arXiv subjects

Svetlana V. Gurevich

Publications and source records attributed to Svetlana V. Gurevich.

At least 37 records · Page 2Linked to original sources

arXiv2020

How carrier memory enters the Haus master equation of mode-locking

We present a generalization of the Haus master equation in which a dynamical boundary condition allows to describe complex pulse trains such as the Q-switched and harmonic transitions of passive mode-locking as well as the weak interactions between localized states. As an example, we investigate the influence of group velocity dispersion on the stability boundaries of the Q-switched regime. We compare our results with that of a time-delayed system.

physics.optics↗

arXiv2020

Phase-field crystal description of active crystallites: elastic and inelastic collisions

The active Phase-Field-Crystal (aPFC) model combines elements of the Toner-Tu theory for self-propelled particles and the classical Phase-Field-Crystal (PFC) model that describes the transition between liquid to crystalline phases. In the liquid-crystal coexistence region of the PFC model, crystalline clusters exist in the form of localized states that coexist with the homogeneous background. At sufficiently strong self-propulsion strength (or activity) they start to travel. We employ numerical path continuation and direct time simulations to first investigate the existence regions of different types of localized states for a one-dimensional system. The results are summarized in morphological phase diagrams in the parameter plane spanned by activity and mean concentration. Then we focus on the interaction of traveling localized states studying their collision behavior. As a result we distinguish 'elastic' and 'inelastic' collisions. In the former, localized states recover their properties after a collision while in the latter they may annihilate or form resting or traveling bound states. In passing, we describe oscillating and modulated traveling localized states that have as the steadily traveling localized states no counterpart in the classical PFC model.

nlin.PS↗

arXiv2020

Two-dimensional patterns in dip coating -- first steps on the continuation path

We present a brief comparative investigation of the bifurcation structure related to the formation of two-dimensional deposition patterns as described by continuum models of Cahn-Hilliard type. These are, on the one hand a driven Cahn-Hilliard model for Langmuir-Blodgett transfer of a surfactant layer from the surface of a bath onto a moving plate and on the other hand a driven thin-film equation modelling the surface acoustic wave-driven coating of a plate by a simple liquid. In both cases, we present selected two-dimensional steady states corresponding to deposition patterns and discuss the main structure of the corresponding bifurcation diagrams.

nlin.PS↗

arXiv2020

Bound States of Light Bullets in Passively-Mode-Locked Semiconductor Lasers

In this paper, we analyze the dynamics and formation mechanisms of bound states (BSs) of light bullets in the output of a laser coupled to a distant saturable absorber. First we approximate the full three-dimensional set of Haus master equations by a reduced equation governing the dynamics of the transverse profile. This effective theory allows us to perform a detailed multiparameter bifurcation study and to identify the different mechanisms of instability of BSs. In addition, our analysis reveals a non-intuitive dependence of the stability region as a function of the linewidth enhancement factors and the field diffusion. Our results are confirmed by direct numerical simulations of the full system.

nlin.PS↗

arXiv2020

Discrete Light Bullets in Passively Mode-Locked Semiconductor Lasers

In this paper, we analyze the formation and dynamical properties of discrete light bullets (dLBs) in an array of passively mode-locked lasers coupled via evanescent fields in a ring geometry. Using a generic model based upon a system of nearest-neighbor coupled Haus master equations we show numerically the existence of dLBs for different coupling strengths. In order to reduce the complexity of the analysis, we approximate the full problem by a reduced set of discrete equations governing the dynamics of the transverse profile of the dLBs. This effective theory allows us to perform a detailed bifurcation analysis via path-continuation methods. In particular, we show the existence of multistable branches of discrete localized states (dLSs), corresponding to different number of active elements in the array. These branches are either independent of each other or are organized into a snaking bifurcation diagram where the width of the dLS grows via a process of successive increase and decrease of the gain. Mechanisms are revealed by which the snaking branches can be created and destroyed as a second parameter, e.g., the linewidth enhancement factor or the coupling strength are varied. For increasing couplings, the existence of moving bright and dark dLSs is also demonstrated.

nlin.PS↗

arXiv2020

Topological Localized states in the time delayed Adler model: Bifurcation analysis and interaction law

The time-delayed Adler equation is arguably the simplest model for an injected semiconductor laser with coherent injection and optical feedback. It is able to reproduce the existence of topological localized structures (LSs) and their rich interactions. In this paper we perform the first extended bifurcation analysis of this model and we explore the mechanisms by which LSs emerge. We also derive the effective equations governing the motion of distant LSs and we stress how the lack of parity in time-delayed systems leads to exotic, non-reciprocal, interactions between topological localized states.

