Modulational Instability of Polarized ...

The polarized electromagnetic wave in cylindrical fibers is described by a system of four component vector nonlinear Schrödinger equations. We have investigated analytically and numerically the modulational instability of this system. Several types of modulational instability are shown to exist depending on the sign of the dispersion coefficients. The results indicate that the group-velocity mismatch and the four wave mixing terms influence considerably the shape, position and especially the number of the spectral regions of the gain spectra of the modulation instability. Numerical simulations of the four component vector nonlinear Schrödinger equation show that the phenomenon of modulational instability gives rise to periodic pulse arrays of waves train. The presence of the four wave mixing terms influences considerably the evolution of the periodic pulse.