OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 6 — Mar. 25, 2013
  • pp: 7082–7095

Mie scattering and optical forces from evanescent fields: A complex-angle approach

Aleksandr Y. Bekshaev, Konstantin Y. Bliokh, and Franco Nori  »View Author Affiliations

Optics Express, Vol. 21, Issue 6, pp. 7082-7095 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (4248 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Mie theory is one of the main tools describing scattering of propagating electromagnetic waves by spherical particles. Evanescent optical fields are also scattered by particles and exert radiation forces which can be used for optical near-field manipulations. We show that the Mie theory can be naturally adopted for the scattering of evanescent waves via rotation of its standard solutions by a complex angle. This offers a simple and powerful tool for calculations of the scattered fields and radiation forces. Comparison with other, more cumbersome, approaches shows perfect agreement, thereby validating our theory. As examples of its application, we calculate angular distributions of the scattered far-field irradiance and radiation forces acting on dielectric and conducting particles immersed in an evanescent field.

© 2013 OSA

OCIS Codes
(240.6690) Optics at surfaces : Surface waves
(290.4020) Scattering : Mie theory
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optical Trapping and Manipulation

Original Manuscript: November 27, 2012
Revised Manuscript: February 6, 2013
Manuscript Accepted: February 6, 2013
Published: March 13, 2013

