Quasi-Gaussian beam analytical basis and comparison with an alternative approach (L)

A superposition of propagating Bessel beams was recently numerically demonstrated to approximate a Gaussian beam and was used to evaluate the scattering by a sphere centered on the focal point of the beam. An analytical beam synthesis used in optics by Agrawal and Pattanayak [J. Opt. Soc. Am. 69, 575-578 (1979)] is found here to be recovered as the weak focusing limit of the quasi-Gaussian beam when evanescent contributions are omitted from the analytical synthesis. The propagating-wave part of the analytical synthesis has similarities to, and differences from, the recent quasi-Gaussian approximation.