Modulation instability of finite energy Airy pulse in optical fiber

We have investigated and analyzed the modulation instability (MI) of finite energy Airy pulse (FEAP) in an optical fiber in order to reveal the impact of truncation coefficient on the nonlinear propagation dynamics of FEAP with or without amplitude perturbation. We have also characterized the difference between the propagation process of smooth FEAP and that of modulated FEAP. It is shown that, for a smooth FEAP, the side lobes prior to the main lobe first undergo compression and then break up into multiple sub-pulses during propagation in the case of small truncation coefficient; while the opposite occurs in the case of large truncation coefficient. For a FEAP with amplitude modulation, the breakup of the main lobe induced by MI precedes that of side lobes for arbitrary values of truncation coefficients; but the evolution of secondary lobes is made by a transition from splitting process to a simple compression process with increasing truncation coefficient. The propagation dynamics of secondary lobes with number symbol larger 2, marked the secondary lobes starting number 1 from near to far according the distance between itself and the main lobe, is insensitive to the truncation coefficients variation in both cases. Finally, the MI gain spectra of FEAP with different truncation coefficients are obtained by numerically solving the nonlinear Schrödinger equation and the results have been compared with the theoretical predictions.