Abstract
When chromatic dispersion operates together with two-dimensional diffraction, the degenerate optical parametric oscillator exhibits three-dimensional (3D) localized structures in a regime devoid of Turing or modulational instabilities. They consist of single lamella, cylinder, or light drops. These 3D structures are generated spontaneously from a weak random noise. We construct 3D bifurcation diagrams associated with these structures. We show that a single cylinder and a single light drop exhibit an overlapping domain of stability. Finally, for a large input intensity, we identify a self-pulsing behavior affecting the stability of 3D localized structures.
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