Based on the generalized Huygens-Fresnel diffraction integral and in consideration of astigmatism introduced by a lens, a closed-form propagation equation of Gaussian beams passing through the astigmatic lens is derived, which enables us to discuss the focusing properties of astigmatic Gaussian beams both analytically and numerically. Furthermore, the beam propagation factor (M 2 -factor) and power in the bucket (PIB) are chosen as the criteria, the beam quality of astigmatic Gaussian beams is analyzed. It is shown that the effects of astigmatic lens on the irradiance distribution and PIB are determined by a combined parameter C 52 +C 62 , and the astigmatism results in a decrement of the PIB.
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