Quantitative comparison of self-healing ability between Bessel-Gaussian beam and Airy beam

The self-healing ability during propagation process is one of the most important properties of non-diffracting beams. This ability has crucial advantages to light sheet-based microscopy to reduce scattering artefacts, increase the quality of the image and enhance the resolution of microscopy. Based on similarity between two infinite-dimensional complex vectors in Hilbert space, the ability to a Bessel-Gaussian beam and an Airy beam have been studied and compared. Comparing the evolution of the similarity of Bessel-Gaussian beam with Airy beam under the same conditions, we find that Bessel-Gaussian beam has stronger self-healing ability and is more stable than that of Airy beam. To confirm this result, the intensity profiles of Bessel-Gaussian beam and Airy beam with different similarities are numerically calculated and compared.