arXiv subjects

Svetlana V. Gurevich

Publications and source records attributed to Svetlana V. Gurevich.

At least 19 recordsLinked to original sources

arXiv2026

Disentangling Memory and Nonlinearity in Time-Multiplexed Optical Reservoir Computing

We analyze and disentangle the individual and combined roles of nonlinearity, transient dynamics, and delayed feedback, and investigate how these mechanisms contribute to different task requirements in photonic reservoir computing. This is achieved using a passive linear photonic reservoir in which a photodiode at the optical-to-electrical interface provides the sole source of nonlinearity. We demonstrate how the requirements of different tasks can be quantified and compared to the dynamics provided by the reservoir by explicitly calculating and comparing the contributing monomials. Our findings include that a reservoir with uncoupled virtual nodes and a quadratic nonlinearity can already achieve good performance for tasks derived from dynamical systems with quadratic nonlinearities, such as the Lorenz63 system. Furthermore, transient coupling and delayed feedback significantly enhance the computational capabilities by compensating for missing higher-order monomials through an effective multi-step integration scheme, given the minimum nonlinearity required for the task is present in the reservoir.

nlin.CD↗

arXiv2026

Impact of phase modulation on the dynamics of temporal localized structures in injected Kerr microcavities

We theoretically investigate how phase modulation alters the dynamics of temporal localized structures (TLSs) in vertically emitting Kerr micro-cavities under detuned optical injection operating in the normal dispersion regime. We show that the emergence of TLSs in general is governed by a synchronization between the imposed modulation and the intrinsic pulse dynamics. We perform a multi-parameter bifurcation analysis of the underlying delay-algebraic equation model in the uniform field limit and demonstrate that weakly nonlinear and dissipative Hermite-Gauss modes shape the dynamics of dark TLSs, leading to a complex hybrid bifurcation structure. Beyond the uniform field limit, both bright and dark modulated TLSs are shown to exist and to occupy distinct equilibrium positions within the cavity. An effective equation of motion for the TLS positions is derived, showing a good agreement with the full model.

nlin.PS↗

arXiv2025

Time Crystals in Actively Mode-locked Lasers

We report the first experimental observation of discrete time-crystal phases and crystallites in an actively mode-locked semiconductor laser. By tuning either the bias current or the modulation frequency, the system undergoes a spontaneous symmetry-breaking transition from the harmonically mode-locked state towards robust, highly coherent time-crystal states that persist indefinitely. Two equivalent time-crystal configurations, shifted by one driving period, can coexist as domains separated by sharp, long-lived boundaries analogous to domain walls. The phenomenon is quantitatively reproduced by a time-delayed model adapted to the large gain and losses of semiconductor systems. Our findings demonstrate that mode-locked semiconductor lasers offer a readily accessible platform to explore and control non-equilibrium phases of light, enabling practical implementations of time-crystal physics in photonic systems.

physics.optics↗

arXiv2025

Coherent pulse interactions in mode-locked semiconductor lasers

We study the dynamics of multipulse solutions in mode-locked lasers in presence of time-delayed feedback stemming, e.g., from reflections upon optical elements, and carrier dynamics. We demonstrate that the dynamics of such a high dimensional problem can be successfully described by some effective equations of motion for the pulses' phases and positions. Analyzing the reduced vector field permits disclosing a highly complex dynamics where coherent and incoherent interactions compete. The latter lead to regimes in which pulses can be equidistant or non-equidistant and also have different phase relations. Multi-stability between regimes is also observed as well as emerging limit cycles and global heteroclinic bifurcations in phase space.

nlin.PS↗

arXiv2024

Thermo-optical spiking and mixed-mode oscillations in injected Kerr microcavities

