TY - JOUR

T1 - Vector-soliton collision dynamics in nonlinear optical fibers

AU - Goodman, Roy H.

AU - Haberman, Richard

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2005/5

Y1 - 2005/5

N2 - 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 low-dimensional 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 two-bounce or two-pass 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.

AB - 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 low-dimensional 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 two-bounce or two-pass 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.

UR - http://www.scopus.com/inward/record.url?scp=26944494063&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26944494063&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.71.056605

DO - 10.1103/PhysRevE.71.056605

M3 - Article

AN - SCOPUS:26944494063

VL - 71

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 5

M1 - 056605

ER -