All-optical soliton switching for the asymmetric fiber couplers

Abstract

Coupled nonlinear Schrodinger (CNLS) equations for the fiber couplers with asymmetric self-phase modulation (SPM) and cross-phase modulation (XPM) are studied. With symbolic computation, one- and two-soliton solutions are obtained for the constant- and variable-coefficient CNLS equations. Switching dynamics of the solitons is discussed, and effects of the second-order group-velocity dispersion β 2, SPM coefficient σ 1, XPM coefficient σ 2 and Kerr nonlinear intensity γ on the all-optical switching properties are studied, while other coefficients in those equations are seen not to affect the all-optical switching properties. For the constant-coefficient CNLS equations, we find that |β 2| is proportional to the optical switching speed, and the optical extinction ratios increase with the decrease of σ 1/σ 2 and increase of |β 2| and γ. A numerical simulation by the split-step Fourier and Runge-Kutta methods is presented on the constant-coefficient CNLS equations to analyse the stability of the one- and two-solitons with the random initial perturbations. For the variable-coefficient CNLS equations, effects of σ 1/σ 2, β 2(z) = a 2 e bz and γ(z) = a 3 e bz on the optical switching are analyzed (where a 2, a 3 and b are all constants, and z gives the direction of propagation in the fiber couplers): optical switching speed increases with the increase of |a 2| and decrease of |b|, and optical extinction ratios increase with the increase of |a 2| and decrease of σ 1/σ 2 and |a 3|.