Symbiotic optical solitons and modulational instability

Abstract

The interaction due to cross phase modulation of dark and bright solitons propagating in optical fibers is studied analytically, within the frame work of a variational approach as well as numerically. It is demonstrated that the interaction of a bright soliton in the anomalous dispersion regime with a dark soliton in the normal dispersion regime is described by a repulsive effective potential. In the reverse case when a bright soliton in the normal dispersion regime intracts with a dark soliton in the anomalous dispersion regime, the dark and bright solitons may form a symbiotic soliton, which is stable with respect to small mismatches in group velocity and initial relative position of the separate solitons. The influence of the symbiotic soliton on the modulational instability of the carrier c.w. background is also analysed. Analytical results are in good agreement with numerical simulations.