Integral representations for solutions of maxwell's equations for anisotropic media
V.V. Kotlyar
, S.S. Stafeev, R.V. Skidanov, A.G. Nalimov, O.Y. Moiseev, S.D. Poletaev

Image Processing Systems Institute of the RAS,
Samara State Aerospace University

Full text of article: Russian language.

Abstract:
We investigated binary axicons with periods 4 um, 6 um and 8 um, manufactured by photolithography technology with resolution 1 mm, depth 500 nm and diameter 4 mm. It is shown experimentally that in the near diffraction zone along the optical axis at a distance of up to 40 um from the axicon appear focal spot with a diameter of 3,5λ up to 4,5λ (for the axicon with a period T=4 um) and from 5λ to 8λ (for the axicon with a period T=8 um), λ - wavelength of light (λ=0.532 um). First focus arises at a distance of 2 um (T=4 um), and focal spots appear with a period of 2 um (for T=4 um) and 4 um (for T=8 um). We produced simulation of diffraction of plane and diverging linearly polarized light waves with the program FullWAVE (RSoft) and the original program R-FDTD, that implement finite difference methods for 3D solution of Maxwell's equations in Cartesian and cylindrical coordinate systems. Numerical values of the diameters of focal spots on the optical axis in the near diffraction zone for the axicon with a period T=4 um agree with experimental data.

Key words: binary microaxicon, diameter of the axial beam, FDTD-method, optical experiment..

References:

  1. Kim, J.K. Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens / J.K. Kim, J.Kim, Y.Jung, W.Ha, Y.S.Jeong, S.Lee, A.Tunnermann, K.Oh // Opt.Lett. – 2009. – V.34, -. 19. – P.2973-2975.
  2. Kurt, H. Limited-diffraction light propagation with axicon-shape photonic crystal / H. Kurt // J. Opt. Soc. Am. B. – 2009. – Vol. 26. - 5. – P. 981-986
  3. Chen, W. Realization of an evanescent Bessel beam via surface Plasmon interference exited by a radially polarized beam / W. Chen, Q.Zhan // Opt. Lett. – 2009. – V. 34. -. 6. – P.722-724.
  4. Watanabe, K. Localized surface plasmon microscope with an illumination system employing a radially polarized zeros-order Bessel beam / K.Watanabe, G. Terakedo, H.Kano // Opt.Lett. – 2009. – vol.34, no.8. – p.1180-1182.
  5. Fu,Y. Hybrid Au-Ag subwavelength metallic structures with variant periods for superfocusing / Y.Fu, W.Zhan // J. Nanophotonics. – 2009. – V.3. – P. 033504.
  6. Fu, Y. Experimental study of plasmonic structures with variant periods for sub-wavelength focusing: analysis of characterization errors / Y. Fu, R.G. Mote, Q.Wang, W.Zhou // J. Mod. Opt. – 2009. – V.56, -.14. – P.1550-1556.
  7. Wei, P. Focusing subwavelength light by using nanoholes in a transparent thin film / P.Wei, W.Chang, K.Lee, E.Lin // Opt. Lett. – 2009. – V.34, -. 12. – P.1867-1869.
  8. Schonbrun, E. Scanning microscory using a short-focal-length Fresnel zone plate / E. Schonbrun, W.N.Ye, E.B.Crozier // Opt. Lett. – 2009. – V.34, -.4. – P.228-2230.
  9. Vahimaa, P. Electromagnetic analysis of nonparaxial Bessel beams generated by diffractive axicon / P.Vahimaa, V. Kettunen, M.Knittinm, J.Turunen // J.Opt.Soc.Am. A. – 1997. – V.4, -. 8. – P. 1817-1824.
  10. Kizuka, T. Characteristics of a laser beam spot focused by a binary diffractive axicon / T. Kizuka, M. Yamanchi, Y.Matsuoka // Opt.Eng. – 2008. – V.45. - 5. – P.053401.
  11. Prudnikov, A.P. Integrals and Series. Special functions / A.P. Prudnikov, Y.A. Brychkov, O.I. Marichev. -.: Science, 1983. – (in Russian)
  12. Snyder, A. Optical waveguide theory / A. Snyder, J. Love. - .: Radio and Communications, 1987. – (in Russian)
    13.Osterberg H. Closed solutions of Rayleigh’s diffraction integral for axial points / H. Osterberg, L.Smith // J.Opt.Soc.Am. – 1961. – V.51. – P.1050-1054.
  13. Kotlyar, V.V. Sharp focusing of radially polarized light with microlenses / V.V. Kotlyar, A.A. Kovalev, S.S. Stafeev // Computer Optics. – 2008. – V.32, -. 2. – P.155-167. – ISSN 0134-2452. – (in Russian).

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