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

Socpus ID

84979467655 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84979467655

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