|
When diffraction and dispersion have a comparable influence in the nonlinear ring cavity, three-dimensional dissipative structures are formed. They consist of either periodic crystals or localized light drops (or bullets) [1,2,3]. Recently, three-dimensional localized structures have been found in a non mean-field model describing a nonlinear resonator with a saturable absorber [4]. In this system chromatic dispersion plays a negligible role and localized structures are formed in the transverse and longitudinal directions.
All previous work reported on three-dimensional systems have been performed in regimes of modulational instabilities. In the present work, we report on localized structures or light drops formation in nonlinear optical systems in the regime far from any modulational instability. We illustrate the formation of these structures in the degenerate optical parametric oscillator in the mean-field approximation. Their existence is related to phase indetermination. They correspond to domain walls or phase solitons. We demonstrate the existence of stable 3D localized structures consisting of single lamellae, cylinder, or light drop (or bullet). They emerge spontaneously from small amplitude noise. Bifurcation diagrams are constructed for each of these structures showing an overlapping domain of stability. Such three-dimensional localized structures have been previously reported in the particular limit of the "nascent bistability" [2,3]. By contrast, our investigation applies on the full degenerate optical parametric oscillator mean-field model. For large input field intensities, the 3D localized structures become unstable through a time oscillatory bifurcation: the widths as well as the intensity of both signal and pump fields exhibit periodic time oscillations. We thus study the formation of three-dimensional localized structures in the fully degenerate optical parametric oscillator, and show a new dynamical regime associated with a time-oscillatory instability affecting these localized structures. [1] (a) M. Tlidi, M. Haelterman, and P. Mandel, Europhy. Lett. 42, 505 (1998). [2] K. Staliunas, Phys. Rev. Lett. 81, 81 (1998). [3] M. Tlidi and P. Mandel, Phys. Rev. Lett. 83, 4995 (1999). [4] M. Brambilla, T. Maggipinto, G. Patera, and L. Columbo, Phys. Rev. Lett. 93, 203901 (2004). |
|