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We present experimental and theoretical results of noise-induced attractor hopping between dynamical states found in a single transverse mode vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. These transitions involve dynamical states with different polarizations of the light emitted by the VCSEL. We report an experimental map identifying, in the injected power-frequency detuning plane, regions where attractor hopping between two, or even three, different states occur. The transition between these behaviors is characterized by using residence time distributions. We find multistability regions that are characterized by heavy-tailed residence time distributions. These distributions are characterized by a -1.83±0.17 power law. Between these regions we find coherence enhancement of noise-induced attractor hopping in which transitions between states occur regularly. Simulation results show that frequency detuning variations and spontaneous emission noise play a role in causing switching between attractors. We also find attractor hopping between chaotic states with different polarization properties. In this case, simulation results show that spontaneous emission noise inherent to the VCSEL is enough to induce this hopping., This work has been funded by the Ministerio de Economía y Competitividad (MINECO/FEDER, UE), Spain under project TEC2015-65212-C3-1-P. A.Q. acknowledges FWO for support from a Postdoc fellowship and K.P. is grateful to the Methusalem Foundation for financial support.

We report an experimental study of the polarization nonlinear dynamics in a 1550 nm single-mode vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. Experimentally measured stability maps identifying regions of different nonlinear dynamics for various values of bias current are reported. We show that VCSELs with more than a 35 dB polarization mode suppression ratio can have rich nonlinear dynamics in both linear polarizations, including periodic and chaotic behaviors appearing simultaneously in both polarization modes., Ministerio de Economía y Competitividad (MINECO) (TEC2015-65212-C3-1-P); Fonds Wetenschappelijk Onderzoek (FWO); Agence Nationale de la Recherche (ANR) (ANR-12-JS03-005); Prefecture de Region Grand-Est (Chair in Photonics, FEDER [PHOTON, APOLLO], FNADT[APOLLO, PIANO]); AIRBUS-GDI Simulation; Metz Metropole; Conseil Departemental de Moselle; Conseil Regional Grand-Est.

We theoretically demonstrate the possibility to synchronize polarization chaos generated by a free-running vertical-cavity surface-emitting laser (VCSEL). We highlight two distinct synchronization regimes: 1) a high-quality synchronization regime where all polarization modes and total intensity are synchronized, which shows good robustness against parameter mismatch, and 2) a "slow time-scale" synchronization where the slower part of the dynamics-that is, the random-like hopping between the two scrolls of the chaotic attractor-synchronizes while the faster oscillations remain unsynchronized. (C) 2016 Optical Society of America

International audience; We investigate theoretically the synchronization properties of the polarization chaos dynamics generated by a free-running vertical-cavity surface-emitting laser (VCSEL). Here, we focus on a one-way master-slave configuration - or unidirectional coupling - with two chaotic VCSELs. The spin-flip model is used to model the two devices and derived to account for the coupling between them. We demonstrate that the chaotic dynamics generated by the two lasers can indeed synchronize in the proposed configuration. The synchronization appears to be of high quality as we obtain a high-level of similarity between the emission characteristics of the master and slave laser dynamics.

International audience; We investigate the behaviour of a multimode two-color quantum dot laser subject to optical feedback. In particular, we focus on the effects of a variation of the external cavity length at the micrometer scale on the laser emission characteristics and especially on its optical spectrum. For each mode, we observe oscillations of the output power with different spectral amplitudes. No clustering or mode grouping effect is observed. Theoretically, we demonstrate a good agreement with a multimode two-color quantum dot laser model.