nlin.PS↗

arXiv2020

Dispersive instabilities in Passively Mode-Locked Integrated External-Cavity Surface-Emitting Lasers

We analyze the dynamics of passively mode-locked integrated external-cavity surface-emitting Lasers (MIXSELs) using a first-principle dynamical model based upon delay algebraic equations. We show that the third order dispersion stemming from the lasing micro-cavity induces a train of decaying satellites on the leading edge of the pulse. Due to the nonlinear interaction with carriers, these satellites may get amplified thereby destabilizing the mode-locked states. In the long cavity regime, the localized structures that exist below the lasing threshold are found to be deeply affected by this instability. As it originates from a global bifurcation of the saddle-node infinite period type, we explain why the pulses exhibit behaviors characteristic of excitable systems. Using the multiple time-scale and the functional mapping methods, we derive rigorously a master equation for MIXSELs in which third order dispersion is an essential ingredient. We compare the bifurcation diagram of both models and assess their good agreement.

physics.optics↗

arXiv2019

Effects of time-periodic forcing in a Cahn-Hilliard model for Langmuir-Blodgett transfer

The influence of a temporal forcing on the pattern formation in Langmuir-Blodgett transfer is studied employing a generalized Cahn-Hilliard model. The occurring frequency locking effects allow for controlling the pattern formation process. In the case of one-dimensional (i.e., stripe) patterns one finds various synchronization phenomena such as entrainment between the distance of deposited stripes and the forcing frequency. In two dimensions, the temporal forcing gives rise to the formation of intricate complex patterns such as vertical stripes, oblique stripes and lattice structures. Remarkably, it is possible to influence the system in the spatial direction perpendicular to the forcing direction leading to synchronization in two spatial dimensions.

nlin.PS↗

arXiv2019

Impact of high-order effects on soliton explosions in the complex cubic-quintic Ginzburg-Landau equation

We investigate the impact of higher-order nonlinear and dispersive effects on the onset of soliton explosions in the complex cubic-quintic Ginzburg-Landau equation. We show how the interplay of the high order effects (HOEs) results in the splitting of symmetric explosion modes and to the formation of right- or left-side periodic explosions. In addition, we demonstrate that HOEs induce a series of pulsating instabilities, leading to a significant reduction of the stability region of the single soliton solution.

nlin.PS↗

arXiv2019

Self-organised dip-coating patterns of simple, partially wetting, nonvolatile liquids

When a solid substrate is withdrawn from a bath of simple, partially wetting, nonvolatile liquid, one typically distinguishes two regimes, namely, after withdrawal the substrate is macroscopically dry or homogeneously coated by a liquid film. In the latter case, the coating is called a Landau-Levich film. Its thickness depends on the angle and velocity of substrate withdrawal. We predict by means of a numerical and analytical investigation of a hydrodynamic thin-film model the existence of a third regime. It consists of the deposition of a regular pattern of liquid ridges oriented parallel to the meniscus. We establish that the mechanism of the underlying meniscus instability originates from competing film dewetting and Landau-Levich film deposition. Our analysis combines a marginal stability analysis, numerical time simulations and a numerical bifurcation study via path-continuation.

physics.flu-dyn↗

arXiv2019

Stabilization of localized structures by inhomogeneous injection in Kerr resonators

We consider the formation of temporal localized structures or Kerr comb generation in a microresonator with inhomogeneities. We show that the introduction of even a small inhomogeneity in the injected beam widens the stability region of localized solutions. The homoclinic snaking bifurcation associated with the formation of localized structures and clusters of them with decaying oscillatory tails is constructed. Furthermore, the inhomogeneity allows not only to control the position of localized solutions, but strongly affects their stability domains. In particular, a new stability domain of a single peak localized structure appears outside of the region of multistability between multiple peaks of localized states. We identify a regime of larger detuning, where localized structures do not exhibit a snaking behavior. In this regime, the effect of inhomogeneities on localized solutions is far more complex: they can act either attracting or repelling. We identify the pitchfork bifurcation responsible for this transition. Finally, we use a potential well approach to determine the force exerted by the inhomogeneity and summarize with a full analysis of the parameter regime where localized structures and therefore Kerr comb generation exist and analyze how this regime changes in the presence of an inhomogeneity.

nlin.PS↗

arXiv2018

Stationary localized structures and the effect of the delayed feedback in the Brusselator model

The Brusselator reaction-diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the Brusselator model. By using numerical continuation methods in two spatial dimensions, we establish a bifurcation diagram showing the emergence of localized spots. We characterize the transition from a single spot to an extended pattern in the form of squares. In the second part, we incorporate delayed feedback control and show that delayed feedback can induce a spontaneous motion of both localized and periodic dissipative structures. We characterize this motion by estimating the threshold and the velocity of the moving dissipative structures.

