Calculation of diffraction of the linearly-polarized limited beam with uniform intensity on high-aperture binary micro-axicons in a near zone
S.N. Khonina, A.V. Ustinov, S.G. Volotovsky, A.A. Kovalev
Image Processing Systems Institute, Russian Academy of Sciences,
Samara State Aerospace University
Full text of article: Russian language.
Abstract:
With application of the electromagnetic theory of diffraction the opportunity of superresolution achievement by means of binary high-aperture axicons is considered at linear polarization of radiation falling on an element. It is shown, that increase of the central light spot, which inevitably arises at linear polarization of the beam illuminating the high-aperture axicon, can be compensated by means of linear phase jump in the illuminating beam or due to use of bi-axicon instead of axially-symmetric axicon. Thus in immediate proximity from an optical element surface the light spot with size on 37 % less than the diffractive limit is formed.
Key words:
binary diffractive axicon, high-aperture optical element, linear polarization, the superresolution.
References:
- McLeod, J.H. The axicon: a new type of optical element / J.H. McLeod // J. Opt. Soc. Am. – 1954. – V. 44. – P. 592-597.
- Durnin, J. Diffraction-free beams / J. Durnin, J.J. Miceli, Jr., and J.H. Eberly // Phys. Rev. Lett. – 1987. – V. 58. – P. 1499-1501.
- Turunen, J. Holographic generation of diffraction-free beams / J. Turunen, A. Vasara, and A.T. Friberg // Appl. Opt. – 1988. – V. 27. – P. 3959-3962.
- Vasara, A. Realization of general nondiffracting beams with computer-generated holograms / A. Vasara, J. Turunen, and A.T. Friberg // J. Opt. Soc. Am. A. – 1989. – V. 6. – P. 1748-1754.
- Indebetouw, G. Nondiffracting optical ?elds: some remarks on their analysis and synthesis / G. Indebetouw // J. Opt. Soc. Am. A. – 1989. – V. 6. – P. 150-152.
- 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. – V. 39(5). – P. 1147-1154.
- Jabczynski, J.K. A ‘diffraction-free’ resonator / J.K.Jabczynski // Opt. Commun. – 1990. – V. 77. – P. 292-294.
- Cox, A.J. Holographic reproduction of a diffraction-free beam / A.J. Cox and D.C. Dibble // Appl. Opt. – 1991. – V. 30. – P. 1330-1332.
- Herman, R.M Production and uses of diffractionless beams / R.M. Herman and T.A. Wiggins // J. Opt. Soc. Am. A. – 1991.– V. 8(6). – P. 932-942.
- Cox, A.J. Nondiffracting beam from a spatially ?ltered Fabry-Perot resonator / A.J. Cox and D.C. Dibble // J. Opt. Soc. Am. A. – 1992. – V. 9. – P. 282-286.
- MacDonald, R.P. Holographic formation of a diode laser nondiffracting beam / R.P. MacDonald, J. Chrostowski, S.A. Boothroyd, and B.A. Syrett // Appl. Opt. – 1993. – V. 32. – P. 6470-6474.
- Rosen, J. Pseudo-nondiffracting beams generated by radial harmonic functions / J. Rosen, B. Salik, and A. Yariv // J. Opt. Soc. Am. A. – 1995. – V. 12. – P. 2446-2457.
- Davis, J.A. Intensity and phase measurements of nondiffracting beams generated with a magneto-optic spatial light modulator / J.A. Davis, E. Carcole, and D.M. Cottrell // Appl. Opt. – 1996. – V. 35. – P. 593-598.
- Niggl, L. Properties of Bessel beams generated by periodic gratings of circular symmetry / L. Niggl, T. Lanzl, and Max Maier // J. Opt. Soc. Am. A. – 1997. – Vol. 14, No. 1. – P. 27-33.
- Paakkonen, P. Rotating optical fields: experimental demonstration with diffractive optics / P. Paakkonen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S.N. Khonina, V.V. Kotlyar, V.A. Soifer, A.T. Friberg // Journal of Modern Optics. – 1998. – V. 45(11). – P. 2355-2369.
- Tervo, J. Generation of vectorial propagation-invariant fields by polarization-grating axicons / J. Tervo, J. Turunen // Opt. Commun. – 2001. – V. 192. – P. 13–18.
- Niv, A. Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam–Berry phase optical elements / Avi Niv, Gabriel Biener, Vladimir Kleiner, and Erez Hasman // Optics Letters. – 2004. – Vol. 29, No. 3. – P. 238-240.
- Golub, I. Solid immersion axicon: maximizing nondiffracting for Bessel beam resolution / Ilya Golub // Optics Letters. – 2007. – Vol. 32, No. 15.– P. 2161-2163.
- Belyi, V.N. Generation of TE- and TH-polarized Bessel beams using one-dimensional photonic crystal / V.N. Belyi, N.S. Kazak, S.N. Kurilkina, N.A. Khilo // Optics Communications. – 2009. – V. 282. – P. 1998–2008.
- Kotlyar, V.V. Light spot diameter in the near zone of binary diffractive microaxicon / V.V. Kotlyar, S.S. Stafeev, R.V. Skidanov, A.G. Nalimov, O.Y. Moiseev, S.D. Poletaev // Computer Optics. – 2010. – V. 34, No. 1. – P. 24-34. – (in Russian).
