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.
In this paper, the propagation dynamics of the Pearcey Gaussian beam modeled by the fractional Schrödinger equation in linear potential have been investigated. Different from the propagation properties of the Pearcey Gaussian beam described by the standard Schrödinger equation, the diffraction-free phenomenon which is presented under the fractional Schrödinger equation with linear potential or not, is influenced by Lévy index. When the linear potential is considered, the periodic evolution of the Pearcey Gaussian beams is given, and results show that transmission period is inversely proportional to the linear potential coefficient. And the direction of beam propagation can be controlled by the symbol of linear potential parameters. The propagation of incident beam with transverse wave velocity have been studied. Moreover, the chirp does not influence the evolution period of the Pearcey Gaussian beam but the intensity distribution. These properties can be well implemented to the promising applications of Pearcey Gaussian beam in optical manipulation and optical switch.
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