A general theory of second-harmonic generation, including all the effects of group-velocity dispersion, is given for coherent ultrashort pulses with arbitrary shapes and carrier chirps. Ultrashort-pulse second-harmonic generation is analyzed for transform-limited fundamental pulses. The effects of intrapulse group-velocity dispersion (IGVD) on the second-harmonic (SH) pulse shape are investigated for parameters representative of popular phase-matchable crystals and wavelength, including Ti:sapphire lasers. In phase-matched structures IGVD at the SH cannot 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. External dispersive shaping of the SH pulses distorted by group-velocity mismatch (GVM) is examined, and some pulse shortening is found possible. It is shown that the effect of IGVD at the SH wavelength on the pulse is similar to that of the spectral quadratic phase provided by an external pulse shaper. Group-velocity-matched configurations are also investigated. IGVD at both the fundamental and the SH wavelengths is found 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 terms of the IGVD and pulse bandwidths for group-velocity-matched configurations.
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