Pt Symmetry In A Fractional Schrödinger Equation
Keywords
Conical diffraction; Fractional Schrödinger equation; symmetry
Abstract
We investigate the fractional Schrödinger equation with a periodic PT-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 PT-symmetric potential. This investigation may find applications in novel on-chip optical devices.
Publication Date
5-1-2016
Publication Title
Laser and Photonics Reviews
Volume
10
Issue
3
Number of Pages
526-531
Document Type
Letter
Personal Identifier
scopus
DOI Link
https://doi.org/10.1002/lpor.201600037
Copyright Status
Unknown
Socpus ID
84979467655 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84979467655
STARS Citation
Zhang, Yiqi; Zhong, Hua; Belić, Milivoj R.; Zhu, Yi; and Zhong, Weiping, "Pt Symmetry In A Fractional Schrödinger Equation" (2016). Scopus Export 2015-2019. 4619.
https://stars.library.ucf.edu/scopus2015/4619