Fresnel diffraction patterns as accelerating beams

¹ Key Laboratory for Physical Electronics and Devices of the Ministry of Education and Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University - Xi'an 710049, China
² Science Program, Texas A&M University at Qatar - P.O. Box 23874 Doha, Qatar
³ Institute of Applied Physics, Xi'an University of Arts and Science - Xi'an 710065, China
⁴ School of Information and Communication Engineering, Tianjin Polytechnic University - Tianjin 300160, China

^(a) zhangyiqi@mail.xjtu.edu.cn
^(b) milivoj.belic@qatar.tamu.edu
^(c) ypzhang@mail.xjtu.edu.cn

Received: 13 August 2013
Accepted: 6 November 2013

Abstract

We demonstrate that beams originating from Fresnel diffraction patterns are self-accelerating in free space. In addition to accelerating and self-healing, they also exhibit parabolic deceleration property, which is in stark contrast to other accelerating beams. We find that the trajectory of Fresnel paraxial accelerating beams is similar to that of nonparaxial Weber beams. Decelerating and accelerating regions are separated by a critical propagation distance, at which no acceleration is present. During deceleration, the Fresnel diffraction beams undergo self-smoothing, in which oscillations of the diffracted waves gradually focus and smooth out at the critical distance.