25 May 2000 Ž . Optics Communications 179 2000 1–7 www.elsevier.comrlocateroptcom Focusing light to a tighter spot 1 S. Quabis, R. Dorn ) , M. Eberler, O. Glockl, G. Leuchs ¨ Physics Department, Chair for Optics, UniÕersity Erlangen-Nuremberg, Staudtstr. 7 r B2, D-91058 Erlangen, Germany Received 28 October 1999; received in revised form 30 December 1999; accepted 30 December 1999 Abstract The smallest spot sizes are reached by focusing an annular shaped light beam with a high aperture lens. We show theoretically that the focal area is further reduced when using a novel radially polarized instead of a linearly polarized light wx annulus. In the vicinity of the focus there is a large longitudinally polarized field component 1 which is still narrower and has no pronounced side lobes. A special photosensitive layer prepared to be sensitive only to this longitudinal field component may be used to reach an even smaller focal area, 0.1 l 2 , which is determined by the contour of the intensity distribution at half the maximum value. The radially polarized doughnut mode may also be used to build improved near field sensors having a substantially increased brightness. q 2000 Elsevier Science B.V. All rights reserved. PACS: 42.25.Ja; 42.15.E; 42.15.D Keywords: Focusing properties; Doughnut-mode; Diffraction; Radial polarization; Apodization 1. Introduction At some point we started to wonder about the limitation of the spot size which can be reached by focusing light waves. In the Feynman lectures we found a brief discussion of inward and outward-going wx spherical waves 2 along with the reminder that Maxwell’s equations are symmetric with respect to ) Corresponding author. E-mail: dorn@physik.uni-erlangen.de 1 This article is dedicated to Marlan O. Scully on the occasion of his 60th birthday. We very much appreciate his enormous contribution to science. But above all we like his approach. When told ‘‘Sir, I have a problem which cannot be solved and above all it’s crazy’’ his typical answer will be ‘‘Tell me more about it, I am interested. I give you five minutes’’. time reversal. There it is stated that the amplitude of the outward-going spherical wave emitted by an atom falls off as the inverse of the radial distance but that the value of the amplitude is limited close to the origin in the region where the moving electric charges generate the outward-going wave. Most exciting was the thought that if one could time-reverse the evolu- tion of the resulting field it would travel inward ever increasing its amplitude way beyond the point where the diameter of the wave front is of the order of the wavelength. In this line of thought the increase would be stopped only when the spherical wave fronts finally reach atomic dimensions. This seems to be in contradiction to the resolution limit in mi- croscopy as discussed by Abbe and Rayleigh. Inter- estingly, both lines of thought seem to be correct when applied to the proper situation. The first exam- ple describes the situation where the outward-going 0030-4018r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0030-4018 99 00729-4