Abstract
The mechanism of pulse switching is investigated analytically and numerically for a family of initial conditions with a solitonlike pulse in one channel and no signal on the other channel of the coupler. This investigation is performed directly in the coupled nonlinear Schroedinger equations that describe the directional coupler. This mechanism appears to be based on the simultaneous existence of the asymmetric and the symmetric soliton states: Switching then can take place for values of coupling constant and total energy for which the asymmetric soliton is stable and the symmetric soliton is unstable. The crucial features of the phase portrait in the infinite-dimensional space are described. In particular, near the switching threshold, a switching solution passes near the unstable symmetric soliton on its way to a new state with the energies in the channels reversed. On the basis of this mechanism a necessary condition for switching is found, which is confirmed numerically for some families of pulse shaped initial conditions. In the case of soliton switching with the energy as the switching parameter, this condition appears to give an accurate prediction of the actual switching threshold. The infinite-dimensional phase portrait has a simple structure, so that its features for a large part can be captured in a three-dimensional phase space.
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Valkering, T.P., De Boer, P.T. & Hoekstra, H.J.W.M. Soliton switching in directional couplers. Japan J. Indust. Appl. Math. 16, 65 (1999). https://doi.org/10.1007/BF03167525
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DOI: https://doi.org/10.1007/BF03167525