Optimization of binary doe for formation of the “light bottle”
D.G. Kachalov, K.A. Gamazkov, V.S. Pavelyev, S.N. Khonina

Image Processing Systems Institute, Russian Academy of Sciences,

Samara State Aerospace University

Full text of article: Russian language.

Abstract:
The numerical procedure for optimization of binary diffractive optical elements forming light distribution “light bottle” is developed and investigated. The developed numerical procedure is based on modification of well-known genetic algorithm. The results of numerical experiments are presented.

Key words:
genetic algorithm, light bottle, binary diffractive optical elements.

References:

  1. Ozeri, R. Long spin relaxation times in a single-beam blue-detuned optical trap / R. Ozeri, L. Khaykovich, N. Davidson // Phys. Rev. A. – 1999. – Vol. 59(3). – P. R1750– R1753.
  2. Arlt, J. Generation of beamwith a dark focus surrounded by regions of higher intensity: the optical bottle beam // Opt. Lett. – 2000. – Vol. 25(4). – P. 191–193.
  3. Yelin, D. Generating an adjustable three-dimensional dark focus / D. Yelin, B. E. Bouma, G. J. Tearney // Opt. Lett. – 2004. – Vol. 29(7). – P. 661–663.
  4. Ashkin, A. Observation of a single-beam gradient force optical trap for dielectric particles / A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chuk //. Opt. Lett. – 1986. – Vol 11(5). – P. 288–290.
  5. Soifer, V.A. Optical manipulation of microobjects: achievements and new abilities which allows diffractive optics / V.A. Soifer, V.V. Kotlyar, S.N. Khonina // Physics of elementary particles and atomic nucleus. – 2004. – Vol. 35(6). – P. 1368-1432 (in Russian).
  6. Gahagan, K. T. Optical vortex trapping of particles / K. T. Gahagan, G. A. Swartzlander // Opt. Letters. – 1996. – Vol. 21(11). – P. 827-829.
  7. Kuga, T. Novel optical trap of atoms with a doughnut beam / T. Kuga, Y. Torii, N. Shiokawa, T. Hirano Y. Shimizu, H. Sasada // Phys. Rev. Lett. – 1997. – Vol. 78. – P. 4713-4716.
  8. Manek, I. Generation of a hollow laser beam for atom trapping using an axicon / I. Manek, Yu. B. Ovchinnikov, R. Grimm // Opt. Comm. – 1998. – Vol. 147. – P. 67-70.
  9. Khonina, S.N. Rotation of microparticles with Bessel beams generated by diffractive elements / S.N. Khonina, V.V. Kotlyar, R.V. Skidanov, V.A. Soifer, K. Jefimovs, J. Simonen, J. Turunen // Journal of Modern Optics. – 2004. – Vol. 51(14). – P. 2167–2184.
  10. Soifer, V.A. Rotation of microparticles in light fields / V.A. Soifer, V.V. Kotlyar, S.N Khonina., R.V. Skidanov // Computer Optics. – 2008. – N 28. –  P. 5-17(in Russian).
  11. Khonina, S.N. The phase rotor filter / S.N. Khonina, V.V. Kotlyar, M.V. Shinkaryev, V.A. Soifer, G.V. Uspleniev // J. Modern Optics. – 1992. Vol. 39(5). – P. 1147-1154.
  12. Kotlyar, V.V. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate / V.V. Kotlyar, A.A. Almazov, S. N. Khonina, V.A. Soifer, H. Elfstrom, J. Turunen // J. Opt. Soc. Am. A. – 2005. – Vol. 22(5). – P. 849-861.
  13. Kotlyar, V.V. Diffraction of a plane, finite-radius wave by a spiral phase plate / V.V. Kotlyar, S.N. Khonina, A.A. Kovalev, V.A. Soifer, H. Elfstrom, J. Turunen // Opt. Lett. – 2006. – Vol. 31. – P. 1597-1599.
