Sequence Of Solitons Research Articles

Highly controllable stabilization and switching of multiple colliding soliton sequences with generic Ginzburg–Landau gain–loss

We investigate propagation of J soliton sequences in a nonlinear optical waveguide array with generic weak Ginzburg–Landau (GL) gain–loss and nearest-neighbor (NN) interaction. The propagation is described by a system of J perturbed coupled nonlinear Schrödinger (NLS) equations. The NN interaction property leads to the elimination of collisional three-pulse interaction effects, which prevented the observation of stable multisequence soliton propagation with J>2 sequences in the presence of generic GL gain–loss in all previous studies. We show that the dynamics of soliton amplitudes can be described by a generalized J-dimensional Lotka–Volterra (LV) model. Stability and bifurcation analysis for the equilibrium points of the LV model, which is augmented by an application of the Lyapunov function method, is used to develop setups that lead to robust and scalable transmission stabilization and switching for a general J value. The predictions of the LV model are confirmed by extensive numerical simulations with the perturbed coupled-NLS model with J=3, 4, and 5 soliton sequences. Furthermore, soliton stability and the agreement between the LV model’s predictions and the simulations are not reduced with increasing value of J. Therefore, our study provides the first demonstration of robust control of multiple colliding sequences of NLS solitons in the presence of generic weak GL gain–loss with an arbitrary number of sequences. Due to the robustness and scalability of the results, they can have important applications in stabilization and switching of broadband soliton-based optical waveguide transmission.

Controlling intracavity dual-comb soliton motion in a single-fiber laser.

Ultrafast science builds on dynamic compositions of precisely timed light pulses, and evolving groups of pulses are observed in almost every mode-locked laser. However, the underlying physics has rarely been controlled or used until now. Here, we demonstrate a general approach to control soliton motion inside a dual-comb laser and the programmable synthesis of ultrashort pulse patterns. Introducing single-pulse modulation inside an Er:fiber laser, we rapidly shift the timing between two temporally separated soliton combs. Their superposition outside the cavity yields ultrashort soliton sequences. On the basis of real-time spectral interferometry, we observe the deterministic switching of intersoliton separation arising from the interplay of attracting and repulsing forces via ultrafast nonlinearity and laser gain dynamics. Harnessing these insights, we demonstrate the high-speed all-optical synthesis of nano- to picosecond pump-probe delays and programmable free-form soliton trajectories. This concept may pave the way to a new class of all-optical delay generators for ultrafast measurements at unprecedented high tuning, cycling, and acquisition speeds.

Dissipative microwave photonic solitons in spontaneous frequency-hopping optoelectronic oscillators

Dissipative solitons relying on the double balance between nonlinear and linear effects as well as cavity loss and gain have attracted increasing attention in recent years, since they give rise to novel operating states of various dissipative nonlinear systems. An optoelectronic oscillator (OEO) is a dissipative nonlinear microwave photonic system with a high quality factor that has been widely investigated for generating ultra-low noise single-frequency microwave signals. Here, we report a novel operating state of an OEO related to dissipative solitons, i.e., spontaneous frequency hopping related to the formation of dissipative microwave photonic solitons. In this operating state, dissipative microwave photonic solitons occur due to the double balance between nonlinear gain saturation and linear filtering as well as cavity loss and gain in the OEO cavity, creating spontaneous frequency-hopping microwave signals. The generation of wideband tunable frequency-hopping microwave signals with a fast frequency-hopping speed up to tens of nanoseconds is observed in the experiment, together with the corresponding soliton sequences. This work reveals a novel mechanism between the interaction of nonlinear and linear effects in an OEO cavity, extends the suitability and potential applications of solitons, and paves the way for a new class of soliton microwave photonic systems for the generation, processing, and control of microwave and RF signals.

On the amplitude dynamics of solitons in waveguide systems with the generic Kerr nonlinearity coefficient and nonlinear gain-loss

We study the transmission of optical solitons in a nonlinear waveguide with the generic Kerr nonlinearity coefficient, the frequency dependent linear gain-loss, and the Ginzburg-Landau (GL) gain-loss profile. We first derive the expression for the collision-induced amplitude dynamics of two fast single solitons in the presence of weak cubic loss and weak quintic loss. This expression is then used to study the amplitude dynamics of solitons in multichannel optical waveguide systems. We show that the dynamics of soliton amplitudes in two-sequence transmission with the GL gain-loss profile are described by a Lotka-Volterra (LV) model. The stability analysis for the LV model is used to obtain the simple conditions on the physical parameters and to calculate the linear amplifier gain-loss for the transmission stabilization of the soliton sequences. The theoretical calculations are then confirmed by numerical simulations with the corresponding nonlinear Schrödinger (NLS) models. Furthermore, the optimal value of the Kerr nonlinearity coefficient for the robust transmission stabilization of the soliton sequences with the GL gain-loss profile is also proposed.

