Desynchronization of temporal solitons in Kerr cavities with pulsed injection.

A numerical and analytical study was conducted to investigate the bifurcation mechanisms that cause desynchronization between the soliton repetition frequency and the frequency of external pulsed injection in a Kerr cavity described by the Lugiato-Lefever equation (LLE). The results suggest that desynchronization typically occurs through an Andronov-Hopf (AH) bifurcation. Additionally, a simple and intuitive criterion for this bifurcation to occur is proposed.

Bifurcation structure of a swept-source laser.

We numerically analyze a delay differential equation model of a short-cavity semiconductor laser with an intracavity frequency-swept filter and reveal a complex bifurcation structure responsible for the asymmetry of the output characteristics of this laser. We show that depending on the direction of the frequency sweep of a narrow-band filter, there exist two bursting cycles determined by different parts of a continuous-wave solutions branch.

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.

Dynamics of a class-A nonlinear mirror mode-locked laser.

Using a delay differential equation model we study theoretically the dynamics of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror. We perform linear stability analysis of the continuous-wave regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by an instability leading to the appearance of square-waves. We investigate the formation of square waves and mode-locked pulses in the system. We show that mode-locked pulses are asymmetric with exponential decay of the trailing edge in positive time and faster-than-exponential (superexponential) decay of the leading edge in negative time. We discuss asymmetric interaction of these pulses leading to a formation of harmonic mode-locked regimes.

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)'.

Delayed feedback control of self-mobile cavity solitons in a wide-aperture laser with a saturable absorber.

We investigate the spatiotemporal dynamics of cavity solitons in a broad area vertical-cavity surface-emitting laser with saturable absorption subjected to time-delayed optical feedback. Using a combination of analytical, numerical, and path continuation methods, we analyze the bifurcation structure of stationary and moving cavity solitons and identify two different types of traveling localized solutions, corresponding to slow and fast motion. We show that the delay impacts both stationary and moving solutions either causing drifting and wiggling dynamics of initially stationary cavity solitons or leading to stabilization of intrinsically moving solutions. Finally, we demonstrate that the fast cavity solitons can be associated with a lateral mode-locking regime in a broad-area laser with a single longitudinal mode.

Bound Pulse Trains in Arrays of Coupled Spatially Extended Dynamical Systems.

We study the dynamics of an array of nearest-neighbor coupled spatially distributed systems each generating a periodic sequence of short pulses. We demonstrate that, unlike a solitary system generating a train of equidistant pulses, an array of such systems can produce a sequence of clusters of closely packed pulses, with the distance between individual pulses depending on the coupling phase. This regime associated with the formation of locally coupled pulse trains bounded due to a balance of attraction and repulsion between them is different from the pulse bound states reported earlier in different laser, plasma, chemical, and biological systems. We propose a simplified analytical description of the observed phenomenon, which is in good agreement with the results of direct numerical simulations of a model system describing an array of coupled mode-locked lasers.

Multi-stability and polariton solitons in microcavity wires.

Nonlinear polaritons in microcavity wires are demonstrated to exhibit multi-stable behavior and rich dynamics, including filamentation and soliton formation. We find that the multi-stability originates from co-existence of different transverse cavity modes. Modulational stability and conditions for multi-mode polariton solitons are studied. Soliton propagation in tilted, relative to the pump momentum, microcavity wires is demonstrated, and a critical tilt angle for the soliton propagation is found.

Effect of dynamical instability on timing jitter in passively mode-locked quantum-dot lasers.

We study the effect of noise on the dynamics of passively mode-locked semiconductor lasers both experimentally and theoretically. A method combining analytical and numerical approaches for estimation of pulse timing jitter is proposed. We investigate how the presence of dynamical features such as wavelength bistability in a quantum-dot laser affects timing jitter.

Bistability and hysteresis in an optically injected two-section semiconductor laser.

The effect of coherent single frequency injection on two-section semiconductor lasers is studied numerically using a model based on a set of delay differential equations. The existence of bistability between different continuous-wave and nonstationary regimes of operation is demonstrated in the case of sufficiently large linewidth enhancement factors.

Cavity solitons in vertical-cavity surface-emitting lasers.

