Transformation properties of annular beams passing through an astigmatic lens

The model of annular beams is given based on the model of flattened multi-Gaussian beams proposed by Tovar. Using the generalized Huygens-Fresnel diffraction integral, the transformation and focusing properties of annular beams passing through an astigmatic lens are studied and analyzed. Furthermore, the effect of astigmatism on the beam quality of the annular beams passing through an astigmatic lens is also discussed. The results show that the annular beams become non-rotational symmetric after passing through an astigmatic lens. The focusing intensity decreases gradually with the increasing of the astigmatic coefficients. The azimuth angle of focusing spot is determined merely by astigmatic coefficients. For the given beam orders and the wavelength of the annular beams, the transformatio