Bistable and addressable localized vortices in semiconductor lasers

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.

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.

Coexistence and Interactions between Nonlinear States with Different Polarizations in a Monochromatically Driven Passive Kerr Resonator

We report on experimental observations of coexistence and interactions between nonlinear states with different polarizations in a passive Kerr resonator driven at a single carrier frequency. Using a fiber ring resonator with adjustable birefringence, we partially overlap nonlinear resonances of two orthogonal polarization modes, achieving coexistence between different nonlinear states by locking the driving laser frequency at various points within the overlap region. In particular, we observe coexistence between temporal cavity solitons and modulation instability patterns, as well as coexistence between two nonidentical cavity solitons with different polarizations. We also observe interactions between the distinctly polarized cavity solitons, as well as spontaneous excitation and annihilation of solitons by a near-orthogonally polarized unstable modulation instability pattern. By demonstrating that a single frequency driving field can support coexistence between differentially polarized solitons and complex modulation instability patterns, our work sheds light on the rich dissipative dynamics of multimode Kerr resonators. Our findings could also be of relevance to the generation of multiplexed microresonator frequency combs.

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

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.

Observing Dissipative Topological Defects with Coupled Lasers

Topological defects have been observed and studied in a wide range of systems, such as cosmology, spin systems, cold atoms, and optics, as they are quenched across a phase transition into an ordered state. These defects limit the coherence of the system and its ability to approach a fully ordered state, so revealing their origin and control is becoming an increasingly important field of research. We observe dissipative topological defects in a one-dimensional ring of phased-locked lasers, and show how their formation is related to the Kibble-Zurek mechanism and is governed in a universal manner by two competing time scales. The ratio between these two time scales depends on the system parameters, and thus offers the possibility of enabling the system to dissipate to a fully ordered, defect-free state that can be exploited for solving hard computational problems in various fields.

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.

Holographic optical metasurfaces: a review of current progress

In this article, we review recent developments in the field of surface electromagnetic wave holography. The holography principle is used as a tool to solve an inverse engineering problem consisting of designing novel plasmonic interfaces to excite either surface waves or free-space beams with any desirable field distributions. Leveraging on the new nanotechnologies to carve subwavelength features within the large diffracting apertures of conventional holograms, it is now possible to create binary holographic interfaces to shape both amplitude phase and polarization of light. The ability of the new generation of ultrathin and compact holographic optical devices to fully address light properties could find widespread applications in photonics.

Breatherlike solitons extracted from the Peregrine rogue wave

Based on the Peregrine solution (PS) of the nonlinear Schrödinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breatherlike solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realistic values of coefficients accounting for the anomalous dispersion, Kerr nonlinearity, and higher-order effects. The results demonstrate that the breathing solitons stably propagate in the fibers. Their robustness against small random perturbations applied to the initial background is demonstrated too.

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.

Pattern formation by kicked solitons in the two-dimensional Ginzburg-Landau medium with a transverse grating

We consider the kick- (tilt-) induced mobility of two-dimensional (2D) fundamental dissipative solitons in models of bulk lasing media based on the 2D complex Ginzburg-Landau equation including a spatially periodic potential (transverse grating). The depinning threshold, which depends on the orientation of the kick, is identified by means of systematic simulations and estimated by means of an analytical approximation. Various pattern-formation scenarios are found above the threshold. Most typically, the soliton, hopping between potential cells, leaves arrayed patterns of different sizes in its wake. In the single-pass-amplifier setup, this effect may be used as a mechanism for the selective pattern formation controlled by the tilt of the input beam. Freely moving solitons feature two distinct values of the established velocity. Elastic and inelastic collisions between free solitons and pinned arrayed patterns are studied too.

Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation

We demonstrate that, in a two-dimensional dissipative medium described by the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) equation with the viscous (spectral-filtering) term, necklace rings carrying a mixed radial-azimuthal phase modulation can evolve into polygonal or quasipolygonal stable soliton clusters, and into stable fundamental solitons. The outcome of the evolution is controlled by the depth and azimuthal anharmonicity of the phase-modulation profile, or by the radius and number of "beads" in the initial necklace ring. Threshold characteristics of the evolution of the patterns are identified and explained. Parameter regions for the formation of the stable polygonal and quasipolygonal soliton clusters, and of stable fundamental solitons, are identified. The model with the CQ terms replaced by the full saturable nonlinearity produces essentially the same set of basic dynamical scenarios; hence this set is a universal one for the CGL models.

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

We use the cubic complex Ginzburg-Landau equation linearly coupled to a dissipative linear equation as a model for lasers with an external frequency-selective feedback. This system may also serve as a general pattern-formation model in media driven by an intrinsic gain and selective feedback. While, strictly speaking, the approximation of the laser nonlinearity by a cubic term is only valid for small field intensities, it qualitatively reproduces results for dissipative solitons obtained in models with a more complex nonlinearity in the whole parameter region where the solitons exist. The analysis is focused on two-dimensional stripe-shaped and vortex solitons. An analytical expression for the stripe solitons is obtained from the known one-dimensional soliton solution, and its relation with vortex solitons is highlighted. The radius of the vortices increases linearly with their topological charge m, therefore the stripe-shaped soliton may be interpreted as the vortex with m=∞, and, conversely, vortex solitons can be realized as unstable stripes bent into stable rings. The results for the vortices are applicable for a broad class of physical systems.

Stability conditions for moving dissipative solitons in one- and multidimensional systems with a linear potential

We analyze stability of moving dissipative solitons in the one-, two, and three-dimensional cubic-quintic complex Ginzburg-Landau equations in the presence of a linear potential (linear refractive index modulation). The expressions of stability conditions and propagation trajectory of solitons are derived by means of a generalized variational approximation. Predictions of the variational analysis are fully confirmed by direct numerical simulations. The results have potential applications to using spatial dissipative solitons in optics as individually addressable and shift registers of the all-optical data processing systems.