Realization of a semiconductor-based cavity soliton laser

Time localized tilted beams in nearly-degenerate laser cavities

We show that nearly-degenerate Vertical External-Cavity Surface-Emitting Lasers may emit a set of tilted beams of individually addressable mode-locked pulses. These time localized beams feature a Gaussian profile and they are emitted in pairs with opposite transverse k-vector. Because they are phase locked, their interference leads to a non homothetic pattern in the near-field emission of the laser. In the simplest situation, when a single pair is emitted, this is a stripe pattern. Our analysis discloses the role of third order (spherical) aberrations of the cavity in stabilizing this spatio-temporal mode-locked regime and in selecting the value of the transverse k-vector.

Operating regimes of cavity solitons by virtue of a graphene flake saturable absorber

Exploiting the. broadband operating frequency regimes of a graphene flake saturable absorber (GFSA), a cavity soliton (CS) is excited in heretofore unexplored ultraviolet and visible regions. A broad-area device, namely, a vertical cavity surface emitting laser (VCSEL) is taken as a host of CSs; a two-dimensional (2D) transverse soliton, which is quite different from the conventional propagating one. The VCSEL with an embedded 2D homogeneous transverse layer of a GFSA is coupled with a frequency selective feedback. A CS is also generated in the infrared region, especially at the optical communication wavelength. Spontaneous dynamics and interaction behavior of CSs as well as generation of CS molecules and the push-broom effect are reported in this broad cross-sectional device. In comparison with other existing and potential models, the proposed VCSEL with GFSA model shows greater efficiency.

Photon thermalization and a condensation phase transition in an electrically pumped semiconductor microresonator

We report on an experimental study of photon thermalization and condensation in a semiconductor microresonator in the weak-coupling regime. We measure the dispersion relation of light and the photon mass in a single-wavelength, broad-area resonator. The observed luminescence spectrum is compatible with a room-temperature, thermal-equilibrium distribution. A phase transition, identified by a saturation of the population at high energies and a superlinear increase of the occupation at low energy, takes place when the phase-space density is of order unity. We explain our observations by Bose-Einstein condensation of photons in equilibrium with a particle reservoir and discuss the relation with laser emission.

Temporal cavity solitons in a laser-based microcomb: a path to a self-starting pulsed laser without saturable absorption

We theoretically present a design of self-starting operation of microcombs based on laser-cavity solitons in a system composed of a micro-resonator nested in and coupled to an amplifying laser cavity. We demonstrate that it is possible to engineer the modulational-instability gain of the system's zero state to allow the start-up with a well-defined number of robust solitons. The approach can be implemented by using the system parameters, such as the cavity length mismatch and the gain shape, to control the number and repetition rate of the generated solitons. Because the setting does not require saturation of the gain, the results offer an alternative to standard techniques that provide laser mode-locking.

Control of topology of two-dimensional solitons in a laser with saturable absorption by means of a coherent holding radiation

We propose a simple method to control the topology of laser vortex solitons and their complexes in a wide-aperture laser with saturable absorption by means of weak coherent holding radiation. The holding radiation acting on initial "free" vortex solitons induces the appearance of new peripheral vortices and the splitting of multiple central vortices, as well as reconfiguration of energy flow topology. A wide variety of these stable vortex structures makes the scheme promising for topologically protected information processing.

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.

Formation of optical supramolecular structures in a fibre laser by tailoring long-range soliton interactions

Self-assembly of fundamental elements through weak, long-range interactions plays a central role in both supramolecular DNA assembly and bottom-up synthesis of nanostructures. Optical solitons, analogous in many ways to particles, arise from the balance between nonlinearity and dispersion and have been studied in numerous optical systems. Although both short- and long-range interactions between optical solitons have attracted extensive interest for decades, stable soliton supramolecules, with multiple aspects of complexity and flexibility, have thus far escaped experimental observation due to the absence of techniques for enhancing and controlling the long-range inter-soliton forces. Here we report that long-range soliton interactions originating from optoacoustic effects and dispersive-wave radiations can be precisely tailored in a fibre laser cavity, enabling self-assembly of large numbers of optical solitons into highly-ordered supramolecular structures. We demonstrate several features of such optical structures, highlighting their potential applications in optical information storage and ultrafast laser-field manipulation.

