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Proceedings Paper

Lyapunov exponents maps and dynamics of nonlinear optical systems
Author(s): Krzysztof Grygiel; Przemyslaw Szlachetka
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Paper 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.

Paper Details

Date Published: 21 November 2003
PDF: 9 pages
Proc. SPIE 5259, 13th Polish-Czech-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics, (21 November 2003); doi: 10.1117/12.545171
Show Author Affiliations
Krzysztof Grygiel, Adam Mickiewicz Univ. (Poland)
Przemyslaw Szlachetka, Adam Mickiewicz Univ. (Poland)

Published in SPIE Proceedings Vol. 5259:
13th Polish-Czech-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics
Jerzy Nowak; Marek Zajac; Jan Masajada, Editor(s)

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