Diffraction-free beams in fractional Schrdinger equation. Academic Article uri icon


  • We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrdinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories z=2(x-x0), which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone z = 2(x(2) + y(2)) and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE.

published proceedings

  • Sci Rep

altmetric score

  • 0.25

author list (cited authors)

  • Zhang, Y., Zhong, H., Beli, M. R., Ahmed, N., Zhang, Y., & Xiao, M.

citation count

  • 94

complete list of authors

  • Zhang, Yiqi||Zhong, Hua||Belić, Milivoj R||Ahmed, Noor||Zhang, Yanpeng||Xiao, Min

publication date

  • April 2016