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.

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.

Spontaneous Formation of Vector Vortex Beams in Vertical-Cavity Surface-Emitting Lasers with Feedback

The spontaneous emergence of vector vortex beams with nonuniform polarization distribution is reported in a vertical-cavity surface-emitting laser (VCSEL) with frequency-selective feedback. Antivortices with a hyperbolic polarization structure and radially polarized vortices are demonstrated. They exist close to and partially coexist with vortices with uniform and nonuniform polarization distributions characterized by four domains of pairwise orthogonal polarization. The spontaneous formation of these nontrivial structures in a simple, nearly isotropic VCSEL system is remarkable and the vector vortices are argued to have solitonlike properties.

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.

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.

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.

Stark effect induced microcavity polariton solitons

This paper proposes a way of generating polariton solitons (PSs) in a semiconductor microcavity using Stark effect as the trigger mechanism. A Stark pulse performing as the writing beam is used to excite non-resonant fluctuations of polariton, which finally evolves into bright PSs. It is found that a branch of PS solutions versus pump parameters could be found through optimizing parameters of the Stark pulse, and polarization of the generated PS is dependent on the writing beam.

Topological solitons as addressable phase bits in a driven laser

Optical localized states are usually defined as self-localized bistable packets of light, which exist as independently controllable optical intensity pulses either in the longitudinal or transverse dimension of nonlinear optical systems. Here we demonstrate experimentally and analytically the existence of longitudinal localized states that exist fundamentally in the phase of laser light. These robust and versatile phase bits can be individually nucleated and canceled in an injection-locked semiconductor laser operated in a neuron-like excitable regime and submitted to delayed feedback. The demonstration of their control opens the way to their use as phase information units in next-generation coherent communication systems. We analyse our observations in terms of a generic model, which confirms the topological nature of the phase bits and discloses their formal but profound analogy with Sine-Gordon solitons.

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.

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.

Complexity in pulsed nonlinear laser systems interrogated by permutation entropy

Permutation entropy (PE) has a growing significance as a relative measure of complexity in nonlinear systems. It has been applied successfully to measuring complexity in nonlinear laser systems. Here, PE and weighted permutation entropy (WPE) are discovered to show an unexpected inversion to higher values, when characterizing the complexity at the characteristic frequencies of nonlinear drivers in laser systems, for output power sequences which are pulsed. The cause of this inversion is explained and its presence can be used to identify when irregular dynamics transform into a fairly regular pulsed signal (with amplitude and timing jitter). When WPE is calculated from experimental output power time series from various nonlinear laser systems as a function of delay time, both the minimum value of WPE, and the width of the peak in the WPE plot are shown to be indicative of the level of amplitude variation and timing jitter present in the pulsed output. Links are made with analysis using simulated time series data with systematic variation in timing jitter and/or amplitude variations.

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.

Experimental observation of localized structures in medium size VCSELs

We report experimental evidence of spontaneous formation of localized structures in a 80 μm diameter Vertical-Cavity Surface-Emitting Laser (VCSEL) biased above the lasing threshold and under optical injection. Such localized structures are bistable with the injected beam power and the VCSEL current. We experimentally investigate the formation of localized structures for different detunings between the injected beam and the VCSEL, and different injection beam waists.

Holding spatial solitons in a pumped cavity with the help of nonlinear potentials

We introduce a one-dimensional model of a cavity with the Kerr nonlinearity and saturated gain designed so as to hold solitons in the state of shuttle motion. The solitons are always unstable in the cavity bounded by the usual potential barriers, due to accumulation of noise generated by the linear gain. Complete stabilization of the shuttling soliton is achieved if the linear barrier potentials are replaced by nonlinear ones, which trap the soliton, being transparent to the radiation. The removal of the noise from the cavity is additionally facilitated by an external ramp potential. The stable dynamical regimes are found numerically, and their basic properties are explained analytically.

