Periodic and chaotic spatiotemporal states in a phase-conjugate resonator using a photorefractive BaTiO_3 phase-conjugate mirror

Abstract

The dynamics of an externally pumped phase-conjugate resonator that uses four-wave mixing in BaTiO₃ is investigated experimentally. The emergence of spatiotemporal instabilities as the degree of transverse confinement is varied by changing the Fresnel number is described in detail. Local intensity time series show that relaxing the transverse confinement leads the system from a stationary state to periodic, then to quasi-periodic, motions and finally to chaotic behavior. In some regions of parameter space two frequencies are identified in the power spectra of the time series, indicating a route to chaos following the Ruelle–Takens–Newhouse scheme [ Commun. Math. Phys. 64, 35– 40 ( 1978)]. Wave-front topological defects are identified by interferometry. As the system’s confinement is varied, the phase-defect density and the spatial correlation index are found to follow similar trends, indicating that the observed spatiotemporal dynamics may indeed be an example of defect-mediated turbulence.