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International audience; We make an in-depth analysis of a bifurcation scenario that leads to chaotic hopping between two elliptically polarized modes in VCSELs. Our work brings new light on recent experiments using quantum dot VCSELs.

International audience; We report on experimental and theoretical results showing how mode competition in quantum dot semiconductor lasers can result in new nonlinear dynamics. A first example is a competition between non-orthogonal elliptically polarized modes that manifests itself in a polarization switching at a given injection current and in a polarization mode hopping dynamics at different time-scales. A second example is a pulsating dynamics in a quantum dot laser with optical injection, which originates from the simultaneous lasing in the ground and excited modes.

This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the general framework underlying this filter and show that it corresponds to a recursive expression of the least-square optimal estimation of the density operator in the presence of measurement imperfections. By measurement imperfections, we mean in a very general sense unread measurement performed by the environment (decoherence) and active measurement performed by non-ideal detectors. However, we assume to know precisely all the Kraus operators and also the detection error rates. Such recursive expressions combine well known methods from quantum filtering theory and classical probability theory (Bayes' law). We then demonstrate that such a recursive filter is always stable with respect to its initial condition: the fidelity between the optimal filter state (when the initial filter state coincides with the real quantum state) and the filter state (when the initial filter state is arbitrary) is a sub-martingale., Comment: Submitted to the American Control Conference 2012

International audience; We study the dynamics of an optically injected quantum-dot laser accounting for excited states. Mapping of the bifurcations in the plane frequency detuning vs. injection strength shows that the relaxation rate scales the regions of locking and single- and double-period solutions, while the capture rate has a minor effect. Within the regions of time-periodic solutions, close to the saddle-node bifurcation boundary, we identify subregions where the output signal resembles excitable pulses as a result of the bottleneck phenomenon. We show that such emission is determined mainly by fluctuations in the occupation of the excited states. The interpulse time follows an inverse square root scaling law as a function of the detuning. In a deterministic system the pulses are periodic regardless of the detuning, but in the presence of noise, close to the locking region, the interpulse time follows a positively skewed normal distribution. For a fixed frequency detuning, increasing the noise strength can shift the mean of the interpulse time distribution and make the pulsations more periodic.

International audience; We analyze the influence of the excited states (ES) on the dynamics of optically injected quantum dot lasers. In our model carriers from the wetting layer are first being captured into the excited state and then relax to the ground state. Our results indicate that the dynamics of optically injected QD lasers are driven by the relaxation time in the sense that it scales the regions where the laser exhibits distinct behaviors. It also influences the size of the locking region. The capture time has minor effect and influences mainly static characteristics. Bifurcation maps are studied with the main focus on self-pulsations. In particular our results show that the dynamics of self-pulsations is consistent with experimental observations of excitable dynamics. To utilize the self-pulsations we propose and investigate properties and limitation of the system used for all-optical signal processing. In our approach the slave laser is switched by the information signal acting as a master laser between the locking region and the region of self-pulsations. The maximum bit rate of such a system has been estimated to be 0.5 GHz. This value can be improved to 1 GHz by applying correction to the detection algorithm. The correction reflects the nature of self-pulsations and is calculated from the distribution of the time the system needs to fire a pulse.

Threshold photoelectron spectra (TPES) of the isotopomers of the methyl radical (CH(3), CH(2)D, CHD(2), and CD(3)) have been recorded in the 9.5-10.5 eV VUV photon energy range using third generation synchrotron radiation to investigate the vibrational spectroscopy of the corresponding cations at a 7-11 meV resolution. A threshold photoelectron-photoion coincidence (TPEPICO) spectrometer based on velocity map imaging and Wiley-McLaren time-of-flight has been used to simultaneously record the TPES of several radical species produced in a Ar-seeded beam by dc flash-pyrolysis of nitromethane (CH(x)D(y)NO(2), x + y = 3). Vibrational bands belonging to the symmetric stretching and out-of-plane bending modes have been observed and P, Q, and R branches have been identified in the analysis of the rotational profiles. Vibrational configuration interaction (VCI), in conjunction with near-equilibrium potential energy surfaces calculated by the explicitly correlated coupled cluster method CCSD(T*)-F12a, is used to calculate vibrational frequencies for the four radical isotopomers and the corresponding cations. Agreement with data from high-resolution IR spectroscopy is very good and a large number of predictions is made. In particular, the calculated wavenumbers for the out-of-plane bending vibrations, nu(2)(CH(3)(+)) = 1404 cm(-1), nu(4)(CH(2)D(+)) = 1308 cm(-1), nu(4)(CHD(2)(+)) = 1205 cm(-1), and nu(2)(CD(3)(+)) = 1090 cm(-1), should be accurate to ca. 2 cm(-1). Additionally, computed Franck-Condon factors are used to estimate the importance of autoionization relative to direct ionization. The chosen models globally account for the observed transitions, but in contrast to PES spectroscopy, evidence for rotational and vibrational autoionization is found. It is shown that state-selected methyl cations can be produced by TPEPICO spectroscopy for ion-molecule reaction studies, which are very important for the understanding of the planetary ionosphere chemistry.

