Journal of Russian Laser Research

, Volume 34, Issue 5, pp 468–476 | Cite as

A Highly Efficient Superresolving Phase Filter for a Radially Polarized Beam

  • Huifang Chen
  • Huimin Yan
  • Zhihua Ding
  • Xiuda Zhang


We simulate the focal intensity distribution of a radially polarized beam, in view of the vector diffraction theory. We summarize two important rules: (i) the marginal ray of the aperture determines the focal size on the focal plane; (ii) the ratio of the longitudinal component to the transversal component affects the shape of the focus. We design a continuous phase filter using these rules for a confocal system. We chose the tangent of the semi-aperture angle to build up the phase function, because it is sensitive to the marginal rays, which have large aperture angles. To achieve a flexible modulation, we use a quadratic function for unwrapping the phase. We optimize the parameters of the quadratic function and achieve a transverse superresolving focus. Aiming at different Strehl ratios, we obtain a series of superresolution phase filters. Compared with others, the filter proposed has the advantages of superior superresolution effect and higher energy utilization ratios. The phase-filter design is universal and proved to be valid. It can be employed in either high or low NA systems, superresolving or donut focus applications.


superresolution radial polarization confocal microscope phase filter 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Z. L. Mao, C. Wang, and Y. Cheng, Chin. J. Laser, 35, 1283 (2008).CrossRefGoogle Scholar
  2. 2.
    S. W. Hell and J. Wichmann, Opt. Lett., 19, 780 (1994).ADSCrossRefGoogle Scholar
  3. 3.
    S. W. Hell, Cytometry A, 71, 742 (2007).Google Scholar
  4. 4.
    M. Gu and C. J. R. Shepard, J. Mod. Opt., 38, 2247 (1991).ADSCrossRefGoogle Scholar
  5. 5.
    V. A. Andreev and K. V. Indukaev, J. Russ. Laser Res., 24, 220 (2003).CrossRefGoogle Scholar
  6. 6.
    V. A. Andreev and K. V. Indukaev, J. Russ. Laser Res., 26, 380 (2005).CrossRefGoogle Scholar
  7. 7.
    V. A. Andreev, K. V. Indukaev, O. K. Ioselev, et al., J. Russ. Laser Res., 26, 394 (2005).CrossRefGoogle Scholar
  8. 8.
    H. Fukuda and R. Yamanaka, Appl. Phys., 31, 4126 (1992).CrossRefGoogle Scholar
  9. 9.
    Y. L. Zhang and J. P. Bai, Opt. Exp., 17, 3698 (2009).ADSCrossRefGoogle Scholar
  10. 10.
    N. M. Mojarad and M. Agin, Opt. Exp., 17, 117 (2009).ADSCrossRefGoogle Scholar
  11. 11.
    W. R. Chen and Q. Zhan, Chin. Opt. Lett., 5, 709 (2007).Google Scholar
  12. 12.
    G. T. Francia, Nuovo Cimento Suppl., 9, 426 (1952).CrossRefGoogle Scholar
  13. 13.
    C. J. R. Sheppard and Z. S. Hegedus, J. Opt. Soc. Am., 5, 643 (1988).ADSCrossRefGoogle Scholar
  14. 14.
    C. M. Martinez, P. Andres, and Z. Rodriguez, Opt. Commun., 165, 267 (1999).ADSCrossRefGoogle Scholar
  15. 15.
    Y. L. Xie, J. M. Wang, and Y. W. Liu, Acta Opt. Sin., 30, 1464 (2010).MathSciNetCrossRefGoogle Scholar
  16. 16.
    M. J. Yun, W. Liang, W. J. Kong, et al., Opt. Commun., 283, 2079 (2010).ADSCrossRefGoogle Scholar
  17. 17.
    B. R. Boruah, Appl. Opt., 49, 701 (2010).ADSCrossRefGoogle Scholar
  18. 18.
    L. Liu and G. Y. Wang, Optik, 119, 481 (2008).ADSCrossRefGoogle Scholar
  19. 19.
    L. M. Zou, J. Q. Qu, S. L. Hou, and X. M. Ding, Opt. Commun., 285, 2022 (2012).ADSCrossRefGoogle Scholar
  20. 20.
    W. Wang, C. H. Zhou, and J. J. Yu, Acta Phys. Sin., 60, 024201 (2011).Google Scholar
  21. 21.
    D. M. Juana, J. E. Oti, and V. F. Canales, Opt. Lett., 28, 607 (2003).ADSCrossRefMATHGoogle Scholar
  22. 22.
    Q. Zhan, Adv. Opt. Photon., 1, 1 (2009).CrossRefGoogle Scholar
  23. 23.
    K. S. Youngworth and T. G. Brown, Proc. SPIE, 3919, 75 (2000).ADSCrossRefGoogle Scholar
  24. 24.
    Y. Kozawa, T. Hibi, A. Sato, et al., Opt. Exp., 19, 15947 (2011).ADSCrossRefGoogle Scholar
  25. 25.
    S. Quabis, R. Dorn, and M. Eberler, Opt. Commun., 179, 1 (2000).ADSCrossRefGoogle Scholar
  26. 26.
    R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett., 91, 233901 (2003).ADSCrossRefGoogle Scholar
  27. 27.
    C. J. R. Sheppard and A. Choudhury, Appl. Opt., 43, 4322 (2004).ADSCrossRefGoogle Scholar
  28. 28.
    Q. Zhan and J. R. Leger, Opt. Exp., 10, 324 (2002).ADSCrossRefGoogle Scholar
  29. 29.
    X. Hao, C. F. Kuang, T. T. Wang, and X. Liu, J. Opt., 12, 115707 (2010).ADSCrossRefGoogle Scholar
  30. 30.
    Q. F. Tang, K. Cheng, Z. H. Zhou, and G. F. Jin, J. Opt. Soc. Am. A, 27, 1355 (2010).ADSCrossRefGoogle Scholar
  31. 31.
    W. T. Tang, E. Yew, and C. J. R. Sheppard, Opt. Lett., 34, 2147 (2009).ADSCrossRefGoogle Scholar
  32. 32.
    K. S. Youngworth, D. P. Biss, and T. G. Brown, Proc. SPIE, 4261, 14 (2001).CrossRefGoogle Scholar
  33. 33.
    J. Kim, D. C. Kim, and S. H. Back, Microscop. Res. Tech., 72, 441 (2009).CrossRefGoogle Scholar
  34. 34.
    M. Born and E. Wolf, Principles of Optics, Cambridge University Press (1999).Google Scholar
  35. 35.
    B. Richards and E. Wolf, Proc. R. Soc. A, 253, 358 (1959).ADSCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Huifang Chen
    • 1
    • 2
  • Huimin Yan
    • 1
  • Zhihua Ding
    • 1
  • Xiuda Zhang
    • 1
  1. 1.State Key Laboratory of Modern Optical InstrumentationsZhejiang UniversityHangzhouChina
  2. 2.College of Optical and Electronic TechnologyChina Jiliang UniversityHangzhouChina

Personalised recommendations