Modulation instability in inhomogenous nonlinear optical fiber

We investigate the Modulation Instability in inhomogenous nonlinear optical fiber having higher-order effects and external potential, governed by the variable-coeffcients Hirota equation. The inhomogeneities are traduced by space dependent Group Velocity Dispersion and Kerr coefficients. A new skill of dispersion management is used, which consists of continuous spatial variation of the dispersion coefficient instead of discrete variation that used to be taken from one positive value to a negative value alternatively. Continuous distribution of dispersion is considered in four patherns: sinusoidal function, triangular Fourrier series function, rectangular Fourrier series function and saw tooth Fourrier series function. From the continuous wave analysis, it appears that the MI gain is space dependent. The numerical analysis reveals that the MI gain varies similarly to the dispersion function.