Ultrashort-pulse second-harmonic generation (USP SHG) is examined for fundamental pulses that are not transform limited but still possess coherent spectra. Pulses whose spectra contain various orders of nonlinear phases are considered, and spectral phase compensation (compression) in either the fundamental pulse (FP) or the second harmonic (SH) is investigated with regard to optimizing final SH pulse duration and overall conversion efficiency. For Gaussian shaped or similarly smooth spectra with only quadratic phase it is found that such a phase maps proportionally over to the spectrum of the SH, and the compressed SH pulse shapes and durations are independent of whether the compensation is performed in the FP or in the SH. The optimum compensation configuration and the conversion efficiency depend on the nonlinear interaction length. For a FP with multiple peaked spectra, compensation in the SH gives poor results, accentuating the structure inherent in the pulses. FP’s with higher-order spectral phases were found to give different results for the two different compensation schemes. In particular, it was found that second-plus fourth-order phases are easier to compensate than second- plus third-order. In all the cases examined, the optimum nonlinear interaction length is one to three times the pulse-width-preservation length. These results are useful for both understanding and experimental optimization of USP SHG with state-of-the-art systems and pulses 10 fs or shorter in duration.
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