Airyprime beams and their propagation characteristics

A type of Airyprime beam is introduced in this document. An analytical expression of Airyprime beams passing through a separable ABCD paraxial optical system is derived. The beam propagation factor of the Airyprime beam is proved to be 3.676. An analytical expression of the kurtosis parameter of an Airyprime beam passing through a separable ABCD paraxial optical system is also presented. The kurtosis parameter of the Airyprime beam passing through a separable ABCD paraxial optical system depends on the two ratios B/(Azrx) and B/(Az(ry)). As a numerical example, the propagation characteristics of an Airyprime beam is demonstrated in free space. In the source plane, the Airyprime beam has nine lobes, one of which is the central dominant lobe. In the far field, the Airyprime beam becomes a darkhollow beam with four uniform lobes. The evolvement of an Airyprime beam propagating in free space is well exhibited. Upon propagation, the intensity distribution of the Airyprime beam becomes flatter and the kurtosis parameter decreases from the maximum value 2.973 to a saturated value 1.302. The Airyprime beam is also compared with the second-order elegant Hermite-Gaussian beam. The novel propagation characteristics of Airyprime beams denote that they could have potential application prospects such as optical trapping.