Multisoliton Regime Research Articles

Strategies for accessing the multipulse regime of mode-locked fiber lasers

Important ongoing research on mode-locked fiber lasers aims at developing new types of multisoliton regimes, such as soliton molecules, molecular complexes, or soliton crystals. The on-demand generation of such multipulse structures is a major challenge, whereas experiments generally involve a tedious trial-and-error adjustment of the laser parameters. Here we present an approach based on a gradual and calibrated adjustment of the system configuration, which employs efficient parameter routes to reach well-defined multipulse regimes. Our numerical simulations show that once the mode-locking threshold is reached, we can adjust the laser parameters gradually to force the evolution of the laser dynamics towards multipulse structures with fewer distortion in their intensity profiles, which are accessible at reduced pump power levels.

Two-Dimensional Nonlinear Thouless Pumping of Matter Waves.

We consider theoretically the nonlinear quantized Thouless pumping of a Bose-Einstein condensate loaded in two-dimensional dynamical optical lattices. We encountered three different scenarios of the pumping: a quasilinear one occurring for gradually dispersing wave packets, transport carried by a single two-dimensional soliton, and a multisoliton regime when the initial wave packet splits into several solitons. The scenario to be realized depends on the number of atoms in the initial wave packet and on the strength of the two-body interactions. The magnitude and direction of the displacement of a wave packet are determined by Chern numbers of the populated energy bands and by the interband transitions induced by two-body interactions. As a case example we explore a separable potential created by optical lattices whose constitutive sublattices undergo relative motion in the orthogonal directions. For such potentials, obeying parity-time symmetry, fractional Chern numbers, computed over half period of the evolution, acquire relevance. We focus mainly on solitonic scenarios, showing that one-soliton pumping occurs at relatively small as well as at sufficiently large amplitudes of the initial wave packet, while at intermediate amplitudes the transport is multisolitonic. We also describe peculiarities of the pumping characterized by two different commensurate periods of the modulations of the lattices in the orthogonal directions.

Dynamic behaviors of multiple-soliton pulsation in an L-band passively mode-locked fiber laser with anomalous dispersion.

As a universal phenomenon in nonlinear optical systems, the soliton pulsating behavior is useful to achieve high pulse energy and can further enrich the complex soliton dynamics. To the best of our knowledge, herein we have demonstrated the observation of multiple-soliton pulsations in an L-band mode-locked fiber laser based on a nonlinear amplifying loop mirror with anomalous dispersion for the first time. Based on the dispersive Fourier transform method, we find that the pulsations in the multi-soliton regime are accompanied with the pulse width breathing and spectrum oscillation. In addition, the corresponding number of pulsating solitons increases linearly from 8 to 16 with the pump power. Our findings can facilitate a better understanding of the complex mechanism of soliton pulsations.

Generation of multi-solitons and noise-like pulses in a high-powered thulium-doped all-fiber ring oscillator.

We report a study on the switching of the generation regimes in a high-powered thulium-doped all-fiber ring oscillator that is passively mode-locked with nonlinear polarization evolution technique with different pumping rates and cavity dispersion values. In one experimental setup, switching was observed between the noise-like pulse and the multi-soliton (in the forms of soliton bunches and soliton rain) regimes by the adjustment of the intracavity polarization controllers. We attributed this to the crucial influence of the nonlinear polarization evolution strength determined by such key parameters as saturation (over-rotation) power, linear phase bias, and nonlinear losses on the pulse evolution and stability. So the soliton collapse effect (leading to noise-like pulse generation) or the peak power clamping effect (generating a bunch of loosely-bound solitons) may determine pulse dynamics. Both the spectrum bandwidth and coherence time were studied for noise-like pulses by varying the cavity length and pump power, as well as the duration of solitons composing bunches. As a result, both noise-like pulses (with spectrum as broad as 32 nm bandwidth) and multi-soliton formations (with individual pulse-widths ranging from 748 to 1273 fs with a cavity length increase from 12 to 53 m) with up to 730 mW average power were generated at a wavelength of around 1.9 μm. The results are important for the realization of the broadband and smooth supercontinuum which can be used as a source for mid-IR vibrational spectroscopy of gas samples for breath analysis and environmental sensing.

Mutually ignited soliton explosions in a fiber laser.

Soliton explosions are among the most intriguing nonlinear dynamics in dissipative systems, manifesting themselves as a self-recovered localized structure when suffering explosive instabilities. Herein, we report on the investigation of soliton explosions in an ultrafast fiber laser operating in the multi-soliton regime. It is demonstrated that explosion of one soliton could be induced by another one through the soliton interactions mediated by the transient gain response of an erbium-doped fiber. We denote this phenomenon as "mutually ignited soliton explosions" when referring to the multi-soliton regime. The results provide the first investigation of soliton explosions in the multi-soliton regime and, therefore, will enhance a more comprehensive understanding of the soliton exploding phenomenon.

Intermittent burst of a super rogue wave in the breathing multi-soliton regime of an anomalous fiber ring cavity.

