties deviate from Gaussian and depend on the pump power.