OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 3 — Feb. 29, 2012

Multipole theory for tight focusing of polarized light, including radially polarized and other special cases

Thanh Xuan Hoang, Xudong Chen, and Colin J. R. Sheppard  »View Author Affiliations

JOSA A, Vol. 29, Issue 1, pp. 32-43 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (2513 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A multipole expansion, based on spherical harmonics, provides an efficient method for calculating the field in the focal region of a lens for radially polarized illumination, or other illumination polarization and phase distributions, including vortex beams. The multipole approach also has the benefit of providing a simple measure of the purity of the longitudinal field mode. The method is also convenient for calculation of fields scattered by particles and calculation of optical trapping forces.

© 2012 Optical Society of America

OCIS Codes
(180.0180) Microscopy : Microscopy
(260.5430) Physical optics : Polarization
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Diffraction and Gratings

Original Manuscript: September 15, 2011
Manuscript Accepted: October 9, 2011
Published: December 7, 2011

Virtual Issues
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics

Thanh Xuan Hoang, Xudong Chen, and Colin J. R. Sheppard, "Multipole theory for tight focusing of polarized light, including radially polarized and other special cases," J. Opt. Soc. Am. A 29, 32-43 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. W. Davis and G. Patsakos, “TM and TE electromagnetic beams in free space,” Opt. Lett. 6, 22–23 (1981). [CrossRef] [PubMed]
  2. R. D. Romea and W. D. Kimura, “Modeling of inverse Cherenkov laser acceleration with axicon laser-beam focusing,” Phys. Rev. D 42, 1807–1818 (1990). [CrossRef]
  3. Z. Bouchal and M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995). [CrossRef]
  4. C. J. R. Sheppard and P. Török, “Electromagnetic field in the focal region of an electric dipole wave,” Optik 104, 175–177(1997).
  5. C. J. R. Sheppard and S. Saghafi, “Transverse-electric and transverse-magnetic beam modes beyond the paraxial approximation,” Opt. Lett. 24, 1543–1545 (1999). [CrossRef]
  6. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87(2000). [CrossRef] [PubMed]
  7. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7(2000). [CrossRef]
  8. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “The focus of light—theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109–113 (2001). [CrossRef]
  9. L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161–172(2001). [CrossRef]
  10. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003). [CrossRef] [PubMed]
  11. C. C. Sun, “Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation,” Opt. Lett. 28, 99–101 (2003). [CrossRef] [PubMed]
  12. C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327(2004). [CrossRef] [PubMed]
  13. E. Y. S. Yew and C. J. R. Sheppard, “Tight focusing of radially-polarized Gaussian and Bessel–Gauss beams,” Opt. Lett. 32, 3417–3419 (2007). [CrossRef] [PubMed]
  14. C. J. R. Sheppard and E. Y. S. Yew, “Performance parameters for focusing of radial polarization,” Opt. Lett. 33, 497–499(2008). [CrossRef] [PubMed]
  15. H. F. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nature Photon. 2, 501–506(2008). [CrossRef]
  16. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959). [CrossRef]
  17. C. J. R. Sheppard and P. Török, “Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion,” J. Mod. Opt. 44, 803–818 (1997). [CrossRef]
  18. A. A. Asatryan, C. J. R. Sheppard, and C. M. de Sterke, “Vector treatment of second harmonic generation produced by tightly focused vignetted Gaussian beams,” J. Opt. Soc. Am. B 21, 2206–2212 (2004). [CrossRef]
  19. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971). [CrossRef]
  20. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991). [CrossRef]
  21. T. Wohland, A. Rosin, and E. H. K. Stelzer, “Theoretical determination of the influence of polarization on forces exerted by optical tweezers,” Optik 102, 181–190 (1996).
  22. K. F. Ren, G. Grehan, and G. Gousebet, “Prediction of reverse radiation pressure by generalized Lorentz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996). [CrossRef] [PubMed]
  23. T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation and optical measurement of laser trapping forces on non-spherical particles,” J. Quant. Spectrosc. Radiat. Transfer 70, 627–637 (2001). [CrossRef]
  24. J. M. Taylor and G. D. Love, “Multipole expansion of Bessel and Gaussian beams for Mie scattering calculations,” J. Opt. Soc. Am. A 26, 278–282 (2009). [CrossRef]
  25. T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 1005–1017 (2003). [CrossRef]
  26. T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical vortex trapping and the dynamics of particle rotation,” in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, D.L.Andrews, ed. (Elsevier, 2008), pp. 195–236.
  27. S. H. Simpson and S. Hanna, “Optical angular momentum transfer by Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 26, 625–638 (2009). [CrossRef]
  28. T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett. 33, 122–124 (2008). [CrossRef] [PubMed]
  29. J. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  30. W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism, 2nd ed. (Wiley, 1962).
  31. A. J. Devaney and E. Wolf, “Multipole expansions and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974). [CrossRef]
  32. E. T. Whittaker, “On the partial differential equations of mathematical physics,” Math. Ann. 57, 333–355 (1903). [CrossRef]
  33. H. Weyl, “Ausbreitung elektromagnetische Wellen über einem ebenen Leiter,” Ann. Phys. 60, 481–500 (1919). [CrossRef]
  34. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, 1966).
  35. G. C. Sherman, J. J. Stamnes, and E. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976). [CrossRef]
  36. A. J. Devaney and G. C. Sherman, “Plane-wave representations for scalar wave fields,” SIAM Rev. 15, 765–786 (1973). [CrossRef]
  37. Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10, 324–331 (2002). [PubMed]
  38. C. J. R. Sheppard and K. G. Larkin, “Optimal concentration of electromagnetic radiation,” J. Mod. Opt. 41, 1495–1505 (1994). [CrossRef]
  39. C. J. R. Sheppard and S. Rehman, “Highly convergent focusing of light based on rotating dipole polarization,” Appl. Opt. 50, 4463–4467 (2011). [CrossRef] [PubMed]
  40. C. J. R. Sheppard, N. K. Balla, and S. Rehman, “Performance parameters for highly-focused electromagnetic waves,” Opt. Commun. 282, 727–734 (2009). [CrossRef]
  41. J. J. Stamnes and V. Dhayalan, “Focusing of electric dipole waves,” Pure Appl. Opt. 5, 195–226 (1996). [CrossRef]
  42. C. J. R. Sheppard, “Fundamentals of superresolution,” Micron 38, 772 (2007). [CrossRef]
  43. S. H. Goh and C. J. R. Sheppard, “High aperture focusing through a spherical interface: application to refractive solid immersion lens (RSIL) for subsurface imaging,” Opt. Commun. 282, 1036–1041 (2009). [CrossRef]
  44. K. M. Lim, G. C. F. Lee, C. J. R. Sheppard, J. C. H. Phang, C. L. Wong, and X. Chen, “The effect of polarization on a solid immersion lens of arbitrary thickness,” J. Opt. Soc. Am. A 28, 903–911 (2011). [CrossRef]
  45. X. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35, 3928–3930 (2010). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited