Modulation instability induced by cross-phase modulation with the fourth-order dispersion in dispersion-decreasing fiber

The modulation instability （MI） induced by cross-phase modulation （XPM） in dispersion-decreasing fiber （DDF）, whose dispersion decreases along the direction of propagation, is solved and analyzed by the pertur- bation method for the extended nonlinear SchrSdinger equation, considering the higher-order dispersion. The change of the gain spectra with incident power and dispersion decaying factor are also given respec- tively. Due to the fourth-order dispersion, XPM occurs at two gain spectral regions in both the normal and the anomalous dispersion regimes of DDF. The two gain spectral regions in the anomalous dispersion regime are larger than those in the normal dispersion ond region in the anomalous dispersion regime is near regime. Moreover, the gain spectrum of the sec- zero compared with that in the normal dispersion regime, indicating that XPM can be easily produced in the anomalous dispersion regime. The spectral width increases with the increase of the incident optical power and the dispersion decaying factor.