The interferogram of a high index phase mask of 200 nm period under normal incidence of a collimated beam at 244 nm wavelength with substantially suppressed zeroth order produces a 100 nm period grating in a resist film under immersion. The paper describes the phase mask design, its fabrication, the effect of electron-beam lithographic stitching errors and optical assessment of the fabricated sub-cutoff grating. (C) 2010 Optical Society of America

International audience; I summarize here some of our recent contributions to the understanding and applications of semiconductor nonlinear dynamics. Interplay between polarization switching properties of VCSELs and external optical injection/optical feedback/current modulation gives rise to a rich variety of new dynamical phenomena characterized by multimode behavior, bistability, self-pulsing, noise-induced or noise-sustained instabilities. In these configurations control of polarization is possible but also new perspectives can be expected where the dynamical complexity would help for all-optical signal processing. I will conclude with recent theoretical and experimental works on polarization and nonlinear dynamical properties of quantum dot semiconductor lasers.

International audience; We demonstrate experimental evidence of polarization switching accompanied by polarization-mode hopping in quantum-dot vertical-cavity surface-emitting lasers. In our case, the polarization switching is associated with a change of linearly polarized light to elliptically polarized one, hence switching takes place between elliptically polarized states. Current-modulation measurements show that the polarization switching is of thermal origin.

International audience; We review our recent results related to nonlinear polarization dynamics and chaos in VCSELs. The possibility to generate multimode chaos motivates the study of chaos synchronization in coupled VCSELs and its application for secure communications.

International audience; In this paper, we summarize our recent results on nonlinear polarization- and transverse-mode dynamics of vertical-cavity surface-emitting lasers (VCSELs) induced by optical injection (OI) or current modulation. Due to the surface emission and cylindrical symmetry, VCSELs lack strong polarization anisotropy and may undergo polarization switching (PS). Furthermore, VCSELs may emit light in multiple transverse modes. This provides new features to the rich nonlinear dynamics induced in VCSELs by an external perturbation. We demonstrate for the case of orthogonal OI that new Hopf bifurcation on a two-polarization-mode solution delimits the injection locking (IL) region and that PS and IL of first-order transverse mode lead to a new resonance tongue for large positive detunings. Similarly, the underlying polarization-mode competition leads to chaotic-like behavior in case of gain switching and the presence of two transverse modes additionally reduces the possibility of regular dynamics.

International audience; We experimentally observe in-phase and anti-phase synchronization of chaos in two mutually-coupled vertical-cavity surface-emitting lasers. We investigate leader-laggard relationship between two chaotic waveforms and find that the laser with longer wavelength becomes the leader.

International audience; We present experimental and theoretical results on polarization nonlinear dynamics in Vertical-Cavity Surface-Emitting Lasers subject to optical injection or current modulation. We discuss polarization switching, rich nonlinear dynamics, multi-transverse modes and their bifurcation routes.

