Dissipative Phase Solitons in Semiconductor Lasers

Temporal dissipative solitons in the Morris-Lecar model with time-delayed feedback

We study the dynamics and bifurcations of temporal dissipative solitons in an excitable system under time-delayed feedback. As a prototypical model displaying different types of excitability, we use the Morris-Lecar model. In the limit of large delay, soliton like solutions of delay-differential equations can be treated as 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 pulse solutions and to explain their dependence on the system parameters. In particular, we show how a homoclinic orbit flip of a single-pulse soliton leads to the destabilization of equidistant multi-pulse solutions and to the emergence of stable pulse packages. It turns out that this transition is induced by a heteroclinic orbit flip in the system without feedback, which is related to the excitability properties of the Morris-Lecar model.

Generation of ultra-low jitter radio frequency phase pulses by a phase-locked oscillator

We demonstrate a novel, to the best of our knowledge, method for mode locking of an oscillator, which is based on the injection of a strong sinusoidal signal from an external source into the cavity. The oscillator generates a low phase noise carrier signal with a train of ultra-low jitter, short 2π phase pulses at a repetition period equal to the cavity round-trip time. Both the carrier signal and phase pulses are phase-locked to the external source. We demonstrate the effect in an optoelectronic oscillator that generates a train of short phase pulses at a high carrier frequency with the broadband spectrum of a dense RF frequency comb. The phase pulses can be converted to short, ultra-low jitter intensity RF pulses by beating the oscillator signal with the external source, used for locking.

Control of single and multiple phase solitons in a ring cavity

Phase solitons are localized structures characterized by phase jumps of 2π or multiples arising in forced ring lasers. Here, we show numerically that they can be created by superimposing to the constant driving field a suitable control beam matched in frequency with a different cavity mode for a time of the order of ten cavity round trip times. If the two beams are separated in frequency by n free spectral ranges of the cavity, a train of solitons like a perfect soliton crystal consisting of n equispaced phase solitons is generated. This may represent a simple way to produce frequency combs with flexible frequency spacing and high power per line.

Unifying Frequency Combs in Active and Passive Cavities: Temporal Solitons in Externally Driven Ring Lasers

Frequency combs have become a prominent research area in optics. Of particular interest as integrated comb technology are chip-scale sources, such as semiconductor lasers and microresonators, which consist of resonators embedding a nonlinear medium either with or without population inversion. Such active and passive cavities were so far treated distinctly. Here we propose a formal unification by introducing a general equation that describes both types of cavities. The equation also captures the physics of a hybrid device-a semiconductor ring laser with an external optical drive-in which we show the existence of temporal solitons, previously identified only in microresonators, thanks to symmetry breaking and self-localization phenomena typical of spatially extended dissipative systems.

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.

Properties of Phase Solitons in an Optically Driven Semiconductor Ring Laser

A semiconductor ring laser with a long cavity supports propagating localised structures with a chiral charge, named phase solitons. In this paper we study the dependence of the velocity and of the duration of the phase solitons on the characteristic time scales of the laser, namely the photon lifetime and the carrier lifetime. We show numerically that phase solitons are stable over a large range of those parameters and verify that the propagation velocity decreases linearly with the ratio of the carrier lifetime to the photon lifetime, while the duration is proportional to the ratio of the carrier lifetime to the cavity roundtrip time.

Experimental electric field visualisation of multi-mode dynamics in a short cavity swept laser designed for OCT applications

An experimental study into the modal dynamics of a short cavity, fast frequency-swept laser is presented. This commercially available external cavity swept source is designed for use in optical coherence tomography (OCT) applications and displays a number of dynamic lasing regimes during the course of the wavelength sweep. Interferometric full electric field reconstruction is employed, allowing for measurement of the laser operation in a time-resolved, single-shot manner. Recovery of both the phase and intensity of the laser output across the entire sweep enables direct visualization of the laser instantaneous optical spectrum. The electric field reconstruction technique reveals the presence of multi-mode dynamics, including coherent mode-locked pulses. During the main part of the imaging sweep, the laser is found to operate in a second harmonic sliding frequency mode-locking regime. Examination of the modal evolution of this coherent regime reveals evidence of previously unobserved frequency switching dynamics.

Directional Bistability and Nonreciprocal Lasing with Cold Atoms in a Ring Cavity

We demonstrate lasing into counterpropagating modes of a ring cavity using a gas of cold atoms as a gain medium. The laser operates under the usual conditions of magneto-optical trapping with no additional fields. We characterize the threshold behavior of the laser and measure the second-order optical coherence. The laser emission exhibits directional bistability, switching randomly between clockwise and counterclockwise modes, and a tunable nonreciprocity is observed as the atoms are displaced along the cavity axis.

