The switching dynamics of short optical pulses in a directional coupler made of two single-mode fibers (or waveguides), which is assumed to possess uniform Kerr nonlinearity, is investigated theoretically. When the nonlinearity is weak, the function of the coupler can be described by the beating between the symmetric and the antisymmetric modes of the composite waveguide structure. The group-delay difference between these two modes (intermodal dispersion) can give rise to pulse broadening or even pulse breakup. New normal-mode equations and coupled-mode equations that include the effect of intermodal dispersion are derived and discussed. The intermodal dispersion in the normal-mode formulation is found to be equivalent to the coupling-coefficient dispersion in the coupled-mode formulation. In many practical cases the intermodal dispersion is much more significant than the group-velocity dispersion, and soliton pulses are switched in the same way as any low-power linear pulses. Only in the special case that the intermodal dispersion is negligible, compared with the group-velocity dispersion, do the new coupled-mode equations reduce to the well-known linearly coupled nonlinear Schrödinger equations. A normalized parameter is proposed to determine the relative importance of the two dispersion effects.
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