Phase-controlled suppression of repulsion between fractional dark solitons via periodic dispersion management

It is demonstrated numerically that the relative phase between the conventional and fractional components of a periodic dispersion map allows for control of the interaction between a pair of dark solitons. Propagation is modeled using a generalized fractional nonlinear Schrödinger equation that incorporates Kerr nonlinearity, delayed Raman response, and self-steepening. The dispersive and nonlinear parameters are scaled using a highly nonlinear fiber, HN1550, in the normal dispersion regime as a reference. A joint sweep of the fractional order and the map phase identifies the configuration α = 1.2 and Φ = 150º as the case with the greatest suppression while maintaining a minimum depth greater than 0.85. In this configuration, the secular repulsion rate decreases from 2.21024 ps/km to 1.75562 ps/km, representing a 20.57% reduction. The amplitude of the oscillatory component of the separation decreases simultaneously by 20.36%. Longitudinal convergence is verified by halving the propagation step. The pair maintains a positive separation rate; thus, the observed effect corresponds to the suppression of repulsive dynamics rather than the formation of a bound state.