Dynamics of new optical solitons for the Triki–Biswas model using beta-time derivative

This paper comprises the different types of optical soliton solutions of an important Triki–Biswas model equation with beta-time derivative. The beta derivative is considered as a generalized version of the classical derivative. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation that describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel beta derivative operator and three efficient integration schemes. During this work, a sequence of new optical solitons is produced that may have an importance in optical fiber systems. These solutions are verified and numerically simulated through soft computation.

Propagation of diverse ultrashort pulses in optical fiber to Triki–Biswas equation and its modulation instability analysis

This paper presents the modulation instability (MI) analysis and the different types of optical soliton solutions of the Triki–Biswas model equation. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation which describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel efficient integration scheme. During this work, a sequence of optical solitons is produced that may have an important in optical fiber systems. The results show that the studied model hypothetically has incredibly rich optical soliton solutions. The constraint conditions for valid soliton solutions are also reported. The gained results show that the applied method is efficient, powerful and can be applied to various complex models with the help of representative calculations.

On the Capacity of Amplitude Modulated Soliton Communication over Long Haul Fibers.

The capacity limits of fiber-optic communication systems in the nonlinear regime are not yet well understood. In this paper, we study the capacity of amplitude modulated first-order soliton transmission, defined as the maximum of the so-called time-scaled mutual information. Such definition allows us to directly incorporate the dependence of soliton pulse width to its amplitude into capacity formulation. The commonly used memoryless channel model based on noncentral chi-squared distribution is initially considered. Applying a variance normalizing transform, this channel is approximated by a unit-variance additive white Gaussian noise (AWGN) model. Based on a numerical capacity analysis of the approximated AWGN channel, a general form of capacity-approaching input distributions is determined. These optimal distributions are discrete comprising a mass point at zero (off symbol) and a finite number of mass points almost uniformly distributed away from zero. Using this general form of input distributions, a novel closed-form approximation of the capacity is determined showing a good match to numerical results. Finally, mismatch capacity bounds are developed based on split-step simulations of the nonlinear Schrdinger equation considering both single soliton and soliton sequence transmissions. This relaxes the initial assumption of memoryless channel to show the impact of both inter-soliton interaction and Gordon–Haus effects. Our results show that the inter-soliton interaction effect becomes increasingly significant at higher soliton amplitudes and would be the dominant impairment compared to the timing jitter induced by the Gordon–Haus effect.

Metastable breathers and local diamagnetism in two-dimensional nonlinear metamaterials

This article investigates the dynamic properties of two-dimensional nonlinear magnetic metamaterials consisting of nanoscale elements. The authors propose a model for a two-dimensional lattice of capacitively and inductively coupled split rectangular nanoresonators. It has been shown that the long-wave dynamics of this two-dimensional lattice are described by a regularized two-dimensional nonlinear Klein–Gordon equation, which has been solved in the form of two sequences of two-dimensional dynamic solitons on a pedestal of homogeneous forced oscillations, using an asymptotic method and taking into account the action of electromotive force (EMF) induced by an electromagnetic wave. The authors have calculated a diamagnetic response to an electromagnetic field in the terahertz range in the metamaterial region, where a breather is excited and oscillates in antiphase to a homogeneous background. The evolution of long-lived metastable breathers has been numerically studied, and two scenarios – collapse and decay – have been established for the development of their instability depending on the parameters of the induced EMF and inductive coupling between nanoresonators. It has been found that at the boundary between these scenarios, the final result of the transformation of the breathers is the chimera state of the metamaterial with a large-amplitude breather that generates stochastic waves.

Frequency shifting for solitons based on transformations in the Fourier domain and applications

We develop the theoretical procedures for shifting the frequency of a single soliton and of a sequence of solitons of the nonlinear Schr\"odinger equation. The procedures are based on simple transformations of the soliton pattern in the Fourier domain and on the shape-preserving property of solitons. These theoretical frequency shifting procedures are verified by numerical simulations with the nonlinear Schr\"odinger equation using the split-step Fourier method. In order to demonstrate the use of the frequency shifting procedures, two important applications are presented: (1) stabilization of the propagation of solitons in waveguides with frequency dependent linear gain-loss; (2) induction of repeated soliton collisions in waveguides with weak cubic loss. The results of numerical simulations with the nonlinear Schr\"odinger model are in very good agreement with the theoretical predictions.

