Soliton trapping and harmonic oscillations due to nonlinear interactions in optical fibers

When the fiber dispersion is normal, there exists a pair of bright and dark solitons with orthogonal polarizations. When the power of the dark soliton (pump) on one polarization is stronger than that of the bright pulse (signal) on the other polarization, we found that the bright pulse is trapped into the dip of the dark soliton, and it undergoes harmonic oscillations if the mean frequency of the bright pulse is lower than a certain critical frequency. Otherwise, it escapes the potential well formed by the dark soliton. Analytical expressions derived for the frequency of harmonic oscillations and the asymptotic value of the trapped energy are in good agreement with numerical experiments. This result could have potential applications for ultra-fast all-optical switching and logic gates.