Soliton Resonance Research Articles

Gramian solutions and solitonic interactions of a (2+1)-dimensional Broer–Kaup–Kupershmidt system for the shallow water

PurposeThis paper aims to study the Gramian solutions and solitonic interactions of a (2 + 1)-dimensional Broer–Kaup–Kupershmidt (BKK) system, which models the nonlinear and dispersive long gravity waves traveling along two horizontal directions in the shallow water of uniform depth.Design/methodology/approachPfaffian technique is used to construct the Gramian solutions of the (2 + 1)-dimensional BKK system. Asymptotic analysis is applied on the two-soliton solutions to study the interaction properties.FindingsN-soliton solutions in the Gramian with a real function ζ(y) of the (2 + 1)-dimensional BKK system are constructed and proved, where N is a positive integer and y is the scaled space variable. Conditions of elastic and inelastic interactions between the two solitons are revealed asymptotically. For the three and four solitons, elastic, inelastic interactions and soliton resonances are discussed graphically. Effect of the wave numbers, initial phases and ζ(y) on the solitonic interactions is also studied.Originality/valueShallow water waves are studied for the applications in environmental engineering and hydraulic engineering. This paper studies the shallow water waves through the Gramian solutions of a (2 + 1)-dimensional BKK system and provides some phenomena that have not been studied.

Higher-dimensional extended shallow water equations and resonant soliton radiation

Higher order equations governing long surface waves in shallow water beyond the standard Korteweg-de Vries and Kadomtsev-Petviashvili equations are derived from the full water wave equations. The higher order dispersive and nonlinear terms in these equations lead to resonance between nonlinear wave structures and dispersive radiation. This resonance between solitary waves and dispersive shock waves (undular bores) is studied numerically and analytically using exponential asymptotic theory. A key result is that there is a near node in the resonant wave amplitude for the higher order equations with the water wave coefficients.

Temporal dissipative structures in optical Kerr resonators with transient loss fluctuation.

Dissipative structures are the result of spontaneous symmetry breaking in a dynamic open system, which is induced by either the nonlinear effect or loss fluctuations. While optical temporal dissipative solitons in nonlinear Kerr cavities has been widely studied, their operation is limited to the red-detuned regime. Here, we demonstrate an emergent dissipative soliton state in optical nonlinear cavities in the presence of loss fluctuations, which is accessible by self-evolution of the system on resonance. Based on a modified dissipative and Kerr-nonlinear cavity model, we numerically investigate the effect of the loss modulation on the intracavity field pattern, and in transmission observe a single and bright soliton pulse state at the zero detuning. The effect of the optical saturable absorption is also numerically investigated, which is recognized as an effective approach to the transient loss fluctuation in the cavity. The estimated power efficiency of the resonant bright soliton can be higher than that of the conventional dissipative Kerr soliton, which is determined by the loss modulation depth and the pump intensity. The self-starting soliton state on system's resonance is potentially of wide interest, which physically contributes to insights of the temporal structure formation in dissipative cavities. On application aspect, it may constitute a way to the generation of ultra-fast soliton pulse trains as well as the generation of soliton micro-combs.

Oscillatory motion of dissipative solitons induced by delay-feedback in inhomogeneous Kerr resonators

We investigate the destabilization mechanisms of dissipative solitons in inhomogeneous nonlinear resonators subjected to injection and to time-delayed feedback. We consider the paradigmatic Lugiato-Lefever model describing inhomogeneous driven nonlinear optical resonator. We analyze the pinning-depinning transition of dissipative solitons by introducing a potential induced by the inhomogeneity. Further, we identify conditions under which these structures are destabilized and describe different bifurcation scenarios. We show that the combined influence of inhomogeneities and delayed feedback induces an Andronov-Hopf-bifurcation that leads to oscillations of the dissipative soliton around the inhomogeneity. Finally, we show that for large values of the feedback strength, the dissipative solitons escapes from the potential well and starts to drift.

Nd-Doped Polarization Maintaining All-Fiber Laser With Dissipative Soliton Resonance Mode-Locking at 905 nm

Moving the fiber laser emission to the region below one micron may provide a cheaper, more compact and robust alternatives to the existing solid state lasers. Here, for the first time we report a neodymium mode-locked fiber laser emitting at 905 nm in the all-fiber polarization maintaining configuration. We obtain a self-starting pulse generation in nonlinear amplifying loop mirror (NALM) cavity configuration. To suppress a dominant emission at 1064 nm corresponding to a 4-level laser scheme, we use an active fiber - 920/1064 division multiplexer - active fiber sandwich-like sequence in the NALM loop. A rectangular shape dissipative soliton had nJ energy, 30 pm spectral width and 80 - 430 ps width linearly depending on the pump power. Excellent agreement with numerical simulation allowed us to recover pulse shape and width for the pulses out of autocorrelation window.

