Vectorsoliton collision dynamics in nonlinear optical fibers
Abstract
We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two polarization directions, described by a coupled pair of nonlinear Schrödinger equations. We study a lowdimensional model system of Hamiltonian ordinary differential equations (ODEs) derived by Ueda and Kath and also studied by Tan and Yang. We derive a further simplified model which has similar dynamics but is more amenable to analysis. Sufficiently fast solitons move by each other without much interaction, but below a critical velocity the solitons may be captured. In certain bands of initial velocities the solitons are initially captured, but separate after passing each other twice, a phenomenon known as the twobounce or twopass resonance. We derive an analytic formula for the critical velocity. Using matched asymptotic expansions for separatrix crossing, we determine the location of these “resonance windows.” Numerical simulations of the ODE models show they compare quite well with the asymptotic theory.
 Publication:

Physical Review E
 Pub Date:
 May 2005
 DOI:
 10.1103/PhysRevE.71.056605
 arXiv:
 arXiv:nlin/0502056
 Bibcode:
 2005PhRvE..71e6605G
 Keywords:

 42.65.Tg;
 05.45.Yv;
 42.81.Dp;
 Optical solitons;
 nonlinear guided waves;
 Solitons;
 Propagation scattering and losses;
 solitons;
 Nonlinear Sciences  Pattern Formation and Solitons;
 Nonlinear Sciences  Chaotic Dynamics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 32 pages, submitted to Physical Review E