Neutral delay differential equation model of an optically injected Kerr cavity.

A neutral delay differential equation (NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second- and higher-order dispersion being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the low dissipation limit, where the model can be reduced to the Lugiato-Lefever equation (LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE, the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes.

Decoherence and Turbulence Sources in a Long Laser.

We investigate the turn-on process in a laser cavity where the round-trip time is several orders of magnitude greater than the active medium timescales. In this long delay limit, we show that the universal evolution of the photon statistics from thermal to Poissonian distribution involves the emergence of power dropouts. While the largest number of these dropouts vanish after a few round-trips, some of them persist and seed coherent structures similar to dark solitons or Nozaki-Bekki holes described by the complex Ginzburg-Landau equation. These coherent structures connect stationary laser emission domains having different optical frequencies. Moreover, they emit intensity bursts which travel at a different speed, and, depending on the cavity dispersion sign, they may collide with other coherent structures, thus leading to an overall turbulent dynamics. The dynamics is well-modeled by delay differential equations from which we compute the laser coherence time evolution at each round-trip and quantify the decoherence induced by the collisions between coherent structures.

Short- and long-range temporal cavity soliton interaction in delay models of mode-locked lasers.

Interaction equations governing slow time evolution of the coordinates and phases of two interacting temporal cavity solitons in a delay differential equation model of a nonlinear mirror mode-locked laser are derived and analyzed. It is shown that long-range soliton interaction due to gain depletion and recovery can lead either to a development of a harmonic mode-locking regime or to a formation of closely packed incoherent soliton bound state with weakly oscillating intersoliton time separation. Short-range soliton interaction via electric field tails can result in an antiphase or in-phase stationary and breathing harmonic mode-locking regimes.

Generalized Haus master equation model for mode-locked class-B lasers.

Using an asymptotic technique, we develop a generalized version of the class-B Haus partial differential equation mode-locking model that accounts for both the slow gain response to the averaged value of the field intensity and the fast gain dynamics on the scale comparable to the pulse duration. We show that unlike the conventional class-B Haus mode-locked model, our model is able to describe not only Q-switched instability of the fundamental mode-locked regime but also the leading edge instability leading to harmonic mode-locked regimes with the increase of the pump power.

Turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold: publisher's note.

This publisher's note contains corrections to Opt. Lett.45, 4903 (2020)OPLEDP0146-959210.1364/OL.397840.

Turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold.

We report on the formation of novel turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold. Experimentally, the laser emits a series of power dropouts within a roundtrip, and the number of dropouts per series depends on a set of parameters including the bias current. At fixed parameters, the drops remain dynamically stable, repeating over many roundtrips. By reconstructing the laser electric field in the case where the laser emits one dropout per roundtrip and simulating its dynamics using a time-delayed model, we discuss the reasons for long-term sustainability of these solutions. We suggest that the observed dropouts are closely related to the coherent structures of the cubic complex Ginzburg-Landau equation.

Convective Nozaki-Bekki holes in a long cavity OCT laser.

We show, both experimentally and theoretically, that the loss of coherence of a long cavity optical coherence tomography (OCT) laser can be described as a transition from laminar to turbulent flows. We demonstrate that in this strongly dissipative system, the transition happens either via an absolute or a convective instability depending on the laser parameters. In the latter case, the transition occurs via formation of localised structures in the laminar regime, which trigger the formation of growing and drifting puffs of turbulence. Experimentally, we demonstrate that these turbulent bursts are seeded by appearance of Nozaki-Bekki holes, characterised by the zero field amplitude and π phase jumps. Our experimental results are supported with numerical simulations based on the delay differential equations model.

Dispersive Time-Delay Dynamical Systems.

We present a theoretical approach to investigate the effect of dispersion in dynamical systems commonly described by time-delay models. The introduction of a polarization equation provides a means to introduce dispersion as a distributed delay term. The expansion of this term in power series, as usually performed to study the propagation of waves in spatially extended systems, can lead to the appearance of spurious instabilities. This approach is illustrated using a long cavity laser, where in the normal dispersion regime both the experiment and theory show a stable operation, while a modulation instability, commonly referred as the Benjamin-Feir instability, is observed in the anomalous dispersion regime.

Bistable regimes in an optically injected mode-locked laser.

We study experimentally the dynamics of quantum-dot (QD) passively mode-locked semiconductor lasers under external optical injection. The lasers demonstrated multiple dynamical states, with bifurcation boundaries that depended upon the sign of detuning variation. The area of the hysteresis loops grew monotonically at small powers of optical injection and saturated at moderate powers. At high injection levels the hysteresis decreased and eventually disappeared.

Stripe-array diode-laser in an off-axis external cavity: theory and experiment.

Stripe-array diode lasers naturally operate in an anti-phase supermode. This produces a sharp double lobe far field at angles +/-alpha depending on the period of the array. In this paper a 40 emitter gain guided stripe-array laterally coupled by off-axis filtered feedback is investigated experimentally and numerically. We predict theoretically and confirm experimentally that at doubled feedback angle 2alpha a stable higher order supermode exists with twice the number of emitters per array period. The theoretical model is based on time domain traveling wave equations for optical fields coupled to the carrier density equation taking into account diffusion of carriers. Feedback from the external reflector is modeled using Fresnel integration.

Chaotic soliton walk in periodically modulated media.

We show that a weak transverse spatial modulation in (2+1) nonlinear Schrödinger-type equation can result in nontrivial dynamics of a radially symmetric soliton. We provide examples of chaotic soliton motion in periodic media both for conservative and dissipative cases. We show that complex dynamics can persist even for soliton sizes greater than the modulation period.

Chaotic bound state of localized structures in the complex Ginzburg-Landau equation.

Stable dynamic bound states of dissipative localized structures are found. It is characterized by chaotic oscillations of distance between the localized structures, their phase difference, and the center of mass velocity.

Delay differential equations for mode-locked semiconductor lasers.

We propose a new model for passive mode locking that is a set of ordinary delay differential equations. We assume a ring-cavity geometry and Lorentzian spectral filtering of the pulses but do not use small gain and loss and weak saturation approximations. By means of a continuation method, we study mode-locking solutions and their stability. We find that stable mode locking can exist even when the nonlasing state between pulses becomes unstable.

Vortex induced rotation of clusters of localized states in the complex Ginzburg-Landau equation.

We report existence of a qualitatively distinct class of spiral waves in the two-dimensional cubic-quintic complex Ginzburg-Landau equation. These are stable clusters of localized states rotating around a central vortex core emerging due to interference of the tails of the individual states involved. We also develop an asymptotic theory allowing calculation of the angular frequency and stability analysis of the rotating clusters.

Two-dimensional clusters of solitary structures in driven optical cavities.

Using analytical and numerical approaches we study clusters of the two-dimensional localized structures of light excited in the externally driven optical cavities. Stability and instability properties of clusters of two, three, and four structures are analyzed in detail. We develop a technique for calculation of the expression for the interaction potential through modified Bessel functions that has applicability going beyond the model under consideration. Qualitative differences between stability properties of triangular and square structures are found that emphasize the role of diagonal interactions in the latter.