We demonstrate that dynamical polarization switching in mutually coupled vertical-cavity surface-emitting lasers (VCSELs) has a profound impact on the chaotic dynamics in the system drastically improving the in-phase (anti-phase) synchronization between the modes of the two VCSELs with the same (orthogonal) polarizations. Furthermore, an exchange of the leader-laggard role is observed with the higher (lower) frequency VCSEL being the leader for lower (higher) coupling strength. (C) 2008 Optical Society of America

article de 3 Pages et poster; National audience; L'objectif du présent article est de présenter le kit éducatif développé dans le cadre du réseau d'excellence NEMO (Network of excellence on Micro Optics) du 6ème PCRD [1]. NEMO est un projet visant à rassembler des partenaires de plusieurs pays européen dans le domaine de la micro-optique. Pour convaincre les élèves, dès l'école primaire et jusqu'à la fin du secondaire, des applications et du rôle de l'optique et la micro-optique dans la vie quotidienne ou dans la recherche, plusieurs partenaires de NEMO ont collaborés à la création de ce kit éducatif.

An experimental analysis of the nonlinear dynamics of a multi-transverse-mode vertical-cavity surface-emitting laser (VCSEL) when subject to a high-frequency current modulation is performed. Regular periodic dynamics-with periods equal to the modulation period or twice the modulation period-and irregular pulsating dynamics are obtained. Our results show that the irregular pulsating dynamics in multimode VCSELs subject to large-signal current modulation is due to the competition between different transverse modes. (C) 2008 American Institute of Physics.

In this paper we summarize the recent results on nonlinear dynamics of vertical-cavity surface-emitting lasers (VCSELs) which are bearing the fingerprints of the particular polarization properties of VCSELs. Due to the surface emission and cylindrical symmetry, VCSELs lack strong polarization anisotropy and may undergo polarization switching and polarization mode-hopping. This provides new specificities to the rich nonlinear dynamics induced in VCSELs by an external perturbation. We unveil both experimentally and theoretically these new specificities for the case of optical feedback, optical injection, and unidirectional synchronization between VCSELs.

International audience

International audience; We first discuss the effect of isotropic optical feedback from an extremely short external cavity (ESEC) (K. Petermann, 1195, K. Hsu, et al., 1998) on the emission properties of vertical-cavity surface-emitting lasers (VCSELs). When changing the external cavity length a modulation of the total power and the wavelength emitted by the VCSEL is observed with a period of half the emission wavelength (K. Panajotov et al., 2004). By making use of a two modes rate equation VCSEL model we develop a map of bistability to investigate the parametric dependence of polarization properties of VCSELs in such configuration, finding out a periodic dependence of the polarization switching currents on the ESEC length (K. pajanotov, et al., 2004 and M. A. Arteaga et al., 2006). By increasing the external mirror reflectivity we can make this periodic dependence stronger and strongly asymmetric providing the possibility to prevent PS for any injection current and thus, achieving polarization stabilization in VCSELs (M. A. Arteaga et al., 2006). Further numerical simulations with isotropic and non isotropic feedback show how parameters as gain compression coefficients, frequency splitting between the linearly polarized modes, differential gain and the mirror reflectivity, affect the map of bistability (M. A. Arteaga et al., 2006). The theoretical results are supported by extensive experimental mapping (M. A. Arteaga et al., 2006). The switching currents and the hysteresis width can be widely tuned by varying the external cavity length. The amplitude of modulation of the polarization switching current with the external cavity length is experimentally confirmed to be proportional to the external mirror reflectivity, proving its key role in achieving polarization control of such lasers using optical feedback. Moreover, by a proper choice of the optical feedback parameters, the emission can be stabilized in any of the two linearly polarized modes (M. A. Arteaga et al., 2006). Finally, by maki- - ng use of the fine-polarization tuning provided by the ESEC feedback we report on the experimental observation of coherence resonance in a bistable system with delay (M. A. Arteaga et al., 2006). Our system consists of a VCSEL subject to time-delayed optical feedback simultaneously from a long and from extremely short external cavity. Coherence resonance is experimentally proven by analysis of the residence time distribution of the polarization mode-hopping regime and of the signal to noise ratio in the power spectrum.

We experimentally and numerically report on polarization switching (PS) mechanism which involves a two-mode limit cycle dynamics in a vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection from a master laser (ML). The VCSEL (slave laser, SL) emits a horizontal linearly polarized (LP) fundamental mode, without optical injection. The VCSEL is injected by a vertically polarized light from ML. Dynamical characteristics of the VCSEL are investigated as a function of optical injection parameters, i.e., injection strength and frequency detuning between master and slave lasers. We experimentally resolve an injection parameter region for which, as the injection strength is increased for fixed detunings, a limit cycle dynamics in both non-injected and injected modes is abruptly excited. For larger injection strengths, the VCSEL switches from the two-mode to a single-mode limit cycle dynamics which involves only the injected mode. Using continuation methods, we numerically identify two torus bifurcation mechanisms, namely TR 1 and TR 2 , which support such a switching scenario. We show that both TR 1 and TR 2 originate from a particular Hopf bifurcation which plays a key role in the polarization dynamics of the injected VCSEL. Furthermore, our results reveal that the newly observed switching dynamics are generic features of VCSEL two-mode systems.

