%0 Journal Article
%T Minimizing the Bright/Shadow Focal Spot Size with Controlled Side-Lobe Increase in High-Numerical-Aperture Focusing Systems
%A S. N. Khonina
%A S. G. Volotovskiy
%J Advances in Optical Technologies
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/267684
%X Minimizing the bright/shadow focal spot size for differently polarized incident waves through the additional apodization of the focusing system output pupil by use of an optical element with the vortex phase dependence on angle and the polynomial amplitude dependence on radius is studied. The coefficients of the radial polynomial were optimized with the aim of fulfilling certain conditions such as the energy efficiency preservation and keeping the side lobes under control. The coefficients were chosen so as to minimize the functional using BrentĄ¯s method. 1. Introduction Recent years have seen the publication of a large number of articles dealing with obtaining a smaller transverse size of the focal spot using a high focusing system [1¨C5]. The smallest transverse size of the focal spot has been obtained for a radially polarized beam in which the longitudinal component makes the maximal contribution to the total intensity. There is a variety of techniques to gain the contribution of the longitudinal component to the total intensity, including the use of an annular aperture which allows only the peripheral part of radiation to pass through the lens [1, 2] and the use of additional phase optical elements, which provides a higher energy efficiency [3¨C5]. However, this study is concerned with not simply controlling the contribution of different electric field components into the focal spot region [5], but rather minimizing the (bright/dark) focal spot size by optimally selecting the pupilĄ¯s transmission function. In [6], it was proposed that the focal spot formed by a high focusing system should be reduced in size using radially polarized Laguerre-Gauss modes of higher radial order, devoid of vortex phase component. The positive role of the vortex phase function which allows obtaining a smaller focal spot in individual components of the sharply focused electric field at different polarization types was analyzed in [4], whereas the possibility of obtaining a smaller focal spot in terms of total intensity by introducing additional variations of radius was shown in [5]. The use of the transmission functions in the form of Zernike polynomials, including those containing vortex phase dependence, was considered in [7]. Thus, it has become possible to simultaneously introduce vortex phase dependence and amplitude variations on radius. Note that it has also been shown that it is possible to reduce not only the bright spot but the shadow region as well. In areas such as optical trapping and micromanipulation [8], STED-microscopy [9], and shadow microscopy [10], there
%U http://www.hindawi.com/journals/aot/2013/267684/