Bandwidth-induced saturation in multimode fiber-based absorbers.

Multimode fiber-based saturable absorbers enable mode-locking in lasers, generating ultrafast pulses and providing an exceptional platform for investigating nonlinear phenomena. Previous analyses in the continuous-wave (CW) limit showed that saturable absorption can be obtained due to nonlinear interactions between transverse modes. We find experimentally that saturable absorption can be achieved, thanks to the interplay of single-mode fiber nonlinearity and the wavelength-dependent linear transmission of the multimode fiber, even with negligible intermodal nonlinearities. We further show that even when intermodal nonlinearities are significant, the CW analysis may not be sufficient for long multimode fibers. Understanding the underlying mechanisms of multimode fiber-based saturable absorbers opens new possibilities for developing programmable devices for ultrafast control.

Direct Measurement of Energy Transfer in Strongly Driven Rotating Turbulence.

A short, abrupt increase in energy injection rate into steady strongly driven rotating turbulent flow is used as a probe for energy transfer in the system. The injected excessive energy is localized in time and space and its spectra differ from those of the steady turbulent flow. This allows measuring energy transfer rates, in three different domains: In real space, the injected energy propagates within the turbulent field, as a wave packet of inertial waves. In the frequency domain, energy is transferred nonlocally to the low, quasigeostrophic modes. In wave number space, energy locally cascades toward small wave numbers, in a rate that is consistent with two-dimensional (2D) turbulence models. Surprisingly however, the inverse cascade of energy is mediated by inertial waves that propagate within the flow with small, but nonvanishing frequency. Our observations differ from measurements and theoretical predictions of weakly driven turbulence. Yet, they show that in strongly driven rotating turbulence, inertial waves play an important role in energy transfer, even in the vicinity of the 2D manifold.

Deterministic access of broadband frequency combs in microresonators using cnoidal waves in the soliton crystal limit.

We present a method to deterministically obtain broad bandwidth frequency combs in microresonators. These broadband frequency combs correspond to cnoidal waves in the limit when they can be considered soliton crystals or single solitons. The method relies on moving adiabatically through the (frequency detuning)×(pump amplitude) parameter space, while avoiding the chaotic regime. We consider in detail Si3N4 microresonators with small or intermediate dimensions and an SiO2 microresonator with large dimensions, corresponding to prior experimental work. We also discuss the impact of thermal effects on the stable regions for the cnoidal waves. Their principal effect is to increase the detuning for all the stable regions, but they also skew the stable regions, since higher pump power corresponds to higher power and hence increased temperature and detuning. The change in the detuning is smaller for single solitons than it is for soliton crystals. Without temperature effects, the stable regions for single solitons and soliton crystals almost completely overlap. When thermal effects are included, the stable region for single solitons separates from the stable regions for the soliton crystals, explaining in part the effectiveness of backwards-detuning to obtaining single solitons.

Bidirectional Soliton Rain Dynamics Induced by Casimir-Like Interactions in a Graphene Mode-Locked Fiber Laser.

We study experimentally and theoretically the interactions among ultrashort optical pulses in the soliton rain multiple-pulse dynamics of a fiber laser. The laser is mode locked by a graphene saturable absorber fabricated using the mechanical transfer technique. Dissipative optical solitons aggregate into pulse bunches that exhibit complex behavior, which includes acceleration and bidirectional motion in the moving reference frame. The drift speed and direction depend on the bunch size and relative location in the cavity, punctuated by abrupt changes under bunch collisions. We model the main effects using the recently proposed noise-mediated pulse interaction mechanism, and obtain a good agreement with experiments. This highlights the major role of long-range Casimir-like interactions over dynamical pattern formations within ultrafast lasers.

Universality and hysteresis in slow sweeping of bifurcations.

Bifurcations in dynamical systems are often studied experimentally and numerically using a slow parameter sweep. Focusing on the cases of period-doubling and pitchfork bifurcations in maps, we show that the adiabatic approximation always breaks down sufficiently close to the bifurcation, so the upsweep and downsweep dynamics diverge from one another, disobeying standard bifurcation theory. Nevertheless, we demonstrate universal upsweep and downsweep trajectories for sufficiently slow sweep rates, revealing that the slow trajectories depend essentially on a structural asymmetry parameter, whose effect is negligible for the stationary dynamics. We obtain explicit asymptotic expressions for the universal trajectories and use them to calculate the area of the hysteresis loop enclosed between the upsweep and downsweep trajectories as a function of the asymmetry parameter and the sweep rate.

Soliton synchronization in microresonators with a modulated pump.

