A new criterion for self-healing quantification of structured light beams

Abstract

This paper introduces a new approach to the self-healing quantification of structured light beams. The self-healing is quantitatively determined by defining a self-healing degree (SHD) and a similarity function based on comparing the intensity distributions of the perturbed and unperturbed beams. In addition, the SHD is employed for two other intensity-based methods to compare the methods’ performance. The Bessel beams (BBs) with integer and fractional topological charges (TCs) are examined numerically to verify the method. Further, the effect of superposition of the Bessel and mirrored BBs with respect to the x-axis on the self-healing property is investigated. The perturbation of the beams is applied using a pair of circular masks as a symmetric perturbation. The propagating of perturbed and unperturbed beams is simulated by the angular spectrum method. The obtained quantitative results are confirmed by the intuitive results and also the accuracy of the proposed method is similar to the other used methods. On the other hand, due to using fewer calculations with respect to them and so is less time-consuming (about 57% and 67% reduction in computational time), it can be used as an adequate alternative method. As a result of this method, it is shown that the superposition of BBs with their mirrored ones is an effective factor to improve the self-healing property, in which the SHD of the superposed beams is more than the BBs for each TC. It is also shown that using the fractional TC beams is another advantageous improvement to increase the SHD.