Far-field modeling of obstructed Laguerre-Gauss beams

It was shown in the paper Opt. Lett.40, 3739 (2015)OPLEDP0146-959210.1364/OL.40.003739 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 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 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 LGB_n as a sum of n rings having different radii and widths, we model the 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 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 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 LGB_n could be studied analytically.