Propagation Dynamics of a Light Beam in a Fractional Schrdinger Equation. Academic Article uri icon


  • The dynamics of wave packets in the fractional Schrdinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and numerically the propagation of optical beams in the fractional Schrdinger equation with a harmonic potential. We find that the propagation of one- and two-dimensional input chirped Gaussian beams is not harmonic. In one dimension, the beam propagates along a zigzag trajectory in real space, which corresponds to a modulated anharmonic oscillation in momentum space. In two dimensions, the input Gaussian beam evolves into a breathing ring structure in both real and momentum spaces, which forms a filamented funnel-like aperiodic structure. The beams remain localized in propagation, but with increasing distance display an increasingly irregular behavior, unless both the linear chirp and the transverse displacement of the incident beam are zero.

published proceedings

  • Phys Rev Lett

altmetric score

  • 0.5

author list (cited authors)

  • Zhang, Y., Liu, X., Beli, M. R., Zhong, W., Zhang, Y., & Xiao, M.

citation count

  • 212

complete list of authors

  • Zhang, Yiqi||Liu, Xing||Belić, Milivoj R||Zhong, Weiping||Zhang, Yanpeng||Xiao, Min

publication date

  • October 2015