Interference and tunneling of beams in fractional systems with rectangular potential

The dynamics of hyperbolic secant beams under the competition between the fractional diffraction and rectangular potential is investigated. It is found that the beams can exhibit the reflection, tunneling and interference, forming the bound states, optical lattices or fringes, or solitons under different conditions. In linear regime, when the potential is wide, the beam exhibits the total reflection for deeper potential and smaller incident angle, and presents the reflection and tunneling for shallower potential and larger incident angle. The irregular interference pattern and bound states are generated for the narrow potential. Moreover, the initial chirp causes the appearance of side lobes during beam propagation. When two hyperbolic secant beams are symmetrically incident from inside or outside the potential, the interference lattices or interference fringes are generated inside the potential, which are related to the Lévy index, initial chirp and incident angle of the beams. In nonlinear regime, the hyperbolic secant beam undergoes the collapse, splitting or formation of the periodic-like soliton by selecting appropriate parameters including the Lévy index, initial chirp and incident angle. In addition, the dynamics of two hyperbolic secant beams under the interaction of the nonlinear effect and fractional diffraction is also investigated in detail. This work provides more possibilities for optical lattice generation and optical manipulation.

Graphical abstract