Study of ultrafast pulse coupling dynamics considering retarded nonlinear response and self-steepening effects

The numerical algorithm is presented for solving coupled extended nonlinear Schrödinger equations (NLSEs) including higher-order dispersion, retarded nonlinear response, and self-steepening terms. The numerical results show that the influence of the retarded nonlinear response and self-steepening effect on the coupling dynamics in a nonlinear directional coupler (NLDC) is strongly dependent on the input peak power, input pulse width, and product of the dispersion length and the coupling coefficient (L_Dκ). In the case of L_Dκ≫1, the pulse coupling obeys Jensen´s equation as long as the input pulse width is broader than 250 fs and the coupler is far from zero dispersion. Both the retarded nonlinear response and the self-steepening effect could be ignored if the normalized amplitude of the input pulse is less than 0.5. It was also found that the retarded nonlinear response improves the energy transfer efficiency between the two coupled waveguides.