3 W average-power high-order mode pulse in dissipative soliton resonance mode-locked fiber laser

AbstractRecently high-order modes (HOMs) lasers have been extensively investigated due to their potential applications in mode-division multiplexing. In this paper, we present two schemes of generating HOMs from the mode-locked fiber lasers (MLFLs) in the dissipative soliton resonance (DSR) regime. Watt-level HOM outputs are implemented through intra-cavity mode conversion. 3 W average-power HOMs with an efficiency slope of 25% can be obtained based on an MLFL in the DSR regime, which is achieved by incorporating a long-period fiber grating (LPFG) and a dual-resonant acoustically induced fiber grating (AIFG), respectively. Their different spectrum responses enable flexible mode conversion in the MLFLs. Both fiber mode converters are exploited to show their robust capability of efficient mode manipulation. The MLFL with an LPFG inserted in the cavity can achieve wide-bandwidth intra-cavity optical vortex beams (OVBs) near the dispersion turning around point because of the pulses of the fundamental mode and high-order vortex eigenmodes oscillating in the cavity with the same group velocity to form spatiotemporal mode locking. The MLFL based on a dual-resonant AIFG can perform the function of fast switching (∼0.3 ms) in LP01, LP11a, and LP11bmodes with a high modal purity of 96%. These different modes with high-energy pulses can be flexibly switched with programmable radio frequency modulation. Furthermore, a quarter-wave plate and a polarizer are employed at the output of fiber laser to realize the controllability of the mode field, which is possible to generate a controllable mode field of OVBs based on the first-order Poincaré sphere. This control method can be integrated with the MLFLs to extend the flexibility of high-power HOMs generation.

Multiple solitary wave interactions

Theoretical solutions of two-soliton resonance show the possibility that the amplitude of soliton resonance is four times as large as the incident solitary wave at the critical angle. The two-soliton interaction with a symmetrical configuration is generally categorized into (3142)-type and (2143)-type (O-type). Previous studies demonstrated that amplification factors of (3142)-type and O-type are successfully reproduced by using a function of the modified Miles' prediction, κ, in which (3142)-type and O-type correspond to 0<κ<1 and κ>1. However, a train of solitary waves often occurs in shallow water, resulting in multiple solitary wave interactions. Therefore, it is necessary to investigate the interaction of multiple solitary waves due to soliton resonance. We, thus, applied theoretical solutions to analyze the interaction of multiple solitary waves, which was validated by using numerical simulations based on the variational principle. It was revealed that the second and the subsequent soliton resonances are O-type when κ is larger than zero.

Resonance [formula omitted]-type soliton and hybrid solutions of a (2+1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

In this paper, a (2+1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation is studied. By adding some new constraints to the N-soliton solutions, the resonance Y-type soliton and the interaction solutions between M-resonance Y-type solitons and P-resonance Y-type solitons are obtained. The new types of solutions including the double openings of resonance Y-type soliton solutions and mixed solutions of resonance solitons and breathers are presented. The hybrid solutions consisting of the resonance Y-type solitons and the multiple lump waves are constructed by using restrictions and the long wave limit method. The trajectories of lump waves in hybrid waves are analyzed from the point of view of mathematical mechanism. The results are helpful to explain some new nonlinear phenomena in the theory of solitons.

Resonant line wave soliton solutions and interaction solutions for (2+1)-dimensional nonlinear wave equation

Based on the N-soliton solutions, the resonant line wave soliton and interaction solutions are derived through some constraints in the (2+1)-dimensional nonlinear wave equation. General resonant line wave soliton solutions are firstly presented and their changing routes are illustrated. Then, several interaction solutions including a nonlinear superposition of resonant line wave soliton with breather wave, a hybrid between resonant line wave soliton and lump wave are constructed via long-wave limit method and module resonant mechanism. The characteristics and properties of these interaction solutions are discussed analytically and graphically. Localized wave and interaction solutions of the nonlinear wave models have a great impact on oceanography and physics. The results may be useful in investigating the physical phenomena in shallow water waves and nonlinear optics.

