Unveiling the Link Between Fractional Schrödinger Equation and Light Propagation in Honeycomb Lattice Academic Article uri icon

abstract

  • AbstractWe suggest a real physical system the honeycomb lattice as a possible realization of the fractional Schrdinger equation (FSE) system, through utilization of the DiracWeyl equation (DWE). The fractional Laplacian in FSE causes modulation of the dispersion relation of the system, which becomes linear in the limiting case. In the honeycomb lattice, the dispersion relation is already linear around the Dirac point, suggesting a possible connection with the FSE, since both models can be reduced to the one described by the DWE. Thus, we propagate Gaussian beams in three ways: according to FSE, honeycomb lattice around the Dirac point, and DWE, to discover universal behavior the conical diffraction. However, if an additional potential is brought into the system, the similarity in behavior is broken, because the added potential serves as a perturbation that breaks the translational periodicity of honeycomb lattice and destroys Dirac cones in the dispersion relation.

published proceedings

  • ANNALEN DER PHYSIK

altmetric score

  • 0.25

author list (cited authors)

  • Zhang, D. a., Zhang, Y., Zhang, Z., Ahmed, N., Zhang, Y., Li, F., Belic, M. R., & Xiao, M.

citation count

  • 50

complete list of authors

  • Zhang, Da||Zhang, Yiqi||Zhang, Zhaoyang||Ahmed, Noor||Zhang, Yanpeng||Li, Fuli||Belic, Milivoj R||Xiao, Min

publication date

  • September 2017

publisher