Soliton dynamics in directional couplers

The evolution of an initial condition consisting of one soliton(like) pulse in one channel and no signal in the other channel of the coupler is investigated. We focus upon the energy transfer (switching) between the two channels as function of the energy of the signal. For decreasing energy the switching appears to take place for the first time in the energy region where the symmetric soliton solution of the coupler is unstable, and where at the same time an asymmetric stable soliton exists. The topology of the corresponding level set structure of the Hamiltonian of the governing equations, two linearly coupled nonlinear Schrödinger equations, determines the possibility of switching. This leads to a necessary condition for switching in terms of the Hamiltonian of the incoming signal: its value must be smaller than that of the asymmetric soliton (with the same energy as the incoming pulse). As function of the pulse energy, there appears to be a very distinct transition between switching and non-switching behavior. This opens the possibility for a switching device with an extremely narrow transition region.