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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; We experimentally and theoretically demonstrate the variety of the nonlinear dynamics exhibited by a single frequency semiconductor laser subjected to optical injection from a frequency comb. The injection parameters (the detuning and the injection strength) and the comb properties (comb spacing and the amplitude of the injected comb lines) are varied to unveil several dynamics such as injection locking, wave-mixing, chaotic dynamics, and unlocked time-periodic dynamics corresponding to new comb solutions. The asymmetry of the injected comb is shown to modify the size of the injection locking region in the parameter space, as well as the common properties between the new comb solutions observed and the injected comb.

International audience; This work reports on numerical analysis of the nonlinear dynamics of a semiconductor laser subject to an optical injection with a frequency comb. We identified the fundamental difference between the single mode injection and frequency comb injection. By varying the injection parameters (detuning and injection ratio), the results show that the slave laser is able to reproduce the injected frequency comb (new comb) in different parameters regions. The appearance of the new comb depends on the number of injected comb lines for fixed comb properties.

International audience; We analyze the nonlinear dynamics of a semiconductor laser with optical injection from a frequency comb. When varying both the injection parameters (detuning and injection ratio) and the comb properties (number of comb lines and comb spacing), we identify and select several dynamics, including (1) injection locking with selective amplification of the comb line that shows the smallest detuning from the injected laser, (2) unlocked time-periodic dynamics that correspond to a new frequency comb with a broadened optical spectrum, thereby sharpening the pulse generated at the injected laser output, and (3) unlocked chaotic dynamics.

This paper describes the high-frequency characterizations of a vertical electro-absorption modulator (EAM) to ensure its monolithic integration onto a VCSEL for data communications. Splitting the emitting and the modulating parts is an attractive approach compared to directly current-modulated VCSEL since it releases the intrinsic limitations due to carriers dynamics that occurs in such VCSEL device. It is, in this aim, utmost to thoroughly characterize and understand the properties and performances of the vertically integrated EAM under high frequency operation, as it will be decisive for the application of EAM-VCSEL to very high data-rate communications. EAM measurements, presented up to 40 GHz, require a precise control of the optical fiber coupling and a precise evaluation of the injection losses over the full frequency range.

International audience; VCSELs became dominant laser sources in many short optical link applications such as datacenter, active cables, etc. Actual standards and commercialized VCSEL are providing 25 Gb/s data rates, but new solutions are expected to settle the next device generation enabling 100 Gb/s. Directly modulated VCSEL have been extensively studied and improved to reach bandwidths in the range of 26-32 GHz [Chalmers, TU Berlin], however at the price of increased applied current and thus reduced device lifetime. Furthermore, the relaxation oscillation limit still subsists with this solution. Thus, splitting the emission and the modulation functions as done with DFB lasers is a very promising alternative [TI-Tech, TU Berlin]. Here, we study the vertical integration of an Electro-Absorption Modulator (EAM) within a VCSEL, where the output light of the VCSEL is modulated through the EAM section. In our original design, we finely optimized the EAM design to maximize the modulation depth by implementing perturbative Quantum Confined Stark Effect (QCSE) calculations, while designing the vertical integration of the EAM without penalty on the VCSEL static performances. We will present the different fabricated vertical structures, as well as the experimental electrical and optical static measurements for those configurations demonstrating a very good agreement with the reflectivity and absorption simulations obtained for both the VCSEL and the EAM-VCSEL structures. Finally, to reach very high frequency modulation we studied the BCB electrical properties up to 110 GHz and investigated coplanar and microstrip lines access to decrease both the parasitic capacitance and the influence of the substrate. 100 words: In this presentation, we describe the operation of Multiple-Quantum-Wells Asymmetric Fabry-Perot modulator, vertically integrated into a VCSEL structure for high-speed modulation. First we optimize the Electro-Absorptive Modulator (EAM) and the EAM-VCSEL structures by utilizing a perturbative quantum-confined Stark-effect and transfer matrix calculations. Then we present experimental reflectivity, LIV curves and photocurrent measurements and demonstrate very good agreement with our modelling results. High frequency measurements of BCB electrical response up to 110 GHz are carried out to estimate the parasitic effects due to the pad configuration and the impact of the substrate.