Microresonator frequency comb generation from Kerr solitons has become a cutting edge technology, but challenges remain in creating, maintaining, and controlling the solitons. Pump modulation and dual pumping are promising techniques for meeting these challenges. Here we derive the equation of motion of solitons interacting with a modulated pump in the framework of synchronization theory. It implies that the soliton repetition rate locks to the modulation frequency whenever the latter is within a locking range of frequencies around an integer multiple of the free spectral range of the microresonator. We calculate explicitly, numerically, and in perturbation theory the width of the locking range as a function of the amplitude and frequency of the pump and the modulation phase. We show that a highly red-detuned, strong pump that is amplitude-modulated provides the best conditions for entrainment, and that the width of the locking range is proportional to the square of the modulation frequency, limiting the effectiveness of RF modulation as an entrainment method.

Universal dynamics of spatiotemporal entrainment with phase symmetry.

We study the entrainment of a localized pattern to an external signal via its coupling to zero modes associated with broken symmetries. We show that when the pattern breaks internal symmetries, entrainment is governed by a multiple degrees-of-freedom dynamical system that has a universal structure, defined by the symmetry group and its breaking. We derive explicitly the universal locking dynamics for entrainment of patterns breaking internal phase symmetry, and calculate the locking domains and the stability and bifurcations of entrainment of complex Ginzburg-Landau solitons by an external pulse.

Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser.

We have recently predicted (R. Weill, B. Fischer and O. Gat, Phys. Rev. Lett.104, 173901, 2010) condensation of light in actively mode locked lasers when the laser power increases, or the noise, that takes the role of temperature, decreases. The condensate is characterized by strong light pulses due to the dominance of the lowest eigenmode ("ground state") power. Here, we experimentally demonstrate, for the first time, light mode condensation transition in an actively mode-locked fiber laser. Following the theoretical prediction, the condensation is obtained for modulations that have a power law dependence on time with exponents smaller than 2. The laser light system is strictly one dimensional, a special opportunity in experimental physics. We also discuss experimental schemes for condensation in two- and three-dimensional laser systems.

Noise-induced oscillations in fluctuations of passively mode-locked pulses.

We study the fluctuations of pulses in mode-locked lasers using the statistical light-mode dynamics approach. The analysis is based on a decomposition of the laser waveform into three parts: solitary pulse, intracavity noise continuum, and local overlap. We discover significant features in the fluctuation dynamics, beyond those known in existing theories that disregard the continuum component of the waveform, most notably oscillations in the autocorrelation functions of the pulse power and frequency parameters, and an enhancement of the phase jitter diffusion constant. The theoretical results are corroborated by numerical simulations.

Experimental study of the stability and optimization of multipulse passive mode locking.

We present an experimental study of the stability of passively mode-locked pulses against noise in multipulse operation of an erbium-doped fiber laser. The laser properties are determined by two dimensionless combinations of the laser parameters. Measurements of the pulses' destabilization threshold as a function of those laser parameters show the optimal regions that maximize the mode-locked pulse stability. We find good agreement between the experimental observations and the theoretical predictions.

Light-mode condensation in actively-mode-locked lasers.

We show that the formation of pulses in actively mode-locked lasers exhibits in certain conditions a transition of the laser mode system to a light pulse state that is similar to Bose-Einstein condensation (BEC). The study is done in the framework of statistical light-mode dynamics with a mapping between the distribution of the laser eigenmodes to the equilibrium statistical physics of noninteracting bosons in an external potential. The light-mode BEC transition occurs for a mode-locking modulation that has a power law dependence on time with an exponent smaller than 2.

Forced deterministic dynamics on a random energy landscape: Implications for the physics of amorphous solids.

The dynamics of supercooled liquids and plastically deformed amorphous solids is known to be dominated by the structure of their rough energy landscapes. Recent experiments and simulations on amorphous solids subjected to oscillatory shear at athermal conditions have shown that for small strain amplitudes these systems reach limit cycles of different periodicities after a transient. However, for larger strain amplitudes the transients become longer and for strain amplitudes exceeding a critical value the system reaches a diffusive steady state. This behavior cannot be explained using the current mean-field models of amorphous plasticity. Here we show that this phenomenology can be described and explained using a simple model of forced dynamics on a multidimensional random energy landscape. In this model, the existence of limit cycles can be ascribed to confinement of the dynamics to a small part of the energy landscape which leads to self-intersection of state-space trajectories and the transition to the diffusive regime for larger forcing amplitudes occurs when the forcing overcomes this confinement.

Statistical physics of power fluctuations in mode-locked lasers.

We present an analysis of the power fluctuations in the statistical steady state of a passively mode-locked laser. We use statistical light-mode theory to map this problem to that of fluctuations in a reference equilibrium statistical physics problem and, in this way, study the fluctuations nonperturbatively. The power fluctuations, being noncritical, are Gaussian and proportional in amplitude to the inverse square root of the number of degrees of freedom. We calculate explicit analytic expressions for the covariance matrix of the overall pulse and cw power variables, providing complete information on the single-time power distribution in the laser, and derive a set of fluctuation-dissipation relations between them and the susceptibilities of the steady-state quantities.

