PT symmetry in a fractional Schrodinger equation Academic Article uri icon

abstract

  • AbstractWe investigate the fractional Schrdinger equation with a periodic symmetric potential. In the inverse space, the problem transfers into a firstorder nonlocal frequencydelay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the onedimensional 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 twodimensional 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 onchip optical devices. image

published proceedings

  • LASER & PHOTONICS REVIEWS

altmetric score

  • 0.5

author list (cited authors)

  • Zhang, Y., Zhong, H., Belic, M. R., Zhu, Y. i., Zhong, W., Zhang, Y., Christodoulides, D. N., & Xiao, M.

citation count

  • 131

complete list of authors

  • Zhang, Yiqi||Zhong, Hua||Belic, Milivoj R||Zhu, Yi||Zhong, Weiping||Zhang, Yanpeng||Christodoulides, Demetrios N||Xiao, Min

publication date

  • May 2016

publisher