In this paper, by analyzing the main lobe of the Airy beam and its fitting Gaussian beam, we define the Rayleigh range of Airy beam based on the width of FEAB's main lobe for scaling the propagation characteristic of the Airy beam. The similar diffraction-free distance of FEAB (here, the width of the main lobe expanding to 2~(1/2) times) can be scaled by Rayleigh range, but it is from infinite (Pure non-diffraction beam) to one Rayleigh range (the same with Gaussian beam) when decay factor is from 0 to 1. On the contrary, although the FEAB with smaller decay factor (a < 0.4) can propagate more Rayleigh ranges keeping diffraction-free, the effective energy in the main lobe is low by studying the power in the bucket (PIB). If more energy needing in the main lobe, the FEAB need bigger decay factor (a > 0.4) will become more similar with Gaussian beam which can propagate about one Rayleigh range.
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