OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 10 — May. 9, 2011
  • pp: 9157–9171

On focused fields with maximum electric field components and images of electric dipoles

R. de Bruin, H. P. Urbach, and S. F. Pereira  »View Author Affiliations


Optics Express, Vol. 19, Issue 10, pp. 9157-9171 (2011)
http://dx.doi.org/10.1364/OE.19.009157


View Full Text Article

Enhanced HTML    Acrobat PDF (1081 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We study focused fields which, for a given total power and a given numerical aperture, have maximum electric field amplitude in some direction in the focal point and are linearly polarized along this direction. It is shown that the optimum field is identical to the image of an electric dipole with unit magnification. In particular, the field which is the image of an electric dipole whose dipole vector is parallel to the optical axis, is identical to the field whose longitudinal component is maximum at the image point.

© 2011 OSA

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.6800) General : Theoretical physics

ToC Category:
Physical Optics

History
Original Manuscript: January 5, 2011
Revised Manuscript: March 26, 2011
Manuscript Accepted: March 28, 2011
Published: April 27, 2011

Citation
R. de Bruin, H. P. Urbach, and S. F. Pereira, "On focused fields with maximum electric field components and images of electric dipoles," Opt. Express 19, 9157-9171 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9157


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. V. S. Ignatowsky, “Diffraction by a lens having arbitrary opening,” Trans. Opt. Inst. Petrograd I, paper IV (1919), (in Russian).
  2. V. S. Ignatowsky, “Diffraction by a parabolic mirror having arbitrary opening,” Trans. Opt. Inst. Petrograd , I, paper V (1920), (in Russian).
  3. E. Wolf, “Electromagnetic diffraction in optical systems I. An integral repesentation of the image field,” Proc. R. Soc. London, Ser. A 253, 349–357 (1959). [CrossRef]
  4. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959). [CrossRef]
  5. X. S. Xie and R. C. Dunn, “Probing single molecule dynamics,” Science 265, 361–364 (1994). [CrossRef] [PubMed]
  6. L. Novotny, M. R. Beverluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001). [CrossRef] [PubMed]
  7. Q. W. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12, 3377–3382 (2004). [CrossRef] [PubMed]
  8. L. E. Helseth, “Focusing of atoms with strongly confined light potentials,” Opt. Commun. 212, 343–352 (2002). [CrossRef]
  9. M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A: Mater. Sci. Process. 86, 329–334 (2007). [CrossRef]
  10. Q. Zhan and J. Leger, “Focus Shaping using cylindrical vector beams,” Opt. Express 10, 324–331 (2002). [PubMed]
  11. J. Wang, W. Chen, and Q. Zhan, “Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation,” Opt. Express 18, 21965–21972 (2010). [CrossRef] [PubMed]
  12. N. Sanner, N. Huot, E. Audouard, C. Larat, J.-P. Huignard, and B. Loiseaux, “Programmable focal spot shaping of amplified femtosecond laser pulses,” Opt. Lett. 30, 1479–1481 (2005). [CrossRef] [PubMed]
  13. M. A. A. Neil, F. Massoumian, R. Juskaitis, and T. Wilson, “Method for the generation of arbitrary complex vector wave fronts,” Opt. Lett. 27, 1929–1931 (2002). [CrossRef]
  14. M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21, 1948 (1996). [CrossRef] [PubMed]
  15. I. Iglesias and B. Vohnsen, “Polarization structuring for focal volume shaping in high-resolution microscopy,” Opt. Commun. 271, 40–47 (2007). [CrossRef]
  16. C. J. R. Sheppard and K. G. Larkin, “Optimal concentration of electromagnetic radiation,” J. Mod. Opt. 41, 1495–1505 (1994). [CrossRef]
  17. C. J. R. Sheppard and P. Török, “Electromagnetic field in the focal region of an electric dipole wave,” Optik 104, 175–177 (1997).
  18. A. J. E. M. Janssen, S. van Haver, J. J. M. Braat, and P. Dirksen, “Strehl ratio and optimum focus of high-numerical-aperture beams,” J. Eur. Opt. Soc. Rapid Publ. 2, 07008 (2007). [CrossRef]
  19. V. Dhayalan and J. J. Stamnes, “Focusing of mixed-dipole waves,” Pure Appl. Opt. 6, 317–345 (1997). [CrossRef]
  20. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003). [CrossRef] [PubMed]
  21. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000). [CrossRef]
  22. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “The focus of light–theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B 72, 109–113 (2001).
  23. C. J. R. Sheppard and A. Choudhurry, “Annular pupils, radial polarization and superresolution,” Appl. Opt. 43, 4322–4327 (2004). [CrossRef] [PubMed]
  24. H. P. Urbach and S. F. Pereira, “The field in focus with maximum longitudinal electric component,” Phys. Rev. Lett. 100, 1233904 (2008). [CrossRef]
  25. H. P. Urbach and S. F. Pereira, “Focused fields of given power with maximum electric field components,” Phys. Rev. A 79, 013825 (2009). [CrossRef]
  26. H. P. Urbach and S. F. Pereira, “Erratum: focused fields of given power with maximum electric field components,” Phys. Rev. A 81, 059903 (2010). [CrossRef]
  27. W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12, 045707 (2010) [CrossRef]
  28. E. Wolf and Y. Li, “Conditions for the validity of the Debye integral representation of focused fields,” Opt. Commun. 39, 205–210 (1981). [CrossRef]
  29. J. J. M. Braat, S. van Haver, A. J. E. M. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” in “Progress in Optics ,” Vol. 51, E. Wolf, ed. (Elsevier B.V., 2008), chap. 6, pp. 349–468. [CrossRef]
  30. R. Aarts, J. J. M. Braat, P. Dirksen, S. van Haver, C. van Heesch, and A. Janssen, “Analytic expressions and approximations for the on-axis, aberration-free Rayleigh and Debye integral in the case of focusing fields on a circular aperture,” J. Eur. Opt. Soc. Rapid Publ. 3, 08039 (2008). [CrossRef]
  31. J. J. M. Braat, S. van Haver, A. J. E. M. Janssen, and S. F. Pereira, “Image formation in a multilayer using the extended Nijboer-Zernike theory,” J. Eur. Opt. Soc. Rapid Publ. 4, 09048 (2009). [CrossRef]
  32. L. Novotny and B. Hecht, “Principles of nano-optics,” Section 2.10.2, (Cambridge University Press, 2008).

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