arXiv subjects

Avner Peleg

Publications and source records attributed to Avner Peleg.

At least 19 recordsLinked to original sources

arXiv2026

Transition to spatiotemporal chaos with multiple colliding pulse sequences of the nonlinear Schr\"odinger equation

We present the first demonstration of transition to spatiotemporal chaos with multiple colliding pulse sequences in systems described by perturbed cubic nonlinear Schr\"odinger (NLS) equations. For this purpose, we consider propagation of multiple sequences of optical pulses in two distinct types of nonlinear waveguide arrays with cubic gain and loss. By employing a perturbation theory for NLS solitons, we show that the dynamics of pulse energies in the waveguide array systems is described by generalized Lotka-Volterra (LV) models, which exhibit dissipative chaos in a wide region in parameter space. We test the LV models' predictions for chaotic dynamics of pulse energies by extensive numerical simulations with perturbed systems of coupled-NLS equations. We find excellent agreement between the results of the LV and coupled-NLS models for energy dynamics in both types of waveguide array systems, despite the strong pulse pattern distortions and the strongly nonlinear nature of the dynamics.

nlin.PS↗

arXiv2024

Stabilizing optical solitons by frequency-dependent linear gain-loss and the collisional Raman frequency shift

We study transmission stabilization of optical solitons against emission of radiation in nonlinear optical waveguides in the presence of weak linear gain-loss, cubic loss, and the collisional Raman frequency shift. We first show how the collisional Raman frequency shift perturbation arises in three different physical setups. We then show by numerical simulations with a perturbed nonlinear Schr\"odinger (NLS) model that transmission in waveguides with weak frequency-independent linear gain is unstable. The radiative instability is stronger than the radiative instabilities that were observed in earlier studies for soliton transmission in the presence of weak linear gain, cubic loss, and various frequency-shifting physical mechanisms. In particular, the Fourier spectrum of the radiation is significantly more spiky and broadband than the radiation's Fourier spectra in earlier studies. Moreover, we demonstrate by numerical simulations with another perturbed NLS model that transmission in waveguides with weak frequency-dependent linear gain-loss, cubic loss, and the collisional Raman frequency shift is stable. Despite the stronger radiative instability in the corresponding waveguide setup with weak linear gain, stabilization occurs via the same generic mechanism that was suggested in earlier studies. More precisely, the collisional Raman frequency shift experienced by the soliton leads to the separation of the soliton's and the radiation's Fourier spectra, while the frequency-dependent linear gain-loss leads to efficient suppression of radiation emission. Thus, our study demonstrates the robustness of the proposed generic soliton stabilization method, which is based on the interplay between perturbation-induced shifting of the soliton's frequency and frequency-dependent linear gain-loss.

nlin.PS↗

arXiv2024

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 independent 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.

nlin.PS↗

arXiv2023

Stabilizing solitons of the cubic-quintic nonlinear Schrödinger equation by frequency-dependent linear gain-loss and delayed Raman response

We demonstrate transmission stabilization against radiation emission by frequency-dependent linear gain-loss and perturbation-induced frequency shifting for solitons of the cubic-quintic nonlinear Schrödinger (CQNLS) equation. We consider soliton propagation in a nonlinear optical waveguide with focusing cubic nonlinearity, defocusing quintic nonlinearity, and dissipative perturbations due to weak frequency-dependent linear gain-loss, cubic loss, and delayed Raman response. The frequency shifting is induced by delayed Raman response. Our perturbation analysis and numerical simulations with the perturbed CQNLS equation show that transmission stabilization with CQNLS solitons is indeed possible, and in this way provide the first demonstration of the stabilization method for solitons of a nonintegrable nonlinear wave model. Moreover, we find that transmission stabilization with energetic CQNLS solitons is realized with significantly smaller frequency shifts and pulse distortion compared with stabilization with energetic solitons of the cubic nonlinear Schrödinger equation. Therefore, our study also demonstrates that stabilization of energetic solitons by the method is significantly improved by the presence of defocusing quintic nonlinearity.

