Far-field modeling of obstructed Laguerre-Gauss beams

摘要

It was shown in the paper "Opt lett, V.40 ,N.16, 2015 " that Laguerre-Gauss beams (LGB(n)) of order n and Bessel beams (BB) are asymptotically equivalent for n 1. Here, we demonstrate that an LGB(n) and a BB are equivalent just in the inner multi-ring parts of the two beams. However, the outer multi-ring parts are completely different, this leads us to apply a truncation on the two beams to make them indistinguishable. Since the LGB(n) could be approximated by a BB just in the inner multi-ring part, we suggest another beam that could replace its outer multi-ring part. By considering the LGB(n) as a sum of n rings having different radii and widths, we model the LGB(n) outer multi-ring part, by a sum of what we call in this paper "ring shifted-Gaussian beams". The peer-to-peer comparison of the LGB(n) with the two cited beams, allowed us to provide a new analytical description of the obstructed LGB(n) far-field. These results will be very useful to study many aspects related to the LGBn diffraction by apertures and stops. As an example, we show at the end of this paper, how the self-healing ability of an obstructed LGB(n) could be studied analytically. (C) 2020 Optical Society of America