Co-propagation of two optical fields in a semiconductor doped dispersion decreasing fiber and modulational instability induced by cross-phase modulation

A theoretical study of cross phase modulation (XPM) induced modulational instability (MI) in a semiconductor doped dispersion decreasing fiber (SD-DDF) is presented. The equation is suitably modeled to account for the saturable nonlinearity and dispersion decreasing nature of the fiber. Using linear stability analysis, the exact dispersion relation is obtained and MI analysis is performed. We exclusively analyze the influence of the walk-off effect in the instability spectra of an SD-DDF and an optimum walk-off parameter is identified. The contrasting nature of action of decreasing dispersion and saturating nonlinearity is emphasized, such that the former enhances and the latter suppresses bandwidth. Thus, a suitable combination of the two physical effects can enable one to realize the desired bandwidth profile. MI analysis in the normal dispersion regime is compared with the anomalous counterpart as well as the conventional single pump case and the results are tabulated. Also, our analytical results are compared through direct numerical simulation and the results are documented. Thus, we present a comprehensive study of XPM-MI in an SD-DDF and the influence of various physical effects on the MI dynamics.