Characteristics of a Gaussian beam after n times Airy transforms

Abstract

The optical system of n times Airy transforms is successively composed of n separate and identical Airy transforms. An analytical expression of the optical field of a Gaussian beam after n times Airy transforms is derived, which is concise and separable in two transverse directions. Moreover, analytical expressions of the centroid, the beam spot size, the divergence angle, and the beam propagation factor of a Gaussian beam after n times Airy transforms are derived. The absolute value of the centroid in arbitrary one transverse direction is proportional to the number of Airy transforms. The beam spot size and the beam propagation factor in arbitrary one transverse direction are both positively correlated with the number of Airy transforms. While, the divergence angle in arbitrary one transverse direction is independent of the number of Airy transforms and keeps unvaried. The analytical optical field of a Gaussian beam after n times Airy transforms propagating in free space is also presented. The Gaussian beam after n times Airy transforms propagating in free space follows an upward ballistic trajectory in a cross section. With the increase of number of Airy transforms, the deflection of the ballistic trajectory in free space increases. Two Airy transforms are performed in the experiment, and the corresponding measurements are carried out. The experimental results are consistent with the theoretical predictions. The performances of a Gaussian beam after n times Airy transforms are well demonstrated by this research. The properties of a Gaussian beam after n times Airy transforms have potential applications in optical micro-manipulation and collimation.