Lyapunov exponents maps and dynamics of nonlinear optical systems

Krzysztof Grygiel; Przemyslaw Szlachetka

doi:10.1117/12.545171

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21 November 2003 Lyapunov exponents maps and dynamics of nonlinear optical systems

Krzysztof Grygiel, Przemyslaw Szlachetka

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Proceedings Volume 5259, 13th Polish-Czech-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics; (2003) https://doi.org/10.1117/12.545171
Event: 13th Polish-Czech-Slovak Conference on Wave and Quantum Aspects of contemporary Optics, 2002, Krzyzowa, Poland

Abstract

Characteristic features of a dynamical system are well-represented by Lyapunov exponents map in a parametric space. The order, quasiperiodic and chaotic regions were identified by the first Lyapunov exponent, whereas in the case of hyperchaotic regions the sign of the second Lyapunov exponents was also needed. We used this tool to investigate the system governing second-harmonic generation (SHG) of light with a modulated pump as well as a pulsating external field (square-wave). The influence of the pump parameters on dynamics of the generation process is numerically investigated. Chaotic and hyperchaotic behaviour in the system with a weak damping is found in both cases of pumping. This kind of performance of the system can be employed in communication devices. Especially, all-optical switching via second-harmonic generation in a directional coupler is extensively studied. A good diagnostic of dynamical system is the first steep for development of methods of manipulation and control of generated signals.

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Krzysztof Grygiel and Przemyslaw Szlachetka "Lyapunov exponents maps and dynamics of nonlinear optical systems", Proc. SPIE 5259, 13th Polish-Czech-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics, (21 November 2003); https://doi.org/10.1117/12.545171

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