Propagation of symmetric tunable dual airy beam through ABCD optical system

A simple mathematical model is proposed to describe symmetric tunable dual Airy beam (STDAB) [Opt. Lett. 39 (2014) 2370; Opt. Lett. 38 (2013) 1286; Opt. Lett. 37 (2012) 3402]. This beam is composed of two conventional Airy beams with a tunable parameter which have several distinguishing features. For example, the intensity distribution of the beam can be Gaussian, elliptical Gaussian, rectangular Gaussian or dumbbell shaped with difference tunable parameters. Based on the Collins integral formula, an analytical expression of the STDAB passing through a paraxial ABCD optical system is derived. For special cases, the propagation properties of the beams in free space and in chiral medium, passing a thin lens and passing a fractional Fourier transformation system are studied.