Interaction potential between discrete solitons in waveguide arrays

Using a variational approach, we obtained the interaction potential between two discrete solitons in optical waveguide arrays. The resulting potential bears the two features of soliton-soliton and soliton-waveguide interaction potentials where the former is similar to that of the continuum case and the latter is similar to the effective Pierls-Nabarro potential. The interplay between the two interaction potentials is investigated by studying its effect on the soliton molecule formation. It is found that the two solitons bind if their initial separation equals an odd number of waveguides, while they do not bind if their separation is an even number, which is a consequence of the two solitons being both either at the intersites (unstable) or being onsite (stable). We derived the equations of motion for the solitons' centre of mass and relative separation and provided analytic solutions for some specific cases. Favourable agreement between the analytical and numerical interaction potentials is obtained. Possible applications of our results to all-optical logic gates are pointed out.