ROUTES TO CHAOS IN A PHASE CONJUGATE RESONATOR WITH FAST MEDIUM RESPONSE TIME.

G. Reiner, Pierre Meystre

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The dynamics have been investigated of a high-diffraction phase conjugate resonator in which the phase conjugate mirror is a diffusive Kerr-type medium and operates in the Raman-Nath scattering regime. Results derived on the limit of phase conjugate mirrors with fast response time, such as semiconductor materials, are presented. It is found that when the system is described by a delay-difference equation, the phase conjugate resonator becomes unstable and follows either a period-doubling scenario or a Ruelle-Takens-Newhouse route to chaos, depending on the geometrical aperture of the conventional backreflecting mirror and the Fresnel number of the resonator. In contrast, in the case of the delay-differential description the transition to chaos involves two or three incommensurate frequencies without preceding period-doubling bifurcations. This confirms previous results. In the delay-difference description the route to high-dimensional chaos was analyzed by means of the spectrum of the Lyapunov exponents. This route is found completely different from that of the one-dimensional delay-differential equations.

Original languageEnglish (US)
Title of host publicationUnknown Host Publication Title
PublisherOptical Soc of America
Pages134
Number of pages1
ISBN (Print)0936659513
StatePublished - 1987

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Chaos theory
Resonators
Mirrors
Difference equations
Raman scattering
Differential equations
Diffraction
Semiconductor materials

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Reiner, G., & Meystre, P. (1987). ROUTES TO CHAOS IN A PHASE CONJUGATE RESONATOR WITH FAST MEDIUM RESPONSE TIME. In Unknown Host Publication Title (pp. 134). Optical Soc of America.

ROUTES TO CHAOS IN A PHASE CONJUGATE RESONATOR WITH FAST MEDIUM RESPONSE TIME. / Reiner, G.; Meystre, Pierre.

Unknown Host Publication Title. Optical Soc of America, 1987. p. 134.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Reiner, G & Meystre, P 1987, ROUTES TO CHAOS IN A PHASE CONJUGATE RESONATOR WITH FAST MEDIUM RESPONSE TIME. in Unknown Host Publication Title. Optical Soc of America, pp. 134.
Reiner G, Meystre P. ROUTES TO CHAOS IN A PHASE CONJUGATE RESONATOR WITH FAST MEDIUM RESPONSE TIME. In Unknown Host Publication Title. Optical Soc of America. 1987. p. 134
Reiner, G. ; Meystre, Pierre. / ROUTES TO CHAOS IN A PHASE CONJUGATE RESONATOR WITH FAST MEDIUM RESPONSE TIME. Unknown Host Publication Title. Optical Soc of America, 1987. pp. 134
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