(30) * << * >> * Russian * English * Content * All Issues

Diffraction of a Gaussian beam on a spiral axicon
V.V. Kotlyar1, A.A. Kovalev2, D. Kodzhek3, V. Garbini3, E. Ferrari1, 3

1Image Processing Systems Institute оf the RAS,
2Samara State Aerospace University (SSAU)
3Laboratory for Interdisciplinary Lithography, Trieste, Italy

 PDF, 187 kB

Pages: 30-35.

Full text of article: Russian language.

Abstract:
The study develops analytical relations that describe the Fresnel and Fraunhofer diffractions of a Gaussian beam on a spiral axicon (SA). The expressions are derived in the form of series of hypergeometric functions. The expression for the SA turns into the expression for a spiral phase plate (SPP) if the axicon parameter is set to zero. The functionality of such optical elements is verified both by numerical simulation and physical experiments using a spatial light modulator.

Keywords:
Gaussian Beam, Axicon, spiral axicon, Fraunhofer diffraction, spiral phase plate.

Citation:
Kotlyar VV, Kovalev AA, Kodzhek D, Garbini V, Ferrari E. Diffraction of a Gaussian Beam on a Spiral Axicon. Computer Optics 2006; 30: 30-35.

Acknowledgements:
This work was supported by the Russian-American program “Basic Research and Higher Education” (grant CRDF REC SA-014-02), as well as by the grant of the RFBR 05-08-50298.