- Vahimaa, P. Electromagnetic analysis of nonparaxial Bessel beams generated by diffractive axicons / Pasi Vahimaa, Ville Kettunen, Markku Kuittinen, and Jari Turunen, Ari T. Friberg // J. Opt. Soc. Am. A. – 1997. – Vol. 14, No. 8. – P. 1817-1824.
- Mishra, S.R. A vector wave analysis of a Bessel beam / S.R. Mishra // Opt. Commun. – 1991. – V. 85. – P. 159-161.
- Turunen, J. Electromagnetic theory of re?axicon beams / J. Turunen and A.T. Friberg // Pure Appl. Opt. – 1993. – V. 2. – P. 539-547.
- Bouchal, Z. Non-diffractive vector Bessel beams / Z. Bouchal and M. Oliv?k // J. Mod. Opt. – 1995. – V. 42. – P. 1555-1566.
- Hall, D.G. Vector-beam solutions of Maxwell’s wave equation / D.G. Hall // Opt. Lett. – 1996. – V. 21. – P. 9-11.
- Yu, Y.Z. Vector analyses of nondiffracting bessel beams / Y.Z. Yu and W.B. Dou // Progress In Electromagnetics Research Letters. – 2008. – Vol. 5. – P. 57-71.
- Borghi, R. On a class of electromagnetic diffraction-free beams / Riccardo Borghi, Franco Gori, and Sergey A. Ponomarenko // J. Opt. Soc. Am. A. – 2009. – Vol. 26, No. 11. – P. 2275-2281.
- Kalosha, V.P. Toward the subdiffraction focusing limit of optical superresolution / V.P. Kalosha and I. Golub // Opt. Lett. – 2007. – V. 32. – P. 3540-3542.
- Khonina, S.N. Frañxicon – diffractive optical element with conical focal domain / S.N. Khonina, S.G. Volotovsky // Computer Optics. – 2009. – Vol. 33, No 4. – P. 401-411. – ISSN 0134-2452. – (in Russian).
- Helseth, L.E. Roles of polarization, phase and amplitude in solid immersion lens system / L.E. Helseth // Opt. Commun. – 2001. – V. 191. – P. 161-172.
- Grosjean, T. Conical optics: the solution to con?ne light / T. Grosjean, F. Baida, and D. Courjon // Applied Optics. – 2007. – Vol. 46, No. 11. – P. 1994-2000.
- Kotlyar, V.V. Modeling sharp focus radially-polarized laser mode with conical and binary microaxicons / V.V. Kotlyar, S.S. Stafeev // Computer Optics. – 2009. – V. 33, N 1. – P. 52-60. – (in Russian).
- Khonina, S.N. Fast calculation algorithms for diffraction of radially-vortical laser fields on the microaperture / S.N. Khonina, A.V. Ustinov, S.G. Volotovsky, M.A. Ananin // Izvest. SNC RAS – 2010. – V. 12(3). – P. 15-25. – (in Russian).
- Grosjean, T. Photopolymers as vectorial sensors of the electric ?eld / T. Grosjean and D. Courjon // Opt. Express. – 2006. – Vol. 14, No. 6. – P. 2203-2210.
- Khonina, S.N. Control by contribution of components of vector electric field in focus of a high-aperture lens by means of binary phase structures / S.N. Khonina, S.G. Volotovsky // Computer Optics. – 2010. – Vol. 34, No. 1. – P. 58-68. – (in Russian).
- Khonina, S.N. Propagation of the radially-limited vortical beam in a near zone. Part I. Calculation algorithms / S.N. Khonina, A.V. Ustinov, A.A. Kovalev, S.G. Volotovsky // Computer Optics. – 2010. – Vol. 34, No. 3. – P. 317-332. – (in Russian).
- Khonina, S.N. Propagation of the radially-limited vortical beam in a near zone. Part II. Results of simulation / S.N. Khonina, A.A. Kovalev, A.V. Ustinov, S.G. Volotovsky // Computer Optics. – 2010. – Vol. 34, No. 3. – P. 332-343. – (in Russian).
- Mansuripur, M. Certain computational aspects of vector diffraction problems / M. Mansuripur // J. Opt. Soc. Am. A. – 1989. – Vol. 6, No. 5. – P. 786-805.
- Luneburg, R.K. Mathematical Theory of Optics. / R.K. Luneburg – Berkeley, California: University of California Press, 1966.
- Carter, W.H. Electromagnetic Field of a Gaussian Beam with an Elliptical Cross Section / W.H. Carter // J. Opt. Soc. Am. A. – 1972. – Vol. 62, No. 10. – P. 1195-1201.
- Deng, D. Analytical vectorial structure of radially polarized light beams / D. Deng and Q. Guo // Optics Letters. – 2007. – Vol. 32, No. 18. – P. 2711-2713.
- Pereira, S.F. Superresolution by means of polarisation, phase and amplitude pupil masks / S.F. Pereira, A.S. van de Nes // Opt. Commun. – 2004. – Vol. 234. – P.119-124.
- Zhang, Y. Vector propagation of radially polarized Gaussian beams diffracted by an axicon, / Y. Zhang, L. Wang, C. Zheng // J. Opt. Soc. Am. A. – 2005. – Vol. 22, No. 11. – P. 2542-2546.
- Jenkins, F.A. Fundamentals of Optics / F.A. Jenkins, H.E. White. – 4th edition. – NY: McGraw-Hill Book Company, 1976. – Chapter 25.
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