Periodic evolution of the Pearcey–Gaussian beam in the fractional Schrödinger equation under Gaussian potential

Abstract

The dynamics of the Pearcey-Gaussian beam with Gaussian potential in the fractional Schrödinger equation are investigated. In the free space, varying the Lévy index offers a convenient way to control the splitting and bending angle of the beam. In the presence of Gaussian potential, with the increasing of propagation distance, the process is repeated in a breath-like motion. The periodicity also can be changed by adjusting the potential parameter and incident beam arguments, such as potential height, potential width and transverse wavenumber. The transmission and reflection of the beam can also be controlled by varying the potential parameters. Moreover, when a symmetrical Gaussian potential barrier is selected, total reflection is more likely to occur. These unique characteristics show the possibility in controlling the dynamics of Pearcey-Gaussian beam with the fractional Schrödinger equation system.

Periodic evolution of the Pearcey Gaussian beam under fractional effect

“…In 2019, Deng et al analyzed the Pearcey Gaussian wave packets which are constructed by combining the chirped Pearcey function in the temporal domain and the Pearcey Gaussian function in the spatial domain in a quadratic-index medium [14]. There has now been a new upsurge in research on the transmission characteristics and dynamics of the Pearcey beams in various potential and medium, such as containing in harmonic potential [15], parabolic refractive index medium [16], parabolic potential [17], trapping potential [18] and Gaussian potential [19].…”