This Demonstration simulates the induced spectral broadening caused by SPM. Assume an input pump laser pulse in the time domain is , with a Gaussian profile of and a frequency of 50 Hz. After propagation in a photonic crystal fiber (PCF), some new phase components are introduced due to the SPM effect. The new phase is proportional to the intensity of the pump pulse, given by . The pulse resulting from SPM can be represented by , where the maximum nonlinear phase shift is a constant, determined by the nonlinearity of the PCF and the pump power. The spectral distribution of this pulse in the frequency domain can be calculated by a numerical Fourier transform. Finally, we can compare this pulse in the time and frequency domains, as shown in the two plots. The relationship between and the number of frequency peaks is .