Vertical-cavity surface-emitting lasers (VCSELs) have competitive advantages with respect to conventional edge-emitting lasers such as the fabrication of dense two-dimensional VCSEL arrays for optical interconnects. VCSELs exhibit intriguing polarization properties which are critical in polarization-sensitive applications. Polarization switching (PS) between two VCSEL's preferential orthogonal linearly polarized (LP) modes may be induced by changing the bias current, temperature or, externally, through orthogonally polarized optical injection. Depending on optical injection parameters, i.e., the injected power and the frequency detuning, injection-locking of the VCSEL can be achieved.We contribute to the study of polarization bistability, polarization switching (PS), injection-locking and transverse mode competition in a VCSEL subject to orthogonal continuous-wave optical injection. We experimentally show and theoretically demonstrate that PS and locking may involve rich nonlinear dynamics including wave mixing, limit cycle, subharmonic resonances or a period-doubling route to chaos. In particular, we analyze the interplay between PS and the underlying nonlinear dynamics, and unveil its bifurcation mechanisms. Our study brings a new insight into the physics of polarization dynamics in externally-driven VCSELs.Chaos synchronization of coupled VCSELs is also investigated. A feedback-induced chaotic light from the master VCSEL is unidirectionally injected into the slave VCSEL. We show that the synchronization quality can be significantly enhanced when chaos involves both orthogonal LP modes. This result is interesting for chaos communication schemes based on VCSELs.; Le laser à cavité verticale émettant par la surface (VCSEL ou Vertical-Cavity Surface-Emitting Laser) comporte des avantages compétitifs par rapport aux lasers émettant par le côté. Notamment, l'émission par la surface permet la fabrication de matrices bidimensionnelles de VCSELs intéressants pour les réseaux d'interconnexion et le routage tout optique. Le VCSEL présente souvent deux modes polarisation linéaire orthogonaux avec des fréquences et des gains optiques presque identiques. Dès lors, de faibles perturbations telles que des modifications du courant d'injection ou de la température peuvent facilement induire des basculements de polarisation. Toutefois, en utilisant un schéma d'injection optique, il est possible de contrôler ces instabilités de polarisation.Nous nous intéressons au contrôle du basculement de polarisation ainsi que la compétition des modes transverses d'un VCSEL soumis à injection optique de polarisation orthogonale. Nous montrons expérimentalement et théoriquement la dynamique de basculement de polarisation dans le plan des paramètres d'injection (puissance injectée et désaccord en fréquence entre le laser maître et le VCSEL) implique des dynamiques non linéaires telles le mélange d'ondes, les cycles limites ainsi qu'une route de doublement de période vers le chaos optique. L'analyse des bifurcations sous-jacentes nous a permet de dresser une cartographie de la dynamique de basculement de polarisation du VCSEL.Dans notre thèse, nous étudions également la synchronisation du chaos de VCSELs dans un schéma de couplage unidirectionnel. Nous montrons que la compétition des modes de polarisation linéaire orthogonaux affecte la qualité de la synchronisation du chaos. Ces résultats sont intéressants dans le cadre du développement récent de liaisons de communication sécurisée par chaos optique.

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.; International audience; In this paper, we report on experimental and theoretical investigation on the nonlinear dynamics of the two orthogonal linearly polarized fundamental transverse modes of verticalcavity surface-emitting lasers (VCSELs) under sinusoidal current modulation. Irregular pulses of the power of individual polarizations are measured with a period equal to twice the modulation period. In contrast with individual polarizations, total power displays regular pulsing at twice the modulation period. The variability of pulse streams is characterized by using residence times distributions. We show that the residence time distributions for individual linear polarizations display an exponential decay for large values of that time. Those results are well reproduced by using a theoretical model that includes spontaneous emission fluctuations. However the previous qualitative features remain even in the absence of spontaneous emission noise. Our results therefore suggest that the irregular polarization dynamics have a deterministic origin and can be defined as deterministic chaos.

