Paul Mandel

Bifurcation phenomena in a laser with saturable absorber. II

We investigate the bifurcation diagram of a laser with saturable absorber in the low and medium intensity regimes. The linear stability of the stationary solutions corresponding to these regimes is studied. In the low intensity domain, a Hopf bifurcation point is determined from which a time-periodic solution emerges. This solution is contructed and its stability is analyzed in the vicinity of the bifurcation point. It is shown that this time-periodic solution is stable in a finite domain of the parameter space.

Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers

We study the polarization switching of vertical-cavity surface-emitting lasers based on simulations of the spin-flip model. We show that the switching point depends on the ramp signal used to scan the injected current. Fast current ramps enlarge the hysteresis region since the switching point moves to high pump values for increasing injection and to low pump values for decreasing injection. The delay of the bifurcation follows a power law with the slope of the current ramp.

Transverse-mode dynamics in directly modulated vertical-cavity surface-emitting lasers with optical feedback

Vertical-cavity surface-emitting lasers (VCSELs) with optical feedback are known to exhibit different transverse-mode regimes depending on the injection current. Close to threshold a VCSEL operates on the fundamental transverse mode, while for larger injection the dynamics is often multimode, with the optical feedback inducing either in-phase or anti-phase transverse mode oscillations. In this paper, we study numerically the influence of current modulation on these different feedback-induced transverse-mode regimes. The modulation amplitude and period are taken as control parameters. We find that the in-phase and anti-phase regimes are robust under weak modulation. As the modulation amplitude increases, there is a transition to a dynamics governed by the current modulation, where the total output power follows the injection current and there is either single-mode or in-phase multimode behavior. However, the effect of the current modulation depends on the modulation period. Under fast modulation, the laser cannot follow the modulation and the optical-feedback-induced effects are dominant. On the contrary, under slow modulation there is a superposition of modulation and feedback effects, with the total output following the modulated current and an underlying transverse-mode behavior mainly determined by the optical feedback. A resonant behavior was observed for modulation periods close to the internal oscillation period. In this case, current modulation induces pulsing output intensity with single-mode or in-phase multimode behavior.

Nonlinear control in optical bistability

We study the influence of a small periodic modulation of the input field amplitude in dispersive optical bistability. When the system is initially near one of the two limit points in a stable state, the addition of a small periodic modulation may either stabilize or destabilize the system. We prove that destabilization occurs as a result of critical slowing down when the modulation frequency is decreased.

Dynamics of nascent hysteresis in optical bistability

Abstract We investigate the time-dependent response of an optical bistable system characterized by a nascent hysteresis under the influence of a slowly varying time-periodic external field amplitude. A quantitative as well as a qualitative difference is observed between stationary and time-dependent hystereses.

Switching times in absorptive optical bistability

Abstract We give analytic expressions for the up-switching and the down-switching times of an optical bistable device in the limit of large C. In the case of up-switching the jump time is proportional to the atomic relaxation time. In the case of down-switching, the jump time is proportional to the cavity relaxation time. No assumption on the relative magnitude of the cavity and the atomic relaxation times is introduced.

Slow passage through the laser first threshold: influence of the initial conditions

Abstract We investigate the slow passage through the laser first threshold in the good cavity limit, when the losses are slowly varied in time. We construct an asymptotic solution of the laser intensity equation and analyze the delay of the bifurcation transition. Our analysis is not restricted to the small intensity regime and we show that the dynamics depends critically on the initial value of the control parameter.

Transverse and polarization effects in index-guided vertical-cavity surface-emitting lasers

We study numerically the polarization dynamics of vertical-cavity surface-emitting lasers (VCSELs) operating in the fundamental transverse mode. We use an extension of the spin-flip model that not only accounts for the vector nature of the laser field, but also considers spatial transverse effects. The model assumes two orthogonal, linearly polarized fields, which are coupled to two carrier populations, associated with different spin sublevels of the conduction and valence bands in the quantum-well active region. Spatial effects are taken into account by considering transverse profiles for the two polarizations, for the two carrier populations, and for the carrier diffusion. The optical profile is the LP{sub 01} mode, suitable for describing index-guided VCSELs with cylindrical symmetry emitting on the fundamental transverse mode for both polarizations. We find that in small-active-region VCSELs, fast carrier diffusion induces self-sustained oscillations of the total laser output, which are not present in larger-area devices or with slow carrier diffusion. These self-pulsations appear close to threshold, and, as the injection current increases, they grow in amplitude; however, there is saturation and the self-pulsations disappear at higher injection levels. The dependence of the oscillation amplitude on various laser parameters is investigated, and the results are found to be inmorexa0» good qualitative agreement with those reported by Van der Sande et al. [Opt. Lett. 29, 53 (2004)], based on a rate-equation model that takes into account transverse inhomogeneities through an intensity-dependent confinement factor.«xa0less

Antiphase dynamics in multimode lasers

Controlling chaos represents one of the most interesting and challenging programs in the field of nonlinear dynamics. In the past few years different methods have been proposed based on (i) the determination of the stable and unstable directions in the PoincarP section, (ii) on a self-controlling feedback procedure and (iii) on the introduction of small perturbations? In this paper, accordingly to method (iii), we show that a small parametric perturbation stabilizes the chaotic behavior of a CO laser with modulated losses. It is well knownq that in a single-mode CO2 laser the intensity undergoes a subharmonic sequence of bifurcations leading to chaos when we increase the amplitude V, of a sinusoidal voltage signal V(t) = Vo + V, sin (2nFt) (V, = 600 V, F = 100 KHz) applied to an intracavity electro-optic crystal. The stabilization of periodic orbits within the chaotic region has been obtained by slight modulations of the control parameter V,. Such perturbations consist of sinusoidal signals at f = f, = 50 KHz and f = f2 = 25 KHz with amplitude e and an adjustable phase offset a = mn with respect to the fundamental sign V(t), that is,