Influence of Kerr nonlinearity on the dynamics of second-harmonic generation

Krzysztof Grygiel; Przemyslaw Szlachetka

doi:10.1117/12.638781

6 December 2006 Influence of Kerr nonlinearity on the dynamics of second-harmonic generation

Krzysztof Grygiel, Przemyslaw Szlachetka

Proceedings Volume 5945, 14th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics; 594502 (2006) https://doi.org/10.1117/12.638781
Event: 14th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 2005, Nitra, Slovakia

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⁾_2ω 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⁾ (χ⁽³⁾/χ⁽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.

Citation Download Citation

Krzysztof Grygiel and Przemyslaw Szlachetka "Influence of Kerr nonlinearity on the dynamics of second-harmonic generation", Proc. SPIE 5945, 14th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 594502 (6 December 2006); https://doi.org/10.1117/12.638781

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
9 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Second-harmonic generation

Kerr effect

Modulation

Information operations

Dynamical systems

Complex systems

Resonators

Show All Keywords

Keywords/Phrases

Search In:

Publication Years