Vertical-cavity surface-emitting lasers (VCSELs) have competitive advantages with respect to conventional edge-emitting lasers such as the fabrication of dense two-dimensional VCSEL arrays for optical interconnects. VCSELs exhibit intriguing polarization properties which are critical in polarization-sensitive applications. Polarization switching (PS) between two VCSEL's preferential orthogonal linearly polarized (LP) modes may be induced by changing the bias current, temperature or, externally, through orthogonally polarized optical injection. Depending on optical injection parameters, i.e., the injected power and the frequency detuning, injection-locking of the VCSEL can be achieved.We contribute to the study of polarization bistability, polarization switching (PS), injection-locking and transverse mode competition in a VCSEL subject to orthogonal continuous-wave optical injection. We experimentally show and theoretically demonstrate that PS and locking may involve rich nonlinear dynamics including wave mixing, limit cycle, subharmonic resonances or a period-doubling route to chaos. In particular, we analyze the interplay between PS and the underlying nonlinear dynamics, and unveil its bifurcation mechanisms. Our study brings a new insight into the physics of polarization dynamics in externally-driven VCSELs.Chaos synchronization of coupled VCSELs is also investigated. A feedback-induced chaotic light from the master VCSEL is unidirectionally injected into the slave VCSEL. We show that the synchronization quality can be significantly enhanced when chaos involves both orthogonal LP modes. This result is interesting for chaos communication schemes based on VCSELs., Le laser à cavité verticale émettant par la surface (VCSEL ou Vertical-Cavity Surface-Emitting Laser) comporte des avantages compétitifs par rapport aux lasers émettant par le côté. Notamment, l'émission par la surface permet la fabrication de matrices bidimensionnelles de VCSELs intéressants pour les réseaux d'interconnexion et le routage tout optique. Le VCSEL présente souvent deux modes polarisation linéaire orthogonaux avec des fréquences et des gains optiques presque identiques. Dès lors, de faibles perturbations telles que des modifications du courant d'injection ou de la température peuvent facilement induire des basculements de polarisation. Toutefois, en utilisant un schéma d'injection optique, il est possible de contrôler ces instabilités de polarisation.Nous nous intéressons au contrôle du basculement de polarisation ainsi que la compétition des modes transverses d'un VCSEL soumis à injection optique de polarisation orthogonale. Nous montrons expérimentalement et théoriquement la dynamique de basculement de polarisation dans le plan des paramètres d'injection (puissance injectée et désaccord en fréquence entre le laser maître et le VCSEL) implique des dynamiques non linéaires telles le mélange d'ondes, les cycles limites ainsi qu'une route de doublement de période vers le chaos optique. L'analyse des bifurcations sous-jacentes nous a permet de dresser une cartographie de la dynamique de basculement de polarisation du VCSEL.Dans notre thèse, nous étudions également la synchronisation du chaos de VCSELs dans un schéma de couplage unidirectionnel. Nous montrons que la compétition des modes de polarisation linéaire orthogonaux affecte la qualité de la synchronisation du chaos. Ces résultats sont intéressants dans le cadre du développement récent de liaisons de communication sécurisée par chaos optique.

International audience; We unveil the bifurcations underlying polarization switching and injection locking in a vertical-cavity surface-emitting laser subject to optical injection. A Hopf bifurcation, not reported for conventional edgeemitting lasers, delimits the injection locking region and influences the polarization switching conditions. We furthermore theoretically show and experimentally observe periodic dynamics at the relaxation oscillation frequency in the noninjected mode together with wave-mixing dynamics in the injected mode. These dynamics precede the polarization switching leading to injection locking and are attributed to a torus bifurcation arising on a two-polarization mode solution.

