Dynamics of coupled solitons in nonlinear optical fibers

A system of coupled nonlinear Schr\"odinger equations (NLS) governs the interaction of propagating pulses in two-mode nonlinear optical fibers and directional couplers. Using NLS solitons as trial functions in an averaged Lagrangian formulation, ordinary-differential-equation (ODE) approximations for the pulse dynamics are derived. These ODE's give a criterion for two pulses to attract one another and form a bound state; they also describe the dynamics of the complicated oscillations these pulses undergo in this bound state. In addition, the ODE dynamics show that collisions between these pulses are generally inelastic, in that there is an exchange between translational energy and internal energy (due to pulse-width oscillations). The results of the ODE theory are verified by comparison with numerical solutions of the governing partial differential equations.

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