We investigate experimentally and theoretically the multi-mode dynamics of a two-color quantum dot laser subject to time-delayed optical feedback. We unveil energy exchanges between the longitudinal modes of the excited state triggered by variations of the feedback phase, and observe that the modal competition between longitudinal modes appears independently within the ground state and excited state emission. These features are accurately reproduced with a quantum dot laser model extended to take into account multiple modes for both ground and excited states. Finally, we discuss the significant impact of such behavior on feedback-based control of two-color quantum dot lasers. (C) 2016 Optical Society of America

International audience; In this contribution, we experimentally report recurrent switching between ground and excited state emission in a quantum dot laser controlled by optical feedback. We demonstrate that changing the phase of the optical feedback can efficiently induce switching between the two emission processes of the laser. Experimentally, by using an external mirror placed on a piezo-actuator, we were able to achieve incomplete switching between ground and excited state emission, i.e. without complete extinction of the modes. The switching takes place for variations of the external cavity length at the wavelength scale, i.e. around 1.2 um. Theoretically, we successfully link this switching behaviour with the evolution of the modal gain difference between the two modes induced by the variations of the optical feedback phase.

International audience; The increase in modulation bandwidth of a vertical-cavity surface-emitting laser (VCSEL) can be achieved through the vertical integration of a modulator onto the laser. This approach has already been proposed and demonstrated to be competitive [1-3]. In this specific case, a double mesa structure with three contacts is needed to apply a high-frequency voltage signal to the modulator section and inject a CW current into the underlying VCSEL section. The middle contact serves as a shared ground. Indeed, splitting the emitting and the modulating parts circumvents the carrier dynamics limitation of the modulation bandwidth encountered in direct current-modulated VCSELs. However, the parasitic capacitances of the access line and contact pad play a significant role in the high-frequency limit of such a device. In this paper, we present the design, fabrication and modulation characteristics of an electro-absorption modulator (EAM) vertically-integrated onto an 850-nm VCSEL that is compatible with high-frequency operation. The two optical cavities are such that their mutual optical coupling is small to improve the modulation properties at high frequencies. This EAM-VCSEL device has been successfully fabricated by molecular beam epitaxy, followed by an original technological process [4]. In particular, planarized BCB layers and microstrip access lines have been implemented to optimize the high-frequency signal injection. Thanks to the optimized wavelength detuning between the cavities resonances of the EAM and the VCSEL and respectively to the quantum well absorption tail of the modulator, the EAM modulator exhibits a modulation depth of more than 40% within a 4V span. This vertically integrated EAM-VCSEL approach enables also to minimize the wavelength chirp during the modulation, which in our case is lower than 80 pm. Finally, 3-dB frequency bandwidths up to 29 GHz were measured on both stand-alone vertical EAM devices and vertically-integrated EAM-VCSELs. (a) (b)Fig. 1 (a) Schematics of the EAM-VCSEL structure under study with planarized BCB and (b) high-frequency modulation response of the EAM-VCSEL device with different DC bias voltages applied to the EAM.

International audience

Faraday Discussions, 212, ISSN:1359-6640, ISSN:1364-5498

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.

We investigate experimentally and theoretically the polarization switching found in single-transverse-mode vertical-cavity surface-emitting lasers (VCSELs) when subject to parallel optical injection. Our analysis focuses on a recently observed state in which injection locking of the parallel polarization and excitation of the free-running orthogonal polarization of the VCSEL are obtained. A simple nonlinear dependence between the power of both linear polarizations and the frequency detuning is found. Also, the total power emitted by the VCSEL is constant and independent of the injected optical power and the frequency detuning. We check these results experimentally for a variety of frequency detunings and bias currents applied to the device. We report experimental and theoretical stability maps in the injected power-frequency detuning plane for different bias currents, identifying the regions in which the state is observed. A simple analytical expression that describes the map boundary for large and negative frequency detunings is obtained. This provides a simple method to extract the linear dichroism of the device., Fonds Wetenschappelijk Onderzoek (FWO); Agence Nationale de la Recherche (ANR) (ANR-12-JS03-005); Ser Cymru National Research Network in Advanced Engineering and Materials; Prefecture de Lorraine and SGAR (APOLLO [FEDER/FNADT], PHOTON project [FEDER]); Ministerio de Economia y Competitividad (MINECO/FEDER, UE) (TEC2015-65212-C3-1-P).