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.

International audience; We propose a simplified and easier fabrication process flow for the manufacturing of AlOx-confined VCSELs based on combining the oxidation step with a self-aligned process, allowing the mesa etching and two successive lift-off steps based on a single lithography step. The electro-optical confinement achieved by standard lateral oxidation enables a low threshold and a single mode behaviour for the VCSEL. This simplified process can largely improve VCSEL manufacturing by reducing the processing time and costs compared to the standard VCSEL process. Introduction: Vertical-cavity surface-emitting lasers (VCSEL) have become the preferred light sources in many photonic systems, enabling short-link interconnections [1] but also in other emerging mass-market applications like sensing and detection [2]. The large production volume of VCSELs would benefit from a simplification of the manufacturing process flow that may largely increase the cost-effectiveness. Indeed, compared to the LED and LDs, the VCSEL fabrication process flow requires a large number of elementary steps defined by successive inter-aligned photolithography levels. A precision in the micron range is required to ensure the lateral alignment between the optical waveguide and the electrical injection. For these reasons, one of the most important concerns for the VCSEL manufacturers is to improve the production throughput by lowering the fabrication time and cost per wafer. The development of a self-aligned process is of great interest as already demonstrated for the fabrication of high performance HBT transistors or ridge lasers [3,4]. To that extent, Al-Omari [5] used a top metallic contact deposited over a photoresist layer as a hard mask to dry-etch the VCSEL mesa. Chua [6] developed a pseudo-planar approach by opening via holes down to the AlAs layer to carry out the lateral oxidation. This process has subsequently been improved by Strzelecka [7] to increase the device density. Recently, we have shown that air-post VCSELs could be created using an innovative self-aligned process, which combined several masking and lift-off steps defined by a single lithographic step [8]. In this paper, we extend this work and propose a new process flow to fabricate, in a very simple and straightforward way, the widely-used oxide-confined VCSELs. The demonstrated process drastically simplifies the oxide-confined VCSEL fabrication by reducing the total number of lithographic alignment steps from four or more to only one alignment, with the additional advantage of relieving the required tolerances. This process flow, most suitable for 3D imaging and sensing applications, can also be easily implemented for the fabrication of other optoelectronic devices such as modulators, ridge waveguide lasers, detectors, solar cells or any process combining dry etch, passivation and metallization.

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.

International audience; In this paper, the output characteristics of an oxide-confined AlGaAs-As quantum well vertical-cavity surface-emitting laser (VCSEL) under orthogonal optical injection are 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, for a very large range of frequency detuning (from -82 to 89 GHz). The injection light is polarized orthogonally with respect to the solitary VCSEL output light. As the injection strength increases the VCSEL switches to the master laser polarization. Polarization switching is accompanied by a rich nonlinear dynamics, including limit cycle, wave mixing, subharmonic resonance and period doubling route to chaos. Polarization switching is found with but also without injection locking. Injection locking occurs with the slave fundamental transverse mode or, for large positive detunings, with the first-order transverse mode.

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

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

We consider a controlled quantum system whose finite dimensional state is governed by a discrete-time nonlinear Markov process. In open-loop, the measurements are assumed to be quantum non-demolition (QND). The eigenstates of the measured observable are thus the open-loop stationary states: they are used to construct a closed-loop supermartingale playing the role of a strict control Lyapunov function. The parameters of this supermartingale are calculated by inverting a Metzler matrix that characterizes the impact of the control input on the Kraus operators defining the Markov process. The resulting state feedback scheme, taking into account a known constant delay, provides the almost sure convergence of the controlled system to the target state. This convergence is ensured even in the case where the filter equation results from imperfect measurements corrupted by random errors with conditional probabilities given as a left stochastic matrix. Closed-loop simulations corroborated by experimental data illustrate the interest of such nonlinear feedback scheme for the photon box, a cavity quantum electrodynamics system., Comment: submitted (16 pages, 4 figures)

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; 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.

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; 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

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; 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.

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.

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.

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.