Approximate description for Bessel, Bessel-Gauss, and Gaussian beams with finite aperture

An approximate analysis is derived for the propagation of Bessel, Bessel-Ga uss, and Gaussian beams with a finite aperture. This treatment is based on the fact that the circ function can be expanded into an approximate sum of complex Gaussian functions, so that these three beams are typically express ed as a combination of a set of infinite-aperture Bessel-Gauss beams. Corre spondingly, the evaluation of the diffracted field distribution of the beam s is reduced to the summation of Bessel-Gauss functions. From analytical re sults, the present approach provides a good description of the diffracted b eams in the region far (greater than a factor of the Fresnel distance) from the aperture. A possible extension of this method to other apertured beams is also discussed. (C) 1999 Optical Society of America [S0740-3232(99)0120 6-5].