Interchannel interaction of optical solitons

We study interaction between two solitons from different frequency channels propagating in an optical fiber. The interaction may be viewed as an inelastic collision, in which energy is lost to continuous radiation due to small but finite third order dispersion. We develop a perturbation theory with two small parameters: the third order dispersion coefficient d₃, and the reciprocal of the interchannel frequency difference, 1/β. We find that amplitude of the leading contribution to radiation emitted during the collision is proportional to d₃/β². The source term for this radiation is of the form that would be generated by a variation in the second order dispersion coefficient. In addition, the only other effects up to the combined third order of the perturbation theory are phase changes and position shifts of the solitons. Solitons propagating in a given frequency channel interact via radiation emitted due to collisions with many solitons from other frequency channels. We show that this intrachannel interaction effect, induced by many interchannel collisions, is identical to the radiation mediated intrachannel interaction effect observed for solitons propagating under the influence of disorder in the second order dispersion coefficient.