nlin.PS↗

arXiv2022

Fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2

We investigate the dynamics of fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2. We introduce a two-dimensional perturbation method, which generalizes the perturbation method used for studying two-pulse collisions in spatial dimension 1. We then use the generalized perturbation method to show that a fast collision in spatial dimension 2 leads to a change in the pulse shape in the direction transverse to the advection velocity vector. Moreover, we show that in the important case of a separable initial condition, the longitudinal part in the expression for the amplitude shift has a simple universal form, while the transverse part does not. Additionally, we show that anisotropy in the initial condition leads to a complex dependence of the amplitude shift on the orientation angle between the pulses. Our perturbation theory predictions are in very good agreement with results of extensive numerical simulations with the weakly perturbed diffusion-advection model. Thus, our study significantly enhances and generalizes the results of previous works on fast collisions in diffusion-advection systems, which were limited to spatial dimension 1.

nlin.PS↗

arXiv2022

Strong effects of fast collisions between pulsed optical beams in a linear medium with weak cubic loss

We investigate fast collisions between pulsed optical beams in a linear medium with weak cubic loss that arises due to nondegenerate two-photon absorption. We introduce a perturbation method with two small parameters and use it to obtain general formulas for the collision-induced changes in the pulsed-beam's shape and amplitude. Moreover, we use the method to design and characterize collision setups that lead to strong localized and nonlocalized intensity reduction effects. The values of the collision-induced changes in the pulsed-beam's shape in both setups are larger by one to two orders of magnitude compared with the values obtained in previous studies of fast two-pulse collisions. Furthermore, we show that for nonlocalized setups, the graph of the collision-induced amplitude shift vs the difference between the first-order dispersion coefficients for the two pulsed-beams has two local minima. This finding represents the first observation of a deviation of the graph from the common funnel shape that was obtained in all previous studies of fast two-pulse collisions in the presence of weak nonlinear loss. The predictions of our perturbation theory are in good agreement with results of numerical simulations with the perturbed linear propagation model, despite the strong collision-induced effects. Our results can be useful for multisequence optical communication links and for reshaping of pulsed optical beams.

nlin.PS↗

arXiv2021

Fast two-beam collisions in a linear optical medium with weak cubic loss in spatial dimension higher than 1

We study the dynamics of fast two-beam collisions in linear optical media with weak cubic loss in spatial dimension higher than 1. For this purpose, we extend the perturbation theory that was developed for analyzing two-pulse collisions in spatial dimension 1 to spatial dimension 2. We use the extended two-dimensional version of the perturbation theory to show that the collision leads to a change in the beam shapes in the direction transverse to the relative velocity vector. Furthermore, we show that in the important case of a separable initial condition for both beams, the longitudinal part in the expression for the amplitude shift is universal, while the transverse part is not universal. Additionally, we demonstrate that the same behavior holds for collisions between pulsed optical beams in spatial dimension 3. We check these predictions of the perturbation theory along with other predictions concerning the effects on the collision of partial beam overlap and anisotropy in the initial condition by extensive numerical simulations with the weakly perturbed linear propagation model in spatial dimensions 2 and 3. The agreement between the perturbation theory and the simulations is very good. Therefore, our study significantly extends and generalizes the results of previous works, which were limited to spatial dimension 1.

physics.optics↗

arXiv2019

Radiation dynamics in fast soliton collisions in the presence of cubic loss

We study the dynamics of emission of radiation (small-amplitude waves) in fast collisions between two solitons of the nonlinear Schrödinger (NLS) equation in the presence of weak cubic loss. We calculate the radiation dynamics by a perturbation technique with two small parameters: the cubic loss coefficient $ε_{3}$ and the reciprocal of the group velocity difference $1/β$. The agreement between the perturbation theory predictions and the results of numerical simulations with the full coupled-NLS propagation model is very good for large $β$ values, and is good for intermediate $β$ values. Additional numerical simulations with four simplified NLS models show that the differences between perturbation theory and simulations for intermediate $β$ values are due to the effects of Kerr nonlinearity on interpulse interaction in the collision. Thus, our study demonstrates that the perturbation technique that was originally developed to study radiation dynamics in fast soliton collisions in the presence of conservative perturbations can also be employed for soliton collisions in the presence of dissipative perturbations.

