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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 2, Iss. 8 — Aug. 10, 2007

Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate

Victor V. Kotlyar, Alexey A. Kovalev, Roman V. Skidanov, Oleg Yu. Moiseev, and Victor A. Soifer  »View Author Affiliations


JOSA A, Vol. 24, Issue 7, pp. 1955-1964 (2007)
http://dx.doi.org/10.1364/JOSAA.24.001955


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Abstract

We derive what we believe to be new analytical relations to describe the Fraunhofer diffraction of the finite-radius plane wave by a helical axicon (HA) and a spiral phase plate (SPP). The solutions are deduced in the form of a series of the Bessel functions for the HA and a finite sum of the Bessel functions for the SPP. The solution for the HA changes to that for the SPP if the axicon parameter is set equal to zero. We also derive what we believe to be new analytical relations to describe the Fresnel and Fraunhofer diffraction of the Gaussian beam by a HA are derived. The solutions are deduced in the form of a series of the hypergeometric functions. We have fabricated by photolithography a binary diffractive optical element (a HA with number n = 10 ) able to produce in the focal plane of a spherical lens an optical vortex, which was then used to perform rotation of several polystyrene beads of diameter 5 μ m .

© 2007 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(140.7010) Lasers and laser optics : Laser trapping

ToC Category:
Diffraction and Gratings

History
Original Manuscript: November 15, 2006
Manuscript Accepted: December 30, 2006
Published: June 13, 2007

Virtual Issues
Vol. 2, Iss. 8 Virtual Journal for Biomedical Optics

Citation
Victor V. Kotlyar, Alexey A. Kovalev, Roman V. Skidanov, Oleg Yu. Moiseev, and Victor A. Soifer, "Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate," J. Opt. Soc. Am. A 24, 1955-1964 (2007)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-24-7-1955