Steady state multiple dark spatial solitons in the biased photorefractive-photovoltaic crystals

We theoretically study the evolution of dark solitons in the biased photorefractive-photovoltaic crystal by using beam propagation method (BPM). We find that when the absolute value of the extra bias field is less than the photovoltaic field, the dark screening-photovoltaic (SP) solitons can be observed. The initial width of the dark notch at the entrance face of the crystal is a key parameter for generating an sequence of dark coherent solitons. If the initial width of the dark notch is small, only a fundamental soliton or Y-junction soliton pair is generated. When the initial width of the dark notch is increased, the dark notch tends to split into an odd (or even) number of multiple dark solitons, which realizes a progressive transition from the low-order solitons to a sequence of higher-order solitons.

Large stable oscillations due to Hopf bifurcations in amplitude dynamics of colliding soliton sequences

We demonstrate that the amplitudes of optical solitons in nonlinear multisequence optical waveguide coupler systems with weak linear and cubic gain-loss exhibit large stable oscillations along ultra-long distances. The large stable oscillations are caused by supercritical Hopf bifurcations of the equilibrium states of the Lotka–Volterra (LV) models for dynamics of soliton amplitudes. The predictions of the LV models are confirmed by numerical simulations with the coupled cubic nonlinear Schrödinger (NLS) propagation models with 2 ≤ N ≤ 4 pulse sequences. Thus, we provide the first demonstration of intermediate nonlinear amplitude dynamics in multisequence soliton systems, described by the cubic NLS equation. Our findings are also an important step towards realization of spatio-temporal chaos with multiple periodic sequences of colliding NLS solitons.

Possible spectroscopic signature of wave collapse in edge plasmas

In plasmas coupled to an external energy source like a beam of energetic electrons, one can observe the non‐linear coupling of Langmuir waves with ion sound and electromagnetic waves. This non‐linear interaction of waves changes the structural and radiative properties of plasmas. Coherent wave packets are trapped in regions of high intensity, and are subjected to a wave collapse cycle. We show that the electric field of the wave packets can modify the spectral lines emitted by hydrogen atoms. Our model for this field is a sequence of envelope solitons oscillating at the plasma frequency or the upper hybrid frequency. The calculations presented concern the Hα and Hβ Balmer lines of hydrogen and show the possible modifications of the line shapes if wave collapse conditions affect the edge plasma.

Line shapes in turbulent plasmas

The fluctuations and oscillations observed in turbulent plasmas may affect the line shapes emitted by atoms and ions. We investigate several plasma conditions for which a spectroscopic signature of plasma turbulence can be observed. Starting from the simple model of microturbulence for Doppler profile, we examine how information on turbulent fluctuations is obtained in astrophysics and magnetic fusion plasmas. We recall the potential of a formalism which expresses the measured line shape in function of the probability density function of the fluctuating plasma parameters. New calculations of hydrogen dipole autocorrelation functions and line shapes are presented for plasmas affected by strong Langmuir turbulence and nonlinear wave collapse. We propose a model using a sequence of envelope solitons for the electric field created by the wave packets and felt by the emitters, and show that the line shape may be dominated by the effect of strong Langmuir turbulence.

Study on soliton phase characteristics in 100 Gbps single‐channel telecommunication system

SummaryHere, we demonstrate the peculiar particle nature of soliton pulses with relative to phase, where the adjacent soliton pulses in a sequence attract and repel each other periodically for in‐phase and out‐of‐phase arrangement, respectively. This effect of soliton's interaction and repulsion is studied analytically by using perturbation theory approach. The study of soliton pair characteristics are mainly noted for different relative spacing (qo) between them and for different phase of launched soliton pulses. Following the analytical studies, we analyzed the effect in a 100 Gbps, single channel and uncompensated telecommunication system for different phased soliton sequences. Such that, the performance of the telecommunication system is characterized in terms of Q‐factor (Q) and bit‐error rate to realize the influence of phase on soliton pulses. The system was studied for 1 collision length (LD) of 123.36 km. It is seen that, for 100 Gbps system implemented with standard single mode telecom fiber, with soliton spaced at qo = 5.28, the in‐phase pulses interacted at 61.68 km, which has resulted in Q = 0 (bit‐error rate = 1). It is realized that for small‐phase introduction on soliton pulses, the system yielded fair Q demonstrating the non‐interaction at the Ip as the pulses deviate with respect to increasing phase values. But, it is also shown that large phase between pulses introduces more deviation, which results in overlapping of deviated pulses with adjacent pulses in sequence resulting in degradation of high bitrate system performance.

