Optik 125 (2014) 6870–6873 Contents lists available at ScienceDirect Optik jo ur nal homepage: www.elsevier.de/ijleo Effect of spherical aberration on tightly focused cylindrically polarized vortex beams G. Therese Anita a , C. Amala Prathiba Janet b , K. Prabakaran c , T.V.S. Pillai c , K.B. Rajesh d,∗ a Department of Physics, Arunachala College of Engineering for Women, Nagercoil, Tamil Nadu, India b Department of Physics, St. Xavier’s Catholic College of Engineering, Nagercoil, Tamil Nadu, India c Department of Physics, Periyar Universit- PG Extension Centre, Dharmapuri, Tamil Nadu, India d Department of Physics, Chikkanna Government Arts College, Tiruppur, Tamil Nadu, India a r t i c l e i n f o Article history: Received 5 August 2013 Accepted 5 February 2014 Keywords: Vector diffraction theory Cylindrical vortex beam Polarization Spherical aberration a b s t r a c t In this paper attention is given to the effects of primary spherical aberration on the cylindrical polarized vortex beam based on the vector diffraction theory. It is observed that by properly choosing the polariza- tion angle and topological charge one can obtain many novel focal patterns suitable for optical tweezers, laser printing and material process. However, it is observed that the focusing objective with spherical aberration generates structural modification and positional shift of the generated focal structure. © 2014 Elsevier GmbH. All rights reserved. 1. Introduction In modern optics study and applications of the optical vortex beam have recently generated great research [1–7]. Recently the focusing properties of a circularly, radially, azimuthally or linearly polarized vortex beam by a high numerical-aperture lens have been discussed [8–13]. The radially and the azimuthally polarized beams are of particular importance in many application fields due to unique cylindrical symmetry of polarization. The size and shape of the focused structure of the vortex beam play an important role in many applications such as in microscopy, lithography, data storage, particle trapping, etc. A deformed focused structure may cause serious problems in optical trapping and microscopy. Defor- mation in the focused structure can be due to aberrations. Under realistic experimental conditions, it is inevitable to suffer wave front aberrations even for the well corrected objectives [14–16]. When a tightly focused laser propagates through an interface of two different materials, spherical aberration will be induced due to refractive-index mismatch. Marcinkvcius et al. [17] reported that this interface SA increase the size and distorts the shape of photo damaged regions and thus reduces the spatial resolution of micro fabrication, where the focusing depth inside the glass is no more than 250 m. An important investigation was initiated by Braat ∗ Corresponding author. E-mail address: rajes@gmail.com (K.B. Rajesh). et al. [18] who used extended Nijboer–Zernike representation of the vector field in the focal region of an aberrated high NA optical beam. Biss and Brown [19] have investigated the effect of primary aberrations on the focused structure of the radially polarized vor- tex beam. However no detailed studies seem to have been made on the effect of primary aberrations on the tight focusing of cylindri- cal vortex beam. In view of the importance of the high NA focusing of CVB, in this paper we present the results of our investigation of effect of spherical aberration, on cylindrical vortex beam. 2. Theoretical model A schematic diagram of the suggested method is shown in Fig. 1. The analysis was performed on the basis of Richards and Wolf’s vectorial diffraction method [20] widely used for high-NA focus- ing systems at arbitrary incident polarization. Instead of a radial polarization or an azimuthally polarization, each point of the optical vortex beam has a polarization rotated by ϕ 0 from its radial direc- tion. In this paper, we assume that the cylindrically vortex beam is incident upon a high NA lens. Since this beam can be expressed as a linear combination of the focal fields of radial polarization and azimuthally polarization, we adapted the same analysis method as that in Ref. [21]. The focal field of a cylindrically polarized vortex beam can be written as:  E (r, z) = E r  e r + E z  e z + E ϕ  e ϕ (1) http://dx.doi.org/10.1016/j.ijleo.2014.08.124 0030-4026/© 2014 Elsevier GmbH. All rights reserved.