Influence of optical Airy transform on non-diffracting propagation distance of finite energy Airy beams

Finite energy Airy beams (FEAB) generated in laboratory have a short non-diffracting propagation distance (NDPD), which restricts its application in laser communication, laser detection and other fields. Effects of optical Airy transform (OAT) on NDPD of FEAB is analyzed. By comparing the theoretical formulas of the FEAB before and after the OAT, we find that when the transform parameter alpha of the OAT is larger than zero, the transverse scaling factor of the transformed FEAB is greater than that before the transformation, while the transformed exponential decay factor is smaller than that before the transformation. Using the Huygens-Fresnel diffractive integral, we derive the propagation formula of the transformed FEAB. Initial intensity distribution of FEAB before and after the OAT is compared. Propagation dynamics of the transformed FEAB with different alpha is numerically simulated and its NDPD is quantitatively evaluated. Results show that: with the increase of alpha, side lobes of the transformed FEAB increase, its main lobe and side lobes become wider than that before the transformation, and the inclination of the propagation trajectory decreases. When alpha is greater than half of the transverse scaling factor, the NDPD of the transformed FEAB increases rapidly.