Propagation and Evolution Properties of Finite Energy Airy Beams

The propagation and evolution properties of the finite energy Airy beams generated by exponential attenuation, spatial truncation, frequency truncation, and constant amplitude methods are compared and analyzed using the Huygens-Fresnel diffraction integral. Further, the effects of a transverse scaling factor and aperture truncated width on nondiffracting propagation distance and transverse acceleration are discussed. When the aperture truncated width is constant, the non-diffracting propagation distance and lateral acceleration offset of all types of finite energy Airy beams increase as the transverse scaling factor increases. When the transverse scale factor is constant, the non-diffracting propagation distance of all types of finite energy Airy beams increases as the aperture truncated width increases. When the aperture truncated width and transverse scaling factor are constant, the non-diffracting propagation distance of frequency truncation Airy beam is the shortest, that of the exponential attenuation and spatial truncation Airy beams are longer, and that of the constant amplitude Airy beam is the longest. The results have certain significance for expanding the application of finite energy Airy beams in the long-distance propagation.