Optical spatial solitons: historical overview and recent advances

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

Adler synchronization of spatial laser solitons pinned by defects

Defects due to growth fluctuations in broad-area semiconductor lasers induce pinning and frequency shifts of spatial laser solitons. The effects of defects on the interaction of two solitons are considered in lasers with frequency-selective feedback both theoretically and experimentally. We demonstrate frequency and phase synchronization of paired laser solitons as their detuning is varied. In both theory and experiment the locking behavior is well described by the Adler model for the synchronization of coupled oscillators.

Disorder mapping in VCSELs using frequency-selective feedback

We report on a simple method with a high spectral and spatial resolution for mapping variations in the cavity resonance of a plano-planar broad-area laser based on frequency-selective feedback. The demonstration experiment uses a vertical-cavity surface-emitting-laser (VCSEL), in which growth induced inhomogeneities are of particular importance. It relies only on a standalone laser with a narrow-bandwidth passive filter avoiding the need for an expensive tunable laser or high-resolution spectrometer.

Compensation of spatial inhomogeneities in a cavity soliton laser using a spatial light modulator

Dissipative solitons are self-localized states which can exist anywhere in a system with translational symmetry, but in real systems this translational symmetry is usually broken due to parasitic inhomogeneities leading to spatial disorder, pinning the soliton positions. We discuss the effects of semiconductor growth induced spatial disorder on the operation of a cavity soliton laser based on a vertical-cavity surface-emitting laser (VCSEL). We show that a refractive index variation induced by an external, suitably spatially modulated laser beam can be used to counteract the inherent disorder. In particular, it is demonstrated experimentally that the threshold of one cavity soliton can be lowered without influencing other cavity solitons making two solitons simultaneously bistable which were not without control. This proof of principle paves the way to achieve full control of large numbers of cavity solitons at the same time.

Nonlinear localized modes in bandgap microcavities

We study experimentally an electrically pumped GaAs-based bandgap structure based on a vertical cavity surface emitting laser (VCSEL). We demonstrate that a microcavity embedded into this bandgap VCSEL structure supports localized optical modes without any holding beam. We propose a model of surface-structured VCSELs based on a reduced dissipative wave equation for describing electromagnetic modes in such semiconductor cavities and analyze a crossover between linear and nonlinear solitonlike cavity modes.

Vectorial polariton solitons in semiconductor microcavities

This paper presents numerical studies of vectorial polariton solitons in semiconductor microcavities. In the simulation, polarization degree of freedom of the polariton fields is taken into consideration. In the bistable regime, bright and/or dark solitons are found to bifurcate from the homogonous solutions of the two circular polarization modes. The combinations of solitons in the two polarization directions can be bright-dark, dark-bright, bright-bright, and dark-dark.

Bistable and addressable localized vortices in semiconductor lasers

We demonstrate experimentally that localized emission states in coupled broad-area semiconductor lasers can carry a finite orbital angular momentum. The resulting structures therefore possess the chirality of optical vortices together with the properties of localized structures in dissipative systems, namely, the coexistence with a low intensity homogeneous emission and the mutual independence. These results open the way to the realization of arrays of optically addressable and bistable chiral laser pixels.

Light-bullet routing and control with planar waveguide arrays

Spatial mode-locking in three dimensions can be achieved in a slab waveguide array architecture. This study focuses on using the resulting robust and self-starting light bullet formation for photonics applications. Specifically, light bullets can be manipulated through a simple electronically addressable spatial gain dynamics. By applying gain ramps in time and/or space via electronics technology, complete control and manipulation of the light bullets can be achieved, thus allowing for the construction of the master logic gates of NAND and NOR. Its robustness, self-starting behavior and easy addressability suggest that the slab waveguide array mode-locking merits serious consideration as a next generation photonics device.

Vortex solitons in lasers with feedback

We report on the existence, stability and dynamical properties of two-dimensional self-localized vortices with azimuthal numbers up to 4 in a simple model for lasers with frequency-selective feedback.We build the full bifurcation diagram for vortex solutions and characterize the different dynamical regimes. The mathematical model used, which consists of a laser rate equation coupled to a linear equation for the feedback field, can describe the spatiotemporal dynamics of broad area vertical cavity surface emitting lasers with external frequency selective feedback in the limit of zero delay.

