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 with integer and fractional topological charges are examined numerically to verify the method‎. ‎Further‎, ‎the effect of superposition of the Bessel and mirrored Bessel beams 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 Bessel beams 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 Bessel beams for each topological charge‎. ‎It is also shown that using the fractional topological charge beams is another advantageous improvement to increase the SHD‎.