Dynamics of Airyprime beams with higher-order spectral phase modulation in the fractional Schrödinger equation

In this paper, the effects of spectral phase modulation on propagation characteristics of Airyprime beams modeled by fractional Schrödinger equation are studied, and the propagation dynamics of Airyprime beams are analyzed. It is found that the second and third-order spectral phase modulation significantly affect the beams dynamics. For the second-order spectral phase modulation, an increase in the Lévy index leads to a forward shift of the peak position, and the peak intensity increases for the positive spectral modulation coefficient, while the opposite tendency of the peak intensity is found for the negative spectral modulation coefficient. In addition, the appearance of multiple peaks depends on the positive modulation coefficient. For the third-order spectral phase modulation, the peak intensity increases under the larger spectral phase modulation coefficient with the backward shift of the maximum peak position, and an increase of the Lévy index results in the forward shift of the focusing position. The results show potential applications of Airyprime beams in various fields such as optical controlling and manipulation.