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Radiophysics and Quantum Electronics

, Volume 61, Issue 7, pp 516–527 | Cite as

Scattering of a Plane Electromagnetic Wave by a Multilayer Spherical Lens

  • P. O. Afanasyev
  • A. A. Akopov
  • A.M. Lehrer
  • M.B. Manuilov
Article
  • 12 Downloads

We propose an analytical solution of the problem of diffraction of a plane electromagnetic wave by a multilayer dielectric (including plasmon) sphere. The solution is obtained using the method of separation of variables. New efficient recurrence relationships are obtained for calculations of the fields in layers, as well as formulas for the fields in the near and far diffraction zones. The novelty of the proposed solution is connected with the way of representing its radial part in the form of normalized functions. It is shown that as the number of the lens layers, which approximate the smooth profile of dielectric permittivity, grows, the electric field at the focusing point increases and reaches the maximum value. This allows one to determine the minimum required number of layers in practical problems. Resonance properties of metal-dielectric nanoparticles are studied in the optical band.

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References

  1. 1.
    P.O. Afanasyev, M. B. Manuilov, S. M. Matytsin, and V. A. Sledkov, Antenny, 3, 16 (2015).Google Scholar
  2. 2.
    A. I. Skorodumov, Multichannel antenna systems for new-generation mobile communication with optimal space frequency filtering [in Russian]: Doct. Sci. Theses, Moscow Aviation Inst. (State Techn. Univ.), Moscow (2010).Google Scholar
  3. 3.
    V. A.Kaloshin, in: 13th Intern. Crimean Conf. “Microwave Engineering and Telecommunication Technologies” (KryMiCo-2003), September 18–12, 2003, Sevastopol, Ukraine, p. 387.Google Scholar
  4. 4.
    R.A. Shore, IEEE Antennas and Propag. Magazine, 57, No. 6, 69 (2015).ADSCrossRefGoogle Scholar
  5. 5.
    S.P. Morgan, IRE Transactions Antennas Propag., 7, No. 4, 342 (1959).ADSCrossRefGoogle Scholar
  6. 6.
    V. A.Kaloshin, Radiotekh. Élektron., 1, 26 (1973).Google Scholar
  7. 7.
    V. A.Kaloshin and A. S.Venetsky, in: 7th Intern. Conf. Mathematical Methods in Electromagnetic Theory (MMET), 2–5 June 1998, Kharkov, Ukraine, p. 157.Google Scholar
  8. 8.
    J. R. Sanford, Spherically stratified microwave lenses: Ph.D. Thesis, Ecole Polytechnique Federale de Lausanne, Lausanne, 1992.Google Scholar
  9. 9.
    J. A. Lock, J. Opt. Soc. America A, 25, No. 12, 2971 (2008).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    E. Braun, IRE Transactions on Antennas and Propagation, 4, No. 2, 132 (1956).ADSCrossRefGoogle Scholar
  11. 11.
    T. A. Rhys, IEEE Transactions on Antennas Propagat., 18, No. 4, 497 (1970).ADSCrossRefGoogle Scholar
  12. 12.
    E. G. Zelkin and R.A. Petrova, Lens Antennas [in Russian], Sov. Radio, Moscow (1974).Google Scholar
  13. 13.
    A. S.Venetsky and V.A.Kaloshin, Zhurn. Radio´elektron., 5, Art. no. 3 (2008).Google Scholar
  14. 14.
    B. Schoenlinner, X.Wu, J. P.Ebling, et al., IEEE Trans. Microwave Theory and Techniques, 50, No. 9, 2166 (2002).ADSCrossRefGoogle Scholar
  15. 15.
    C. A. Fernandes, IEEE Antennas and Propagation Magazine, 41, No. 5, 141 (1999).ADSCrossRefGoogle Scholar
  16. 16.
    W. C. Chew, Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York (1990).Google Scholar
  17. 17.
    N. A. Logan, Proc. IEEE, 53, No. 8, 773 (1965).CrossRefGoogle Scholar
  18. 18.
    M. Born and E.Wolf, Principles of Optics, Cambridge Univ. Press (1999).Google Scholar
