Ignace Gatare

Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers

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.

Nonlinear dynamics accompanying polarization switching in vertical-cavity surface-emitting lasers with orthogonal optical injection

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.

Transverse Mode Switching and Locking in Vertical-Cavity Surface-Emitting Lasers Subject to Orthogonal Optical Injection

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

Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers.

We analyze theoretically the effect of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs). Chaos in the master laser is induced by delayed optical feedback, and the slave laser is subject to isotropic optical injection from the master VCSEL. We show that the synchronization quality can be enhanced when the chaotic regime in the master VCSEL involves both fundamental orthogonal linearly polarized modes.

Polarization- and Transverse-Mode Dynamics in Optically Injected and Gain-Switched Vertical-Cavity Surface-Emitting Lasers

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.

Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach

We present a comprehensive study of the bifurcation routes in a generic model of a two-polarization-mode semiconductor laser when subject to orthogonal optical injection, relevant to a single-transverse-mode vertical-cavity surface-emitting laser. For positive detunings, polarization switching (PS) occurs as the intensity of the noninjected mode gradually decreases and eventually shuts down, in some cases accompanied along the way by the onset and the subsequent vanishing of relaxation oscillations. We identify a Hopf bifurcation on a two-polarization-mode solution, which supports the onset of relaxation oscillation time-periodic dynamics in both injected (x-linearly polarized) and noninjected (y-linearly polarized) modes. For sufficiently large negative detunings, PS is a sharp transition occurring either at the injection-locking point or at a subcritical Hopf bifurcation and is often part of a hysteresis cycle.

Nonlinear Dynamics of Vertical-Cavity Surface-Emitting Lasers

Nonlinear dynamics of Vertical-Cavity Surface-Emitting Lasers (VCSELs) induced by optical injection, optical feedback, current modulation and mutual coupling is reviewed. Due to the surface emission and cylindrical symmetry VCSELs lack strong polarization anisotropy and may undergo polarization switching. Furthermore, VCSELs may emit light in multiple transverse modes. These VCSEL properties provide new features to the rich nonlinear dynamics induced by an external perturbation. We demonstrate for the case of orthogonal optical injection that new Hopf bifurcation on a two-polarization-mode solution delimits the injection locking region and that polarization switching and injection locking 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. The bistable property of VCSEL makes it possible to investigate very fundamental problems of bistable systems with time-delay, such as the coherence resonance phenomenon. We also demonstrate that the synchronization quality between unidirectionally coupled VCSELs can be significantly enhanced when the feedback-induced chaos in the master laser involves both orthogonal LP fundamental transverse modes.

Polarization switching in VCSELs induced by optical injection

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

Excitation of a two-mode limit cycle dynamics on the route to polarization switching in a VCSEL subject orthogonal to optical injection

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 TR1 and TR2, which support such a switching scenario. We show that both TR1 and TR2 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.

Light polarization fingerprints on nonlinear dynamics of vertical-cavity surface-emitting lasers

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.