We report the intermittent burst of a super rogue wave in the multi-soliton (MS) regime of an anomalous-dispersion fiber ring cavity. We exploit the spatio-temporal measurement technique to log and capture the shot-to-shot wave dynamics of various pulse events in the cavity, and obtain the corresponding intensity probability density function, which eventually unveils the inherent nature of the extreme events encompassed therein. In the breathing MS regime, a specific MS regime with heavy soliton population, the natural probability of pulse interaction among solitons and dispersive waves exponentially increases owing to the extraordinarily high soliton population density. Combination of the probabilistically started soliton interactions and subsequently accompanying dispersive waves in their vicinity triggers an avalanche of extreme events with even higher intensities, culminating to a burst of a super rogue wave nearly ten times stronger than the average solitons observed in the cavity. Without any cavity modification or control, the process naturally and intermittently recurs within a time scale in the order of ten seconds.

Experimental spatio-temporal analysis on the shot-to-shot coherence and wave-packet formation in quasi-mode-locked regimes in an anomalous dispersion fiber ring cavity

We carry out systematic and dedicated experimental investigations on the shot-to-shot coherence and wave-packet formation in quasi-mode-locked (QML) regimes, including noise-like-pulse, symbiotic, and multi-soliton regimes in an anomalous-dispersion fiber ring cavity. To analyze the regimes in real-time, we take advantage of the spatio-temporal shot-to-shot measurement technique. We show that the individual regimes exhibit significantly different coherence characteristics, depending not only on the amount of nonlinear phase shift accumulated per roundtrip but also on the degree of soliton interaction, the latter of which crucially governs the bunching (i.e., the wave-packet formation) or anti-bunching mechanisms in the corresponding QML regimes. In fact, solitons with higher intensities tend to undergo higher nonlinear phase shift and stronger soliton interactions. Subsequently, the intensified soliton interactions among the individual solitons in the multi-soliton-regime cavity trigger them to form a bunched soliton-group, i.e., a wave packet, thereby resulting in QML pulses in the noise-like pulse or symbiotic regime. This complicated nonlinear process, in turn, causes a severe degradation in the shot-to-shot coherence of the resultant QML pulses. In addition, the shot-to-shot coherence trends observed in the experiment are in good agreement with our previous numerical predictions, so that the strong correlation between the shot-to-shot coherence of QML pulses and the corresponding nonlinear phase shift accumulated per roundtrip is confirmed by this experimental observation.

Numerical study on multi-pulse dynamics and shot-to-shot coherence property in quasi-mode-locked regimes of a highly-pumped anomalous dispersion fiber ring cavity.

We numerically investigate quasi-mode-locked (QML) multi-pulse dynamics in a fiber ring laser cavity in the anomalous dispersion regime. We show that the laser cavity can operate in five constitutively different QML regimes, depending on the saturation power of the saturable absorber element and the length of the passive fiber section that parameterize the overall nonlinearity and dispersion characteristic of the laser cavity. We classify them into the incoherent noise-like-pulse, partially-coherent noise-like-pulse, symbiotic, partially-coherent multi-soliton, and coherent multi-soliton regimes, accounting for their coherence and multi-pulse formation features. In particular, we numerically clarify and confirm the symbiotic regime for the first time to the best of our knowledge, in which noise-like pulses and multi-solitons coexist stably in the cavity that has recently been observed experimentally. Furthermore, we analyze the shot-to-shot coherence characteristics of the individual QML regimes relative to the amount of the nonlinear-phase shift per roundtrip, and verify a strong correlation between them. We also show that the net-cavity dispersion plays a critical role in determining the multi-pulse dynamics out of the partially-coherent noise-like-pulse, symbiotic, and partially-coherent multi-soliton regimes, when the cavity bears moderate nonlinearity. We quantify and visualize all those characteristics onto contour maps, which will be very useful and helpful in discussing and clarifying the complex QML dynamics.

Vector nature of multi-soliton patterns in a passively mode-locked figure-eight fiber laser.

The vector nature of multi-soliton dynamic patterns was investigated in a passively mode-locked figure-eight fiber laser based on the nonlinear amplifying loop mirror (NALM). By properly adjusting the cavity parameters such as the pump power level and intra-cavity polarization controllers (PCs), in addition to the fundamental vector soliton, various vector multi-soliton regimes were observed, such as the random static distribution of vector multiple solitons, vector soliton cluster, vector soliton flow, and the state of vector multiple solitons occupying the whole cavity. Both the polarization-locked vector solitons (PLVSs) and the polarization-rotating vector solitons (PRVSs) were observed for fundamental soliton and each type of multi-soliton patterns. The obtained results further reveal the fundamental physics of multi-soliton patterns and demonstrate that the figure-eight fiber lasers are indeed a good platform for investigating the vector nature of different soliton types.

Suppression of transverse instabilities of dark solitons and their dispersive shock waves

We investigate the impact of nonlocality, owing to diffusive behavior, on transverse instabilities of a dark stripe propagating in a defocusing cubic medium. The nonlocal response turns out to have a strongly stabilizing effect both in the case of a single soliton input and in the regime where dispersive shock waves develop "multisoliton regime". Such conclusions are supported by the linear stability analysis and numerical simulation of the propagation.

