Topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems and maps. A topological method is introduced that simplifies the solution of boundary value problems: The activation energy is calculated as a function of a set of parameters characterizing the initial conditions of the escape path. The method is applied explicitly to compute the optimal escape path and the activation energy for a variety of dynamical systems and maps.
We theoretically investigate the possibility of generating pulses in an excitable (asymmetric) semiconductor ring laser (SRL) using optical trigger pulses. We show that the phase difference between the injected field and the electric field inside the SRL determines the direction of the perturbation in phase space. Due to the folded shape of the excitability threshold, this has an important influence on the ability to cross it. A mechanism for exciting multiple consecutive pulses using a single trigger pulse (i.e., multipulse excitability) is revealed. We furthermore investigate the possibility of using asymmetric SRLs in a coupled configuration, which is a first step toward an all-optical neural network using SRLs as building blocks.
We report the first experimental observation of multistable states in a single-longitudinal mode semiconductor ring laser. We show how the operation of the device can be steered to either monostable, bistable, or multistable dynamical regimes in a controlled way. We observe that the dynamical regimes are organized in well-reproducible sequences that match the bifurcation diagrams of a two-dimensional model. By analyzing the phase space in this model, we predict how the stochastic transitions between multistable states take place and confirm it experimentally.
We investigate both theoretically and experimentally the stochastic switching between two counter-propagating lasing modes of a semiconductor ring laser. Experimentally, the residence time distribution cannot be described by a simple one parameter Arrhenius exponential law and reveals the presence of two different mode-hop scenarios with distinct time scales. In order to elucidate the origin of these two time scales, we propose a topological approach based on a two-dimensional dynamical system. 42.55.Px,42.60.Mi Fluctuations in active optical systems such as lasers is one of today's technological challenges as well as a fundamental problem of modern physics as they are the result of the quantum nature of the interaction between light and matter [1]. Fluctuations are e.g. responsible for longitudinal mode switching in semiconductor lasers [2], polarization mode-hopping in Vertical Cavity Surface Emitting Lasers (VCSELs) [3][4][5], and they play a fundamental role in stochastic and coherence resonances of optical systems [6][7][8].Semiconductor ring lasers (SRLs) are a particular class of lasers whose operation is strongly affected by stochastic fluctuations. The circular geometry of the active cavity allows a SRL to operate in two possible directions, namely clockwise mode (CW ) and counter-clockwise mode (CCW ). From the application point of view, SRLs are ideal candidates for all-optical information-storage. [9][10][11]. From a theoretical point of view, SRLs represent the optical prototype of nonlinear Z 2 -symmetric systems [12], which appear in many fields of physics.Fluctuations induce spontaneous abrupt changes in the SRL's directional operation from CW to CCW and vice versa, and therefore represent a major limitation to their successful applications for instance as optical memories. An in-depth understanding of the mode-hopping in SRLs would shed light on the stochastic properties of the large class of Z 2 -symmetric systems. In spite of its importance, the problem of spontaneous directional switches in SRLs remains unaddressed, partly due to the high dimensionality of the models that have been proposed for SRLs [9,13].In this paper, we address the problem of such fluctuations both theoretically and experimentally. We experimentally investigate the properties of the residence time distribution (RTD) that quantifies the mode hopping. Our theoretical analysis is based on an asymptotic reduction of a full rate-equation model to a Z 2 -symmetric planar system [14].We consider here an InP-based multiquantum-well SRL with a racetrack geometry and a free-spectralrange of 53.6 GHz. The device operates in a singletransverse, single-longitudinal mode regime at wavelength λ = 1.56µm. However, it will be clear from the rest of the discussion that our analysis is general and applies to any kind of ring geometry. A waveguide has been integrated on the same chip in order to couple power out from the ring. This bus waveguide can be independently biased in order to reduce absorption losses. The waveguide crosses the fa...
We theoretically investigate optical injection in semiconductor ring lasers and disclose several dynamical regimes. Through numerical simulations and bifurcation continuation, two separate parameter regions in which two different injection-locked solutions coexist are revealed, in addition to a region in which a frequency-locked limit cycle coexists with an injection-locked solution. Finally, an anti-phase chaotic regime without the involvement of any carrier dynamics is revealed. Parallels are drawn with the onset of chaos in the periodically forced Duffing oscillator.
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