Conservative Solitons and Reversibility in Time Delayed Systems.

Time delayed dynamical systems have proven to be a fertile framework for the study of physical phenomena. In natural sciences, their uses have been limited to the study of dissipative dynamics. In this Letter, we demonstrate the existence of nonlinear reversible conservative time delayed systems. We consider the example of a dispersive microcavity containing a Kerr medium coupled to a distant external mirror. At low energies and in the long delay limit, a multiscale analysis shows the equivalence with the nonlinear Schrödinger equation. We unveil some of the symmetries and conserved quantities, as well as bright temporal solitons. While elastic collisions occur for shallow wave packets, we observe the lack of integrability at higher energies. We recover the Lugiato-Lefever equation in the weakly dissipative regime.

Simplified description of dynamics in neuromorphic resonant tunneling diodes.

In this article, the standard theoretical model accounting for a double barrier quantum well resonant tunneling diode (RTD) connected to a direct current source of voltage is simplified by representing its current-voltage characteristic with an analytically approachable, anti-symmetric N-shaped function. The time and variables involved are also transformed to reduce the number of parameters in the model. Responses observed in previous, more physically accurate studies are reproduced, including slow-fast dynamics, excitability, and bistability, relevant for spiking signal processing. A simple expression for the refractory time of the excitable response is derived and shown to be in good agreement with numerical simulations. In particular, the refractory time is found to be directly proportional to the circuit's intrinsic inductance. The presence or absence of bistability in the dependence of the parameters is also discussed thoroughly. The results of this work can serve as a guideline in prospective endeavors to design and fabricate RTD-based neuromorphic circuits for power and time-efficient execution of neural network algorithms.

Manipulation of temporal localized structures in a vertical external-cavity surface-emitting laser with optical feedback.

We analyze the effect of optical feedback on the dynamics of an external-cavity passively mode-locked surface-emitting laser operating in the regime of temporal localized structures. Depending on the ratio between the cavity round trip time and the feedback delay, we show experimentally that feedback acts as a solution selector that either reinforces or hinders the appearance of one of the multistable harmonic arrangements of pulses. Our theoretical analysis reproduces well the experiment and allows us to evidence asymmetrical resonance tongues due to the parity symmetry-breaking induced by gain depletion.

Hopping and emergent dynamics of optical localized states in a trapping potential.

The position and motion of localized states of light in propagative geometries can be controlled via an adequate parameter modulation. Here, we show theoretically and experimentally that this process can be accurately described as the phase locking of oscillators to an external forcing and that non-reciprocal interactions between light bits can drastically modify this picture. Interactions lead to the convective motion of defects and to an unlocking as a collective emerging phenomenon.

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

The time-delayed Adler equation is the simplest model for an injected semiconductor laser with coherent injection and optical feedback. It is, however, 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.

Tunable Kerr frequency combs and temporal localized states in time-delayed Gires-Tournois interferometers.

In this Letter, we study theoretically a new setup allowing for the generation of temporal localized states (TLSs) and frequency combs. The setup is compact (a few centimeters) and can be implemented using established technologies, while offering tunable repetition rates and potentially high power operation. It consists of a vertically emitting micro-cavity, operated in the Gires-Tournois regime, containing a Kerr medium strong time-delayed optical feedback, and detuned optical injection. We disclose sets of multistable dark and bright TLSs coexisting on their respective bistable homogeneous backgrounds.

Third Order Dispersion in Time-Delayed Systems.

Time-delayed dynamical systems materialize in situations where distant, pointwise, nonlinear nodes exchange information that propagates at a finite speed. However, they are considered devoid of dispersive effects, which are known to play a leading role in pattern formation and wave dynamics. We show how dispersion may appear naturally in delayed systems and we exemplify our result by studying theoretically and experimentally the influence of third order dispersion in a system composed of coupled optical microcavities. Dispersion-induced pulse satellites emerge asymmetrically and destabilize the mode-locking regime.

Temporal localized structures in mode-locked vertical external-cavity surface-emitting lasers.

Temporal localized states (TLSs) are individually addressable structures traveling in optical resonators. They can be used to obtain bits of information and generate frequency combs with tunable spectral density. We show that a pair of specially designed nonlinear mirrors, a 1/2 vertical-cavity surface-emitting laser and a semiconductor saturable absorber, coupled in self-imaging conditions, can lead to the generation of such TLSs. Our results indicate how a conventional passive mode-locking scheme can be adapted to provide a robust and simple system emitting TLSs and paves the way towards the observation of three dimensional confined states, the so-called light bullets.

Light bullets in a time-delay model of a wide-aperture mode-locked semiconductor laser.

Recently, a mechanism of formation of light bullets (LBs) in wide-aperture passively mode-locked lasers was proposed. The conditions for existence and stability of these bullets, found in the long cavity limit, were studied theoretically under the mean field (MF) approximation using a Haus-type model equation. In this paper, we relax the MF approximation and study LB formation in a model of a wide-aperture three section laser with a long diffractive section and short absorber and gain sections. To this end, we derive a non-local delay-differential equation (NDDE) model and demonstrate by means of numerical simulations that this model supports stable LBs. We observe that the predictions about the regions of existence and stability of the LBs made previously using MF laser models agree well with the results obtained using the NDDE model. Moreover, we demonstrate that the general conclusions based upon the Haus model that regard the robustness of the LBs remain true in the NDDE model valid beyond the MF approximation, when the gain, losses and diffraction per cavity round trip are not small perturbations anymore.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Functional mapping for passively mode-locked semiconductor lasers.

