Amplification of ultra-short pulses in optical fibers can be degraded by the nonlinear phenomenon of self-phase modulation (SPM), resulting in considerable spectral broadening and distortion. Variation in the refractive index of the medium is caused by the optical Kerr effect.

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

e^{-2t2}. 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

.