Analytical Analysis of Residual Chromatic Dispersion and Self-Phase Modulation Optimal Compensation in the Fractional Domain

We present an analytical expression of residual chromatic dispersion and self-phase modulation optimal compensation with a chirped Gaussian pulse in the fractional domain. The accuracy of the expression is confirmed by the simulation platform, which is based on the split-step Fourier method. Moreover, the simulation of a 28-GBd RZ-DQPSK optical fiber communication system is carried out to verify the correctness when the transmission distance is less than 800 km in a standard single-mode fiber and non-zero dispersion-shifted fiber.