Soliton dynamics of megawatt ultrashort light pulses in a hollow photonic-crystal fiber: Effect of high-order dispersion and retarded nonlinearity

The properties of megawatt optical solitons in hollow photonic-crystal fibers (PCFs) are studied. We demonstrate regimes where high-power laser pulses can be compressed to a few cycles of light field and identify the main tendencies in the soliton dynamics of ultrashort laser pulses in hollow PCFs originating from dispersion properties and limited transmission band of such waveguides. The influence of retarded nonlinearity on the soliton dynamics of high-power laser pulses in a hollow PCF is analyzed. In a multisoliton regime, retarded nonlinearity and high-order dispersion are shown to result in the formation of high-power pulses displaying no oscillations of their temporal envelope, which would be typical of standard high-order solitons.

Multisoliton regime of pulse generation by lasers passively mode locked with a slow saturable absorber

We perform a study of soliton generation by a passively mode-locked laser using a slow saturable absorber. We show theoretically that multisoliton regimes of generation are possible. The values of the parameters are found where one-, two-, or three-soliton solutions exist.

Phase Pinning by EPR Probe in Biphenyl Doped with Naphthalene

The naphthalene Electronic Paramagnetic Resonance probe used to study the phase transitions in biphenyl does not account for the plane wave modulation of the incommensurate phase II. Its EPR spectra yields a phase distribution which looks like a multi-soliton regime. Moreover, the splitting between the edge singularities is not symmetrical, in contradiction with a linear one. This behaviour is not exhibited by the phenanthrene EPR probe whose spectra account well enough for the plane wave modulation with a linear coupling to the order parameter. To analyse the defect behaviour of the probe, we first introduce a coupling between the probe and the modulation wave and determine the phase distribution within the phenomenological Landau theory. Furthermore, a calculation based on intermolecular interaction is performed in order to describe the microscopic origin of this distribution and is applied to naphthalene and phenanthrene molecular probes.

Domain structure in biphenyl incommensurate phase II observed by electron paramagnetic resonance

The domain structure in incommensurate phase II of single biphenyl crystal has been observed by investigations of the optically excited states of the Electronic Paramagnetic Resonance (E.P.R.) deuterated naphthalene molecular probes which substitute biphenyl molecules. Our results confirm that this phase is a 1q bi-domain one. The analysis of the spectra obtained in X band (9.5 GHz) experiments, in relation with the spin Hamiltonian parameter properties permits us to show that the E.P.R. probe rotates around a direction perpendicular to its long axis while the biphenyl molecule undergoes a twist movement around this axis. They also account for a regime which is like a “ multi-soliton regime while the modulation is a plane wave one in the pure single crystal. The two molecules of the high temperature cell do not exactly experience the saure displacement field in the incommensurate phase and consequently the two domains can be distinguished. The spin Hamiltonian parameters which characterize the E.P.R. probes have been determined in the incommensurate phase II of biphenyl.

ESR and X-rays investigations of the incommensurate-commensurate phase transition in Rb2ZnCl4and [Rb(1−x)Kx]2ZnCl4

Abstract ‘‘Pure'’ and mixed Bridgman crystals, Rb2ZnCl4 and [Rb((1−x)Kx]2ZnCl4, doped in the melt with Mn2+ ions, are studied by E.P.R. and X-rays. In the multisoliton regime, we measure the density of the Mn2+ ions which occupy nearly the same sites as in the commensurate phase, and we obtain an estimation of the thermal evolution of the soliton density Ns(T). Nevertheless, these local measurements do not give any information about their long range ordering and involve measurements on the site occupied by an impurity. Therefore, using samples cleaved from the same Bridgman batch, only doped with Mn2+ ions, we compare the results of X-rays and E.P.R. investigations.

E.P.R. investigation on the multisoliton regime in betaine calcium chloride dihydrate

Abstract In this paper some results concerning an E.P.R. study of Mn2+ doped BCCD crystal are reported. We focused in a temperature range (130 K- 122 K) around the phase transition between the first incommensurate phase and the commensurate phase (q=2/7). A multisoliton regime with metastables states is evidenced.

Spin-wave envelope solitons in thin ferromagnetic films (invited)

The process of spin-wave (SW) envelope soliton formation and propagation has been studied experimentally in thin yttrium-iron-garnet (YIG) films at microwave frequencies. The formation of solitons has been observed in perpendicularly and tangentially magnetized YIG films in the spectral regions of high dispersion near the ‘‘dipole gaps’’ in the dipole-exchange SW spectrum. With the increase of the input pulse duration or/and amplitude, the multisoliton regime of SW propagation and the regime of SW modulational instability have been observed. With a further increase of input power the spectrum of SW modulational instability became more complicated and a SW strange attractor was formed through the destruction of two-frequency quasiperiodic motion. The theoretical interpretation of the observed nonlinear SW phenomena is given in the framework of nonlinear Schrodinger equation (NSE) model taking into account peculiarities of the thin-film dipole-exchange SW spectrum. The results of numerical calculations of SW envelope profiles performed using NSE model are compared to the results of the experiments.