Tight focusing of double ring shaped radially polarized beam with high NA lens axicon K.B. Rajesh a,n , N. Veerabagu Suresh b , P.M. Anbarasan c , K. Gokulakrishnan b , G. Mahadevan d a Department of Physics, Anna University Tirunelveli, Tirunelveli 627 027, India b Department of Electrical and Electronics, Anna University Tirunelveli, Tirunelveli 627 007, India c Department of Physics, Periyar University, Salem 636 011, India d Department of Mathematics, Anna University Tirunelveli, Tirunelveli 627007, India article info Article history: Received 13 April 2010 Received in revised form 13 July 2010 Accepted 14 November 2010 Available online 6 April 2011 Keywords: Longitudinal polarized beam Lens axicon Radial polarized beam abstract A method is presented for generation of a sub wavelength (0.45l) longitudinally polarized beam, which propagates without divergence over lengths of about 8l in free space. This is achieved by tight focusing of double ring shaped radially polarized beam with a high NA lens axicon that utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distributions were calculated based on the vector diffraction theory and it was observed that in the case of high numerical aperture (NA) lens axicon, the distribution of the total intensity near the focus had little effect on the degree of truncation of the incident beam by the pupil. & 2010 Elsevier Ltd. All rights reserved. 1. Longitudinally polarized beam Cylindrical polarized laser beams due to their unique electric vector distribution have recently gained considerable research interest. Radial and azimuthal polarizations are two distinctive cases of such cylindrical vector beams. Radially polarized beams are of particular interest, due to their unique properties of generating a fully symmetric focus spot with added resolution enhancement [1] and providing a longitudinal electric component [2,3] under high numerical aperture focusing. The existence of a strong longitudinal field of tightly focused radially polarized beam has many attractive applications such as particle acceleration [4], fluorescent imaging [5], second harmonic generation [6] and Raman spectroscopy [7]. Several methods to enhance the longitudinal field component have been suggested [8,9]; however all of them have insufficient optical efficiency and non-uniform axial field strength. 2. Tight focusing of R-TEM11* mode beam with high NA lens axicon Recently a double-ring-shaped beam was experimentally observed as a higher-order radially polarized mode (R-TEM11*) directly from a laser cavity [10]. In addition, these higher-order mode beams may be generated by a particular laser cavity designed to oscillate only with radial polarization [11,12]. It was theoretically reported that a double-ring shaped radially polarized beam has the potential to form an optical bottle beam under a particular focusing condition [13], and can generate a sharp focal spot of the longitudinal component under tight focusing [14]. The axicon lens, invented in 1954, can focus a light beam with a long depth of focus. However, the axial intensity of the beam generated by the axicon lens increases with the propagation distance and it has difficulty in realizing sub wavelength focusing [15,16]. The idea of using spherical aberration to produce an axicon from ordinary lenses was first suggested by Steel [17] in 1960. It has been thoroughly investigated both analytically and numerically [18–20]. The experimental aspect of designing the lens axicon is investigated in Ref. [21]. Recently we have introduced the possible design of high NA lens axicon with nano scale resolution [22]. The high NA lens axicon is a system of a cemented doublet-lens axicon, where the virtual focal segment created by the aberrated diverging lens can be converted to a real focal segment, of the forward type with a nano scale resolution, by adding a high numerical aperture (NA) converging lens. The advantage of such a system is that spherical surfaces are routinely produced in any optical workshop, so the lens axicon is easy and inexpensive to manufacture. In this paper we describe a numerical study, based on the vector diffraction theory, of a property of a double ring-shaped R-TEM11* mode beam that is tightly focused by a high-NA-lens axicon. Here we consider only systems that comprise a diverging lens that has third-order spherical aberration and a perfect high NA converging lens. A schematic diagram of the suggested method is shown in Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optlastec Optics & Laser Technology 0030-3992/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2010.11.009 n Corresponding author. E-mail address: rajeskb@gmail.com (K.B. Rajesh). Optics & Laser Technology 43 (2011) 1037–1040