Applied Physics B

, Volume 110, Issue 1, pp 7–14

Twisted longitudinally polarized field in the focal region



We calculate the field distribution based on the vector diffraction theory for a superposition of spirally phase shifted radially polarized beams. Twisted longitudinally polarized field is found in the focal region. The total intensity as well as the polarization components rotates around the beam axis near the focus. Calculation of the Poynting vector at the focal plane shows that the electromagnetic energy is redistributed between different polarization components. Nonzero value of transverse components of the Poynting vector implies the transverse flow of the energy in the focal region.


  1. 1.
    Q. Zhan, Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon. 1, 1–57 (2009)CrossRefGoogle Scholar
  2. 2.
    Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, S. Sato, Lateral resolution enhancement of laser scanning microscopy by a higher order radially polarized mode beam. Opt. Express 19, 15947–15954 (2011)ADSCrossRefGoogle Scholar
  3. 3.
    Y. Kozawa, S. Sato, Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams. Opt. Express 18, 10828–10833 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    Y.I. Salamin, Direct particle acceleration by two identical cross radially polarized laser beams. Phys. Rev. A 82, 013823 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    Y. Kozawa, S. Sato, Focusing properties of a double-ring-shaped radially polarized beam. Opt. Lett. 31, 820–822 (2006)ADSCrossRefGoogle Scholar
  6. 6.
    Y.Q. Zhao, Q. Zhan, Y.L. Zhang, Y.P. Li, Creation of a three-dimensional optical chain for controllable particle delivery. Opt. Lett. 30, 848–850 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, C.T. Chong, Creation of a needle of longitudinally polarized light in vacuum using binary optics. Nat. Photonics 2, 501–505 (2008)CrossRefGoogle Scholar
  8. 8.
    S.H. Tao, X.-C. Yuan, J. Lin, R.E. Burge, Residue orbital angular momentum in interferenced double vortex beams with unequal topological charges. Opt. Express 14, 535–541 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    C.H.J. Schmitz, K. Uhrig, J.O. Spatz, J.E. Curtis, Tuning the orbital angular momentum in optical vortex beams. Opt. Express 14, 6604–6612 (2006)ADSCrossRefGoogle Scholar
  10. 10.
    I.D. Maleev, G.A. Swartzlander Jr, Composite optical vortices. J. Opt. Soc. Am. B 20, 1169–1176 (2003)ADSCrossRefGoogle Scholar
  11. 11.
    S.M. Baumann, D.M. Kalb, L.H. MacMillan, E.J. Galvez, Propagation dynamics of optical vortices due to Gouy phase. Opt. Express 17, 9818–9827 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, T. Inoue, Structure of optical singularities in coaxial superpositions of Laguerre-Gaussian modes. J. Opt. Soc. Am. A 27, 2603–2612 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    D. Yang, J. Zhao, T. Zhao, L. Kong, Generation of rotating intensity blades by superposing optical vortex beams. Opt. Commun. 284, 3597–3600 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    R. Zambrini, S.M. Barnett, Angular momentum of multimode and polarization patterns. Opt. Express 15, 15214–15227 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    Y.Y. Schechner, R. Piestun, J. Shamir, Wave propagation with rotating intensity distribution. Phys. Rev. E 54, R50 (1996)ADSCrossRefGoogle Scholar
  16. 16.
    A. Jesacher, S. Fürhapter, S. Bernet, M. Ritsch-Marte, Size selective trapping with optical “cogwheel” tweezers. Opt. Express 12, 4129–4135 (2004)ADSCrossRefGoogle Scholar
  17. 17.
    S. Franke-Arnold, J. Leach, M.J. Padgett, V.E. Lembessis, D. Ellinas, A.J. Wright, J.M. Girkin, P. Ohberg, A.S. Arnold, Optical ferries wheel for ultracold atoms. Opt. Express 15, 8619–8625 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    M.P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K. Dholakia, Creation and manipulation of three-dimensional optically trapped structures. Science 296, 1101–1103 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    S. Sato, Y. Kozawa, Hollow vortex beams. J. Opt. Soc. Am. A 26, 142–146 (2009)CrossRefGoogle Scholar
