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A modification of the hybrid projection method for analysis of electromagnetic scattering by radially inhomogeneous dielectric sphere


A.R. Gabdullina – Student, Moscow Institute of Physics and Technology (State University) E-mail: O.N. Smolnikova – Ph. D. (Eng.), Associate Professor, Moscow Aviation Institute (National Research University); Head of Department, PJSC «Radiofizika» (Moscow) E-mail: S.P. Skobelev – Dr. Sc. (Phys.-Math.), Leading Research Scientist, PJSC «Radiofizika» (Moscow); Associate Professor, Moscow Institute of Physics and Technology (State University) E-mail:

A modification of the hybrid projection method is proposed in the paper for analysis of electromagnetic scattering by a radially inho-mogeneous dielectric sphere. The modification is based on projection matching of the fields on the boundaries of spherical regions, projection of the Maxwell equations on transverse spherical vector functions, and application of the one-dimensional method of finite elements in the projection form to the ordinary differential equations obtained as a result of projection of the Maxwell equations for reducing the differential equations to algebraic systems with three-diagonal matrices. Some advantages of the proposed modification over other numerical methods are shown and discussed. High effectiveness of the modification is shown by numerical results charac-terizing convergence of the method and by comparison of the results with the data available in the literature for some partial cases. Characteristics of plane wave scattering by a Lunegurg-like lens with simultaneously negative permittivity and permeability (a negative Luneberg lens) are obtained and compared to the appropriate characteristics corresponding a conventional Luneburg lens.


  1. Bilgin E., Yapar A. Electromagnetic scattering by radially inhomogeneous dielectric spheres // IEEE Trans. Antennas Propagat. 2015. V. 63. № 6. P. 2677−2685.
  2. Shore R.A. Scattering of an electromagnetic linearly polarized plane wave by a multilayered sphere // IEEE Antennas & Propagat. Mag. 2015. № 6. P. 69−116.
  3. Gutman A.L. Primenenie metoda poperechnykh sechenijj k resheniju zadachi o difrakcii ehlektromagnitnojj volny na neodnorodnojj sfere // Radiotekhnika i ehlektronika. 1965. T. 10. № 9. S. 1583−1593.
  4. Permjakov V.A. Difrakcija ehlektromagnitnykh voln na radialno neodnorodnykh plazmennom share i cilindre // Izvestija vuzov. Ser. Radiofizika. 1968. T. 11. № 4. S. 531−542.
  5. Stratton J.A. Electromagnetic Theory. New York: McGraw-Hill. 1941. P. 563−565.
  6. Wyatt P.J. Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects // Physical Review. 1962. V. 127. № 5. P. 1837−1843.
  7. Volakis J.L., Chatterjee A., Kempel L.C. Finite Element Method for Electromagnetics. New York: IEEE Press. 1998.
  8. Skobelev S.P. Fazirovannye antennye reshetki s sektornymi parcialnymi diagrammami napravlennosti. M.: Fizmatlit. 2010.
  9. Mikulski J.J., Murphy E.L. The computation of electromagnetic scattering from concentric spherical structures // IEEE Trans. Antennas Propagat. 1963. V. AP-11. № 2. P. 169−177.
  10. Boren K., KHafmen D. Pogloshhenie i rassejanie sveta malymi chasticami. M.: Mir. 1986.
  11. Balanis C. Advanced engineering electromagnetics. N.Y.: John Wiley & Sons. 1989.
  12. Rozenfeld P. The electromagnetic theory of three-dimensional inhomogeneous lenses // IEEE Trans. Antennas Propagat. 1976. V. AP-24. № 3. P. 365−370.
  13. Miroshnichenko A.E. Non-Rayleigh limit of the Lorenz-Mie solution and suppression of scattering by spheres of negative refractive index // Physical Review. A. 2009. V. 80. P. 02138-1-02138-6.
  14. Gutman A.S. Modified Luneberg lens // Journal of Applied Physics. 1954. V. 25. № 7. P. 855−859.


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