We investigate the nonlinear dynamics of vertically emitting Kerr microcavities under detuned optical injection, considering the impact of slow thermal effects. Our model integrates thermal detuning caused by refractive index shifts due to heating. Through numerical and analytical approaches, we uncover a rich spectrum of dynamical behaviors, including excitable thermo-optical pulses, mixed-mode oscillations, and chaotic spiking, governed by a higher-dimensional canard scenario. Introducing a long external feedback loop with time delays comparable to the microcavity photon lifetime but shorter than thermal relaxation timescales, reveals how delay affects excitability and stabilizes temporal localized states. Our findings extend the understanding of excitable systems, demonstrating how thermal and feedback mechanisms interplay to shape nonlinear optical dynamics. Further, our approach paves the way for the study of cavity stabilization and cavity cooling using an additional control beam.

physics.optics↗

arXiv2024

Pulse instabilities in harmonic active mode-locking: a time-delayed approach

We propose a time-delayed model for the study of active mode-locking that is valid for large values of the round-trip gain and losses. It allows us to access the typical regimes encountered in semiconductor lasers and to perform an extended bifurcation analysis. Close to the harmonic resonances and to the lasing threshold, we recover the Hermite-Gauss solutions. However, the presence of the linewidth enhancement factor induces complex regimes in which even the fundamental solution becomes unstable. Finally, we discover a global bifurcation scenario in which a single pulse can jump, over a slow time scale, between the different minima of the modulation potential.

physics.optics↗

arXiv2024

Excitability and memory in a time-delayed optoelectronic neuron

We study the dynamics of an optoelectronic circuit composed of an excitable nanoscale resonant-tunneling diode (RTD) driving a nanolaser diode (LD) coupled via time-delayed feedback. Using a combination of numerical path-continuation methods and time simulations, we demonstrate that this RTD-LD system can serve as an artificial neuron, generating pulses in the form of temporal localized states (TLSs) that can be employed as memory for neuromorphic computing. In particular, our findings reveal that the prototypical delayed FitzHugh-Nagumo model previously employed to model the RTD-LD resembles our more realistic model only in the limit of a slow RTD. We show that the RTD time scale plays a critical role in memory capacity as it governs a shift in pulse interaction from repulsive to attractive, leading to a transition from stable to unstable multi-pulse TLSs. Our theoretical analysis uncovers features and challenges previously unknown for the RTD-LD system, including the multistability of TLSs and attractive interaction forces, stemming from the previously neglected intrinsic dynamics of the laser. These effects are crucial to consider since they define the memory properties of the RTD-LD.

nlin.PS↗

arXiv2023

Square Waves and Bykov T-points in a Delay Algebraic Model for the Kerr-Gires-Tournois Interferometer

We study theoretically the mechanisms of square wave formation of a vertically emitting micro-cavity operated in the Gires-Tournois regime that contains a Kerr medium and that is subjected to strong time-delayed optical feedback and detuned optical injection. We show that in the limit of large delay, square wave solutions of the time-delayed system can be treated as relative homoclinic solutions of an equation with an advanced argument. Based on this, we use concepts of classical homoclinic bifurcation theory to study different types of square wave solutions. In particular, we unveil the mechanisms behind the collapsed snaking scenario of square waves and explain the formation of complex-shaped multistable square wave solutions through a Bykov T-point. Finally we relate the position of the T-point to the position of the Maxwell point in the original time-delayed system.

nlin.PS↗

arXiv2023

Stationary broken parity states in active matter models

We demonstrate that several nonvariational continuum models commonly used to describe active matter as well as other active systems exhibit nongeneric behavior: each model supports asymmetric but stationary localized states even in the absence of pinning at heterogeneities. Moreover, such states only begin to drift following a drift-transcritical bifurcation as the activity increases. Asymmetric stationary states should only exist in variational systems, i.e., in models with gradient structure. In other words, such states are expected in passive systems, but not in active systems where the gradient structure of the model is broken by activity. We identify a "spurious" gradient dynamics structure of these models that is responsible for this nongeneric behavior, and determine the types of additional terms that render the models generic, i.e., with asymmetric states that appear via drift-pitchfork bifurcations and are generically moving. We provide detailed illustrations of our results using numerical continuation of resting and steadily drifting states in both generic and nongeneric cases.

cond-mat.soft↗

arXiv2023

Temporal localized states and square-waves in semiconductor micro-resonators with strong time-delayed feedback

In this paper we study the dynamics of a vertically-emitting micro-cavity operated in the Gires-Tournois regime that contains a semiconductor quantum-well and that is subjected to strong time-delayed optical feedback and detuned optical injection. Using a first principle time-delay model for the optical response, we disclose sets of multistable dark and bright temporal localized states coexisting on their respective bistable homogeneous backgrounds. In the case of anti-resonant optical feedback, we disclose square-waves with a periodic of twice the round-trip in the external cavity. Finally, we perform a multiple time-scale analysis in the good cavity limit. The resulting normal form is in good agreement with the original time-delayed model.

nlin.PS↗

arXiv2022

Exploring Bifurcations in Bose-Einstein Condensates via Phase Field Crystal Models

To facilitate the analysis of pattern formation and of the related phase transitions in Bose-Einstein condensates (BECs) we present an explicit approximate mapping from the nonlocal Gross-Pitaevskii equation with cubic nonlinearity to a phase field crystal (PFC) model. This approximation is valid close to the superfluid-supersolid phase transition boundary. The simplified PFC model permits the exploration of bifurcations and phase transitions via numerical path continuation employing standard software. While revealing the detailed structure of the bifurcations present in the system, we demonstrate the existence of localized states. Finally, we discuss how higher-order nonlinearities change the structure of the bifurcation diagram representing the transitions found in the system.

nlin.PS↗

arXiv2022

Square wave generation in vertical external-cavity Kerr-Gires-Tournois interferometers

We study theoretically the mechanisms of square-wave (SW) formation in vertical external-cavity Kerr-Gires-Tournois interferometers in presence of anti-resonant injection. We provide simple analytical approximations for their plateau intensities and for the conditions of their emergence. We demonstrate that SWs may appear via a homoclinic snaking scenario, leading to the formation of complex-shaped multistable SW solutions. The resulting SWs can host localized structures and robust bound-states.

physics.optics↗

arXiv2022

A normal form for frequency combs and localized states in Kerr-Gires-Tournois interferometers

We elucidate the mechanisms that underly the formation of temporal localized states and frequency combs in vertical external-cavity Kerr-Gires-Tournois interferometers. We reduce our first principle model based upon delay algebraic equations to a minimal pattern formation scenario. It consists in a real cubic Ginzburg-Landau equation modified by high-order effects such as third order dispersion and nonlinear drift. The latter are responsible for generating localized states via the locking of domain walls connecting the high and low intensity levels of the injected micro-cavity. We interpret the effective parameters of the normal form in relation with the configuration of the optical setup. Comparing the two models, we observe an excellent agreement close to the onset of bistability.

physics.optics↗

arXiv2022

Influence of time-delayed feedback on the dynamics of temporal localized structures in passively mode-locked semiconductor lasers

In this paper, we analyze the effect of optical feedback on the dynamics of a passively mode-locked ring laser operating in the regime of temporal localized structures. This laser system is modeled by a system of delay differential equations, which include delay terms associated with the laser cavity and the feedback loop. Using a combination of direct numerical simulations and path-continuation techniques, we show that the feedback loop creates echos of the main pulse whose position and size strongly depend on the feedback parameters. We demonstrate that in the long-cavity regime, these echos can successively replace the main pulses, which defines their lifetime. This pulse instability mechanism originates from a global bifurcation of the saddle-node infinite-period type. In addition, we show that, under the influence of noise, the stable pulses exhibit forms of behavior characteristic of excitable systems. Furthermore, for the harmonic solutions consisting of multiple equispaced pulses per round-trip we show that if the location of the pulses coincide with the echo of another, the range of stability of these solutions is increased. Finally, it is shown that around these resonances, branches of different solutions are connected by period doubling bifurcations.

nlin.PS↗

arXiv2021

Wiggling Instabilities of Temporal Localized States in Passively Mode-Locked Vertical External-Cavity Surface-Emitting Lasers

We analyze the emergence of wiggling temporal localized states in a passively mode-locked Vertical External- Cavity Surface-Emitting Laser composed by a gain chip and a resonant saturable absorber mirror. We show that the wiggling instability stems from the interplay between the third-order dispersion induced by the micro-cavities and their frequency mismatch. The latter is identified as an experimentally crucial parameter defining the range of existence of stable emission. We reveal the homoclinic scenario underlying the wiggling phenomenon and we show how it allows to control the oscillation.

physics.optics↗

arXiv2021

Phase incoherent photonic molecules in V-shaped mode-locked VECSELs

Passively mode-locked vertical external-cavity surface-emitting semiconductor lasers (VECSELs) composed of a gain chip and a semiconductor saturable absorber have been drawing much attention due to their excellent performance figures. In this work we investigate how localized structures and incoherent, non-locally bound, pulse molecules emerge in a long cavity VECSELs using a V-shaped cavity geometry. We show that these states are bistable with the laser off state and that they are individually addressable. Using a model based upon delay differential equations, we demonstrate that pulse clusters result from the cavity geometry and from the non-local coupling with the gain medium; this leads to locally independent, yet globally bound phase, incoherent photonic molecules. Using a multiple time-scale analysis, we derive an amplitude equation for the field that allows us to predict analytically the distance between the elements of a cluster.

physics.optics↗

arXiv2020

Two-dimensional localized states in an active phase-field-crystal model

The active phase-field-crystal (active PFC) model provides a simple microscopic mean field description of crystallization in active systems. It combines the PFC model (or conserved Swift-Hohenberg equation) of colloidal crystallization and aspects of the Toner-Tu theory for self-propelled particles. We employ the active PFC model to study the occurrence of localized and periodic active crystals in two spatial dimensions. Due to the activity, crystalline states can undergo a drift instability and start to travel while keeping their spatial structure. Based on linear stability analyses, time simulations and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of resting and traveling states. We explore, for instance, how the slanted homoclinic snaking of steady localized states found for the passive PFC model is modified by activity. The analysis is carried out for the model in two spatial dimensions. Morphological phase diagrams showing the regions of existence of various solution types are presented merging the results from all the analysis tools employed. We also study how activity influences the crystal structure with transitions from hexagons to rhombic and stripe patterns. This in-depth analysis of a simple PFC model for active crystals and swarm formation provides a clear general understanding of the observed multistability and associated hysteresis effects, and identifies thresholds for qualitative changes in behavior.

cond-mat.soft↗

arXiv2020

Localized states in passive and active phase-field-crystal models

The passive conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) corresponds to a gradient dynamics for a single order parameter field related to density. It provides a simple microscopic description of the thermodynamic transition between liquid and crystalline states. In addition to spatially extended periodic structures, the model describes a large variety of steady spatially localized structures. In appropriate bifurcation diagrams the corresponding solution branches exhibit characteristic slanted homoclinic snaking. In an active PFC model, encoding for instance the active motion of self-propelled colloidal particles, the gradient dynamics structure is broken by a coupling between density and an additional polarization field. Then, resting and traveling localized states are found with transitions characterized by parity-breaking drift bifurcations. Here, we first briefly review the snaking behavior of localized states in passive and active PFC models before discussing the bifurcation behavior of localized states in systems of (i) two coupled passive PFC equations described by common gradient dynamics, (ii) two coupled passive PFC where the coupling breaks the gradient dynamics structure, and (iii) a passive PFC coupled to an active PFC.

cond-mat.soft↗