Dispersive wave in the modulation instability spectrum in the presence of noise

We present the dispersive wave (DW) in the dispersion-shifted fibre (DSF) based on numerical simulations, which causes the symmetry-breaking of the modulation instability (MI) spectrum. It is demonstrated that the DW power is related to both pump power and three-order dispersion (TOD). It is found in particular that different levels of noise also have relations with the generation of a DW, which essentially results from the fact that MI is initiated from noise and there exists power transfer between the MI (soliton) and DW. Furthermore, we study the spectral autocorrelation within the Stokes and anti-Stokes bands in the presence of the DW, which show the property of very weak autocorrelation for a continuous wave (CW) or quasi-CW. The results provide further understanding of the symmetry and correlation of the MI spectrum.