Dissipative solitons for bistable delayed-feedback systems

We study how nonlinear delayed-feedback in the Ikeda model can induce solitary impulses, i.e., dissipative solitons. The states are clearly identified in a virtual space-time representation of the equations with delay, and we find that conditions for their appearance are bistability of a nonlinear function and negative character of the delayed feedback. Both dark and bright solitons are identified in numerical simulations and physical electronic experiment, showing an excellent qualitative correspondence and proving thereby the robustness of the phenomenon. Along with single spiking solitons, a variety of compound soliton-based structures is obtained in a wide parameter region on the route from the regular dynamics (two quiescent states) to developed spatiotemporal chaos. The number of coexisting soliton-based states is fast growing with delay, which can open new perspectives in the context of information storage.

Exponentially decaying interaction potential of cavity solitons

We analyze the interaction of two cavity solitons in an optically injected vertical cavity surface emitting laser above threshold. We show that they experience an attractive force even when their distance is much larger than their diameter, and eventually they merge. Since the merging time depends exponentially on the initial distance, we suggest that the attraction could be associated with an exponentially decaying interaction potential, similarly to what is found for hydrophobic materials. We also show that the merging time is simply related to the characteristic times of the laser, photon lifetime, and carrier lifetime.

Dynamics of a broad-band quantum cascade laser: from chaos to coherent dynamics and mode-locking

The dynamics of a multimode quantum cascade laser, are studied in a model based on effective semiconductor Maxwell-Bloch equations, encompassing key features for the radiation-medium interaction such as an asymmetric frequency dependent gain and refractive index as well as the phase-amplitude coupling provided by the linewidth enhancement factor. By considering its role and that of the free spectral range, we find the conditions in which the traveling wave emitted by the laser at the threshold can be destabilized by adjacent modes, thus leading the laser emission towards chaotic or regular multimode dynamics. In the latter case our simulations show that the field oscillations are associated to self-confined structures which travel along the laser cavity, bridging mode-locking and solitary wave propagation. In addition, we show how a RF modulation of the bias current leads to active mode-locking yielding high-contrast, picosecond pulses. Our results compare well with recent experiments on broad-band THz-QCLs and may help in the understanding of the conditions for the generation of ultrashort pulses and comb operation in mid-IR and THz spectral regions.

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.

Direct experimental measurement of single-mode and mode-hopping dynamics in frequency swept lasers

A time-resolved study is presented of the single-mode and mode-switching dynamics observed in swept source vertical cavity surfing emitting lasers and swept wavelength short external cavity lasers. A self-delayed interferometric technique is used to experimentally measure the phase and intensity of these frequency swept lasers, allowing direct examination of the modal dynamics. Visualisation of the instantaneous optical spectrum reveals mode-hop free single mode lasing in the case of the vertical cavity laser, with a tuning rate of 6.3 GHz/ns. More complex mode-switching behaviour occurs in the external cavity laser, with the mode-hopping dynamics found to be dominated by the deterministic movement of the spectral filter. Evidence of transient multi-mode operation and mode-pulling is also presented.

Abnormal chiral events in a semiconductor laser with coherent injection

We study experimentally and theoretically the dynamics of a spatially extended (along the propagation direction) oscillatory medium with coherent forcing. We observe abnormally high events, responsible for a different statistics of intensity and pulse height, in a regime where solitons and roll patterns are unstable. We focus on the formation of these high-peak events and their connection to the phase dynamics. Each abnormal event can be associated with a change in the slope of the phase time trace. Furthermore, the coexistence of ±2π phase rotations inside the cavity can be associated to the observation of abnormal events, similarly to recent predictions in bidimensional vortex turbulence.

Extreme events induced by collisions in a forced semiconductor laser

We report on the experimental study of an optically driven multimode semiconductor laser with a 1 m cavity length. We observed a spatiotemporal regime where real-time measurements reveal very high-intensity peaks in the laser field. Such a regime, which coexists with the locked state and with stable phase solitons, is characterized by the emergence of extreme events that produce heavy tail statistics in the probability density function. We interpret the extreme events as collisions of spatiotemporal structures with opposite chirality. Numerical simulations of the semiconductor laser model, showing very similar dynamical behavior, substantiate our evidences and corroborate the description of interactions such as collisions between phase solitons and transient structures with different phase rotations.

Real-Time Observation of Internal Motion within Ultrafast Dissipative Optical Soliton Molecules

Real-time access to the internal ultrafast dynamics of complex dissipative optical systems opens new explorations of pulse-pulse interactions and dynamic patterns. We present the first direct experimental evidence of the internal motion of a dissipative optical soliton molecule generated in a passively mode-locked erbium-doped fiber laser. We map the internal motion of a soliton pair molecule by using a dispersive Fourier-transform imaging technique, revealing different categories of internal pulsations, including vibrationlike and phase drifting dynamics. Our experiments agree well with numerical predictions and bring insights to the analogy between self-organized states of lights and states of the matter.

Observation of Mode-Locked Spatial Laser Solitons

A stable nonlinear wave packet, self-localized in all three dimensions, is an intriguing and much sought after object in nonlinear science in general and in nonlinear photonics in particular. We report on the experimental observation of mode-locked spatial laser solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback from an external cavity. These spontaneously emerging and long-term stable spatiotemporal structures have a pulse length shorter than the cavity round-trip time and may pave the way to completely independent cavity light bullets.

Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser

We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.