Nonlinear propagation of optical pulse in laser amplifying medium

After considering Kerr nonlinear effect, group velocity dispersion of host and gain distribution of active particle in laser amplifying medium, a basic equation describing the propagation of an optical pulse in laser amplifying medium has been deduced. Besides, the profile and power spectrum of a ps superGaussion pulse along Nd３＋：glass laser amplifying medium length have been disscussed when its central frequency coincides with peak frequency of gain of laser amplifying medium.