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References

  1. S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. V. Shinkaryev, and G. V. Uspleniev, "Trochoson," Opt. Commun. 91, 158-162 (1992). [CrossRef]
  2. S. N. Khonina, V. V. Kotlyar, M. V. Shinkarev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992). [CrossRef]
  3. J. A. Davis, E. McNamara, D. M. Cottrell, and J. Campos, "Image processing with the radial Hilbert transform: theory and experiments," Opt. Lett. 25, 99-101 (2000). [CrossRef]
  4. C. Guo, Y. Han, J. Xu, and J. Ding, "Radial Hilbert transform with Laguerre-Gaussian spatial filters," Opt. Lett. 31, 1394-1396 (2006). [CrossRef] [PubMed]
  5. S. Furhapter, A. Jesacher, S. Beraet, and M. Ritsch-Marte, "Spiral interferometry," Opt. Lett. 30, 1953-1955 (2005). [CrossRef] [PubMed]
  6. S. Bernet, A. Jesacher, S. Furhapter, C. Maurer, and M. Ritsch-Marte, "Quantitative imaging of complex samples by spiral phase contrast microscopy," Opt. Express 14, 3792-3805 (2006). [CrossRef] [PubMed]
  7. I. G. Foo, D. M. Palecios, and G. A. Swartzlander, "Optical vortex coronograph," Opt. Lett. 30, 3308-3310 (2005). [CrossRef]
  8. J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 1.33901-1-3 (2003). [CrossRef]
  9. J. Lin, X. Yuan, S. H. Tao, and R. E. Burge, "Synthesis of multiple collinear helical modes generated by a phase-only element," J. Opt. Soc. Am. A 23, 1214-1218 (2006). [CrossRef]
  10. J. A. Davis, J. Guertin, and D. M. Cottrell, "Diffraction-free beam generated with programmable spatial light modulators," Appl. Opt. 32, 6368-6370 (1993). [CrossRef] [PubMed]
  11. J. A. Davis, E. Carcole, and D. M. Cottrell, "Intensity and phase measurements of nondiffracting beams generated with the magneto-optic spatial light modulator," Appl. Opt. 35, 593-598 (1996). [CrossRef] [PubMed]
  12. J. A. Davis, E. Carcole, and D. M. Cottrell, "Nondiffracting interference patterns generated with programmable spatial light modulators," Appl. Opt. 35, 599-602 (1996). [CrossRef] [PubMed]
  13. N. Chattrapiban, E. A. Rogers, D. Cofield, W. T. Hill, and R. Roy, "Generation of nondiffracting Bessel beams by use of a spatial light modulator," Opt. Lett. 28, 2183-2185 (2003). [CrossRef] [PubMed]
  14. A. Hakola, A. Shevchenko, S. C. Buchter, M. Kaivola, and N. V. Tabiryan, "Creation of a narrow Bessel-like laser beam using a nematic liquid crystal," J. Opt. Soc. Am. B 23, 637-641 (2006). [CrossRef]
  15. R. Chakraborty and A. Ghosh, "Generation of an elliptic Bessel beam," Opt. Lett. 31, 38-40 (2006). [CrossRef] [PubMed]
  16. J. B. Bentley, J. A. Davis, M. A. Bandres, and J. C. Gutiérrez-Vega, "Generation of helical Ince-Gaussian beams with a liquid-crystal display," Opt. Lett. 31, 649-651 (2006). [CrossRef] [PubMed]
  17. F. K. Fatemi and M. Bashkansky, "Generation of hollow beams by using a binary spatial light modulator," Opt. Lett. 31, 864-866 (2006). [CrossRef] [PubMed]
  18. V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, J. Turunen, "Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate," J. Opt. Soc. Am. A 22, 849-861 (2005). [CrossRef]
  19. V. V. Kotlyar, S. N. Khonina, A. A. Kovalev, V. A. Soifer, H. Elfstrom, and J. Turunen, "Diffraction of a plane, finite-radius wave by a spiral phase plate," Opt. Lett. 31, 1597-1599 (2006). [CrossRef] [PubMed]
  20. V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, "Diffraction of conic and Gaussian beams by a spiral phase plate," Appl. Opt. 45, 2656-2665 (2006). [CrossRef] [PubMed]
  21. B. P. S. Ahluwalia, W. C. Cheong, X.-C. Yuan, L.-S. Zhang, S.-H. Tao, J. Bu, and H. Wang, "Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids," Opt. Lett. 31, 987-989 (2006). [CrossRef] [PubMed]
  22. D. Rozas, C. T. Law, and G. A. Swartzlander, "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3065 (1997). [CrossRef]
  23. M. R. Dennis, "Rows of optical vortices from elliptically perturbing a high-order beam," Opt. Lett. 31, 1325-1327 (2006). [CrossRef] [PubMed]
  24. D. Ling, J. Li, and J. Chen, "Analysis of eigenfields in the axicon-based Bessel-Gauss resonator by the transfer-matrix method," J. Opt. Soc. Am. A 23, 912-918 (2006). [CrossRef]
  25. W. C. Cheong, W. M. Lee, X.-C. Yuan, L.-S. Zhang, K. Dholakia, and H. Wang, "Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation," Appl. Phys. Lett. 85, 5784-5786 (2004). [CrossRef]
  26. C. Guo, X. Liu, X. Ren, and H. Wang, "Optimal annular computer-generated holograms for the generation of optical vortices," J. Opt. Soc. Am. A 22, 385-390 (2005). [CrossRef]
  27. J. Lin, X. Yuan, S. H. Tao, and R. E. Burge, "Variable-radius focused optical vortex with suppressed sidelobes," Opt. Lett. 31, 1600-1602 (2006). [CrossRef] [PubMed]
  28. J. Courtial, G. Whyte, Z. Bouchel, and J. Wagner, "Iterative algorithm for holographic shaping of non-diffracting and self-imaging light beams," Opt. Express 14, 2108-2116 (2006). [CrossRef] [PubMed]
  29. G. Whyte and J. Courtial, "Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm," New J. Phys. 7, 1-12 (2005). [CrossRef]
  30. Q. Wang, X. W. Sun, P. Shum, and X. J. Yin, "Dynamic switching of optical vortices with dynamic gamma-correction liquid-crystal spiral phase plate," Opt. Express 13, 10285-10291 (2005). [CrossRef] [PubMed]
  31. J. Lin, X. Yuan, S. H. Tao, X. Peng, and H. B. Nin, "Deterministic approach to the generation of modified helical beams for optical manipulation," Opt. Express 13, 3862-3867 (2005). [CrossRef] [PubMed]
  32. J. Hahn, H. Kim, K. Choi, and B. Lee, "Real-time digital holographic beam-shaping system with a genetic feedback tuning loop," Appl. Opt. 45, 915-924 (2006). [CrossRef] [PubMed]
  33. D. Cojoc, E. Di Fabrizio, L. Businaro, S. Carbini, F. Romanato, L. Vaccari, and M. Altissimo, "Design and fabrication of diffractive optical elements for optical tweezer arrays by means of e-beam lithography," Microelectron. Eng. 61-62, 963-969 (2002). [CrossRef]
  34. G. A. Swartzlander, "Broadband nulling of a vortex phase mask," Opt. Lett. 30, 2876-2878 (2005). [CrossRef] [PubMed]
  35. A. P. Prudnikov, Y. A. Brichkov, and O. I. Marichev, Integrals and Series. Special Functions (Nauka, 1983).
  36. V.A.Soifer, ed., Method for Computer Design of Diffractive Optical Elements (Wiley, 2002).

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