Three-dimensional intensity distribution in the far zone of focused fields in systems with different Fresnel numbers

Three-dimensional intensity distribution near the focus in systems with different Fresnel numbers has been investigated by Li and Wolf on the basis of the Huygens-Fresnel principle and Lommel analysis [J. Opt. Soc. Am. A1, 801 (1984)JOAOD61084-752910.1364/JOSAA.1.000801]. Their computed results have been summarized into a group of isophotes of intensity distribution near the focus. In order to show the behavior of focused fields beyond the focal region, this study enlarges the research scope from intensity distribution near the focus to that in the half-space from the focal plane to infinity. To this end, a mapping transformation function is proposed that allows the plotting of isophotes within a finite area. Using this technique, both analytical and numerical expressions of far-zone behavior predicted by the Huygens-Fresnel principle for systems with different Fresnel numbers and the predictions of the Rayleigh diffraction integrals for systems with high relative aperture are obtained and compared with the predictions of Debye's theory of focusing, which is found to be unable to describe the far-zone behavior correctly in most cases but is able to give an approximation to systems with high Fresnel numbers.