Drifting instabilities of cavity solitons in vertical cavity surface-emitting lasers with frequency selective feedback

In this paper we study the formation and dynamics of self-propelled cavity solitons (CSs) in a model for vertical cavity surface-emitting lasers (VCSELs) subjected to external frequency selective feedback (FSF), and build their bifurcation diagram for the case where carrier dynamics is eliminated. For low pump currents, we find that they emerge from the modulational instability point of the trivial solution, where traveling waves with a critical wavenumber are formed. For large currents, the branch of self-propelled solitons merges with the branch of resting solitons via a pitchfork bifurcation. We also show that a feedback phase variation of 2\pi can transform a CS (whether resting or moving) into a different one associated to an adjacent longitudinal external cavity mode. Finally, we investigate the influence of the carrier dynamics, relevant for VCSELs. We find and analyze qualitative changes in the stability properties of resting CSs when increasing the carrier relaxation time. In addition to a drifting instability of resting CSs, a new kind of instability appears for certain ranges of carrier lifetime, leading to a swinging motion of the CS center position. Furthermore, for carrier relaxation times typical of VCSELs the system can display multistability of CSs.Comment: 11 pages, 12 figure

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 coupled to a dissipative linear equation as a model of lasers with an external frequency-selective feedback. It is known that the feedback can stabilize the one-dimensional (1D) self-localized mode. We aim to extend the analysis to 2D stripe-shaped and vortex solitons. The radius of the vortices increases linearly with their topological charge, $m$, therefore the flat-stripe soliton may be interpreted as the vortex with $m=\infty$, while vortex solitons can be realized as stripes bent into rings. The results for the vortex solitons are applicable to a broad class of physical systems. There is a qualitative agreement between our results and those recently reported for models with saturable nonlinearity.Comment: Submitted to PR

A generic travelling wave solution in dissipative laser cavity

A large family of cosh-Gaussian travelling wave solution of a complex Ginzburg–Landau equation (CGLE), that describes dissipative semiconductor laser cavity is derived. Using perturbation method, the stability region is identified. Bifurcation analysis is done by smoothly varying the cavity loss coefficient to provide insight of the system dynamics. He’s variational method is adopted to obtain the standard sech-type and the notso-explored but promising cosh-Gaussian type, travelling wave solutions. For a given set of system parameters, only one sech solution is obtained, whereas several distinct solution points are derived for cosh-Gaussian case. These solutions yield a wide variety of travelling wave profiles, namely Gaussian, near-sech, flat-top and a cosh-Gaussianwith variable central dip. A split-step Fourier method and pseudospectral method have been used for direct numerical solution of the CGLE and travelling wave profiles identical to the analytical profiles have been obtained. We also identified the parametric zone that promises an extremely large family of cosh-Gaussian travelling wave solutions with tunable shape. This suggests that the cosh-Gaussian profile is quite generic and would be helpful for further theoretical as well as experimental investigation on pattern formation, pulse dynamics andlocalization in semiconductor laser cavity

Self-localized states in species competition

We study the conditions under which species competition, as described by competitive Lotka- Volterra models in a homogeneous niche space, can support localized states, i.e. patches of species with enhanced population surrounded by species with smaller densities. Using some approximations we show analytically and numerically that for strong enough self-interaction, such states exist and are stable, representing self-enhanced populations arising from the interactions, and not by any preferred niche location or better fitness. These structures can be thought as portions of stable periodic density patterns (which are also supported by the system), inserted in the background of homogeneous density of species.We acknowledge financial support from FEDER and MINECO (Spain) through Grant No. FIS2012-30634 INTENSE@COSYP, and from Comunitat Autónoma de les Illes Balears. D.G. acknowledges support from CSIC (Spain) through Grant No. 201050I016.Peer reviewe

Adler synchronization of spatial laser solitons pinned by defects

Spatial disorder due to growth fluctuations in broad-area semiconductor lasers induces pinning and frequency shifts of spatial laser solitons. We demonstrate frequency and phase-locking between two spatial solitons in VCSELs with frequency-selective feedback

Frequency and phase locking of laser cavity solitons

Edited by B. A. Malomed.Self-localized states or dissipative solitons have the freedom of translation in systems with a homogeneous background. When compared to cavity solitons in coherently driven nonlinear optical systems, laser cavity solitons have the additional freedom of the optical phase. We explore the consequences of this additional Goldstone mode and analyze experimentally and numerically frequency and phase locking of laser cavity solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback. Due to growth-related variations of the cavity resonance, the translational symmetry is usually broken in real devices. Pinning to different defects means that separate laser cavity solitons have different frequencies and are mutually incoherent. If two solitons are close to each other, however, their interaction leads to synchronization due to phase and frequency locking with strong similarities to the Adler-scenario of coupled oscillators.P.V.P. acknowledges support from SFB 910; C.M., and Y.N. from EPSRC DTA; P.C. from MICINN and Feder (FIS2007-60327, FISICOS, TEC2009-14101, DeCoDicA). Y.N. and C.M. were supported by EPSRC DTA/DTG grants.Peer reviewe

Observation of laser vortex solitons in a self-focusing semiconductor laser

We report the observation of single and multiple vortex solitons in a self-focusing dissipative system, a broad-area vertical-cavity surface-emitting laser (VCSEL) with frequency-selective feedback by a volume Bragg grating. They are bistable and the transitions between different soliton structures are analysed. The observations qualitatively verify theoretical predictions based on simplified models for a semiconductor laser with frequency-selective feedback