LAUSR

In this work, we establish the relationship existing between astigmatic Gaussian beams and Bessel-modulated Gaussian beams with quadratic radial dependence. We introduce an alternative representation of quadratic Bessel-Gaussian beams. This result permits us to expand the astigmatic Gaussian beams in a Fourier series with respect to the polar azimuthal angle with coefficients that are expressible in terms of Bessel-modulated Gaussian beams with quadratic radial dependence. The analysis presented also includes an analytic derivation of the power azimuthal spectral distribution associated with the decomposition in orbital angular momentum eigenmodes and a comprehensive characterization of the properties of this distribution as the beam parameters are varied.