Numerical investigation of a periodically driven laser with an intracavity saturable absorber

Lauterborn, Werner; Eick, Ingo

doi:10.1364/josab.5.001089

Cited by 23 publications

(10 citation statements)

References 12 publications

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“…These results agree well with experimental facts and data of numerical simulation of system (20) [10][11][12][13][14].…”

Section: Maps In the Presence Of Saturable Absorber And A High Level supporting

confidence: 90%

“…Then, after a single application of a short external pulse of pumping, the phase-trajectory coordinates can be found from the map described by Eqs. (12) and (13), in which p is a root of the equation…”

Section: Map In the Case Of An Additional Short Pulsed Forcingmentioning

confidence: 99%

“…Within the framework of the proposed method of reduction to the Poincaré map, it is convenient to allow for additional physical factors which are often encountered in the experiment and especially important for semiconductor lasers [10][11][12][13][14], namely, the presence of dopants with saturable absorption, a high level of spontaneous emission to the laser mode, the multimode oscillation, the inertia (finite passband) of modulators, and different combinations of the above-mentioned additional conditions. Below we briefly outline the results of such analysis.…”

Section: Maps In the Presence Of Saturable Absorber And A High Level mentioning

confidence: 99%

“…If spontaneous emission is neglected ( = 0), then the relaxation self-oscillations are determined by iterations of the same two-dimensional map given by Eqs. (12) and (13), in which the pulse energy p is found from Eq. (6) and the interval T between the pulses, from the equation a(T, c, ϕ) = bT .…”

Section: Maps In the Presence Of Saturable Absorber And A High Level mentioning

confidence: 99%

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Poincar� maps for studying relaxation oscillations in periodically pumped solid-state lasers

Grigorieva

2004

Radiophys Quantum Electron

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We present an asymptotic analysis of relaxation oscillations in periodically pumped single-and multimode class-B lasers. Discrete maps which allow one to describe the hierarchy of coexisting periodic attractors are obtained and their bifurcations leading to period-doubling regimes and quasi-periodic and chaotic oscillations are studied analytically. For systems of coupled longitudinal modes, the maps determine conditions for antiphase dynamics.

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“…These results agree well with experimental facts and data of numerical simulation of system (20) [10][11][12][13][14].…”

Section: Maps In the Presence Of Saturable Absorber And A High Level supporting

confidence: 90%

Section: Map In the Case Of An Additional Short Pulsed Forcingmentioning

confidence: 99%

Section: Maps In the Presence Of Saturable Absorber And A High Level mentioning

confidence: 99%

Section: Maps In the Presence Of Saturable Absorber And A High Level mentioning

confidence: 99%

See 2 more Smart Citations

Poincar� maps for studying relaxation oscillations in periodically pumped solid-state lasers

Grigorieva

2004

Radiophys Quantum Electron

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“…In the biological domain, circle maps have been useful in modelling mode-locking (Bauer & Martienssen, 1991), cardiac arrythmias (Bub & Glass, 1995;Glass, 1991;Glendinning, 1995) and neural networks (Aihara et al, 1990;Bressloff & Stark, 1990;Zeller et al, 1995). In addition, they have been applied to, for example, models of Josephson junctions (Jensen et al, 1983), electrical conductivity in barium sodium niobate (Martin & Martienssen, 1986), lasing (Marriott & Delisle, 1989) and chemical reactions (Lauterborn & Eick, 1988).…”

Section: A Piecewise Linear Discontinuous Circle Mapmentioning

confidence: 99%

Neuronal population dynamics with post inhibitory rebound:A reduction to piecewise linear discontinuous circle maps

Coombes

Doole

1996

Dynamics and Stability of Systems

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Post inhibitory rebound (PZR) is a nonlinear phenomenon present in a variety of nerve cells. It is an important mechanism underlying central pattern generationfor heartbeat, swimming and other motor patterns in many neuronal systems. In this paper, we propose an extension of the binary threshold neuron model to incorporate the efects of PZR. For a single neuron, the dynamics can be described by a piecewise linear circle map with two discontinuities. Both frequency-locking and chaos can occur. The Liapunov exponent of the map is evaluated and used to dejine transitions between these two distinct types of asymptotic behaviour. Hysteresis between periodic orbits is also observed. A small network of these model neurons, with reciprocal inhibition, is shown to exhibit 'self-sustained' anti-phase oscillations, making PZR a plausible mechanism for central pattern generation in neuronal systems. Unlike coupled oscillator theories, network oscillations emerge naturally as a consequence of the biological description from which the neuronal dynamics is derived. The simplicity of the dynamical model allows for the possibility of large population studies in contrast to other classical models of single neuron dynamics that incorporate active processes.

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Influence of electron heating and cooling on the dynamic behaviour of a semiconductor laser with a saturable absorber

Plyavenek¹

1993

Optics Communications

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Numerical investigation of a periodically driven laser with an intracavity saturable absorber

Cited by 23 publications

References 12 publications

Poincar� maps for studying relaxation oscillations in periodically pumped solid-state lasers

Poincar� maps for studying relaxation oscillations in periodically pumped solid-state lasers

Neuronal population dynamics with post inhibitory rebound:A reduction to piecewise linear discontinuous circle maps

Influence of electron heating and cooling on the dynamic behaviour of a semiconductor laser with a saturable absorber

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