Theoretical Calculation of Ultrashort-Pulse Optical Parametric Generation

A general theory of optical parametric generation that accounts for pump depletion, loss, phase mismatch, group-velocity mismatch among the pump, signal and idler pulses, and intrapulse group- velocity dispersion is proposed for coherent ultrashort pulses with arbitrary shapes and carrier chirps. The coupled differential equations are numerically solved using a symmetric split-step beam-propagation method. The general solutions of these equations are obtained and the optical parametric generation process is theoretically investigated. Results show that the major factors, which remarkably affect the optical parametric conversion efficiency and durations of the pulses in phase-matched structure, are the group velocity mismatch and the intrapulse group velocity dispersion.