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Focal-plane field when lighting double-ring phase elements
Ustinov A.V.

Image Processing Systems Institute оf RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Samara, Russia,
Samara National Research University, Samara, Russia

 PDF 234 kB

DOI: 10.18287/2412-6179-2017-41-4-515-520

Pages: 515-520.

The focal-plane field amplitude is calculated when lighting double-ring phase elements by flat and Gaussian beams. Emerging conditions in the minimum or maximum centers, including flat-top maxima, are given. For the field amplitude, we obtain equations that define the radius of the first zero-intensity ring based on the deduced expressions. The root values are listed for several parameters of optical elements and incident beams due to the lack of analytical solutions. Numerical simulation results are given for flat incident beams; they are fully consistent with the theoretical calculations.

phase optical elements, double-ring phase elements, focal spot size.

Ustinov AV. Focal-plane field when lighting double-ring phase elements. Computer Optics 2017; 41(4): 515-520. DOI: 10.18287/2412-6179-2017-41-4-


  1. Khonina SN, Kotlyar VV, Skidanov RV, Soifer VA. Leveling the focal spot intensity of the focused Gaussian beam. J Mod Opt 2000; 47(5): 883-904. DOI: 10.1080/09500340008235098.
  2. Veldkamp WB. Laser beam profile shaping with interlaced binary diffraction gratings. Appl Opt 1982; 21(17): 3209-3212. DOI: 10.1364/AO.21.003209.
  3. Han C-Y, Ishii Y, Murata K. Reshaping collimated laser beams with Gaussian profile to uniform profiles. Appl Opt 1983; 22(22): 3644-3647. DOI: 10.1364/AO.22.003644.
  4. Cordingley J. Application of a binary diffractive optics for beam shaping a semiconductor processing by lasers. Appl Opt 1993; 32(14): 2538-2542. DOI: 10.1364/AO.32.002538.
  5. Passilly N, Fromager M, Mechin L, Gunther C, Eimer S, Mohammed-Brahim T, Ait-Ameur K. 1-D laser beam shaping using an adjustable binary diffractive optical element. Opt Commun 2004; 241(4-6): 465-473. DOI: 10.1016/j.optcom.2004.07.036.
  6. Novotny L, Sánchez EJ, Xie XS. Near-field imaging using metal tips illuminated by higher-order Hermite-Gaussian beams. Ultramicroscopy 1998; 71(1-4): 21-29. DOI: 10.1016/S0304-3991(97)00077-6.
  7. Khonina SN, Golub I. Optimization of focusing of linearly polarized light. Optics Letters 2011; 36(3): 352-354. DOI: 10.1364/OL.36.000352.
  8. Khonina SN, Nesterenko DV, Morozov AA, Skidanov RV, Soifer VA. Narrowing of a light spot at diffraction of linearly-polarized beam on binary asymmetric axicons. Optical Memory and Neural Networks (Information Optics), Allerton Press 2012; 21(1): 17-26. DOI: 10.3103/S1060992X12010043
  9. Khonina SN. Simple phase optical elements for narrowing of a focal spot in high-numerical-aperture conditions. Optical Engineering 2013; 52(9): 091711. DOI: 10.1117/1.OE.52.9.091711.
  10. Khonina SN, Alferov SV, Karpeev SV. Strengthening the longitudinal component of the sharply focused electric field by means of higher-order laser beams. Optics Letters 2013; 38(17): 3223-3226. DOI: 10.1364/OL.38.003223.
  11. Alferov SV, Khonina SN, Karpeev SV. Study of polarization properties of fiber-optics probes with use of a binary phase plate. J Opt Soc Am A 2014; 31(4): 802-807. DOI: 10.1364/JOSAA.31.000802.
  12. Bokor N, Davidson N. Tight parabolic dark spot with high numerical aperture focusing with a circular p phase plate. Opt Commun 2007; 270(2): 145-150. DOI: 10.1016/j.opt­com.2006.09.022.
  13. Helseth LE. Mesoscopic orbitals in strongly focused light. Opt Commun 2003; 224(4-6): 255-261. DOI: 10.1016/j.opt­com.2003.07.017.
  14. Jabbour TG, Kuebler SM. Vector diffraction analysis of high numerical aperture focused beams modified by two- and three-zone annular multi-phase plates. Opt Express 2006; 14(3): 1033-1043. DOI: 10.1364/OE.14.001033.
  15. Gao X, Wang J, Gu H, Xu W. Focusing properties of concentric piecewise cylindrical vector beam. Optik 2007; 118(6): 257-265. DOI: 10.1016/j.ijleo.2006.10.006.
  16. Xu Q, Chen J. The creation of double tight focus by a concentric multi-belt pure phase filter. Opt Commun 2012; 285(7): 1642-1645. DOI: 10.1016/j.optcom.2011.11.116.
  17. Khonina SN, Ustinov AV. Sharper focal spot for a radially polarized beam using ring aperture with phase jump. Journal of Engineering 2013; 2013: 512971. DOI: 10.1155/2013/512971.
  18. Khonina SN, Savelyev DA, Ustinov AV. Diffraction of laser beam on a two-zone cylindrical microelement. Computer Optics 2013; 37(2): 160-169.
  19. Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and Series. Volume 2: Special Functions. Amsterdam: Gordon and Breach Science Publishers; 1983. ISBN: 2-88124-097-6.

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