ULTRASHORT-PULSE 2ND-HARMONIC GENERATION .1. TRANSFORM-LIMITED FUNDAMENTAL PULSES

A general theory of second-harmonic generation, including all the effe cts of group-velocity dispersion, is given for coherent ultrashort pul ses with arbitrary shapes and carrier chirps. Ultrashort-pulse second- harmonic generation is analyzed for transform-limited fundamental puls es. The effects of intrapulse group-velocity dispersion (IGVD) on the second-harmonic (SH) pulse shape are investigated for parameters repre sentative of popular phase-matchable crystals and wavelength, includin g Ti:sapphire lasers. In phase-matched structures IGVD at the SK canno t be neglected for pulses approaching 10 fs. It results in a spectral quadratic phase on the SH and in some cases can shorten the pulse. Ext ernal dispersive shaping of the SH pulses distorted by group-velocity mismatch (GVM) is examined, and some pulse shortening is found possibl e. It is shown that the effect of IGVD at the SH wavelength on the pul se is similar to that of the spectral quadratic phase provided by an e xternal pulse shaper. Group-velocity-matched configurations are also i nvestigated. IGVD at both the fundamental and the SH wavelengths is fo und to Limit the optimum thickness of the nonlinear medium. A measure of the interaction length in which the pulse width of the fundamental pulse is preserved in the SH is introduced. It is defined in terms of the GVM and the pulse bandwidth for phase-matched structures and in te rms of the IGVD and pulse bandwidths for group-velocity-matched config urations.