International audience; We report theoretically on the dynamics of two vertical-cavity surface-emitting lasers (VCSELs) coupled unidirectionally through their optical fields, in the context of chaos synchronization and its use for chaos secure communications. One of the two VCSELs is rendered chaotic by optical feedback effects and injects its chaotic output into a second, slave VCSEL. Two different injection schemes are analyzed. A first configuration is such that the master VCSEL injects light polarized orthogonal to that emitted by the free-running slave VCSEL. The orthogonal optical injection induces polarization switching of the slave VCSEL, leading to polarization synchronization between master and slave. A second configuration considers a polarization-preserving optical injection. We report on anticipative and isochronous polarization synchronization and interestingly, we show that VCSEL polarization mode competition enhances the synchronization quality.

Poster; International audience; An experimental and theoretical investigation of polarization switching (PS) and transverse mode locking of a vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection was provided. Experimental mapping of the polarization switching and transverse modes competition in the plane of frequency detuning vs. injection power was performed. It is shown that PS is achieved with bistability over the whole frequency detuning range.

International audience; In this paper, we investigate theoretically the interplay between polarization switching (PS) and nonlinear dynamics in a vertical-cavity surface emitting laser (VCSEL) subject to orthogonal optical injection from a master laser (ML). The free-running VCSEL is biased such that only the horizontal (x) linearly polarized fundamental (LP) mode is excited. The injected VCSEL is then modeled using an extension of the spin flip model (SFM). We perform a bifurcation analysis using continuation techniques that allow tracking bifurcation of both stable and unstable solutions.

Poster; International audience; It is shown numerically that two fundamentally different regimes (I and II) of isochronous synchronization are possible, depending on the detuning between the lasers and the strength of the optical injection into the slave. We consider a master laser subjected to isotropic optical feedback and which is optically coupled, in a unidirectional way, to an open-loop slave laser. A master laser which exhibits a dominant x-LP mode and a weak y-LP mode was chosen. The x-LP mode was selected, rotate it to y direction, and optically inject it in the slave laser, which, under free-running conditions, emits x-polarized light.

Poster; International audience; This work investigates numerically the impact of the polarization mode competition and the frequency detuning between the two lasers on the chaos synchronization of mutually coupled VCSELs. To this aim , a simple rate-equation model of single transverse-mode VCSEL is implemented.

[poster]

International audience; We will present a survey on our experimental and theoretical studies on polarization dynamics in Vertical-Cavity Surface-Emitting Lasers (VCSELs) in three situations, namely optical injection, unidirectional synchronization under optical feedback and mutual coupling.

International audience; In this paper we report on a theoretical investigation of the nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers (VCSELs) under current modulation. Special attention is given to the comparison with a previously studied case of single-transverse mode VCSEL emitting in two orthogonal polarizations. The consideration of spatial effects in VCSEL modifies the polarization dynamics that accompanies the period doubling route to chaos for large modulation amplitudes. Depending on the modulation parameters, the excitation of a higher order transverse mode may either induce chaotic pulsing in an otherwise regularly pulsating VCSEL, or induce a time-periodic pulsing dynamics in an otherwise chaotic VCSEL. Bifurcation diagrams obtained for different modulation frequencies, several values of the dichroism, and different transverse mode characteristics allow us to identify the different scenarios of polarization dynamics in a directly modulated VCSEL. Temporal analysis of carrier number radial profile reveals considerable changes for the multitransverse mode case only constituting the physical origin of the reported changes in the temporal and polarization dynamics.

International audience; We report theoretically on a pure frequency-induced polarization bistability in a vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection, i.e., the master laser light polarization is orthogonal to that of the slave VCSEL. As the frequency detuning is scanned from negative to positive values and for a fixed injected power, the VCSEL exhibits two successive and possibly bistable polarization switchings. The first switching (from the slave laser polarization to the injected light polarization) exhibits a bistable region whose width is maximum for a given value of the injected power. Such a dependency of hysteresis width on the injected power is similar to that recently found experimentally by Hong et al.[Electron. Lett. 36, 2019 (2000)]. The bistability accompanying the second switching (from the injected light polarization back to the slave laser free-running polarization) exhibits, however, significantly different features related to the occurrence of optical chaos. Interestingly, the width of the bistable region can be tuned over a large range not only by modifying the injection parameters but also by modifying the device parameters, in particular the VCSEL linewidth enhancement factor.

