4-photon homoclinic instabilities in nonlinear highly birefringent media

Year: 1995

Authors: De Angelis C., Santagiustina M., Trillo S.

Autors Affiliation: Dipartimento di Elettronica e Informatica, Universitā di Padova, Via Gradenigo 6/a, 35131 Padova, Italy;
Fondazione Ugo Bordoni, Via B. Castiglione 59, 00142 Roma, Italy

Abstract: We investigate the nonlinear dynamics of a nonconventional (i.e., pumped by a mixed-mode wave) modulational instability in a highly birefringent nonlinear dispersive medium. We find that the depleted regime of propagation beyond the linearized stage can be described analytically in a proper region of the parameter space. In this case the governing coupled nonlinear Schrödinger equations, which are not integrable, are reduced to an integrable one-dimensional nonlinear oscillator that rules the propagation of the pump wave and a single sideband pair. This approach permits us to predict the existence of stable and unstable manifolds of time-periodic solutions of the coupled nonlinear Schrödinger equations. The nonlinear dynamics governed by these equations mimics the period-doubling instabilities associated with the homoclinic separatrices in the reduced phase space. Moreover, our approach is also capable of describing the onset of spatial chaos that occurs when the parameter values are such that the additional degree of freedom represented by the conjugated sidebands becomes effective.

Journal/Review: PHYSICAL REVIEW A

Volume: 51 (1)      Pages from: 774  to: 791

KeyWords: Nonlinear Optics
DOI: 10.1103/PhysRevA.51.774

Citations: 20
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