Comparison of the propagation characteristics of Bessel, Bessel–Gauss, and Gaussian beams diffracted by a circular aperture

TLDR

We analytically derived axial and transverse intensity distributions for plane, Bessel, Gaussian, and Bessel–Gauss beams diffracted by a circular aperture using the scalar Kirchhoff–Huygens integral with Fresnel and Fraunhofer approximations. The Bessel–Gauss beam exhibits lower axial intensity and a shorter propagation distance than the Bessel beam, and its transverse diffraction‑free performance depends strongly on the aperture radius, beam waist, and transverse wave number.

Abstract

We use the scalar Kirchhoff–Huygens diffraction integral to obtain analytic expressions for both axial and transverse intensity distributions, assuming normal incidence on a circular aperture for four types of incident field: (1) plane wave, (2) Bessel beam, (3) Gaussian beam, and (4) Bessel–Gauss beam. We use the Fresnel approximation to obtain the axial intensity as a function of distance from the aperture. We consider both Fresnel and Fraunhofer diffraction for the case of the transverse intensity distributions. For the axial case, we find that the Bessel–Gauss beam performs worse than the Bessel beam, in terms both of the magnitude of intensity and of its ability to extend a distance from the aperture. In the transverse case, we find that the Bessel–Gauss beam performance in terms of remaining nearly diffraction free over a given distance is highly dependent on the relationship among the aperture radius, the beam waist parameter, and the transverse wave number.