Poster

We present a quantitative study on the fabrication of microlenses using a low-cost polymer dispending technique. Our method is based on the use of a silicon micro-cantilever robotized spotter system. We first give a detailed description of the technique. In a second part, the fabricated microlenses are fully characterized by means of SEM (Scanning Electron Microscope), AFM (Atomic Force Microscopy) non contact optical profilometry and Mach-Zehnder interferometry. Diameters in the range [25-130 mu m] are obtained with an average surface roughness of 2.02nm. Curvature radii, focal lengths as well as aberrations are also measured for the first time: the fabricated microlenses present focal lengths in the range [55-181 mu m] and exhibit high optical quality only limited by diffraction behaviour with RMS aberration lower than lambda/14. (C) 2007 Optical Society of America.

International audience; Round-Robin measurements on the linewidth enhancement factor are carried out in many laboratories participating to EU COST 288 Action. Up to 7 different techniques are applied to DFB, VCSELs, QCL, and QD lasers, and results are compared.

International audience; We analyze theoretically the polarization dynamics in unidirectionally coupled vertical-cavity surface-emitting lasers ͑VCSELs͒. The master VCSEL is subject to an isotropic optical feedback. The slave VCSEL is subject to an orthogonal optical injection from the master VCSEL, i.e., only the linearly polarized mode orthogonal to the dominant linearly polarized mode of the free-running slave VCSEL is injected into the slave VCSEL. This laser configuration may lead the slave VCSEL polarization to switch to that of the injected master laser field. The injected power required for polarization switching depends on the frequency detuning. We identify in the plane of the injection parameters two regions of enhanced synchronization between the injected LP mode and the corresponding slave LP mode. In the so-called region II the slave VCSEL exhibits anticorrelated dynamics in its two LP modes while in the so-called region I the slave VCSEL exhibits dynamics in only one LP mode, which corresponds to the polarization of the injected field. The two regions exhibit different synchronization properties in both the LP mode dynamics and total intensity dynamics. We furthermore analyze the dependency of the synchronization quality on the parameter mismatch between master and slave VCSELs and on the polarization switching properties of each VCSEL.

International audience; We present experimental and theoretical studies of nonlinear dynamics induced by optical feedback in vertical cavity surface emitting lasers (VCSELs) focusing on the impact of polarization mode competition. We unveil the bifurcation mechanism leading to multiple channels of interchanging linearly polarized (LP) steady states, study the way of their destabilization and the role of the external cavity modes and the polarization of light in this process. We distinguish two situations depending on the dichroism present in the VCSEL. In the first one, as typical for semiconductor lasers, with increasing the optical feedback strength the VCSEL exhibits a Hopf bifurcation from steady state to a limit cycle followed by a torus bifurcation to quasiperiodic behavior and then can become chaotic. Bistability between different single polarization dynamics: steady-state, periodic, quasi-periodic and chaotic dynamics is possible, however, the suppressed polarization mode is never excited. In the second case, when the VCSEL is biased in the region of polarization bistability, increasing the feedback strength can not only cause polarization switching but can also lead to chaotic emission in the two LP modes. Polarization switching can happen from a limit cycle in the x-LP mode to a steady state in the y-LP mode which then undergoes consecutive Hopf and torus bifurcations and becomes chaotic. Bistability between chaotic two LP mode emission and periodic single LP mode emission is demonstrated. We also consider the case of polarization selective optical feedback and the influence of the spontaneous emission noise or external noise in the system. For the last situation we demonstrate slow antiphase hopping between the two LP modes together with rapid anticorrelated oscillations in the LP intensities at the external-cavity frequency. These last dynamics can be strongly enhanced by the noise leading to the phenomenon of coherence resonance. Finally, we consider the transition from long to short external cavity and show that the typical low-frequency fluctuation chaotic dynamics is anticipated by a regime of regular dynamics - fast pulses at the delay time modulated by a slow time periodic envelope. We discuss the interplay of optical feedback and polarization dynamics in this regime, too.

International audience

International audience; We present an experimental investigation of a vertical-cavity surface-emitting laser (VCSEL) submitted to orthogonal optical injection, i.e., the injected light is linearly polarized and orthogonal to that emitted by the solitary VCSEL. Bifurcation boundaries of qualitatively different dynamics are mapped out in the frequency detuning-injection strength plane. We unveil rich and complex dynamics including injection locking, limit cycle, wave mixing, and period doubling route to chaos.