Selected Lectures; International audience; We report on chaotic polarization fluctuations generated from a free-running vertical-cavity surface-emitting laser, and investigate in details the VCSEL dynamics and its potential application. We provide new experimental evidences of asymmetrical behaviour of VCSEL polarization dynamics, and show that considering a slight misalignment of the anisotropies of the laser cavity allows to reproduce these dynamics numerically. Finally, we propose a simple scheme for random bit generation exploiting polarization chaos , and experimentally demonstrate a 100 Gbps random generation rate.

©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.; In this paper, we report on theoretical and experimental investigation on polarization and transverse mode behavior of vertical-cavity surface-emitting lasers (VCSELs) under orthogonal optical injection as a function of the injection strength and of the detuning between the injection frequency and the free-running frequency of the solitary laser. As the injection strength increases the VCSEL switches to the master laser polarization. We find that the injection power necessary to obtain such polarization switching is minimum at two different values of the frequency detuning: the first one corresponds to the frequency splitting between the two linearly polarized fundamental transverse modes, and the second one appears at a larger positive frequency detuning, close to the frequency difference between the first-order and the fundamental transverse modes of the solitary VCSEL. We show theoretically that both the depth and the frequency corresponding to the second minimum increase when the relative losses between the two transverse modes decrease. Bistability of the polarization switching is obtained for the whole frequency detuning range. Such a bistability is found for the fundamental mode only or for both transverse modes, depending on the value of the detuning. The theoretical and experimental optical spectra are in good agreement showing that the first-order transverse mode appears locked to the external injection.

We demonstrate the physical generation of random bits at high bit rates (> 100 Gb/s) using optical chaos from a solitary laser diode and therefore without the complex addition of either external optical feedback or injection. This striking result is obtained despite the low dimension and relatively small bandwidth of the laser chaos, i.e. two characteristics that have been so far considered as limiting the performances of optical chaos-based applications. We unambiguously attribute the successful randomness at high speed to the physics of the laser chaotic polarization dynamics and the resulting growth rate of the dynamical entropy., 14 pages, 3 figures, submitted

We report experimentally a bistability between two limit cycles (i.e. time-periodic dynamics) in a free-running vertical-cavity surface-emitting laser. The two limit cycles originate from a bifurcation on two elliptically polarized states which exhibit a small frequency difference and whose main axes are symmetrical with respect to the linear polarization eigenaxes at threshold. We demonstrate theoretically that this peculiar behavior can be explained in the framework of the spin-flip model model by taking into account a small misalignment between the phase and amplitude anisotropies. (C) 2014 Optical Society of America

This special issue of Optical and Quantum Electronics is related to the workshops PHASE 2007 and IPSSO 2007, which took place in Supelec, Metz (France) on March 28–30, 2007. The acronym PHASE stands for “PHysics and Applications of SEmiconductor LASERs”. The acronym IPSSO stands for “Instabilities, Patterns and Spatial SOlitons”. The workshops brought together the photonics community in Europe and the scientific program was built to both acknowledge recent advances and emphasize modern trends in this field. The workshop PHASE 2007 was organized in the framework of the European Action COST 288 “Nanoscale andUltrafast Photonics”. COST is the acronym (in French) for “European Cooperation in the Field of Scientific and Technical Research”. It is a framework for international research and development cooperation, allowing for coordination of national research at European level. The main objective of the COST 288 Action is to advance the application of ultrafast nanophotonics to develop high capacity photonic communication infrastructures, as well as to provide a forum to bring forward advanced research on novel topics such as advanced optical signal processing and optical logic, microwave photonics and exploratory technologies (based on nanophotonics) such as quantum communication. PHASE 2007 was a continuation of the workshop PHASE 2005 which also took place at

Summary form only given. When using quantum dot (QD) as an active region for semiconductor laser, one can confine more than one energy level, thus allowing laser effect to take place in the ground state (GS), the excited state (ES) or both simultaneously [1]. In this contribution we theoretically consider the impact of optical feedback on the mode competition between GS and ES emission. Using an analytical approach, continuation techniques and numerical integration we provide a detailed analysis of the steady-states and bifurcation scenarios predicted, thus bringing new light on recent experiments [2].

