A tensor method is used to formulate the on-axis scintillation index for an elliptical Gaussian beam (EGB; astigmatic Gaussian beam) propagating in a weak turbulent atmosphere. Variations of the on-axis scintillation of an EGB are studied. It is interesting to find that the scintillation index of an EGB can be smaller than that of a circular Gaussian beam in a weakly turbulent atmosphere under certain conditions and is closely related to the ratio of the beam waist size along the long axis to that along the short axis of the EGB, the wavelength, and the structure constant of the turbulent atmosphere.
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Cai et al. (2007) studied this question.
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