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 language||English (US)|
|Title of host publication||Unknown Host Publication Title|
|Publisher||Optical Soc of America|
|Number of pages||1|
|Publication status||Published - 1987|
ASJC Scopus subject areas