Dynamics of finite energy Airy beams modeled by the fractional Schrödinger equation with a linear potential

The dynamics of finite energy Airy beams modeled by the fractional Schrödinger equation (FSE) with a linear potential are numerically investigated. Different from the propagation properties of Airy beams described by the standard Schrödinger equation, the splitting phenomenon, which is presented under the FSE without potential, is influenced by the quadratic chirp and the Lévy index. As the linear potential is considered, the periodic evolution of Airy beams is shown, and the period is inversely proportional to the linear potential coefficient. The beam width can undergo an abrupt decrease or increase depending on the sign of potential coefficient. The beam deviation distance increases with the beam width greatly changed if the Lévy index increases. Moreover, the quadratic chirp does not influence the evolution period but the intensity distribution. In addition, the intriguing properties are analytically clarified. All these features confirm the promising applications of Airy beams in optical manipulation and optical switch.