Abstract

It was shown in the paper Opt. Lett. 40, 3739 (2015) [CrossRef]   that Laguerre–Gauss beams $({{\rm LGB}_n})$ of order $n$ and Bessel beams (BB) are asymptotically equivalent for $n \gg 1$. Here we demonstrate that an ${{\rm LGB}_n}$ and a BB are equivalent just in the inner multiring parts of the two beams. However, the outer multiring parts are completely different, and this leads us to apply a truncation on the two beams to make them indistinguishable. Since the ${{\rm LGB}_n}$ could be approximated by a BB only in the inner multiring part, we suggest another beam that could replace its outer multiring part. By considering the ${{\rm LGB}_n}$ as a sum of $n$ rings having different radii and widths, we model the ${{\rm LGB}_n}$ outer multiring part by a sum of what we call in this paper “ring shifted-Gaussian beams.” The peer-to-peer comparison of the ${{\rm LGB}_n}$ with the two cited beams allowed us to provide a new analytical description of the obstructed ${{\rm LGB}_n}$ far field. These results will be very useful to study many aspects related to the ${{\rm LGB}_n}$ diffraction by apertures and stops. As an example, we show at the end of this paper how the self-healing ability of an obstructed ${{\rm LGB}_n}$ could be studied analytically.

© 2020 Optical Society of America

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