Airy transformation of Airyprime beam

As a remarkable optical transformation enabling mutual conversion between Gaussian and Airy beams, the Airy transformation raises intriguing questions when applied to Airyprime beam—an advanced variant of conventional Airy beam. To answer these questions, numerical simulations and experimental verification are combined in this study. The results show two different operation regimes: when the Airy coefficient exceeds the negative transverse scale factor, the Airy-transformed optical field of Airyprime beam in any transverse direction becomes equivalent to the superposition of eccentric Airy beam and eccentric Airyprime beam; when the Airy coefficient equals the negative transverse scale factor, the transformed optical field equivalently corresponds to the sum of two displaced elegant Hermite-Gaussian beams. Analytical expressions for centroid and beam half width under both regimes are rigorously derived and validated experimentally by using Airy transformation of Airyprime beams to systematically measure the influences of Airy coefficientson intensity distribution, centroid displacement, and beam half width. This investigation provides a novel method for generating complex beam profiles while enhancing the potential application value of such beams in optical communication and beam-splitting technology.