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

Diffraction of a conical wave and a Gaussian beam by a spiral phase plate

V.V. Kotlyar1,2 A.A. Kovalev1,2 S.N. Khonina1,2 R.V. Skidanov1,2 V.A. Soifer1,2 J. Turunen3
1Image Processing Systems Institute of RAS 

2Samara State Aerospace University named after academician S.P. Korolev 

3University of Joensuu, Finland 


 PDF, 853 kB

Pages: 29-36.

Abstract:
An analytical expression is obtained for the diffraction in the far zone of a conical wave on a spiral phase plate (SPP) with an arbitrary integer order of singularity n. Diffraction of a conical wave by an SPP is equivalent to the diffraction of a plane wave on a screw axicon. The diffraction of a conical wave and a Gaussian beam by an SPP is compared analytically. It is shown that in both cases a light ring is formed and the intensity function for small values of the radial variable ρ increases in proportion ρ2n, and for large ρ decreases as n2ρ-4. A 32-level second-order SPP with a diameter of 5 mm was made by way of direct recording with an electron beam on a resist. Using this SPP, a beam of a helium-neon laser was converted into a beam with a phase singularity and an annular intensity distribution.

Keywords:
Gaussian beam, conical wave, spiral phase plate, axicon, diffraction of a conical wave, helium-neon laser

Citation:
Kotlyar VV, Kovalev AA, Khonina SN, Skidanov RV, Soifer VA, Turunen J. Diffraction of a conical wave and a Gaussian beam by a spiral phase plate. Computer Optics 2005; 28: 29-36.

References:
  1. Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and series. Volume 2: Special functions. Amsterdam: Gordon and Breach Science Publishers; 1998. 
  2. Alonzo CA, Rodrigo PJ, Gluckstad J. Helico-conical optical beams: a product of helical and conical phase fronts. Opt Expr 2005; 13(5): 1749-1760. 
  3. Cheong WG, Lee WM, 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. 
  4. Furhapter S, Jesacher A, Bernet S, Ritsch-Marte M. Spiral phase contrast imaging in microscopy. Opt Express 2005; 13(3): 689-694. 
  5. Ganic D, Gan X, Gu M. Focusing of doughnut laser beams by a high numerical-aperture objective in free space. Opt Express 2003; 11(21): 2747-2752. 
  6. Khonina SN, Kotlyar VV, Shinkaryev MV, Soifer VA, Uspleniev GV. The rotor phase filter. J Mod Opt 1992; 39(5): 1147-1154. DOI: 10.1080/09500349214551151. 
  7. Khonina SN, Kotlyar VV, Skidanov RV, Soifer VA, Jefimos K, Simonen J, Turunen J. Rotation of microparticles with Bessel beams generated by diffractive elements. J Mod Opt 2004; 51(14): 2167-2184. DOI: 10.1080/09500340408232521. 
  8. 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. 
  9. Koltyar 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. 
  10. Lee WM, Ahluwalia BPS, Yuan X-C, Cheong WC, Dholakia K. Optical steering of high and low index microparticles by manipulating an off-axis optical vortex. J Opt A Pure Appl Opt 2005; 7: 1-6. 
  11. Niv A, Biener G, Kleiner V, Hasman E. Spiral phase elements obtained by use of discrete space-variant subwavelength gratings. Opt Commun 2005; 251: 306-314. 
  12. Oemrawsingh SSR, van Houwelinger JAW, Eliel ER, Woerdman JR, Vestegen EJK, Kloosterboer JG, Hooft GW. Production and characterization of spiral phase plates for optical wavelengths. Appl Opt 2004; 43(3): 688-694. 
  13. Paterson C, Smith R. Higher-order Bessel waves produced by axicon-type computer-generated holograms. Opt Commun 1996; 124: 123-130. 
  14. Saks ZS, Rozes D, Swatzlander GA. Holographic formation of optical-vortex filaments. J Opt Soc Am B 1998; 15: 2226-2234. 
  15. Sueda K, Miyaji G, Miyanaga N, Nakatsura M. Laguerre-Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses. Opt Expr 2004; 12(15): 3548-3553. 
  16. Sundbeck S, Gruzberg I, Grier DG. Structure and scalling of helical modes of light. Opt Lett 2005; 30(5): 1-13.

© 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