Abstract
First, the nonparaxial integral expression of fractional-order Bessel–Gauss (FBG) beams during propagation is rigorously derived by using the virtual source technique and the principle of independent transmission and superposition of light, together with Weber integral formula and Fourier–Bessel transform pair. Then, the analytic expression of the important axial optical field amplitude of FBG beams is obtained. Finally, the on-axis intensity and phase of FBG beams are calculated on the basis of the analytic expression. Calculated results quantitatively revealed some important intensity information regarding the near-field propagation characteristic of FBG beams.
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