光子学报 ›› 2019, Vol. 48 ›› Issue (10): 1048005-1048005.doi: 10.3788/gzxb20194810.1048005

• “光孤子”专题 • 上一篇    下一篇

基于分数薛定谔方程对高斯光束的操控

王栋栋, 臧峰, 李禄   

  1. 山西大学 理论物理研究所 太原 030006
  • 收稿日期:2019-09-09 出版日期:2019-10-25 发布日期:2019-09-23
  • 通讯作者: 李禄(1960-),男,教授,博士,主要研究方向为光学传输理论与非线性动力学.Email:llz@sxu.edu.cn E-mail:llz@sxu.edu.cn
  • 作者简介:王栋栋(1995-),男,硕士研究生,主要研究方向为光学传输理论.Email:515908517@qq.com
  • 基金资助:

    国家自然科学基金(Nos.61475198,11705108)

Manipulation of Gaussian Beam Based on Fractional Schrödinger Equation

WANG Dong-dong, ZANG Feng, LI Lu   

  1. Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
  • Received:2019-09-09 Online:2019-10-25 Published:2019-09-23
  • Contact: 2019-09-23 E-mail:llz@sxu.edu.cn
  • Supported by:

    The National Natural Science Foundation of China (Nos. 61475198, 11705108)

摘要:

基于具有谐振势阱的分数薛定谔方程,数值研究了Lévy指数、啁啾参量和势阱深度对啁啾高斯光传输动力学的影响.研究发现,在啁啾参量与势阱深度一定的情况下,随着Lévy指数增大,光束演化周期会减小,偏移中心轴的距离则变大;在Lévy指数与势阱深度一定的情况下,光束演化周期和偏移距离随着啁啾参量增大而增大;无论Lévy指数值与啁啾参量是多少,周期与偏移中心轴的最大距离都和势阱深度成反比.研究结果表明,通过调节Lévy指数、啁啾参量与势阱深度可以有效地控制光传输,为光开关提供了新的设计思路.

关键词: Lévy指数, 谐振势阱, 分数薛定谔方程, 操控, 啁啾高斯光束

Abstract:

The influences of Lévy index, chirp parameter and potential depth on the propagation dynamics of chirped Gaussian beam are investigated numerically based on the fractional Schrödinger equation with a harmonic potential. It is found that, for fixed chirp parameter and potential depth, the propagation period decreases and the deviation distance increases with increasing of Lévy index. For fixed Lévy index and potential depth, the propagation period and the deviation distance increase as the chirp parameter increases. The period and the deviation distance are inversely proportional to the potential coefficient regardless of the values of Lévy index and chirp parameter. The results indicate that the beam propagation can be effectively controlled by adjusting Lévy index, chirp parameter and potential depth, which can inspire new ideas in the manufacture of optical switches.

Key words: Manipulation, Fractional Schrödinger equation, Lévy index, Chirped Gaussian beam, Harmonic potential

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