nlin.PS↗

arXiv2018

Resting and Traveling Localized States in an Active Phase-Field-Crystal Model

The conserved Swift-Hohenberg equation (or Phase-Field-Crystal [PFC] model) provides a simple microscopic description of the thermodynamic transition between fluid and crystalline states. Combining it with elements of the Toner-Tu theory for self-propelled particles Menzel and Löwen [Phys. Rev. Lett. 110, 055702 (2013)] obtained a model for crystallization (swarm formation) in active systems. Here, we study the occurrence of resting and traveling localized states, i.e., crystalline clusters, within the resulting active PFC model. Based on linear stability analyses and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of periodic and localized, resting and traveling states in a one-dimensional active PFC model. This allows us, for instance, to explore how the slanted homoclinic snaking of steady localized states found for the passive PFC model is amended by activity. A particular focus lies on the onset of motion, where we show that it occurs either through a drift-pitchfork or a drift-transcritical bifurcation. A corresponding general analytical criterion is derived.

nlin.PS↗

arXiv2018

Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.

physics.flu-dyn↗

arXiv2018

A Functional Mapping for Passively Mode-Locked Semiconductor Lasers

We present a novel approach for the analysis of passively mode-locked semiconductor lasers that allows for efficient parameter sweeps and time jitter analysis. It permits accessing the ultra-low repetition rate regime where pulses become localized states. The analysis including slow (e.g. thermal) processes or transverse dynamics becomes feasible. Our method bridges the divide between the phenomenological, yet highly efficient, pulse iterative model that is the Haus master equation, and the more involved first principle descriptions relying on time delayed equations. Our iterative functional mapping exploits the fundamental division of the mode-locking regime between fast and slow stages and allows computing the dynamics only in the pulse vicinity. Reductions of the simulation times and of the memory footprint up to two orders of magnitudes are demonstrated. Finally, the mapping also provides a general framework for deducing the Haus master equation from first principle models based upon delayed differential equations.

physics.optics↗

arXiv2017

Dynamics of Temporal Localized States in Passively Mode-Locked Semiconductor Lasers

We study the emergence and the stability of temporal localized structures in the output of a semiconductor laser passively mode-locked by a saturable absorber in the long cavity regime. For large yet realistic values of the linewidth enhancement factor, we disclose the existence of secondary dynamical instabilities where the pulses develop regular and subsequent irregular temporal oscil- lations. By a detailed bifurcation analysis we show that additional solution branches that consist in multi-pulse (molecules) solutions exist. We demonstrate that the various solution curves for the single and multi-peak pulses can splice and intersect each other via transcritical bifurcations, lead- ing to a complex web of solution. Our analysis is based upon a generic model of mode-locking that consists in a time-delayed dynamical system, but also upon a much more numerically efficient, yet approximate, partial differential equation. We compare the results of the bifurcation analysis of both models in order to assess up to which point the two approaches are equivalent. We conclude our analysis by the study of the influence of group velocity dispersion, that is only possible in the framework of the partial differential equation model, and we show that it may have a profound impact on the dynamics of the localized states.

physics.optics↗

arXiv2017

Effect of Cherenkov radiation on localized states interaction

We study theoretically the interaction of temporal localized states in all fiber cavities and microresonator-based optical frequency comb generators. We show that Cherenkov radiation emitted in the presence of third order dispersion breaks the symmetry of their interaction and greatly enlarges the interaction range thus facilitating the experimental observation of the soliton bound states. Analytical derivation of the reduced equations governing slow time evolution of the positions of two interacting localized states in the Lugiato-Lefever model with third order dispersion term is performed. Numerical solutions of the model equation are in close agreement with analytical predictions.

physics.optics↗

arXiv2017

Nudged Elastic Band calculation of the binding potential for liquids at interfaces

The wetting behavior of a liquid on solid substrates is governed by the nature of the effective interaction between the liquid-gas and the solid-liquid interfaces, which is described by the binding or wetting potential $g(h)$ which is an excess free energy per unit area that depends on the liquid film height $h$. Given a microscopic theory for the liquid, to determine $g(h)$ one must calculate the free energy for liquid films of any given value of $h$; i.e. one needs to create and analyze out-of-equilibrium states, since at equilibrium there is a unique value of $h$, specified by the temperature and chemical potential of the surrounding gas. Here we introduce a Nudged Elastic Band (NEB) approach to calculate $g(h)$ and illustrate the method by applying it in conjunction with a microscopic lattice density functional theory for the liquid. We show too that the NEB results are identical to those obtained with an established method based on using a fictitious additional potential to stabilize the non-equilibrium states. The advantages of the NEB approach are discussed.

cond-mat.soft↗