Virtual Issues
Vol. 8, Iss. 4 Virtual Journal for Biomedical Optics

Aleksandr Y. Bekshaev, Konstantin Y. Bliokh, and Franco Nori, "Mie scattering and optical forces from evanescent fields: A complex-angle approach," Opt. Express 21, 7082-7095 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
  2. M. Born and E. Wolf, Principles of Optics, 7th ed. (London: Pergamon, 2005).
  3. H. C. Van de Hulst, Light Scattering by Small Particles (New York: Chapman & Hall, 1957).
  4. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (New York: Wiley, 1983).
  5. M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008). [CrossRef]
  6. I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52(3), 133–201 (1979). [CrossRef]
  7. M. A. Paesler and P. J. Moyer, Near–Field Optics (New York: John Wiley & Sons, 1996).
  8. M. Nieto-Vesperinas and N. Garcia, eds., Optics at the nanometer scale, NATO ASI Series (Dordrecht: Kluwer Academic Publishing, 1996).
  9. S. A. Maier, Plasmonics: Fundamentals and Applications (New York: Springer, 2007).
  10. H. Chew, D.-S. Wang, and M. Kerker, “Elastic scattering of evanescent electromagnetic waves,” Appl. Opt. 18(15), 2679–2687 (1979). [CrossRef] [PubMed]
  11. C. Liu, T. Kaiser, S. Lange, and G. Schweiger, “Structural resonances in a dielectric sphere illuminated by an evanescent wave,” Opt. Commun. 117(5-6), 521–531 (1995). [CrossRef]
  12. M. Quinten, A. Pack, and R. Wannemacher, “Scattering and extinction of evanescent waves by small particles,” Appl. Phys. B 68(1), 87–92 (1999). [CrossRef]
  13. E. Almaas and I. Brevik, “Radiation forces on a micrometer-sized sphere in an evanescent field,” J. Opt. Soc. Am. B 12(12), 2429–2438 (1995). [CrossRef]
  14. I. Brevik, T. A. Sivertsen, and E. Almaas, “Radiation forces on an absorbing micrometer-sized sphere in an evanescent field,” J. Opt. Soc. Am. B 20(8), 1739–1749 (2003). [CrossRef]
  15. H. Y. Jaising and O. G. Hellesø, “Radiation forces on a Mie particle in the evanescent field of an optical waveguide,” Opt. Commun. 246(4-6), 373–383 (2005). [CrossRef]
  16. S. Chang, J. T. Kim, J. H. Jo, and S. S. Lee, “Optical force on a sphere caused by the evanescent field of a Gaussian beam; effects of multiple scattering,” Opt. Commun. 139(4-6), 252–261 (1997). [CrossRef]
  17. Y. G. Song, B. M. Han, and S. Chang, “Force of surface plasmon-coupled evanescent fields on Mie particles,” Opt. Commun. 198(1-3), 7–19 (2001). [CrossRef]
  18. J. Y. Walz, “Ray optics calculation of the radiation forces exerted on a dielectric sphere in an evanescent field,” Appl. Opt. 38(25), 5319–5330 (1999). [CrossRef] [PubMed]
  19. P. C. Chaumet and M. Nieto-Vesperinas, “Electromagnetic force on a metallic particle in the presence of a dielectric surface,” Phys. Rev. B 62(16), 11185–11191 (2000). [CrossRef]
  20. J. R. Arias-González and M. Nieto-Vesperinas, “Optical forces on small particles: attractive and repulsive nature and plasmon-resonance conditions,” J. Opt. Soc. Am. A 20(7), 1201–1209 (2003). [CrossRef] [PubMed]
  21. M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, “Near-field photonic forces,” Philos. Transact. A Math. Phys. Eng. Sci. 362(1817), 719–737 (2004). [CrossRef] [PubMed]
  22. M. Nieto-Vesperinas and J. J. Saenz, “Optical forces from an evanescent wave on a magnetodielectric small particle,” Opt. Lett. 35(23), 4078–4080 (2010). [CrossRef] [PubMed]
  23. M. Nieto-Vesperinas and J. R. Arias-González, “Theory of forces induced by evanescent fields,” arXiv: 1102.1613 (2011).
  24. S. Kawata and T. Sugiura, “Movement of micrometer-sized particles in the evanescent field of a laser beam,” Opt. Lett. 17(11), 772–774 (1992). [CrossRef] [PubMed]
  25. S. Kawata and T. Tani, “Optically driven Mie particles in an evanescent field along a channeled waveguide,” Opt. Lett. 21(21), 1768–1770 (1996). [CrossRef] [PubMed]
  26. M. Vilfan, I. Muševi?, and M. ?opi?, “AFM observation of force on a dielectric sphere in the evanescent field of totally reflected light,” Europhys. Lett. 43(1), 41–46 (1998). [CrossRef]
  27. K. Sasaki, J.-I. Hotta, K.-I. Wada, and H. Masuhara, “Analysis of radiation pressure exerted on a metallic particle within an evanescent field,” Opt. Lett. 25(18), 1385–1387 (2000). [CrossRef] [PubMed]
  28. L. N. Ng, M. N. Zervas, J. S. Wilkinson, and B. J. Luff, “Manipulation of colloidal gold nanoparticles in the evanescent field of a channel waveguide,” Appl. Phys. Lett. 76(15), 1993–1995 (2000). [CrossRef]
  29. G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. 96(23), 238101 (2006). [CrossRef] [PubMed]
  30. M. Šiler, T. ?ižmár, M. Šerý, and P. Zemánek, “Optical forces generated by evanescent standing waves and their usage for sub-micron particle delivery,” Appl. Phys. B 84(1-2), 157–165 (2006). [CrossRef]
  31. S. Gaugiran, S. Gétin, J. M. Fedeli, and J. Derouard, “Polarization and particle size dependence of radiative forces on small metallic particles in evanescent optical fields. Evidences for either repulsive or attractive gradient forces,” Opt. Express 15(13), 8146–8156 (2007). [CrossRef] [PubMed]
  32. D. C. Prieve and J. Y. Walz, “Scattering of an evanescent surface wave by a microscopic dielectric sphere,” Appl. Opt. 32(9), 1629–1641 (1993). [CrossRef] [PubMed]
  33. A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13(5), 053001 (2011). [CrossRef]
  34. K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012). [CrossRef]
  35. F. I. Fedorov, “To the theory of total reflection,” Dokl. Akad. Nauk SSSR 105, 465–468 (1955) (reprinted in J. Opt. 15, 014002 (2013)).
  36. C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D Part. Fields 5(4), 787–796 (1972). [CrossRef]
  37. S. H. Simpson and S. Hanna, “Orbital motion of optically trapped particles in Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 27(9), 2061–2071 (2010). [CrossRef] [PubMed]
  38. A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, “Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows,” Phys. Rev. A 86(2), 023847 (2012). [CrossRef]

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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited