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We demonstrate that in the parametrically driven Ginzburg-Landau equation arbitrarily small nongradient corrections lead to qualitative differences in the dynamical properties of domain walls in the vicinity of the transition from rest to motion. These differences originate from singular rotation of the eigenvector governing the transition. We present(More)
We consider some features of spatial solitary-wave switching in a unidirectional ring cavity that is partially filled with a fast and saturably self-focusing nonlinear medium. Large (part-beam switched) solitary arrays are considered. It is found that prescribed binary patterns may be encoded in the duration of a single cavity transit and subsequently(More)
Separatrices and scaling laws in the switching dynamics of spatial solitary wave pixels are investigated. We show that the dynamics in the full model are similar to those in the plane-wave limit. Switching features may be indicated and explained by the motion of the (complex) solitary wave amplitude in the phase plane. We report generalization, into the(More)
Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits(More)
We study experimentally the nonlinear dynamics of two-color optical vortex beams in the presence of second-harmonic generation combined with the effects of photo-and thermal refraction, as well as self-and induced-phase modulation. We use an iron-doped lithium niobate crystal as a nonlinear medium for the vortex propagation and observe experimentally,(More)
Pulse dynamics in an actively mode-locked laser" (2003). Math. Paper 1. Abstract. We consider pulse formation dynamics in an actively mode-locked laser. We show that an amplitude-modulated laser is subject to large transient growth and we demonstrate that at threshold the transient growth is precisely the Petermann excess noise factor for a laser governed(More)
We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schrödinger equations. Varying the relative strength of cross-phase and self-phase effects we show the existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical(More)
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