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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 7 — Jul. 1, 2014
  • pp: 1657–1665

Nonparaxial propagation and focusing properties of azimuthal-variant vector fields diffracted by an annular aperture

Bing Gu, Danfeng Xu, Yang Pan, and Yiping Cui  »View Author Affiliations

JOSA A, Vol. 31, Issue 7, pp. 1657-1665 (2014)

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Based on the vectorial Rayleigh–Sommerfeld integrals, the analytical expressions for azimuthal-variant vector fields diffracted by an annular aperture are presented. This helps us to investigate the propagation behaviors and the focusing properties of apertured azimuthal-variant vector fields under nonparaxial and paraxial approximations. The diffraction by a circular aperture, a circular disk, or propagation in free space can be treated as special cases of this general result. Simulation results show that the transverse intensity, longitudinal intensity, and far-field divergence angle of nonparaxially apertured azimuthal-variant vector fields depend strongly on the azimuthal index, the outer truncation parameter and the inner truncation parameter of the annular aperture, as well as the ratio of the waist width to the wavelength. Moreover, the multiple-ring-structured intensity pattern of the focused azimuthal-variant vector field, which originates from the diffraction effect caused by an annular aperture, is experimentally demonstrated.

© 2014 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(260.1960) Physical optics : Diffraction theory
(260.5430) Physical optics : Polarization
(350.5500) Other areas of optics : Propagation

ToC Category:
Diffraction and Gratings

Original Manuscript: April 8, 2014
Manuscript Accepted: June 2, 2014
Published: June 30, 2014

Bing Gu, Danfeng Xu, Yang Pan, and Yiping Cui, "Nonparaxial propagation and focusing properties of azimuthal-variant vector fields diffracted by an annular aperture," J. Opt. Soc. Am. A 31, 1657-1665 (2014)

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  1. C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrafast pulses,” Phys. Rev. Lett. 106, 123901 (2011). [CrossRef]
  2. C. Min, Z. Shen, J. Shen, Y. Zhang, H. Fang, G. Yuan, L. Du, S. Zhu, T. Lei, and X. Yuan, “Focused plasmonic trapping of metallic particles,” Nat. Commun. 4, 3891 (2013). [CrossRef]
  3. G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12, 3207–3212 (2012). [CrossRef]
  4. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002). [CrossRef]
  5. X. L. Wang, J. P. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32, 3549–3551 (2007). [CrossRef]
  6. Z. Y. Rong, Y. J. Han, S. Z. Wang, and C. S. Guo, “Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators,” Opt. Express 22, 1636–1644 (2014). [CrossRef]
  7. M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012). [CrossRef]
  8. K. Ding, L. Yin, M. T. Hill, Z. Liu, P. J. van Veldhoven, and C. Z. Ning, “An electrical injection metallic cavity nanolaser with azimuthal polarization,” Appl. Phys. Lett. 102, 041110 (2013). [CrossRef]
  9. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18, 8790–8799 (2010). [CrossRef]
  10. L. Pan and D. B. Bogy, “Data storage: heat-assisted magnetic recording,” Nat. Photonics 3, 189–190 (2009). [CrossRef]
  11. Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. D. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447, 1098–1101 (2007). [CrossRef]
  12. J. Li, Y. Chen, and Q. Cao, “Analytical vectorial structure of Bessel-Gauss beam in the near field,” Opt. Laser Technol. 45, 734–747 (2013). [CrossRef]
  13. B. Lü and K. Duan, “Nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture,” Opt. Lett. 28, 2440–2442 (2003). [CrossRef]
  14. X. Jia, Y. Wang, and B. Li, “Nonparaxial analyses of radially polarized beams diffracted at a circular aperture,” Opt. Express 18, 7064–7075 (2010). [CrossRef]
  15. X. Jia and Y. Wang, “Vectorial structure of far field of cylindrically polarized beams diffracted at a circular aperture,” Opt. Lett. 36, 295–297 (2011). [CrossRef]
  16. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003). [CrossRef]
  17. Y. Yang, X. Li, and K. Duan, “Nonparaxial propagation of vectorial hollow Gaussian beams diffracted at an annular aperture,” Opt. Eng. 50, 078001 (2011). [CrossRef]
  18. J. L. Chen, “Nonparaxial propagation of a radially polarized beam diffracted by an annular aperture,” Chin. Phys. Lett. 28, 124202 (2011). [CrossRef]
  19. R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, 1966).
  20. V. V. Kotlyar and A. A. Kovalev, “Nonparaxial propagation of a Gaussian optical vortex with initial radial polarization,” J. Opt. Soc. Am. A 27, 372–380 (2010). [CrossRef]
  21. B. Gu and Y. Cui, “Nonparaxial and paraxial focusing of azimuthal-variant vector beams,” Opt. Express 20, 17684–17694 (2012). [CrossRef]
  22. K. Duan and B. Lü, “Vectorial nonparaxial propagation equation of elliptical Gaussian beams in the presence of a rectangular aperture,” J. Opt. Soc. Am. A 21, 1613–1620 (2004). [CrossRef]
  23. P. Liu, B. Lü, and K. Duan, “Propagation of vectorial nonparaxial Gaussian beams through an annular aperture,” Opt. Laser Technol. 38, 133–137 (2006). [CrossRef]

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