Propagation dynamics of the circular airy beam in the fractional Schrodinger equation under three kinds of potentials

In this paper, using a split -step Fourier method, we discuss the propagation dynamics of the circular airy beam (CAB) modeled by the fractional Schro center dot dinger equation (FSE) with the linear, parabolic and Gaussian potentials. Results show that the CAB is deflected with the action of the linear potential, and the deflecting direction of the beam is controlled by a positive or negative linear potential coefficient. The magnitude of the linear potential is inversely proportional to the evolution period of the beam. And as the Le ' vy index decreases to one, the beam is no longer focused but gradually splits into two symmetric beams with a part of energy in the middle. With the influence of the parabolic potential, the CAB undergoes periodic evolution of autofocusing and auto-defocusing behaviors. And the period is inversely proportional to the parabolic potential coefficient. The intensity of the beam grows larger with a decreasing Le ' vy index when it is suddenly self-focusing. In the presence of a Gaussian potential barrier, the CAB is reflected when it encounters the barrier, and the Gaussian potential well has the same phenomenon. However, the critical potential intensity required for total reflection of the beam with a potential well is greater than that with a barrier. It is shown that we can control the propagation trajectory of CABs by rationally tuning the Le ' vy index and various potential parameters in the fractional Schro center dot dinger optical system. It has a great potential in the application of optical operation and optical switching.