  19. 19.
    G. Mie, Annalen der Physik, 330, No. 3, 377 (1908).ADSCrossRefGoogle Scholar
  20. 20.
    W. Hergert and T.Wriedt, The Mie Theory: Basics and Applications. Springer Series in Optical Sciences. Springer, Berlin (2012).Google Scholar
  21. 21.
    P. Debye, Annalen der Physik, 335, No. 11, 57 (1909).ADSCrossRefGoogle Scholar
  22. 22.
    A. L. Aden and M.Kerker, J. Appl. Phys., 22, No. 10, 1242 (1951).Google Scholar
  23. 23.
    J.R.Wait, Applied Scientific Research B, 10, No. 5–6, 441 (1962).Google Scholar
  24. 24.
    Z. S.Wu and Y. P.Wang, Radio Science, 26, No. 6, 1393 (1991).Google Scholar
  25. 25.
    J.A. Stratton, Electromagnetic Theory, McGraw-Hill, New York (1941).zbMATHGoogle Scholar
  26. 26.
    R. F. Harrington, Time-harmonic electromagnetic fields, McGraw-Hill, New York (1961).Google Scholar
  27. 27.
    J. Mikulski and E. L.Murphy, IEEE Trans. Anten. Propag., 11, No. 2, 169 (1963).Google Scholar
  28. 28.
    H. Mieras, IEEE Trans. Anten. Propag., 30, No. 6, 1221 (1982).ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    S. Vinogradov, E. Vinogradova, and P. Smith, in: Intern. Conf. Electromagnetics in Advanced Applications, September, 15–17, 1999, Torino, Italy, p. 277.Google Scholar
  30. 30.
    L.-W. Li, P.-S.Kooi, M.-S. Leong, et al., IEEE Trans. Microwave Theory and Techniques, 42, No. 12, 2302 (1994).Google Scholar
  31. 31.
    E. V.Komarova, Antenna and Diffraction Properties of the Multilayer Luneberg Lens [in Russian]. Cand. Tech. Sci. Theses, Urals Federal Univ., Ekaterinburg (2012).Google Scholar
  32. 32.
    J. R. Sanford, IEEE Trans. Anten. Propag., 42, No. 5, 690 (1994).ADSCrossRefGoogle Scholar
  33. 33.
    B.Fuchs, S.Palud, L. Le Coq, et al., IEEE Trans. Anten. Propag., 56, No. 2, 450 (2008).Google Scholar
  34. 34.
    S. Rondineau, A. I.Nosich, D. Jean-Pierre, et al., IEEE Trans. Anten. Propag., 52, No. 5, 1270 (2004).Google Scholar
  35. 35.
    V. V. Akhiyarov, Zhurn. Radio´elektron., 12, Art. no. 13 (2015).Google Scholar
  36. 36.
    A. Lerer, I. Donets, and S. Bryzgalo, J. Electromagnetic Waves and Applications, 10, No. 6, 765 (1996).CrossRefGoogle Scholar
  37. 37.
    G. Godi, R. Sauleau, and D.Thouroude, IEEE Trans. Anten. Propag., 53, No. 4, 1278 (2005).Google Scholar
  38. 38.
    A. D. Greenwood and J.-M. Jin, IEEE Trans. Anten. Propag., 47, No. 8, 1260 (1999).ADSCrossRefGoogle Scholar
  39. 39.
    D.P. Zoric, D. I. Olcan, and B.M.Kolundzija, in: 2012 Intern. Symposium on Antennas and Propag. (ISAP), October 29–November 2, 2012, Nagoya, Japan, p. 918.Google Scholar
  40. 40.
    Z. Sipus, N.Burum, and J.Bartolic, Microwave and Optic. Techn. Lett., 36, No. 4, 276 (2003).Google Scholar
  41. 41.
    V. V.Klimov, Nanoplasmonics [in Russian], Fizmatlit, Moscow (2009).Google Scholar
  42. 42.
    S.Peng, J.M.McMahon, G.C. Schatz, et al., Proc. Nath. Acad. Sci. USA, 107, No. 33, 14530 (2010).Google Scholar
  43. 43.
    P.K. Jain, K. S. Lee, I. H. el-Sayed, and M. A. el-Sayed, J. Phys. Chem. B, 110, 7238 (2006).Google Scholar
  44. 44.
  45. 45.
  46. 46.
    B.Fuchs, L. le Coq, O. Lafond, and S.Rondineau, IEEE Trans. Anten. Propag., 55, No. 2, 283 (2007).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • P. O. Afanasyev
    • 1
  • A. A. Akopov
    • 2
  • A.M. Lehrer
    • 2
  • M.B. Manuilov
    • 3
  1. 1.National University of IrelandMaynoothIreland
  2. 2.Rostov-on-Don Research Institute of RadiocommunicationsRostov-on-DonRussia
  3. 3.Southern Federal UniversityRostov-on-DonRussia

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