Q-switched dissipative soliton resonance operation in GeTe based fiber laser

Q-switched dissipative soliton resonance (DSR) operation in a germanium telluride (GeTe) based erbium-doped fiber laser is investigated experimentally. The modulation depth of the GeTe based saturable absorber is about 12.3%. For the Q-switched envelope of the DSR operation in this laser, its repetition rate increases monotonically from 6.95 to 14.09 kHz and full-width at half-maximum decreases from 24.46 to 18.37 μs when pump power changes from 39.1 to 101.1 mW. With increase of pump power, the width of DSR pulse increases from 13.3 to 20.7 ns, and the average output power varies from 1.1 to 2.1 mW. The highest average single-pulse energy of DSR is calculated as 2.44 nJ at pump power of 101.1 mW. This result show that Q-switched DSR operation can be obtained in a nanocrystal based fiber laser, which will broaden the application of nanocrystals in fiber lasers.

Space-Curved Resonant Line Solitons in a Generalized (2 + 1)-Dimensional Fifth-Order KdV SystemSupported by the National Natural Science Foundation of China (Grant Nos. 11775121 and 11435005), and the K. C. Wong Magna Fund at Ningbo University.

On the basis of N-soliton solutions, space-curved resonant line solitons are derived via a new constraint proposed here, for a generalized (2+1)-dimensional fifth-order KdV system. The dynamic properties of these new resonant line solitons are studied in detail. We then discuss the interaction between a resonance line soliton and a lump wave in greater detail. Our results highlight the distinctions between the generalized (2+1)-dimensional fifth-order KdV system and the classical type.

Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System

Under investigation in this paper is the higher-order Broer-Kaup(HBK) system, which describes the bidirectional propagation of long waves in shallow water. Via the standard truncated Painlevé expansion method, the residual symmetry of this system is derived. By introducing an appropriate auxiliary-dependent variable, the residual symmetry is successfully localized to Lie point symmetries. Via solving the initial value problems, the finite symmetry transformations are presented. However, the solution which obtained from the residual symmetry is a special group invariant solutions. In order to find more general solution of HBK system, we further generalize the residual symmetry method to the consistent tanh expansion (CTE) method and prove that the HBK system is CTE solvable, then the resonant soliton solutions and interaction solutions among different nonlinear excitations are obtained by the CET method.

Soliton Molecules and Full Symmetry Groups to the KdV-Sawada-Kotera-Ramani Equation

By N -soliton solutions and a velocity resonance mechanism, soliton molecules are constructed for the KdV-Sawada-Kotera-Ramani (KSKR) equation, which is used to simulate the resonances of solitons in one-dimensional space. An asymmetric soliton can be formed by adjusting the distance between two solitons of soliton molecule to small enough. The interactions among multiple soliton molecules for the equation are elastic. Then, full symmetry group is derived for the KSKR equation by the symmetry group direct method. From the full symmetry group, a general group invariant solution can be obtained from a known solution.

Soliton gas in bidirectional dispersive hydrodynamics.

The theory of soliton gas had been previously developed for unidirectional integrable dispersive hydrodynamics in which the soliton gas properties are determined by the overtaking elastic pairwise interactions between solitons. In this paper, we extend this theory to soliton gases in bidirectional integrable Eulerian systems where both head-on and overtaking collisions of solitons take place. We distinguish between two qualitatively different types of bidirectional soliton gases: isotropic gases, in which the position shifts accompanying the head-on and overtaking soliton collisions have the same sign, and anisotropic gases, in which the position shifts for head-on and overtaking collisions have opposite signs. We construct kinetic equations for both types of bidirectional soliton gases and solve the respective shock-tube problems for the collision of two "monochromatic" soliton beams consisting of solitons of approximately the same amplitude and velocity. The corresponding weak solutions of the kinetic equations consisting of differing uniform states separated by contact discontinuities for the mean flow are constructed. Concrete examples of bidirectional Eulerian soliton gases for the defocusing nonlinear Schrödinger (NLS) equation and the resonant NLS equation are considered. The kinetic equation of the resonant NLS soliton gas is shown to be equivalent to that of the shallow-water bidirectional soliton gas described by the Kaup-Boussinesq equations. The analytical results for shock-tube Riemann problems for bidirectional soliton gases are shown to be in excellent agreement with direct numerical simulations.

Generation of dissipative soliton resonance in a fiber laser based on a nonlinear optical loop mirror

We experimentally demonstrate generation of mode-locked pulses in dissipative soliton resonance (DSR) regime. The DSR pulses are obtained from a passively mode-locked figure-8 Er:Yb doped fiber laser operating in large net anomalous dispersion regime. The modelocked laser emission is based on a polarization-imbalanced nonlinear optical loop mirror (NOLM), acting as artificial saturable absorber. Stable square DSR pulses, obtained by carefully adjusting the NOLM properties, increase their duration from 2.47 ns to 46.52 ns as the pump power is increased from 0.68 to 6.31 W. With the maximum pump power launched, average output power of 73.95 mW with pulse energy of 53.39 nJ is achieved.

