Diffraction-free beams in fractional Schrödinger equation.
We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories z = ±2(x - x0), which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone z = 2√(x(2) + y(2)) and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE.
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.
Yiqi
Y
Zhang
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.
Hua
H
Zhong
Science Program, Texas A&M University at Qatar, P.O. Box 23874 Doha, Qatar.
Milivoj R
MR
Belić
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.
Noor
N
Ahmed
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.
Yanpeng
Y
Zhang
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.
Min
M
Xiao