中国物理B ›› 2020, Vol. 29 ›› Issue (5): 54201-054201.doi: 10.1088/1674-1056/ab7b4c

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Trajectory engineering via a space-fractional Schrödinger equation with dynamic linear index potential

Yunji Meng(孟云吉), Youwen Liu(刘友文), Haijiang Lv(吕海江)   

  1. 1 School of Information Engineering, Huangshan University, Huangshan 245041, China;
    2 College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
  • 收稿日期:2019-10-09 修回日期:2019-12-26 出版日期:2020-05-05 发布日期:2020-05-05
  • 通讯作者: Yunji Meng E-mail:meng_yunji@msn.com
  • 基金资助:
    Project supported by the Natural Science Research Project of Anhui Provincal Education Department of China (Grant Nos. KJHS2018B01 and KJ2018A0407), the National Natural Science Foundation of China (Grant No. 11804112), the Natural Science Foundation of Anhui Province of China (Grant No. 1808085QA22), and Start-up Fund of Huangshan University, China (Grant No. 2015xkjq001).

Trajectory engineering via a space-fractional Schrödinger equation with dynamic linear index potential

Yunji Meng(孟云吉)1, Youwen Liu(刘友文)2, Haijiang Lv(吕海江)1   

  1. 1 School of Information Engineering, Huangshan University, Huangshan 245041, China;
    2 College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
  • Received:2019-10-09 Revised:2019-12-26 Online:2020-05-05 Published:2020-05-05
  • Contact: Yunji Meng E-mail:meng_yunji@msn.com
  • Supported by:
    Project supported by the Natural Science Research Project of Anhui Provincal Education Department of China (Grant Nos. KJHS2018B01 and KJ2018A0407), the National Natural Science Foundation of China (Grant No. 11804112), the Natural Science Foundation of Anhui Province of China (Grant No. 1808085QA22), and Start-up Fund of Huangshan University, China (Grant No. 2015xkjq001).

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摘要： We theoretically and numerically study the propagation dynamics of a Gaussian beam modeled by the fractional Schrödinger equation with different dynamic linear potentials. For the limited case α=1 (α is the Lévy index) in the momentum space, the beam suffers a frequency shift which depends on the applied longitudinal modulation and the involved chirp. While in the real space, by precisely controlling the linear chirp, the beam will exhibit two different evolution characteristics: one is the zigzag trajectory propagation induced by multi-reflection occurring at the zeros of spatial spectrum, the other is diffraction-free propagation. Numerical simulations are in full accordance with the theoretical results. Increase of the Lévy index not only results in the drift of those turning points along the transverse direction, but also leads to the delocalization of the Gaussian beam.

关键词: trajectory engineering, space-fractional Schrö, dinger equation, dynamic linear index potential

Abstract: We theoretically and numerically study the propagation dynamics of a Gaussian beam modeled by the fractional Schrödinger equation with different dynamic linear potentials. For the limited case α=1 (α is the Lévy index) in the momentum space, the beam suffers a frequency shift which depends on the applied longitudinal modulation and the involved chirp. While in the real space, by precisely controlling the linear chirp, the beam will exhibit two different evolution characteristics: one is the zigzag trajectory propagation induced by multi-reflection occurring at the zeros of spatial spectrum, the other is diffraction-free propagation. Numerical simulations are in full accordance with the theoretical results. Increase of the Lévy index not only results in the drift of those turning points along the transverse direction, but also leads to the delocalization of the Gaussian beam.

Key words: trajectory engineering, space-fractional Schrö, dinger equation, dynamic linear index potential

中图分类号:  (Wave propagation, transmission and absorption)

  • 42.25.Bs
42.25.Fx (Diffraction and scattering) 42.30.Kq (Fourier optics)