International audience; We investigate theoretically the impact of optical feedback on quantum dot two-color laser dynamics when emitting from both the excited and the ground states. Detailed analysis of the laser dynamics is provided by numerical integrations and continuation techniques, as well as by analytical methods. As the feedback strength is increased the quantum dot laser undergoes a sequence of bifurcations involving steady-states, external cavity modes, self-pulsations and chaos. Furthermore, we report on two interesting mode competition results. First, the optical feedback favors the ground state emission; hence an increase of the feedback strength will generally lead to an increase of the ground state emission output power. Second, the optical feedback can select one lasing state or induce bistable switchings between different steady-states depending on the feedback strength and the injection current.

In this contribution we provide an in depth theoretical analysis of the bifurcations leading to nonlinear polarization dynamics in a free-running vertical-cavity surface-emitting laser (VCSEL). We detail the sequence of bifurcations that occurs when increasing the injection current, and which brings the laser from linear to elliptical polarization emission and then self-pulsating or even more complex chaotic dynamics of the light intensity. Continuation techniques allow us to follow the stable and unstable limit cycle solutions emerging from Hopf bifurcations, and therefore to interpret the frequency of the self-pulsating polarization dynamics. The fundamental frequency of the pulsating dynamics is either close to the laser relaxation oscillation frequency or close to the linear-birefringence-induced polarization mode frequency splitting, depending on the laser parameters. A systematic analysis of the parameter space allows us to identify two scenarios that are in excellent qualitative agreement with those reported in recent experiments. Our results provide, moreover, evidence for an interesting polarization mode hopping mechanism, i.e., a so-called deterministic mode hopping where the laser exhibits a chaotic and therefore random-like hopping between two states that are elliptically polarized and nonorthogonal. DOI: 10.1103/PhysRevA.87.013834

Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos., Comment: 13 pages, 5 figures

International audience

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.

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.

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.

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

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.

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.

©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.

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.

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.

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.

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 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; 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

International audience; We investigate experimentally and theoretically nonlinear dynamics and polarization bistability in a vertical-cavity surface-emitting laser (VCSEL) submitted to an external optical injection with orthogonal polarization, i.e., the injected light from a master laser (ML) is linearly polarized and orthogonal to the polarization direction of the free-running VCSEL (slave laser, SL). Depending on the injection power level and the frequency detuning between ML and SL, our experimental results show that the injected VCSEL may undergo complex dynamics including subharmonic resonances and period-doubling route to chaos that are associated to polarization switching (PS). Using continuation method, we carry out a detailed bifurcation analysis and report on qualitatively different dynamics as we change the injection strength and/or the detuning. We show that PS may be strongly influenced by the presence of those dynamics. Our numerical results reveal period doubling dynamics that emerge from a Hopf bifurcation associated to an elliptical polarized injection locking state. Pure frequency-induced polarization bistability, i.e., when the detuning is changed for fixed injection power, is studied theoretically. Our results show that, depending on the level of the fixed injection strength, frequency induced PS may be achieved with or without hysteresis.

International audience; Bistability as well as dynamics associated to polarization switching in a vertical-cavity surface-emitting laser (VCSEL) submitted to orthogonal optical injection from an external master laser are investigated. Intensity-polarization switching bistability is studied by increasing and decreasing the intensity of the injected beam and for a fixed frequency detuning, i.e. the frequency offset between master and the free running VCSEL. Depending on the frequency detuning, bistable switching is experimentally found to occur with or without injection locking of the fundamental mode to the master laser frequency. For large positive detuning, injection locking of the first-order transverse mode with a strong depression of the fundamental mode has been observed. The case of frequency – polarization switching bistability, i.e. when the frequency detuning is first decreased and then increased for a fixed injected power, has also been theoretically analyzed. Qualitative comparison with previous experimental work is presented for the dependence of the width of the bistable switching region on the injection strength level. Finally we show an experimental result of complicated dynamics including period doubling route to chaos that accompany polarization switching and which motivates future theoretical investigations.