Gaetan Friart

Relaxation and square-wave oscillations in a semiconductor laser with polarization rotated optical feedback.

The rate equations for a laser with a polarization rotated optical feedback are investigated both numerically and analytically. The frequency detuning between the polarization modes is now taken into account and we review all earlier studies in order to motivate the range of values of the fixed parameters. We find that two basic Hopf bifurcations leading to either stable sustained relaxation or square-wave oscillations appear in the detuning versus feedback rate diagram. We also identify two key parameters describing the differences between the total gains of the two polarization modes and discuss their effects on the periodic square-waves.

All-optical controlled switching between time-periodic square waves in diode lasers with delayed feedback

We investigate the square-wave (SW) self-modulation output of an edge-emitting diode laser subject to polarization rotated optical feedback in detail, both experimentally and theoretically. Our experimental results show that the 2τ-periodic SW, where τ is the delay of the feedback, coexists with other SW oscillations of shorter periods. We have found that these new SWs are specific harmonics of the fundamental one and their periods are P(n)≃2τ/(1+2n), where n is an integer. Numerical simulations and analytical studies of laser rate equations confirm the multistability of SW solutions. By adding a weak conventional optical feedback, we show that the switching between the different periodic SWs can be easily controlled. The delay of this feedback control is the key parameter determining the harmonic that is stabilized. Numerical simulations corroborate the effectiveness of our experimental control scheme.

Analytical stability boundaries for quantum cascade lasers subject to optical feedback.

We consider nonlinear rate equations appropriate for a quantum cascade laser subject to optical feedback. We analyze the conditions for a Hopf bifurcation in the limit of large values of the delay. We obtain a simple expression for the critical feedback rate that highlights the effects of key parameters such as the linewidth enhancement factor and the pump. All our asymptotic approximations are validated numerically by using a path continuation technique that allows us to follow Hopf bifurcation points in parameter space.

Stability of steady and periodic states through the bifurcation bridge mechanism in semiconductor ring lasers subject to optical feedback

With the development of new applications using semiconductor ring lasers (SRLs) subject to optical feedback, the stability properties of their outputs becomes a crucial issue. We propose a systematic bifurcation analysis in order to properly identify the best parameter ranges for either steady or self-pulsating periodic regimes. Unlike conventional semiconductor lasers, we show that SRLs exhibit both types of outputs for large and well defined ranges of the feedback strength. We determine the stability domains in terms of the pump parameter and the feedback phase. We find that the feedback phase is a key parameter to achieve a stable steady output. We demonstrate that the self-pulsating regime results from a particular Hopf bifurcation mechanism referred to as bifurcation bridges. These bridges connect two distinct external cavity modes and are fully stable, a scenario that was not possible for diode lasers under the same conditions.

Dynamics of semiconductor microring lasers subject to on-chip filtered optical feedback

Tunable laser diodes are needed in a range of applications including wavelength division multiplexing, optical instrument testing, optical sensing and tera hertz generation. In this work, we investigate the stability of lasers which use filtered optical feedback for wavelength tuning. We investigate experimentally the dynamics induced by this on-chip filtered optical feedback. In this study, we choose to use a compact device which combines a semiconductor ring laser with on-chip filtered optical feedback to achieve wavelength tunability. The filtered optical feedback is realized by employing two arrayed waveguide gratings to split/recombine light into different wavelength channels. Semiconductor optical amplifiers are placed in the feedback loop in order to control the feedback of each wavelength channel independently. Experimental observations show that the stability of the clockwise and counterclockwise propagation modes depends on the feedback strength. Experiments also show that for a specific range of the feedback strength, anti-phase oscillations in the intensity of the clockwise and counterclockwise propagating modes can be induced. These oscillations could not be seen in the same semiconductor ring laser without filtered optical feedback. We investigate how the frequency and the amplitude of these oscillations change under the effect of filtered optical feedback. We also discuss how these anti-phase oscillations can be suppressed by properly choosing the feedback strength.

Two distinct bifurcation routes for delayed optoelectronic oscillators

We investigate the coexistence of low- and high-frequency oscillations in a delayed optoelectronic oscillator. We identify two nearby Hopf bifurcation points exhibiting low and high frequencies and demonstrate analytically how they lead to stable solutions. We then show numerically that these two branches of solutions undergo higher order instabilities as the feedback rate is increased but remain separated in the bifurcation diagram. The two bifurcation routes can be followed independently by either progressively increasing or decreasing the bifurcation parameter.

Multirhythmicity for a Time-Delayed FitzHugh-Nagumo System with Threshold Nonlinearity

A time-delayed FitzHugh-Nagumo (FHN) system exhibiting a threshold nonlinearity is studied both experimentally and theoretically. The basic steady state is stable but distinct stable oscillatory regimes may coexist for the same values of parameters (multirhythmicity). They are characterized by periods close to an integer fraction of the delay. From an asymptotic analysis of the FHN equations, we show that the mechanism leading to those oscillations corresponds to a limit-point of limit-cycles. In order to investigate their robustness with respect to noise, we study experimentally an electrical circuit that is modeled mathematically by the same delay differential equations. We obtain quantitative agreements between numerical and experimental bifurcation diagrams for the different coexisting time-periodic regimes.