1.3\xa0\xb5m dissipative soliton resonance generation in Bismuth doped fiber laser

In this work, a Figure-9 (F9) bismuth-doped fiber laser (BiDFL) operating in the dissipative soliton resonance (DSR) regime is presented. The 1338 nm laser used a BiDF as the active gain medium, while a nonlinear amplifying loop mirror (NALM) in an F9 configuration was employed to obtain high energy mode-locked pulses. The wave breaking-free rectangular pulse widened significantly in the time domain with the increase of the pump power while maintaining an almost constant peak power of 0.6 W. At the maximum pump power, the mode-locked laser delivered a rectangular-shaped pulse with a duration of 48 ns, repetition rate of 362 kHz and a radio-frequency signal-to-noise ratio of more than 60 dB. The maximum output power was recorded at around 11 mW with a corresponding pulse energy of 30 nJ. This is, to the best of the author’s knowledge, the highest mode-locked pulse energy obtained at 1.3 μm as well as the demonstration of an NALM BiDFL in a F9 configuration.

Tunable peak power square-wave pulse based on an all-PM thulium-doped mode-locked fiber laser.

Nanosecond dissipative soliton resonance pulse is a demonstration of an all polarization-maintaining (PM) thulium-doped fiber laser in a nonlinear amplifying loop mirror (NALM)-based figure-eight configuration. Each loop of the apparatus includes a controllable power amplifier. With increased amplifier power, pulse width broadens linearly from 3.6 to 13.5 ns, and maximum single pulse energy can reach 27.5 nJ. Interestingly, the output peak power presents two completely opposite proportional effects in terms of the variation of settings for two amplifiers, respectively. The experimental results show that the NALM loop plays an important role for tunable pulse duration, and the unidirectional ring part makes a significant contribution for power scaling.

Resonant Optical Nonlinearity and Fluorescence Enhancement in Electrically Tuned Plasmonic Nanosuspensions

Controlled orientation and alignment of rod‐shaped plasmonic nanoparticles are of great interest for many applications. Herein, it is demonstrated that the nonlinear optical response of gold nanorod suspensions is dynamically controlled by electric field‐induced orientation. Merely by switching incident light polarization, the longitudinal and transverse surface plasmon resonance (SPR) absorption peaks are modulated with opposite trends, and the resulting optical nonlinearity is revealed from self‐trapping of plasmonic resonant solitons. Moreover, even with a very low concentration of fluorescent molecules, a significant increase in the fluorescent signal is observed with a transmittance‐type volume detection scheme. Such an enhancement is attributed to a combined action of optical force‐induced nonlinearity and electric field‐induced nanorod orientation, as explained by the theoretical analyses. Herein, new possibilities for engineering nonlinear plasmonic soft matter and detecting low‐concentration (yet a large total number of moleculesas needed) fluorescent samples are brought out.

Coherence characterization of nanosecond rectangular pulses in passively mode-locked fiber lasers

Dissipative soliton resonance (DSR) phenomenon is a recent concept of pulse formation proposed to achieve a high-energy passively mode-locked fiber laser. Such pulses have general features, e.g., flat-top temporal profile, energy scalability, and temporal coherence. To identify the nature of various rectangular pulses which share most of DSR features, it is important to verify their coherence. When a pulse is in the nanosecond range, the experimental study of the coherence is a complex task, which is overlooked in the literature. In this work, a novel approach is proposed for the first time to study the coherence of nanosecond rectangular pulses. It is based on two different methods: Mach-Zehnder interferometer (MZI) and dispersive Fourier transformation (DFT).

Sub-nanosecond gain-switched Ytterbium-doped fiber laser pumped by 1030 nm dissipative soliton resonance mode-locked fiber laser

In this work we report on a tandem pumped gain-switched Yb-doped fiber laser. We used an amplified dissipative soliton resonance mode-locked fiber laser with the wavelength of 1030 nm as a source of high repetition rate pulsed pump, incorporated with a CW diode laser at the wavelength of 976 nm in hybrid pump scheme. Sub-nanosecond narrow line-width gain-switched pulses with peak power of 10 kW at 1064 nm have been achieved. The line-width of the gain-switched laser is less than 0.06 nm and the repetition rate is 683 kHz.