International audience

International audience; We perform a theoretical investigation of the polarization dynamics in a vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection, i.e., the injected field has a linear polarization (LP) orthogonal to that of the free-running VCSEL. In agreement with previous experiments [Z. G. Pan et al., Appl. Phys. Lett. 63, 2999 (1993)], an increase of the injection strength may lead to a polarization switching accompanied by an injection locking. We find that this route to polarization switching is typically accompanied by a cascade of bifurcations to wave-mixing dynamics and time-periodic and possibly chaotic regimes. A detailed mapping of the polarization dynamics in the plane of the injection parameters (detuning, injection strength) unveils a large richness of dynamical scenarios. Of particular interest is the existence of another injection-locked solution for which the two LP modes both lock to the master laser frequency, i.e., an elliptically polarized injection-locked (EPIL) steady state. Modern continuation techniques allow us to unveil an unfolding mechanism of the EPIL solution as the detuning varies and also to link the existence of the EPIL solution to a resonance condition between the master laser frequency and the free-running frequency of the normally depressed LP mode in the slave laser. We furthermore report an additional case of bistability, in which the EPIL solution may coexist with the second injection-locked solution (the one being locked to the master polarization). This case of bistability is a result of the interaction between optical injection and the two-polarization-mode characteristics of VCSEL devices.

International audience; In this paper we summarize our recent theoretical and experimental results concerning optical injection in VCSELs. First, we develop phenomenological rate equation model for the normalized photon densities of the two fundamental VCSEL modes with orthogonal linear polarization when injecting external light polarized along the direction of polarization of the nonlazing mode. We then perform a simple analytical analysis of optically induced polarization switching in VCSELs, which takes into account both the current-dependent linear dichroism and the nonlinear dichroism. We also present detailed investigation of polarization dynamics induced by optical injection using an alternative rate equation model for VCSELs which takes into account the microscopic spin-flip processes in the active medium. In particular we predict that two injection locked solutions may coexist: the first one exhibits the polarization of the master laser, while the second one corresponds to an elliptically polarized injection locking. Continuation techniques allow us to find the bifurcation scenario leading to such an elliptically locked state. We also report on our first experimental results on polarization switching and injection locking for the case of an orthogonal optical injection in VCSELs and demonstrate rich dynamical behavior. The polarization switching is accompanied by a cascade of bifurcations to timeperiodic and possibly chaotic dynamics. Our experimental results show evidence of a period doubling route to chaos.

International audience; We will present a survey on our experimental and theoretical studies of polarization dynamics in vertical-cavity surface-emitting lasers (VCSELs) when subject to orthogonal optical injection, i.e. the injected field has a linear polarization (LP) orthogonal to that of the free-running VCSEL. The output characteristics of an oxide-confined AlGaAs-GaAs quantum well VCSEL are experimentally mapped as a function of the strength of the optical injection and the detuning between the injection frequency and the free-running frequency of the solitary laser. Experimentally, we achieve a very large range of frequency detunings: from -82 to 89 GHz. Two border lines at negative and positive detunings form "a tongue" of polarization switch (PS) region; its area expanding to both positive and negative detunings with increasing the injection strength. The two border lines are with a well pronounced region of bistability, the hysteresis width is almost constant for positive detuning and increasing for negative ones. Only in the later case the route to PS occurs through injection locking (both the polarization and the frequency of the VCSEL locks to the ones of the master laser). The route to injection locking can be accompanied by a rich nonlinear dynamics, including limit cycle, wave mixing, subharmonic resonance and possibly period doubling route to chaos. The PS "tongue" is further strongly influenced at large positive detuning, which we identify as being due to an injection locking of the first-order transverse mode of the VCSEL. We carry out theoretical studies of the case of orthogonal injection in VCSELs, which qualitatively match the experimental findings. Furthermore, we predict the existence of new injection locked solution for which the two LP modes both lock to the master laser frequency resulting in an elliptically polarized injection locked (EPIL) steady-state. Modern continuation techniques allow us to unveil an unfolding mechanism of the EPIL solution as the detuning varies and also to link the existence of the EPIL solution to a resonance condition between the master laser frequency and the frequency of the suppressed VCSEL LP mode. This EPIL solution may coexist with the LP injection locked solution, resulting in a new type of bistability in VCSELs