Stable scalable control of soliton propagation in broadband nonlinear optical waveguides

We develop a method for achieving scalable transmission stabilization and switching of $N$ colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in $N$-sequence transmission is described by a generalized $N$-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of $M$ out of $N$ soliton sequences. Numerical simulations for single-waveguide transmission with a system of $N$ coupled nonlinear Schr\"odinger equations with $2 \le N \le 4$ show excellent agreement with the predator-prey model's predictions and stable propagation over significantly larger distances compared with other broadband nonlinear single-waveguide systems. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated by the simulations. We discuss the reasons for the robustness and scalability of transmission stabilization and switching in waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss, and explain their advantages compared with other broadband nonlinear waveguides.

Observations of meteotsunami on the Louisiana shelf: a lone soliton with a soliton pack

The paper reports unique high-resolution observations of meteotsunami by a large array of oceanographic instruments deployed on the Atchafalaya Shelf (Louisiana, USA) in 2008 with the primary aim to study wave dissipation in muddy environments. The meteotsunami event on March 7, 2008, was caused by the passage of a cold front which was monitored by the NOAA NEXRAD radar. The observations of water surface elevations on the shelf show a highly detailed textbook picture of an undular bore (solibore) in the process of its disintegration into a train of solitons. The picture has a striking feature never reported before not only for the meteotsunamis but in other contexts of disintegration of a long-wave perturbation into a sequence of solitons as well—the persistent presence of a single soliton, well ahead of the solibore. Data analysis and simulations based on the celebrated variable-coefficient KdV (vKdV) equation first proposed by Ostrovsky and Pelinovsky (Izv Atmos Ocean Phys 11:37–41, 1975) explain the physics of this phenomenon and suggest that the formation of the lone soliton ahead of the solibore is very likely to be the result of the specific interplay of natural meteotsunami forcing and nearshore bathymetry. The analysis strongly suggests that the patterns of coexisting lone solitons and packets of cnoidal waves should be quite common for meteotsunamis. They were not observed before only because of the scarcity of high-resolution observations. The results highlight the effectiveness of the vKdV equation in providing understanding of the fundamental mechanisms of the complex natural phenomenon that would otherwise require computationally very expensive numerical models.

All-optical bit storage in a fibre laser by optomechanically bound states of solitons

Optomechanically coupled modes in a fibre laser cavity make it possible to generate and robustly store gigahertz-rate soliton sequences.

Sequential formation of multiple lattice gap solitons in defocusing photovoltaic–photorefractive crystals

We show that an odd- or even-numbered sequence of multiple gap solitons (MGSs) supported by optical lattices imprinted in defocusing photovoltaic–photorefractive (PP) crystals is possible. The side lobes of MGSs are the small intensity, which can be controlled by changing the propagation constant. The lobes of MGSs are the same intensity except for the side lobes. The existence domain of MGSs decreases with decreasing the lattice depth and vanishes when the lattice depth decreases to below a certain threshold. The stability of MGSs has been investigated numerically and it has been found that they are stable.

Analysis of chaotic bright spin-wave soliton trains in magnetic films

We have experimentally studied a chaotic dynamics of bright spin-wave soliton trains. Thin yttrium iron garnet films having pinned surface spins were used for the experiments providing propagation of highly dispersive dipole-exchange spin waves. Chaotic soliton trains were excited in the frequency band around low-frequency part of dipole gap of spin wave spectrum. Analysis of fractal dimension, embedding dimension, and Lyapunov exponents was carried out based on measured time profiles of chaotic soliton sequences. We find that the fractal dimension and Lyapunov exponents are weak function of carrier frequency around dipole gap whereas embedding dimension is almost constant.

Robust transmission stabilization and dynamic switching in broadband hybrid waveguide systems with nonlinear gain and loss

We develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with the coupled nonlinear Schr\"odinger equations confirm the predictions of the LV model, and show stable transmission over distances larger by an order of magnitude compared with uniform waveguides with linear gain and cubic loss. Moreover, multiple on-off and off-on dynamic switching events are demonstrated over a wide range of soliton amplitudes, showing the superiority of hybrid waveguides compared with static switching in uniform waveguides, considered in earlier studies.