  14. Tsai, H.-Y. Fabrication of spiral-phase diffractive elements using scanning-electron-beam lithography / H.-Y. Tsai, H. I. Smith, and R. Menon, J. Vac. // Sci. Technol. B. – 2007. – Vol. 25. – P. 2068–2071.
  15. Balalaev, S.A. Investigation of possibility to form hypergeometric laser beams by methods of diffractive optics / S.A. Balalaev, S.N. Khonina, R.V.Skidanov// Izvest. SNC RAS. – 2008. – Vol. 10. – ¹ 3. – P. 694-706 (in Russian).
  16. Khonina, S.N. DOE-generated laser beams with given orbital angular moment: application for micromanipulation// Proc. SPIE Int. Soc. Opt. Eng. – 2005. – Vol. 5962. – P. 59622W.
  17. Skidanov, R.V. Experimental investigation of dielectric spheres moving in light beams with high angle harmonics /R.V. Skidanov, S.N. Khonina, V.V, Kotlyar, V.A. Soifer //Computer Optics. – 2007. – V. 31. – ¹ 1. – P. 14-21.
  18. de Angelis, M. Axially symmetric hollow beams using refractive conical lenses / M. de Angelis, L. Cacciapuoti, G. Pierattini, and G. M. Tino // Opt. Lasers Eng. – 2003. – Vol. 39. – P. 283–291.
  19. Wei, M.-D Adjustable generation of bottle and hollow beams using an axicon / M.-D. Wei, W.-L. Shiao, and Y.-T. Lin // Opt. Commun. – 2005. – Vol. 248. - P. 7–14.
  20. Zeng, X. The analytical description and experiments of the optical bottle generated by an axicon and a lens / X. Zeng and F. Wu // J. Mod. Opt. – 2008. – Vol. 55. – P. 3071–3081.
  21. Methods for Computer Design of Diffractive Optical Elements, ed. Victor A. Soifer – John Wiley & Sons, Inc., New York, 2002. – 765 p.
  22. Doskolovich, L.L. Comparative analysis of analytic and iterative methods for solution of task of focusing into line segment/ L.L. Doskolovich, N.L. Kazanskiy, V.A. Soifer, S.I. Kharitonov// Copmuter Optics. 1993. – ¹ 13. – P.16-29 (in Russian).
  23. Doskolovich, L.L. Comparative analysis of dif­ferent focusators into seg­ment / L.L. Doskolovich, N.L. Kazanskiy, V.A. Soifer // Optics and Laser Technology. – 1995. – Vol.27. – ¹ 4. – P. 207-213.
  24. Doskolovich, L.L. Analysis of quasiperiodic and geometric optical solutions of the prob­lem of focusing into an axial seg­ment / L.L. Doskolovich, N.L. Kazanskiy, V.A. Soifer, A.Ye. Tzaregorodtzev // Optik. – 1995. – Vol.101. – ¹ 2. – P. 37-41.
  25. Doskolovich, L.L. Analysis of quasiperiodic and geometric optical solutions of the axial segment focusing problem / L.L. Doskilovich, N.L. Kazanskiy, V.A. Soifer // Computer Optics. –  1996. – N. 16. – P. 4-8 (in Russian).
  26. Kotlyar, V.V. An algorithm for the generation of laser beams with longitudinal periodicity: rotating images / V.V. Kotlyar, S.N. Khonina, V.A. Soifer // Journal of Modern Optics. – 1997. – Vol. 44. – N. 7. – P. 1409-1416.
  27. Chavez-Cerda, S. Interference of traveling nondiffracting beams / S. Chavez-Cerda, M. A. Meneses-Nava, and J. Miguel Hickmann // Opt. Lett. – 1998. – Vol. 23. – P. 1871–1873.
  28. Golub, Ì.À. Computational experiment with plane optical elements/ M.A. Golub, N.L. Kazanskiy, I.N. Sissakian, V.A. Soifer// Avtometria. – 1988. – ¹ 1. – P. 70-82 (in Russian).
