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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 10 — Oct. 1, 2013
  • pp: 2029–2033

Engineering the smallest 3D symmetrical bright and dark focal spots

Svetlana N. Khonina and Ilya Golub  »View Author Affiliations

JOSA A, Vol. 30, Issue 10, pp. 2029-2033 (2013)

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A simple roadmap is established for the construction of the smallest three-dimensional (3D) isotropic focal spots. It is achieved in a 4Pi configuration by imposing a restriction/condition of equal transverse and longitudinal spot sizes to determine the position of an annular aperture and then optimize its size. The calculations were performed for cylindrically symmetric radial, azimuthal, and circular polarizations for the cases of in-phase and out-of-phase counter-propagating beams as well as when a vortex was added to the beams. A diffraction-limited bright 3D isotropic spot containing solely longitudinal or transverse electric field components is obtained, while the 3D dark spot can be formed from one of two complementary combinations, each containing both transverse and longitudinal field components.

© 2013 Optical Society of America

OCIS Codes
(100.6640) Image processing : Superresolution
(180.0180) Microscopy : Microscopy
(260.1960) Physical optics : Diffraction theory
(260.5430) Physical optics : Polarization

ToC Category:
Physical Optics

Original Manuscript: July 31, 2013
Manuscript Accepted: August 22, 2013
Published: September 18, 2013

Svetlana N. Khonina and Ilya Golub, "Engineering the smallest 3D symmetrical bright and dark focal spots," J. Opt. Soc. Am. A 30, 2029-2033 (2013)

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  1. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009). [CrossRef]
  2. N. Bokor, N. Davidson, “4π focusing with single parabolic mirror,” Opt. Commun. 281, 5499–5503 (2008). [CrossRef]
  3. W. Chen, Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265, 411–417 (2006). [CrossRef]
  4. N. Bokor, N. Davidson, “A three dimensional dark focal spot uniformly surrounded by light,” Opt. Commun. 279, 229–234 (2007). [CrossRef]
  5. Y. Kozawa, S. Sato, “Dark spot formation by vector beams,” Opt. Lett. 33, 2326–2328 (2008). [CrossRef]
  6. X. L. Wang, J. Ding, J. Q. Qin, J. Chen, Y. X. Fan, H. T. Wang, “Configurable three-dimensional optical cage generated from cylindrical beams,” Opt. Commun. 282, 3421–3425 (2009). [CrossRef]
  7. N. Bokor, N. Davidson, “Toward a spherical spot distribution with 4π focusing of radially polarized light,” Opt. Lett. 29, 1968–1970 (2004). [CrossRef]
  8. N. Bokor, N. Davidson, “Generation of a hollow dark spherical spot by 4π focusing of a radially polarized Laguerre–Gaussian beam,” Opt. Lett. 31, 149–151 (2006). [CrossRef]
  9. Z. Chen, D. Zhao, “4Pi focusing of spatially modulated radially polarized vortex beams,” Opt. Lett. 37, 1286–1288 (2012). [CrossRef]
  10. S. Quabis, R. Dorn, M. Eberler, O. Glockl, G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000). [CrossRef]
  11. W. Chen, Q. Zhan, “Creating a spherical focal spot with spatially modulated radial polarization in 4Pi microscopy,” Opt. Lett. 34, 2444–2446 (2009). [CrossRef]
  12. W. Chen, Q. Zhan, “Three dimensional polarization control in 4Pi microscopy,” Opt. Commun. 284, 52–56 (2011). [CrossRef]
  13. J. Wang, W. Chen, Q. Zhan, “Creation of uniform three-dimensional optical chain through tight focusing of space-variant polarized beams,” J. Opt. 14, 055004 (2012). [CrossRef]
  14. E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet, A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010). [CrossRef]
  15. M. Jang, A. Sentenac, C. Yang, “Optical phase conjugation (OPC)-assisted isotropic focusing,” Opt. Express 21, 8781–8792 (2013). [CrossRef]
  16. M. C. Lang, T. Staudt, J. Engelhardt, S. W. Hell, “4Pi microscopy with negligible sidelobes,” New J. Phys. 10, 043041 (2008). [CrossRef]
  17. V. Kalosha, I. Golub, “Toward the subdiffraction focusing limit of optical superresolution,” Opt. Lett. 32, 3540–3542 (2007). [CrossRef]
  18. S. N. Khonina, I. Golub, “Optimization of focusing of linearly polarized light,” Opt. Lett. 36, 352–354 (2011). [CrossRef]
  19. S. N. Khonina, I. Golub, “Enlightening darkness to diffraction limit and beyond: comparison and optimization of different polarizations for dark spot generation,” J. Opt. Soc. Am. A 29, 1470–1474 (2012). [CrossRef]
  20. T. Grosjean, D. Courjon, “Photopolymers as vectorial sensors of the electric field,” Opt. Express 14, 2203–2210 (2006). [CrossRef]
  21. T. Grosjean, D. Courjon, C. Bainier, “Smallest lithographic marks generated by optical focusing systems,” Opt. Lett. 32, 976–978 (2007). [CrossRef]
  22. S. N. Khonina, I. Golub, “How low can STED go? Comparison of different write-erase beam combinations for stimulated emission depletion microscopy,” J. Opt. Soc. Am. A 29, 2242–2246 (2012). [CrossRef]
  23. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the aplanatic system,” Proc. R. Soc. Lond. Ser. A 253, 358–379 (1959). [CrossRef]
  24. M. Dyba, S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88, 163901 (2002). [CrossRef]
  25. J. Bewersdorf, A. Egner, S. W. Hell, Handbook of Biological Confocal Microscopy (Springer, 2006), p. 561.
  26. T. G. Kolda, M. R. Lewis, V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Review 45, 385–482 (2003). [CrossRef]

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