Etienne Averlant

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.

Self-Replicating Spots in the Brusselator Model and Extreme Events in the One-Dimensional Case with Delay

We consider the paradigmatic Brusselator model for the study of dissipative structures in far from equilibrium systems. In two dimensions, we show the occurrence of a self-replication phenomenon leading to the fragmentation of a single localized spot into four daughter spots. This instability affects the new spots and leads to splitting behavior until the system reaches a hexagonal stationary pattern. This phenomenon occurs in the absence of delay feedback. In addition, we incorporate a time-delayed feedback loop in the Brusselator model. In one dimension, we show that the delay feedback induces extreme events in a chemical reaction diffusion system. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical distribution, which is often considered as a signature of the presence of rogue waves, appears for sufficiently strong feedback intensity. The generality of our analysis suggests that the feedback-induced instability leading to the spontaneous formation of rogue waves in a controllable way is a universal phenomenon.

Vector cavity solitons in broad area Vertical-Cavity Surface-Emitting Lasers

We report the experimental observation of two-dimensional vector cavity solitons in a Vertical-Cavity Surface-Emitting Laser (VCSEL) under linearly polarized optical injection when varying optical injection linear polarization direction. The polarization of the cavity soliton is not the one of the optical injection as it acquires a distinct ellipticity. These experimental results are qualitatively reproduced by the spin-flip VCSEL model. Our findings open the road to polarization multiplexing when using cavity solitons in broad-area lasers as pixels in information technology.

Self-organized light bullets in type-I intracavity second-harmonic generation

We study the formation of three-dimensional structures in type-I intracavity second harmonic generation model where polarization degrees of freedom due to the birefringence of the χ(2) crystal is not considered. The device consists of an optical cavity filled with a quadratic nonlinear material and driven by an external beam at the fundamental frequency. The transmitted part of this field is coupled into the cavity where it undergoes second-harmonic conversion. These dissipative structures consist of regular or localized 3D lattices of bright spots travelling at the group velocity of light in the material. We show evidence of stable three dimensional structures such as stripes and cylinders.

Polarization properties of localized structures in VCSELs

Broad area Vertical-Cavity Surface-Emitting Lasers (VCSELs) have peculiar polarization properties which are a field of study by itself.1-3 These properties have already been used for localized structure generation, in a simple configuration, where only one polarization component was used.4 Here, we present new experimental and theoretical results on the complex polarization behavior of localized structures generated in an optically-injected broad area VCSEL. A linear stability analysis of the spin-flip VCSEL model is performed for the case of broad area devices, in a restrained and experimentally relevant parameter set. Numerical simulations are performed, in one and two dimensions. They reveal existence of vector localized structures. These structures have a complex polarization state, which is not simply a linear polarization following the one of the optical injection. Experimental results confirm theoretical predictions. Applications of this work can lead to the encoding of small color images in the polarization state of an ensemble of localized structures at the surface of a broad area VCSEL.

Periodic and Localized Structures in a Photonic Crystal Fiber Resonator

We consider a photonic crystal fiber resonator , driven by a coherent beam. The threshold for appearance of dark localized structures is estimated analytically and numerically by using a weakly nonlinear analysis in the vicinity of the modulational instability threshold. The nonlinear analysis allows to determine the parameter regime where the transition from supercritical to subcritical modulational instability takes place. This transition determines the threshold associated with the formation of dark cavity solitons. Numerical simulations of the governing model equation are in good agreement with the analytical results.

Polarisation properties of cavity solitons in VCSELs: Theory and experiment

Localized structures often called cavity solitons in optics have been observed in various systems of nonlinear science such as chemistry, physics, plant ecology and optics [1]. Scalar cavity solitons have been reported in the broad area [2] and in medium size vertical cavity surface emitting lasers [3]. The polarization degree of freedom was not considered in these works.

Coexistence of cavity solitons with different polarization states and different power peaks in all-fiber resonators

We theoretically investigate a weakly birefringent all-fiber cavity subject to linearly polarized optical injection. We describe the propagation of light inside the cavity using, for each linear polarization component of the electric field, the Lugiato-Lefever model. These two components are coupled by cross-phase modulation. We show that, for a wide range of parameters, there is a coexistence between a homogeneous steady state and two different types of temporal vector cavity solitons, which can be hosted in the same system. They differ by their polarization state and peak intensity. We construct their bifurcation diagram and show that they are connected through a saddle-node bifurcation. Finally, we show that vector cavity solitons exhibit multistability involving different polarization states with different energies.

Localized structures in broad area VCSELS: Experiments and delay-induced motion

We investigate the space-time dynamics of a Vertical-Cavity Surface-Emitting Laser (VCSEL ) subject to optical injection and to delay feedback control. Apart from their technological advantages, broad area VCSELs allow creating localized light structures (LSs). Such LSs, often called Cavity Solitons , have been proposed to be used in information processing, device characterization, and others. After a brief description of the experimental setup, we present experimental evidence of stationary LSs. We then theoretically describe this system using a mean field model. We perform a real order parameter description close to the nascent bistability and close to large wavelength pattern forming regime. We theoretically characterize the LS snaking bifurcation diagram in this framework. The main body of this chapter is devoted to theoretical investigations on the time-delayed feedback control of LSs in VCSELs. The feedback induces a spontaneous motion of the LSs, which we characterize by computing the velocity and the threshold associated with such motion. In the nascent bistability regime, the motion threshold and the velocity of moving LSs depend only on the feedback parameters. However, when considering the previously introduced mean-field model, theoretical predictions indicate that both motion threshold and velocity are strongly affected by the phase of the delay and by the carrier relaxation rate.

Cavity solitons in vertical-cavity surface-emitting lasers

We consider a broad area vertical-cavity surface-emitting laser(VCSEL) subject to injection and to time-delayed feedback. We present analytical and numerical analysis of the dependence of the drift instability threshold and on the feedback strength, feedback phase, and carrier relaxation time. we demonstrate that due to finite carrier relaxation rate the delay induced drift instability can be suppressed to a certain extent. We give analytical estimation of the soliton velocity near the drift instability point which is in a good agreement with numerical results obtained using the full model equations.