Observation of frequency modulation in second-harmonic generation of ultrashort pulses

We study both experimentally and theoretically the intensity and frequency profile of the pulse that is generated by second-harmonic generation with phase mismatch of a pulse with a duration of 50 fs. Experimentally, we determine the shape and the frequency of the generated pulse by correlating it with a second fundamental pulse and by measuring the spectra of the generated pulse. Theoretically, we solve numerically the coupled differential equations that describe the nonlinear interaction. We show that for ultrashort pulses the effects of phase mismatch, depletion, and group-velocity differences between the fundamental and the second harmonic strongly influence the intensity profile and the frequency spectrum of the second-hamonic pulse. We find that in second-harmonic generation with phase mismatch the frequency of the generated pulse becomes modulated.