nlin.PS↗

arXiv2018

Universality of the amplitude shift in fast two-pulse collisions in weakly perturbed linear physical systems

We demonstrate that the amplitude shifts in fast two-pulse collisions in perturbed linear physical systems with weak nonlinear dissipation exhibit universal soliton-like behavior. The behavior is demonstrated for linear optical waveguides with weak cubic loss and for systems described by linear diffusion-advection models with weak quadratic loss. We show that in both systems, the expressions for the collision-induced amplitude shifts due to the nonlinear loss have the same form as the expression obtained for a fast collision between two solitons of the nonlinear Schrödinger equation in the presence of weak cubic loss. Furthermore, we show that the expressions for the amplitude shifts are universal in the sense that they are independent of the exact details of the initial pulse shapes. We demonstrate the universal soliton-like behavior of the collision-induced amplitude shifts by carrying out numerical simulations with the two perturbed coupled linear evolution models with three different initial conditions corresponding to pulses with exponentially decreasing tails, pulses with power-law decreasing tails, and pulses that are initially nonsmooth and that develop significant tails during the collision. In all six cases we observe very good agreement between the analytic predictions for the amplitude shifts and the results of the numerical simulations.

nlin.PS↗

arXiv2018

Enhancement of transmission quality in soliton-based optical waveguide systems by frequency dependent linear gain-loss and the Raman self-frequency shift

We study transmission stabilization against radiation emission in soliton-based nonlinear optical waveguides with weak linear gain-loss, cubic loss, and delayed Raman response. We show by numerical simulations with perturbed nonlinear Schrödinger propagation models that transmission quality in waveguides with frequency independent linear gain and cubic loss is not improved by the presence of delayed Raman response due to the lack of an efficient mechanism for suppression of radiation emission. In contrast, we find that the presence of delayed Raman response leads to significant enhancement of transmission quality in waveguides with frequency dependent linear gain-loss and cubic loss. Enhancement of transmission quality in the latter waveguides is enabled by the separation of the soliton's spectrum from the radiation's spectrum due to the Raman-induced self-frequency shift and by efficient suppression of radiation emission due to the frequency dependent linear gain-loss. Further numerical simulations demonstrate that the enhancement of transmission quality in waveguides with frequency dependent linear gain-loss, cubic loss, and delayed Raman response is similar to transmission quality enhancement in waveguides with linear gain, cubic loss, and guiding filters with a varying central frequency.

physics.optics↗

arXiv2017

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 $2 \le N \le 4$ 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.

nlin.PS↗

arXiv2017

Soliton-like behavior in fast two-pulse collisions in weakly perturbed linear physical systems

We demonstrate that pulses of linear physical systems, weakly perturbed by nonlinear dissipation, exhibit soliton-like behavior in fast collisions. The behavior is demonstrated for linear waveguides with weak cubic loss and for systems described by linear diffusion-advection models with weak quadratic loss. We show that in both systems, the expressions for the collision-induced amplitude shifts due to the nonlinear loss have the same form as the expression for the amplitude shift in a fast collision between two optical solitons in the presence of weak cubic loss. Our analytic predictions are confirmed by numerical simulations with the corresponding coupled linear evolution models with weak nonlinear loss. These results open the way for studying dynamics of fast collisions between pulses of weakly perturbed linear physical systems in an arbitrary spatial dimension.

nlin.PS↗

arXiv2017

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 Schrödinger 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.

nlin.PS↗

arXiv2016

Transmission stability and Raman-induced amplitude dynamics in multichannel soliton-based optical waveguide systems