A dissipative attractor in the spatiotemporal collapse of ultrashort light pulses

Spatiotemporal self-focusing in nonlinear lossy media pushes ultrashort pulses towards a universal, non-solitary and non-conical light bullet wave state defined by the medium solely, and characterized by maximum energy losses. Its stationary propagation relies on a balance between nonlinear losses and the refuelling effect of self-focusing. No balancing gain is required for stationarity. These purely lossy dissipative light-bullets can explain many aspects of the filamentary dynamics in nonlinear media with anomalous dispersion.

Bifurcation to fronts due to delay

The stability of a steady-state front (kink) subject to a time-delayed feedback control (TDFC) is examined in detail. TDFC is based on the use of the difference between system variables at the current moment of time and their values at some time in the past. We first show that there exists a bifurcation to a moving front. We then investigate the limit of large delays but weak feedback and obtain a global bifurcation diagram for the propagation speed. Finally, we examine the case of a two-dimensional front with radial symmetry and determine the critical radius above which propagation is possible.

Spatial mode-locking of light bullets in planar waveguide arrays

A theoretical proposal is presented for the generation of mode-locked light-bullets in planar waveguide arrays, extending the concept of time-domain mode-locking in waveguide arrays to spatial (transverse) mode-locking in slab waveguides. The model presented yields three-dimensional localized states that act as global attractors to the waveguide array system. Single pulse stationary and time-periodic solutions as well as the transition to multi-pulse solutions as a function of gain are observed to be stabilized in such a system.

All-optical memory based on the injection locking bistability of a two-color laser diode

We study the injection locking bistability of a specially engineered two-color semiconductor Fabry-Pérot laser. Oscillation in the uninjected primary mode leads to a bistability of single mode and two-color equilibria. With pulsed modulation of the injected power we demonstrate an all-optical memory element based on this bistability, where the uninjected primary mode is switched with 35 dB intensity contrast. Using experimental and theoretical analysis, we describe the associated bifurcation structure, which is not found in single mode systems with optical injection.

Optical bistability in a GaAs-based polariton diode

We report on a new type of optical nonlinearity in a polariton p-i-n microcavity. Abrupt switching between the strong and weak coupling regime is induced by controlling the electric field within the cavity. As a consequence, bistable cycles are observed for low optical powers (2-3 orders of magnitude less than for Kerr induced bistability). Signatures of switching fronts propagating through the whole 300 x 300 microm2 mesa surface are evidenced.

Homoclinic snaking in a semiconductor-based optical system

We report on experimental observations of homoclinic snaking in a vertical-cavity semiconductor optical amplifier. Our observations in a quasi-one-dimensional and two-dimensional configurations agree qualitatively well with what is expected from recent theoretical and numerical studies. In particular, we show the bifurcation sequence leading to a snaking bifurcation diagram linking single localized states to "localized patterns" or clusters of localized states and demonstrate a parameter region where cluster states are inhibited.

Cavity soliton laser based on mutually coupled semiconductor microresonators

We report on experimental observation of localized structures in two mutually coupled broad-area semiconductor resonators, one of which acts as a saturable absorber. These structures coexist with a dark homogeneous background and they have the same properties as cavity solitons without requiring the presence of a driving beam into the system. They can be switched individually on and off by means of a local addressing beam.

Self-localized structures in vertical-cavity surface-emitting lasers with external feedback

In this paper, we analyze a model of broad area vertical-cavity surface-emitting lasers subjected to frequency-selective optical feedback. In particular, we analyze the spatio-temporal regimes arising above threshold and the existence and dynamical properties of cavity solitons. We build the bifurcation diagram of stationary self-localized states, finding that branches of cavity solitons emerge from the degenerate Hopf bifurcations marking the homogeneous solutions with maximal and minimal gain. These branches collide in a saddle-node bifurcation, defining a maximum pump current for soliton existence that lies below the threshold of the laser without feedback. The properties of these cavity solitons are in good agreement with those observed in recent experiments.