Dynamics and manipulation of Airy beam in fractional system with diffraction modulation and PT-symmetric potential

Abstract

We investigate the dynamics and manipulation of finite energy Airy (FEA) beam in fractional system with diffraction modulation and PT-symmetric potential. In the absence of PT-symmetric potential, we first present the approximate analytical solution of chirp-free FEA beam. Based on the analytical solution, we investigate analytically and numerically the split and collision of chirp-free FEA beam under diffraction modulation, and discuss the possibility of inverse design of diffraction modulation according to the predefined trajectory. Furthermore, through coherent combining technique, we derive the analytical solution of chirped FEA beam, and investigate analytically and numerically the asymmetric evolutions of chirped FEA beam in real space and spectral space, and discuss qualitatively the relation between the asymmetry and the chirp parameter. In the presence of PT-symmetric potential, we derive a general eigenvalue equation dependent on diffraction modulation and present the band structure modulated by varying fractional diffraction. Based on the band structure modulated by varying fractional diffraction, we study numerically the asymmetric conical evolution of chirp-free FEA beam under diffraction modulation, which demonstrates that the propagation channels of FEA beam can be jointly manipulated by diffraction modulation and PT-symmetric potential. For chirped FEA beam, the competition effect between the chirp and the PT-symmetric potential on the beam dynamics is explored in detail.