Controllable transmission of Airy-Gaussian beams in fractional Schro?dinger equation under Gaussian potential

Based on fractional Schro?dinger equation (FSE), we have emphatically investigated the evolution of Airy-Gaussian (AiG) beams under Gaussian potential by split-step Fourier method. Only when beam is incident vertically can splitting occur. When taking Gaussian potentials into account, periodic evolution can be achieved by assigning appropriate values to barrier parameters, avoiding the transmission phenomenon. Transmission and reflection (TR) ratio varies with values of barrier width and height, and period changes accordingly. Critical barrier height increases with the larger Le?vy index as a whole, while it eventually tends to be stable with the larger barrier width. In addition, compared with Gaussian wells, it is easier to achieve total reflection in Gaussian barriers. Based on fractional Schro?dinger equation (FSE), we have emphatically investigated the evolution of Airy-Gaussian (AiG) beams under Gaussian potential by split-step Fourier method. Only when beam is incident vertically can splitting occur. When taking Gaussian potentials into account, periodic evolution can be achieved by assigning appropriate values to barrier parameters, avoiding the transmission phenomenon. Transmission and reflection (TR) ratio varies with values of barrier width and height, and period changes accordingly. Critical barrier height increases with the larger Le?vy index as a whole, while it eventually tends to be stable with the larger barrier width. In addition, compared with Gaussian wells, it is easier to achieve total reflection in Gaussian barriers.

Automated summary

Based on the fractional Schro?dinger equation, the evolution of AiG beams under Gaussian potential was studied using the split-step Fourier method. The study found that beam splitting only occurs when the beam is incident vertically, and periodic evolution can be achieved by assigning appropriate barrier parameters values. The critical barrier height increases with the larger Le?vy index, while total reflection is easier to achieve in Gaussian barriers compared to Gaussian wells.