Stability criterion of coupled soliton states

Abstract

By operator theory, we prove that the stability of coupled fundamental soliton solutions of two coupled nonlinear Schr\odinger equations is determined by $dP/d\ensuremath{\beta}$ criterion (with $P$ the power or energy and \ensuremath{\beta} the propagation constant). Examples of the application of the stability criterion to the coupled fundamental soliton states in nonlinear couplers, birefringent fibers, and birefringent nonlinear planar waveguides are given. The predictions from the analytical stability criterion are consistent with numerical results.