title: Propagation Dynamics of a Light Beam in a Fractional Schrödinger Equation.
abstract: The dynamics of wave packets in the fractional Schrödinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and numerically the propagation of optical beams in the fractional Schrödinger equation with a harmonic potential. We find that the propagation of one- and two-dimensional input chirped Gaussian beams is not harmonic. In one dimension, the beam propagates along a zigzag trajectory in real space, which corresponds to a modulated anharmonic oscillation in momentum space. In two dimensions, the input Gaussian beam evolves into a breathing ring structure in both real and momentum spaces, which forms a filamented funnel-like aperiodic structure. The beams remain localized in propagation, but with increasing distance display an increasingly irregular behavior, unless both the linear chirp and the transverse displacement of the incident beam are zero.
authors.affiliation: Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China.
authors.forename: Yiqi
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China.
authors.forename: Xing
authors.initials: X
authors.lastname: Liu
authors.affiliation: Science Program, Texas A&M University at Qatar, P.O. Box 23874 Doha, Qatar.
authors.forename: Milivoj R
authors.initials: MR
authors.lastname: Belić
authors.affiliation: Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300, China.
authors.forename: Weiping
authors.initials: W
authors.lastname: Zhong
authors.affiliation: Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China.
authors.forename: Yanpeng
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Department of Physics, University of Arkansas, Fayetteville, Arkansas, 72701, USA.|National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China.
authors.forename: Min
authors.initials: M
authors.lastname: Xiao