We investigate second-harmonic generation by an astigmatic partially coherent beam. An explicit expression for the second-order correlation function of the second-harmonic field is obtained. The properties of the generated field and the conversion efficiency for second-harmonic generation are studied numerically. We find that using an astigmatic instead of a stigmatic partially coherent pump beam can increase the conversion efficiency of the second-harmonic generation.
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Cai et al. (2007) studied this question.