We investigate a control of the motion of localized structures (LSs) of light by means of delay feedback in the transverse section of a broad area nonlinear optical system. The delayed feedback is found to induce a spontaneous motion of a solitary LS that is stationary and stable in the absence of feedback. We focus our analysis on an experimentally relevant system, namely the vertical-cavity surface-emitting laser (VCSEL). We first present an experimental demonstration of the appearance of LSs in a 80 µm aperture VCSEL. Then, we theoretically investigate the self-mobility properties of the LSs in the presence of a time-delayed optical feedback and analyse the effect of the feedback phase and the carrier lifetime on the delay-induced spontaneous drift instability of these structures. We show that these two parameters affect strongly the space-time dynamics of two-dimensional LSs. We derive an analytical formula for the threshold associated with drift instability of LSs and a normal form equation describing the slow time evolution of the speed of the moving structure.

Localized structures in dissipative media: from optics to plant ecology.

Localized structures (LSs) in dissipative media appear in various fields of natural science such as biology, chemistry, plant ecology, optics and laser physics. The proposal for this Theme Issue was to gather specialists from various fields of nonlinear science towards a cross-fertilization among active areas of research. This is a cross-disciplinary area of research dominated by nonlinear optics due to potential applications for all-optical control of light, optical storage and information processing. This Theme Issue contains contributions from 18 active groups involved in the LS field and have all made significant contributions in recent years.

Dynamics of Fourier domain mode-locked lasers.

An analysis of the dynamical features in the output of a Fourier Domain Mode Locked laser is presented. An experimental study of the wavelength sweep-direction asymmetry in the output of such devices is undertaken. A mathematical model based on a set of delay differential equations is developed and shown to agree well with experiment.

Long-range interaction and synchronization of oscillating dissipative solitons.

We study the interaction of well-separated oscillating localized structures (oscillons). We show that oscillons emit weakly decaying dispersive waves, which lead to the formation of bound states due to harmonic synchronization. We also show that in optical applications the Andronov-Hopf bifurcation of stationary localized structures leads to a drastic increase in their interaction strength.

Optically injected mode-locked laser.

We study analytically and numerically a delay differential model of a passively mode-locked semiconductor laser subjected to a single-frequency coherent injection. The width of the locking cone is calculated asymptotically in the limit of small injection and zero line-width enhancement factors and compared to that obtained by direct numerical integration of the model equations. The dependence of the locking cone on the laser parameters is discussed.

Spontaneous motion of cavity solitons induced by a delayed feedback.

We study the properties of 2D cavity solitons in a coherently driven optical resonator subjected to a delayed feedback. The delay is found to induce a spontaneous motion of a single cavity soliton that is stationary and stable otherwise. This behavior occurs when the product of the delay time and the feedback strength exceeds some critical value. We derive an analytical formula for the speed of a moving soliton. Numerical results are in good agreement with analytical predictions.

Localized beating between dynamically generated frequencies.

We analyze the beating between intrinsic frequencies that are simultaneously generated by a modulation (Turing) instability in a nonlinear extended system. The model studied is that of a coherently driven photonic crystal fiber cavity. Beating in the form of a slow modulation of fast intensity oscillations is found to be stable for a wide range of parameters. We find that such beating can also be localized and contain only a finite number of slow modulations. These structures consist of dips in the amplitude of the fast intensity oscillations, which can either be isolated or regularly spaced. An asymptotic analysis close to the modulation instability threshold allows us to explain this phenomenon as a manifestation of homoclinic snaking for dissipative localized structures.

Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities.

Taking up to fourth-order dispersion effects into account, we show that fiber resonators become stable for a large intensity regime. The range of pump intensities leading to modulational instability becomes finite and controllable. Moreover, by computing analytically the thresholds and frequencies of these instabilities, we demonstrate the existence of a new unstable frequency at the primary threshold. This frequency exists for an arbitrary small but nonzero fourth-order dispersion coefficient. Numerical simulations for a low and flattened dispersion photonic crystal fiber resonator confirm analytical predictions and open the way to experimental implementation.

Bragg localized structures in a passive cavity with transverse modulation of the refractive index and the pump.

We consider a passive optical cavity containing a photonic crystal and a purely absorptive two-level medium. The cavity is driven by a superposition of two coherent beams forming a periodically modulated pump. Using a coupled mode reduction and direct numerical modeling of the full system we demonstrate the existence of bistability between uniformly periodic states, modulational instabilities and localized structures of light. All are found to exist within the conduction band of the photonic material. Moreover, contrary to similar previously found intra-band structures, we show that these localized structures can be truly stationary states.

Curvature instability in passive diffractive resonators.

We study the stability of localized structures in a passive optical bistable system. We show that there is a critical value of the input field intensity above which localized structures are unstable with respect to a curvature instability. Beyond this instability boundary, a transition from the localized branch of solutions to stable hexagons is found.