  20. 20.
    Y. Xue, C. Kuang, X. Hao, Z. Gu and X. Liu, A method for generating a three-dimensional dark spot using a radially polarized beam. J. Opt. 13, 125704 (9 pp) (2011)Google Scholar
  21. 21.
    X. Hao, C. Kuang, Y. Li, X. Liu, A method for extending depth of focus in STED nanolithography. J. Opt. 14, 045702 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    C. Kuang, X. Hao, X. Liu, T. Wang, Y. Ku, Formation of sub-half-wavelength focal spot with ultra long depth of focus. Opt. Commun. 284, 1766–1769 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    X. Hao, C. Kuang, T. Wang, X. Liu, Effects of polarization on the de-excitation dark focal spot in STED microscopy. J. Opt. 12, 115707 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    B. Harke, C.K. Ullal, J. Keller, S.W. Hell, Three-dimensional nanoscopy of colloidal crystals. Nano Lett. 8, 1309–1313 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    E. Engle, N. Huse, T.A. Klar, S.W. Hell, Creating λ/3 focal holes with a Mach-Zehnder interferometer. Appl. Phys. B. 77, 11–17 (2003)CrossRefGoogle Scholar
  26. 26.
    K.S. Youngworth, T.G. Brown, Focusing of high numerical aperture cylindrical-vector beams. Opt. Express 7, 77–87 (2000)ADSCrossRefGoogle Scholar
  27. 27.
    A. Tovar, Production and propagation of cylindrically polarized Laguerre-Gaussian laser beams. J. Opt. Soc. Am. A 15, 2705–2711 (1998)ADSCrossRefGoogle Scholar
  28. 28.
    G.H. Yuan, S.B. Wei, X.-C. Yuan, Generation of nondiffraction quasi-circular polarization beams using an amplitude modulated phase hologram. J. Opt. Soc. Am. A 28, 1716–1720 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    L. Paterson, M.P. MacDonald, J. Arlt, W. Sibbett, P.E. Bryant, K. Dholakia, Controlled rotation of optically trapped microscopic particles. Science 292, 912–914 (2001)ADSCrossRefGoogle Scholar
  30. 30.
    M.P. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett, K. Dholakia, Revolving interference pattern for the rotation of optically trapped particles. Opt. Commun. 201, 21–28 (2002)ADSCrossRefGoogle Scholar
  31. 31.
    H. Chen, Q. Zhan, Y. Zhang, Y.P. Li, The Gouy phase shift of the highly focused radially polarized beam. Phys. Lett. A 371, 259–262 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    J.A. Rodrigo, A.M. Carvac-Anguirre, T. Alieva, G. Cristóbal, M.L. Calvo, Microparticle moments in optical funnels and pods. Opt. Express 19, 5232–5243 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    S.R.P. Pavani, R. Piestun, Three dimensional tracking of fluorescent microparticle using a photon-limited double-helix response system. Opt. Express 16, 22048–22057 (2008)CrossRefGoogle Scholar
  34. 34.
    M.A. Thompson, M.D. Lew, M. Badierostami, W.E. Moerner, Localizing and tracking single nanoscale emitters in three dimension with high spatiotemporal resolution using a double-helix point spread function. Nano Lett. 10, 211–218 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    J. Hamazaki, Y. Mineta, K. Oka, R. Morita, Direct observation of Gouy phase shift in a propagating optical vortex. Opt. Express 18, 8382–8392 (2006)ADSCrossRefGoogle Scholar
  36. 36.
    Y. Kozawa, S. Sato, Generation of a radially polarized laser beam by use of a conical Brewster prism. Opt. Lett. 30, 3063–3065 (2005)Google Scholar
  37. 37.
    Y. Kozawa, S. Sato, Demonstration and selection of a single-transverse higher-order-mode beam with radial polarization. J. Opt. Soc. Am. A 27, 399–403 (2010)ADSCrossRefGoogle Scholar
  38. 38.
    A. Ito, Y. Kozawa, S. Sato, Generation of hollow scalar and vector beams using a spot-defect mirror. J. Opt. Soc. Am. A 27, 2072–2076 (2010)ADSCrossRefGoogle Scholar
  39. 39.
    H. Kawauchi, Y. Kozawa, S. Sato, T. Sato, S. Kawakami, Simultaneous generation of helical beams with linear and radial polarization by use of a segmented half-wave plate. Opt. Lett. 33, 399–401 (2008)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Multidisciplinary Research for Advanced MaterialsTohoku UniversitySendaiJapan

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