Tailoring the Generalized 2D Airy Beam

Generalized two-dimensional (2D) Airy beam is a kind of self-accelerating beam with variable initial angle between its two wings, manifested itself as an initial angle determined parabolic trajectory during the free-space propagation. However, the independent and flexible manipulation of both the transverse optical field and longitudinal trajectory of the generalized 2D Airy beam has not been achieved yet which limits its application in the various fields. Herein, we report on tailoring of the propagation properties of the generalized 2D Airy beam based on the catastrophe theory, where analytical expression of its propagation trajectory is derived. In order to clarify the relationship between the transverse optical field distribution and the longitudinal trajectory, we analytically put forward a generation vector, facilitating the tailoring of both longitudinal trajectory and transverse distribution of optical field simultaneously. Consequently, we can effectively generate the generalized 2D Airy beam and precisely manipulate the evolution of its peak intensity. Once the initial and terminal points of trajectory are determined in advance, we can flexibly tailor the trajectory of 2D Airy beam, with the help of corresponding generation vector. Meanwhile, when the longitudinal trajectory is fixed, we can flexibly rotate the transverse optical field distribution of the generalized 2D Airy beam and manipulate its initial angle. Experimental verifications of the manipulation capabilities for the longitudinal trajectory, initial angle, and the rotation of transverse optical field are provided to validate our theoretical results.