  29. Golub, M.A. Mathematical model of irradiation focusing by elements of computer optics/ M.A. Golub, N.L. Kazanskiy, V.A. Soifer // Nauchnoe priborostroeniye. – 1993. – V.3, – ¹ 1. – P. 9-23 (In Russian).
  30. Kharitonov, S.I. Asymptotic method of field calculation for zone-structured optical elements/ S.I. Kharitonov, L.L. Doskolovich, N.L. Kazanskiy, M.L. Kalyaev// Computer optics. – 2007. – V. 31. – ¹ 4. – P. 7-18 (in Russian).
  31. Martínez-Corral, M. Tailoring the axial shape of the point spread function using the Toraldo concept / M. Martínez-Corral, M. T. Caballero, E. H. K. Stelzer and J. Swoger // Optics Express. – 2002. – Vol. 10(1). –  P. 98-103.
  32. Chen, W. Three-dimensional focus shaping with cylindrical vector beams / W. Chen and Q. Zhan // Opt. Commun. – 2006. – Vol. 265. – P. 411–417.
  33. Menon, R. Design of diffractive lenses that generate optical nulls without phase singularities / R. Menon, P. Rogge, H.-Y. Tsai // J. Opt. Soc. Am. A – 2009. – Vol. 26(2). – P. 297-304.
  34. Osipov, V.P. Realization of binary radial diffractive optical elements by two-photon polymerization technique / V.P. Osipov, V.S. Pavelyev, D.G. Kachalov, A. Zukauskas, B.N. Chichkov // Opt. Exp. – 2010. – Vol. 18(25) – P. 25808-25814.
  35. Kachalov, D. G. Application of the direct search in solving a problem of forming longitudinal distribution of intensity / D. G. Kachalov, V. S. Pavelyev, S. N. Khonina, R. V. Skidanov, O. Yu Moiseev // J. Mod. Opt. – 2011. – Vol 58. – No 1. – P. 69 - 76.
  36. Golub M.A. Computer generated diffractive multi-focal lens / M.A. Golub, L.L. Doskolovich, N.L. Kazanskiy, S.L. Kharitonov, V.A. Soifer // Journal of Modern Op­tics. – 1992. – Vol.39(6). – P.1245-1251.
  37. Doskolovich, L.L.  Design of two-order focusators/ L.L. Doskolovich, N.L. Kazanskiy, V.A. Soifer // Avtometria. – 1993, – ¹ 1. – P.58-63 (in Russian).
  38. Soifer, V.A. Multifocal diffractive ele­ments / V.A. Soifer, L.L. Doskolovich, N.L. Kazanskiy // Optical Engi­neering. – 1994. – Vol.33(11). – P.3610-3615.
  39. Doskolovich, L.L. Design of diffractive optical elements for focusing into axial radial focal domains / L.L. Doskolovich, N.L. Kazanskiy, V.S. Pavelyev, V.A. Soifer //Avtometria. – 1995, ¹ 1. – P.114-119 (in Russian).
  40. Doskolovich, L.L. Design of binary diffractive optical elements for focusing into pregiven two-dimensional domain/ L.L. Doskolovich, N.L. Kazanskiy, V.A. Soifer// Avtometria. – 1995, ¹ 5. – P.42-50 (in Russian).
  41. Soifer, V.A. Synthesis of a Binary DOE Focusing into an Arbitrary Curve, Using the Electromagnetic Approximation / V.A.  Soifer, N.L. Kazanskiy, S.I. Kharitonov // Optics and Lasers in Engineering. – 1998. – Vol.29(4-5). – P. 237-247.
  42. Kotlyar, V.V. Iterative calculation of diffractive optical elements focusing into a three dimensional domain and the surface of the body of rotation / V.V. Kotlyar, S.N. Khonina, V.A. Soifer // J. Modern Optics. – 1996. – Vol. 43(7). – P. 1509-1524.
  43. Doskolovich, L.L. A method for estimating the DOE's energy efficiency / L.L. Doskolovich, N.L. Kazanskiy, S.I. Khari­tonov, A. Ye. Tzaregorodzev // Optics and Laser Technology. - 1995. - Vol.27(4). - P.219-221.
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