Statistical light-mode dynamics of multipulse passive mode locking.

We study the multipulse formation in passive mode locking in the framework of the statistical light-mode dynamics theory. It is a many-body theory that treats the complex many-mode laser system by statistical mechanics. We give a detailed theory and experimental verification for the important case of multiple-pulse formation in the laser cavity. We follow and extend our former work on the subject. We give a detailed analysis with a rigorous calculation of the partition function, the free energy, and the order parameter in the coarse-graining method within the mean-field theory that is exact in the light-mode system. The outcome is a comprehensive picture of multipulse formation and annihilation, pulse after pulse, in an almost quantized manner, as the noise ("temperature") or the light power is varied. We obtain the phase diagram of the system, showing a series of first-order phase transitions, each belonging to a different number of pulses. We also study the hysteresis behavior, typical for such thermodynamic systems. We elaborate on the role of the saturable absorber structure in determining the multipulse formation. The theoretical results are compared to experimental measurements that we obtained with mode-locked fiber lasers, and we find an excellent agreement.

Self-starting of passive mode locking.

It has been recently understood that mode locking of lasers has the signification of a thermodynamic phase transition in a system of many interacting light modes subject to noise. In the same framework, self starting of passive mode locking has the thermodynamic significance of a noise-activated escape process across an entropic barrier. Here we present the first dynamical study of the light mode system. While accordant with the predictions of some earlier theories, it is the first to give precise quantitative predictions for the distribution of self-start times, in closed form expressions, resolving the long standing self starting problem. Numerical simulations corroborate these results, which are also in good agreement with experiments.

Self-similar relaxation dynamics of a fluid wedge in a Hele-Shaw cell.

Let the interface between two immiscible fluids in a Hele-Shaw cell have, at t = 0, a wedge shape. As a wedge is scale-free, the fluid relaxation dynamics are self-similar. We find the dynamic exponent of this self-similar flow and show that the interface shape is given by the solution of an unusual inverse problem of potential theory. We solve this problem analytically for an almost flat wedge, and numerically otherwise. The wedge solution is useful for analysis of pinch-off singularities.

Solution of a statistical mechanics model for pulse formation in lasers.

We present a rigorous statistical-mechanics theory of nonlinear many mode laser systems. An important example is the passively mode-locked laser that promotes pulse operation when a saturable absorber is placed in the cavity. It was shown by Phys. Rev. Lett. 89, 103901 (2002)] that pulse formation is a first-order phase transition of spontaneous ordering of modes in an effective "thermodynamic" system, in which intracavity noise level is the effective temperature. In this paper we present a rigorous solution of a model of passive mode locking. We show that the thermodynamics depends on a single parameter, and calculate exactly the mode-locking point. We find the phase diagram and calculate statistical quantities, including the dependence of the intracavity power on the gain saturation function, and finite size corrections near the transition point. We show that the thermodynamics is independent of the gain saturation mechanism and that it is correctly reproduced by a mean field calculation. The outcome is a new solvable statistical mechanics system with an unstable self-interaction accompanied by a natural global power constraint, and an exact description of an important many mode laser system.

First-harmonic approximation in nonlinear chirped-driven oscillators.

Nonlinear classical oscillators can be excited to high energies by a weak driving field provided the drive frequency is properly chirped. This process is known as autoresonance (AR). We find that for a large class of oscillators, it is sufficient to consider only the first harmonic of the motion when studying AR, even when the dynamics is highly nonlinear. The first harmonic approximation is also used to relate AR in an asymmetric potential to AR in a "frequency equivalent" symmetric potential and to study the autoresonance breakdown phenomenon.

Violation of smooth observable macroscopic realism in a harmonic oscillator.

We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.

Gain balance of pulses and noise in passive mode locking with slow saturable absorber.

We employ a recently developed gain balance principle to study the problem of passive mode locking with a slow saturable absorber in the presence of noise and solitonic pulse compression. We calculate the compression of the chirped pulse under general conditions and show that there is a minimal achievable pulse width owing to stability requirements. We derive the slow-absorber mode locking parameter, which must exceed a pulse-width-dependent minimal value to sustain mode locking, and calculate the fraction of the total intracavity power that resides in the pulse. We show that choosing the system parameters in an attempt to achieve shorter pulses reduces the pulse power, which, in contrast to fast-absorber passive mode locking, can attain arbitrary small values. Finally, we discuss the modification of the continuum stability condition needed to account for the effect of noise.