Phase-mediated long-range interactions of cavity solitons in a semiconductor laser with a saturable absorber

We numerically study the dynamics of pairs of cavity solitons in a laser. We show that the solitons interact even at distances much greater than their sizes in the intensity and carrier-densities profile. The interaction is mediated by the phase. In a certain range of initial values of the distance, the solitons adjust their position until they form bound states. There are two such bound states, corresponding to different equilibrium distances, in which the solitons display partial phase locking, that is, their relative phase slowly oscillates as in a phase-entrained state. In those states, the two solitons can be switched on and off independently. For smaller initial distances, only one soliton survives. For larger initial distances, the solitons lock in phase and repel each other up to a distance of about ten soliton diameters.