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

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 29, Issue 1, 2012, Pages 32-43

  Hoang, Thanh Xuan ^a   Chen, Xudong ^a   Sheppard, Colin J R ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

LONGITUDINAL FIELDS; MULTIPOLE EXPANSIONS; MULTIPOLE THEORIES; OPTICAL TRAPPING FORCE; PHASE DISTRIBUTION; RADIALLY POLARIZED; SPHERICAL HARMONICS; TIGHT FOCUSING;

OPTICS;

ARTICLE; ELECTRICITY; LIGHT; LIGHT RELATED PHENOMENA; THEORETICAL MODEL;

ELECTRICITY; LIGHT; MODELS, THEORETICAL; OPTICAL PROCESSES;

EID: 84855411589     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.29.000032     Document Type: Article

References (45)

1. L. W. Davis and G. Patsakos, "TM and TE electromagnetic beams in free space," Opt. Lett. 6, 22-23 (1981).
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).
3. Z. Bouchal and M. Olivik, "Non-diffractive vector Bessel beams," J. Mod. Opt. 42, 1555-1566 (1995).
4. C. J. R. Sheppard and P. Török, "Electromagnetic field in the focal region of an electric dipole wave," Optik 104, 175-177 (1997). (Pubitemid 127574670)
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). (Pubitemid 129579986)
6. K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
7. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
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). (Pubitemid 32908927)
9. L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems," Opt. Commun. 191, 161-172 (2001). (Pubitemid 32408500)
10. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
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).
12. C. J. R. Sheppard and A. Choudhury, "Annular pupils, radial polarization, and superresolution," Appl. Opt. 43, 4322-4327 (2004).
13. E. Y. S. Yew and C. J. R. Sheppard, "Tight focusing of radiallypolarized Gaussian and Bessel-Gauss beams," Opt. Lett. 32, 3417-3419 (2007). (Pubitemid 351328359)
14. C. J. R. Sheppard and E. Y. S. Yew, "Performance parameters for focusing of radial polarization," Opt. Lett. 33, 497-499 (2008). (Pubitemid 351431552)
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).
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).
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). (Pubitemid 127597221)
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). (Pubitemid 40060161)
19. P. C. Waterman, "Symmetry, unitarity, and geometry in electromagnetic scattering," Phys. Rev. D 3, 825-839 (1971).
20. M. I. Mishchenko, "Light scattering by randomly oriented axially symmetric particles," J. Opt. Soc. Am. A 8, 871-882 (1991).
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). (Pubitemid 126551890)
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). (Pubitemid 126632583)
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). (Pubitemid 32668029)
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).
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). (Pubitemid 36594969)
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).
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). (Pubitemid 351328256)
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).
32. E. T. Whittaker, "On the partial differential equations of mathematical physics," Math. Ann. 57, 333-355 (1903).
33. H. Weyl, "Ausbreitung elektromagnetische Wellen über einem ebenen Leiter," Ann. Phys. 60, 481-500 (1919).
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).
36. A. J. Devaney and G. C. Sherman, "Plane-wave representations for scalar wave fields," SIAM Rev. 15, 765-786 (1973).
37. Q. Zhan and J. R. Leger, "Focus shaping using cylindrical vector beams," Opt. Express 10, 324-331 (2002).
38. C. J. R. Sheppard and K. G. Larkin, "Optimal concentration of electromagnetic radiation," J. Mod. Opt. 41, 1495-1505 (1994).
39. C. J. R. Sheppard and S. Rehman, "Highly convergent focusing of light based on rotating dipole polarization," Appl. Opt. 50, 4463-4467 (2011).
40. C. J. R. Sheppard, N. K. Balla, and S. Rehman, "Performance parameters for highly-focused electromagnetic waves," Opt. Commun. 282, 727-734 (2009).
41. J. J. Stamnes and V. Dhayalan, "Focusing of electric dipole waves," Pure Appl. Opt. 5, 195-226 (1996).
42. C. J. R. Sheppard, "Fundamentals of superresolution," Micron 38, 772 (2007).
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).
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).
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).