We present a modern approach for the analysis of passively mode-locked semiconductor lasers that allows for efficient parameter sweeps and time jitter analysis. It permits accessing the ultralow 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 magnitude 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.

Interactions and collisions of topological solitons in a semiconductor laser with optical injection and feedback.

We present experimental and numerical results about dynamical interactions of topological solitons in a semiconductor laser with coherent injection and feedback. We show different kind of interactions such as repulsion, annihilation, or formation of soliton bound states, depending on laser parameters. Collisions between single structures and bound states conserve momentum and charge.

Nonlocality Induces Chains of Nested Dissipative Solitons.

Dissipative solitons often behave as quasiparticles, and they may form molecules characterized by well-defined bond distances. We show that pointwise nonlocality may lead to a new kind of molecule where bonds are not rigid. The elements of this molecule can shift mutually one with respect to the others while remaining linked together, in a manner similar to interlaced rings in a chain. We report experimental observations of these chains of nested dissipative solitons in a time-delayed laser system.

Publisher's Note: Refractory period of an excitable semiconductor laser with optical injection [Phys. Rev. E 95, 012214 (2017)].

This corrects the article DOI: 10.1103/PhysRevE.95.012214.

Refractory period of an excitable semiconductor laser with optical injection.

Injection-locked semiconductor lasers can be brought to a neuronlike excitable regime when parameters are set close to the unlocking transition. Here we study experimentally the response of this system to repeated optical perturbations and observe the existence of a refractory period during which perturbations are not able to elicit an excitable response. The results are analyzed via simulations of a set of dynamical equations which reproduced adequately the experimental results.

Asymmetric mode scattering in strongly coupled photonic crystal nanolasers.

We investigate the basic mechanism of nonlinear mode competition in two semiconductor-coupled nanocavities operating in the laser regime. For this, we study energy transfer between bonding (in-phase) and anti-bonding (out-of-phase) modes of the system formed by two strongly coupled photonic crystal nanolasers. We experimentally observe mode switching from the blue-detuned to the red-detuned mode as the pump power is increased. A semi-classical description in terms of mean-field equations allows us to explain this phenomenon as stimulated scattering due to carrier population oscillations in the cavities at the mode splitting frequency. We predict such asymmetrical mode interaction to be universal in arrays of optically coupled semiconductor micro and nanocavities.

Dynamics of Localized Structures in Systems with Broken Parity Symmetry.

A great variety of nonlinear dissipative systems are known to host structures having a correlation range much shorter than the size of the system. The dynamics of these localized structures (LSs) has been investigated so far in situations featuring parity symmetry. In this Letter we extend this analysis to systems lacking this property. We show that the LS drifting speed in a parameter varying landscape is not simply proportional to the parameter gradient, as found in parity preserving situations. The symmetry breaking implies a new contribution to the velocity field which is a function of the parameter value, thus leading to a new paradigm for LSs manipulation. We illustrate this general concept by studying the trajectories of the LSs found in a passively mode-locked laser operated in the localization regime. Moreover, the lack of parity affects significantly LSs interactions which are governed by asymmetrical repulsive forces.

Cavity Light Bullets in Passively Mode-Locked Semiconductor Lasers.

We demonstrate the existence of stable three-dimensional dissipative localized structures in the output of a laser coupled to a distant saturable absorber. These phase invariant cavity light bullets are individually addressable and can be envisioned for three-dimensional optical information storage. An effective theory provides for an intuitive picture and allows us to relate their formation to the morphogenesis of static spatial autosolitons and temporal cellular patterns.

Regenerative memory in time-delayed neuromorphic photonic resonators.

We investigate a photonic regenerative memory based upon a neuromorphic oscillator with a delayed self-feedback (autaptic) connection. We disclose the existence of a unique temporal response characteristic of localized structures enabling an ideal support for bits in an optical buffer memory for storage and reshaping of data information. We link our experimental implementation, based upon a nanoscale nonlinear resonant tunneling diode driving a laser, to the paradigm of neuronal activity, the FitzHugh-Nagumo model with delayed feedback. This proof-of-concept photonic regenerative memory might constitute a building block for a new class of neuron-inspired photonic memories that can handle high bit-rate optical signals.

Arrest of Domain Coarsening via Antiperiodic Regimes in Delay Systems.

Motionless domain walls representing connecting temporal or spatial orbits typically exist only for very specific parameters, around the so-called Maxwell point. This report introduces a novel mechanism for stabilizing temporal domain walls away from this peculiar equilibrium, opening up new possibilities to encode information in dynamical systems. It is based on antiperiodic regimes in a delayed system close to a bistable situation, leading to a cancellation of the average drift velocity. The results are demonstrated in a normal form model and experimentally in a laser with optical injection and delayed feedback.

How lasing localized structures evolve out of passive mode locking.

We investigate the relationship between passive mode locking and the formation of time-localized structures in the output intensity of a laser. We show how the mode-locked pulses transform into lasing localized structures, allowing for individual addressing and arbitrary low repetition rates. Our analysis reveals that this occurs when (i) the cavity round-trip is much larger than the slowest medium time scale, namely the gain recovery time, and (ii) the mode-locked solution coexists with the zero intensity (off) solution. These conditions enable the coexistence of a large quantity of stable solutions, each of them being characterized by a different number of pulses per round-trip and with different arrangements. Then, each mode-locked pulse becomes localized, i.e., individually addressable.