References:
  1. Khonina SN, Kotlyar VV, Soifer VA, Shinkaryev MV, Uspleniev GV. Trochoson. Opt Commun 1992; 91(3-4): 158-162. DOI: 10.1016/0030-4018(92)90430-Y.
  2. Khonina SN, Kotlyar VV, Shinkarev MV, Soifer VA, Uspleniev GV. The phase rotor filter. J Mod Opt 1992; 39(5): 1147-1154. DOI: 10.1080/09500349214551151.
  3. Fürhapter S, Jesacher A, Bernet S, Ritsch-Marte M. Spiral interferometry. Opt Lett 2006; 30(15): 1953-1955. DOI: 10.1364/OL.30.001953.
  4. Bernet S, Jesacher A, Fürhapter S, Maurer C, Ritsch-Marte M. Quantitative imaging of complex samples by spiral phase contrast microscopy. Opt Express 2006; 14(9): 3792-3805. DOI: 10.1364/OE.14.003792.
  5. Foo G, Palecios DM, Swartzlander GA. Optical vortex coronograph. Opt Lett 2005; 30(24): 3308-3310. DOI: 10.1364/OL.30.003308.
  6. Curtis JE, Grier DG. Structure of optical vortices. Phys Rev Lett 2003; 90(13): 133901. DOI: 10.1103/PhysRevLett.90.133901.
  7. Lin J, Yuan X, Tao SH, Burge RE. Synthesis of multiple collinear helical modes generated by a phase-only element. J Opt Soc Am A 2006; 23(5): 1214-1218. DOI: 10.1364/JOSAA.23.001214.
  8. Hakola A, Shevchenko A, Buchter SC, Kaivola M, Tabiryan NV. Creation of a narrow Bessel-like laser beam using a nematic liquid crystal. J Opt Soc Am B 2006; 23(4): 637-641. DOI: 10.1364/JOSAB.23.000637.
  9. Chakraborty R, Ghosh A. Generation of an elliptic Bessel beam. Opt Lett 2006; 31(1): 38-40. DOI: 10.1364/OL.31.000038.
  10. Bentley JB, Davis JA, Bandres MA, Gutiérrez-Vega JC. Generation of helical Ince-Gaussian beams with a liquid-crystal display. Opt Lett 2006; 31(5): 649-651. DOI: 10.1364/OL.31.000649.
  11. Fatemi FK, Bashkansky M. Generation of hollow beams by using a binary spatial light modulator. Opt Lett 2006; 31(7): 864-866. DOI: 10.1364/OL.31.000864.
  12. Whyte G, Courtial J. Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm. New J Phys 2005; 7(1): 117. DOI: 10.1088/1367-2630/7/1/117.
  13. Wang Q, Sun XW, Shum P, Yin XJ. Dynamic switching of optical vortices with dynamic gamma-correction liquid-crystal spiral phase plate. Opt Express 2005; 13(25): 10285-10291. DOI: 10.1364/OPEX.13.010285.
  14. Lin J, Yuan X, Tao SH, Peng X, Nin HB. Deterministic approach to the generation of modified helical beams for optical manipulation. Opt Express 2005; 13(10): 3862-3867.
  15. Hahn J, Kim H, Choi K, Lee B. Real-time digital holographic beam-shaping system with a genetic feedback tuning loop. Appl Opt 2006; 45(5): 915-924. DOI: 10.1364/AO.45.000915.
  16. Courtial J, Whyte G, Bouchel Z, Wagner J. Iterative algorithm for holographic shaping of non-diffracting and self-imaging light beams. Opt Express 2006; 14(6): 2108-2116. DOI: 10.1364/OE.14.002108.
  17. Cojoc D, Di Fabrizio E, Businaro L, Carbini S, Romanato F, Vaccari L, Altissimo M. Design and fabrication of diffractive optical elements for optical tweezer arrays by means of e-beam lithography. Microelectron Eng 2002; 61-62: 963-969. DOI: 10.1016/S0167-9317(02)00426-4.
  18. Kotlyar VV, Almazov AA, Khonina SN, Soifer VA, Elfstrom H, Turunen J. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate. J Opt Soc Am A 2005; 22(5): 849-861. DOI: 10.1364/JOSAA.22.000849.
  19. Kotlyar VV, Khonina SN, Kovalev AA, Soifer VA, Elfstrom H, Turunen J. Diffraction of a plane, finite-radius wave by a spiral phase plate. Opt Lett 2006; 31(11): 1597-1599. DOI: 10.1364/OL.31.001597.
  20. Kotlyar VV, Kovalev AA, Khonina SN, Skidanov RV, Soifer VA, Elfstrom H, Tossavainen N, Turunen J. Diffraction of conic and Gaussian beams by a spiral phase plate. Appl Opt 2006; 45(12): 2656-2665.DOI: 10.1364/AO.45.002656.
  21. Ahluwalia BPS, Cheong WC, Yuan X-C, Zhang L-S, Tao S-H, Bu J, Wang H. Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids. Opt Lett 2006; 31(7): 987-989. DOI: 10.1364/OL.31.000987.
  22. Rozas D, Law CT, Swartzlander GA. Propagation dynamics of optical vortices. J Opt Soc Am B 1997; 14(11): 3054-3065. DOI: 10.1364/JOSAB.14.003054.
  23. Dennis MR. Rows of optical vortices from elliptically perturbing a high-order beam. Opt Lett 2006; 31(9): 1325-1327. DOI: 10.1364/OL.31.001325.
  24. Swartzlander GA. Broadband nulling of a vortex phase mask. Opt Lett 2005; 30(21): 2876-2878. DOI: 10.1364/OL.30.002876.
  25. Cheong WC, Lee W, Yuan X-C, Zhang L-S, Dholakia K, Wang H. Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation. Appl Phys Lett 2004; 85(23): 5784-5786. DOI: 10.1063/1.1830678.
  26. Polin M, Ladavac K, Lee S, Roichman Y, Gviev DG. Optimized holographic optical traps. Opt Express 2005; 13(15): 5831-5845. DOI: 10.1364/OPEX.13.005831.
  27. Prudnikov AP, Brichkov YA, Marichev OI. Integrals and series. Volume 2: Special functions. CRC Press; 1986. ISBN: 978-2-88124-090-4.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20