We study transmission stability and dynamics of pulse amplitudes in $N$-channel soliton-based optical waveguide systems, taking into account second-order dispersion, Kerr nonlinearity, delayed Raman response, and frequency dependent linear gain-loss. We carry out numerical simulations with systems of $N$ coupled nonlinear Schrödinger (NLS) equations and compare the results with the predictions of a simplified predator-prey model for Raman-induced amplitude dynamics. Coupled-NLS simulations for single-fiber transmission with $2 \le N \le 4$ frequency channels show stable oscillatory dynamics of soliton amplitudes at short-to-intermediate distances, in excellent agreement with the predator-prey model's predictions. However, at larger distances, we observe transmission destabilization due to resonant formation of radiative sidebands, which is caused by Kerr nonlinearity. The presence of linear gain-loss in a single fiber leads to a limited increase in transmission stability. Significantly stronger enhancement of transmission stability is achieved in a nonlinear $N$-waveguide coupler due to efficient suppression of radiative sideband generation by the linear gain-loss. As a result, the distances along which stable Raman-induced dynamics of soliton amplitudes is observed are significantly larger in the waveguide coupler system compared with the single-fiber system.

nlin.PS↗

arXiv2016

Stabilizing soliton-based multichannel transmission with frequency dependent linear gain-loss

We report several major theoretical steps towards realizing stable long-distance multichannel soliton transmission in Kerr nonlinear waveguide loops. We find that transmission destabilization in a single waveguide is caused by resonant formation of radiative sidebands and investigate the possibility to increase transmission stability by optimization with respect to the Kerr nonlinearity coefficient $γ$. Moreover, we develop a general method for transmission stabilization, based on frequency dependent linear gain-loss in Kerr nonlinear waveguide couplers, and implement it in two-channel and three-channel transmission. We show that the introduction of frequency dependent loss leads to significant enhancement of transmission stability even for non-optimal $γ$ values via decay of radiative sidebands, which takes place as a dynamic phase transition. For waveguide couplers with frequency dependent linear gain-loss, we observe stable oscillations of soliton amplitudes due to decay and regeneration of the radiative sidebands.

nlin.PS↗

arXiv2014

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 Schrödinger 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.

nlin.PS↗

arXiv2013

Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction

We study propagation and on-off switching of two colliding soliton sequences in the presence of second-order dispersion, Kerr nonlinearity, linear loss, cubic gain, and quintic loss. Employing a Lotka-Volterra (LV) model for dynamics of soliton amplitudes along with simulations with two perturbed coupled nonlinear Schrödinger (NLS) equations, we show that stable long-distance propagation can be achieved for a wide range of the gain-loss coefficients, including values that are outside of the perturbative regime. Furthermore, we demonstrate robust on-off and off-on switching of one of the sequences by an abrupt change in the ratio of cubic gain and quintic loss coefficients, and extend the results to pulse sequences with periodically alternating phases. Our study significantly strengthens the recently found relation between collision dynamics of sequences of NLS solitons and population dynamics in LV models, and indicates that the relation might be further extended to solitary waves of the cubic-quintic Ginzburg-Landau equation.

nlin.PS↗

arXiv2013

Many-body interaction in fast soliton collisions

We study $n$-pulse interaction in fast collisions of $N$ solitons of the cubic nonlinear Schrödinger (NLS) equation in the presence of generic weak nonlinear loss. We develop a reduced model that yields the contribution of $n$-pulse interaction to the amplitude shift for collisions in the presence of weak $(2m+1)$-order loss, for any $n$ and $m$. We first employ the reduced model and numerical solution of the perturbed NLS equation to analyze soliton collisions in the presence of septic loss $(m=3)$. Our calculations show that three-pulse interaction gives the dominant contribution to the collision-induced amplitude shift already in a full-overlap four-soliton collision, and that the amplitude shift strongly depends on the initial soliton positions. We then extend these results for a generic weak nonlinear loss of the form $G(|ψ|^{2})ψ$, where $ψ$ is the physical field and $G$ is a Taylor polynomial of degree $m_{c}$. Considering $m_{c}=3$, as an example, we show that three-pulse interaction gives the dominant contribution to the amplitude shift in a six-soliton collision, despite the presence of low-order loss. Our study quantitatively demonstrates that $n$-pulse interaction with high $n$ values plays a key role in fast collisions of NLS solitons in the presence of generic nonlinear loss. Moreover, the scalings of $n$-pulse interaction effects with $n$ and $m$ and the strong dependence on initial soliton positions lead to complex collision dynamics, which is very different from the one observed in fast NLS soliton collisions in the presence of cubic loss.

nlin.PS↗