Study of the nonparaxial propagation of asymmetric Bessel-Gauss beams by using virtual source method

The virtual source method, which is also known as the complex source point method was used to study the nonparaxial propagation of asymmetric Bessel-Gauss (aBG) beams. According to optical independence transmission and superposition principles of beam propagation, an aBG beam was expanded into superposition of the infinite Bessel-Gauss beams. Superposition of infinite virtual source points of the expanded aBG beams was used to correspond to electric rings generating an aBG beam. Then Fourier-Bessel transform theory was used to derive the nonparaxial integral expression of aBG beams. Finally, the analytic expression of axial optical field amplitude of an aBG beams was derived when they are kept to third-order nonparaxial correction term.