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Proceedings Paper

Influence of Kerr nonlinearity on the dynamics of second-harmonic generation
Author(s): Krzysztof Grygiel; Przemyslaw Szlachetka
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Paper Abstract

In this paper we present analysis of the dynamics of an optical system combining two kinds of nonlinearities. In our model we analyse an optical system in which a second-harmonic generation (SHG) takes place in the resonator configuration with an added intracavity Kerr-like nonlinearity. So, the nonlinear medium in the cavity is characterized by its second χ(2) and third χ(3)ω,-ω,ω nonlinearity parameters (Kerr process affects the fundamental mode only). The extended equations of motion for the fundamental and the second-harmonic amplitudes have been derived for the classical case. We have found that for the special case of a coherent pumping, the equations have an analytical periodic solution. Generally, the system is non-integrable and we have investigated it numerically for two types of external pumping and the results were compared with those obtained for the pure SHG case. For the periodical motion the influence of the Kerr nonlinearity is insignificant because the constant χ(3) is much smaller than χ(2)(3)(2) < 10-4 in our case). The Lyapunov spectrum analysis as well as the analysis of information dimension show that in the chaotic case the influence of Kerr nonlinearity on the dynamics of the system is more significant. We have obtained quite a different dynamics on chaotic attractors. However, the stability of the system remains almost unchanged. The influence of the system parameters on the dynamics and the stability of the SHG process with the Kerr nonlinearity is also investigated.

Paper Details

Date Published: 6 December 2006
PDF: 9 pages
Proc. SPIE 5945, 14th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 594502 (6 December 2006); doi: 10.1117/12.638781
Show Author Affiliations
Krzysztof Grygiel, A. Mickiewicz Univ. (Poland)
Przemyslaw Szlachetka, A. Mickiewicz Univ. (Poland)


Published in SPIE Proceedings Vol. 5945:
14th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics
Anton Štrba; Dagmar Senderákova; Miroslav Hrabovský, Editor(s)

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