On the nonparaxial corrections of Bessel-Gauss beams

The nonparaxial corrections for Bessel-Gauss beams were derived recently using two different approaches [Borghi et al., J. Opt. Soc. Am. A 18, 1618 (2001) and Vaveliuk et al., J. Opt. Soc. Am. A 24, 3297 (2007)]. However, the two obtained results do not agree, so it is necessary to determine which method is correct. In the most recent of those papers, Vaveliuk et al. claimed that their method is correct while the method described by Borghi et al. is incorrect. In the present work, just by solving the rigorous propagation problem, we show that exactly the converse is true.