PT symmetry in a fractional Schrödinger equation
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- 作者：Yiqi Zhang ; Hua Zhong ; Milivoj R. Belić ; Yi Zhu ; Weiping Zhong ; Yanpeng Zhang ; Demetrios N. Christodoulides and Min Xiao
- 刊名：Laser & Photonics Reviews
- 出版年：2016
- 出版时间：May 2016
- 年：2016
- 卷：10
- 期：3
- 页码：526-531
- 全文大小：603K
- ISSN：1863-8899
文摘
We investigate the fractional Schrödinger equation with a periodic -symmetric potential. In the inverse space, the problem transfers into a first-order nonlocal frequency-delay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the one-dimensional case, which results in a nondiffracting propagation and conical diffraction of input beams. If only one channel in the periodic potential is excited, adjacent channels become uniformly excited along the propagation direction, which can be used to generate laser beams of high power and narrow width. In the two-dimensional case, there appears conical diffraction that depends on the competition between the fractional Laplacian operator and the -symmetric potential. This investigation may find applications in novel on-chip optical devices.