Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS

Тел.: +7 (495) 625-9241


Features of electromagnetic scattering by radially inhomogeneous cylinders with positive and negative refraction index


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

The problem of electromagnetic wave scattering by radially inhomogeneous circular cylinder is considered. Two modifications of the hybrid projection method corresponding to the cases of E- and H polarization are developed for its solution. The approach is based on projection matching of the fields on the boundaries of cylindrical regions, projection of the Helmholtz equations on the Fourier harmonics, and application of the one-dimensional method of finite elements in projection form to the derived ordinary differential equations for reducing the latter to algebraic systems with three-diagonal matrices. Some advantages of the proposed approach over other numerical methods are indicated and appropriate numerical results demonstrating the effectiveness of the method are presented. The scattering characteristics for the cylinders with various permittivity profiles including a cylindrical Eaton-Lippman lens, Luneberg lenses with positive and negative refraction index, and generalized Maxwell lenses with positive and negative refraction index are also presented and discussed.

  1. Samaddar S.N. Scattering of plane electromagnetic waves by radially inhomogeneous infinite cylinders // II Nuovo Cimento B. Ser. 10. 1970. V. 66. № 1. P. 33−50.
  2. Alexopoulos N.G. Scattering from inhomogeneous cylindrically symmetric lenses with a line infinity in the index of refraction // Journal of the Optical Society of America. 1972. V. 62. № 9. P. 1088−1094.
  3. Elsherbeni A.Z., Hamid M. Scattering by a cylindrical dielectric shell with inhomogeneous permittivity profile // Int. Journal of Electronics. 1985. V. 58. № 6. P. 949−962.
  4. Richmond J.H. Scattering by a dielectric cylinder of arbitrary cross section shape // IEEE Trans. Antennas Propagat. 1965. V. AP-13. № 3. P. 334−341.
  5. Richmond J.H. TE-wave scattering by a dielectric cylinder of arbitrary cross section shape // IEEE Trans. Antennas Propagat. 1966. V. AP-14. № 4. P. 460−464.
  6. Peterson A.F., Klock P.W. An improved MFIE formulation for TE-wave scattering from lossy, inhomogeneous dielectric cylinders // IEEE Trans. Antennas Propagat. 1988. V. 36. № 1. P. 45−49.
  7. Chang S., Mei K.K. Application of the unimoment method to electromagnetic scattering of dielectric cylinders // IEEE Trans. Antennas Propagat. 1976. V. 24. № 1. P. 35−42.
  8. Jin J., Liepa V.V. Application of hybrid finite element method to electromagnetic scattering from coated cylinders // IEEE Trans. Antennas Propagat. 1988. V. 36. № 1. P. 50−54.
  9. Peterson A.F., Castillo S.P. A frequency-domain differential equation formulation for electromagnetic scattering from inhomogeneous cylinders // IEEE Trans. Antennas Propagat. 1989. V. 37. № 5. P. 601−607.
  10. Jankovic D., LaBelle M., Chang D.C., Dunn J.M., Booton R.C. A hybrid method for the solution of scattering from inhomogeneous dielectric cylinders of arbitrary shape // IEEE Trans. Antennas Propagat. 1994. V. 42. № 9. P. 1215−222.
  11. Rusch W.V.T., Yeh C. Scattering by an infinite cylinder coated with an inhomogeneous and anisotropic plasma sheath // IEEE Trans. Antennas Propagat. 1967. V. 15. № 3. P. 452−457.
  12. Il’inskij A.S., Nekrasov L.M. Chislenny’j metod resheniya zadachi difrakczii na neodnorodnom die’lektricheskom czilindre i ego obosnovanie // Zhurnal vy’chislitel’noj matematiki i matematicheskoj fiziki. 1995. T. 35. № 1. S. 53−70.
  13. Swathi P.S., Tong T.W., Cunnington G.R. Scattering of electromagnetic waves by cylinders with a radially-inhomogeneous layer // J. Quant. Spectrosc. Radiat. Transfer. 1991. V. 46. № 1. P. 281−292.
  14. Kai L., D’Alessio A. Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves // Applied Optics. 1995. V. 34. № 24. P. 5520−5530.
  15. Kotlyar V.V., Lichmanov M.A. Difrakcziya ploskoj e’lektromagnitnoj volny’ na gradientnom die’lektricheskom czilindre // Komp’yuternaya optika. 2003. № 25. S. 11−15.
  16. Gabdullina A.R., Smol’nikova O.N., Skobelev S.P. Modifikacziya gibridnogo proekczionnogo metoda dlya analiza e’lektromagnitnogo rasseyaniya na radial’no neodnorodnoj die’lektricheskoj sfere // Radiotexnika. 2016. № 10. S. 70−79.
  17. Skobelev S.P., Yaparova A.A. Gibridny’j proekczionny’j metod analiza volnovodny’x reshetok s vy’stupayushhimi die’lektricheskimi e’lementami. Dvumerny’e zadachi // Radiotexnika i e’lektronika. 2007. T. 52. № 3. S. 311−321.
  18. Balanis C.A. Advanced engineering electromagnetics. N.Y.: Wiley. 1989.
  19. Peterson A.F. A comparison of integral, differential and hybrid methods for TE-wave scattering from inhomogeneous dielectric cylinders // Journal of Electromagnetic Waves and Applications. 1989. V. 3. № 2. P. 87−106.
  20. Boren K., Xafmen D. Pogloshhenie i rasseyanie sveta maly’mi chasticzami. M.: Mir. 1986.
  21. Nikol’skij V.V. E’lektrodinamika i rasprostranenie radiovoln. M.: Nauka. 1988.
  22. Eaton J.E. On spherically symmetric lenses // IRE Trans. Antennas Propagat. 1952. V. 4. № 1. P. 66−71.
  23. Kornblit S. SVCh optika. Opticheskie princzipy’ v prilozhenii k konstruirovaniyu SVCh antenn. M.: Svyaz’. 1980.
  24. Gutman A.S. Modified Luneberg lens // Journal of Applied Physics. 1954. V. 25. № 7. P. 855−859.
  25. Minano J.C., et al. Design of spherical symmetric gradient index lenses // Proc. SPIE 8485. Nonimaging Optics: Efficient Design for Illumination and Solar Concentration IX, 848508 (11 October 2012). doi:10.1117/12.931505.
  26. Minano J.C. Perfect imaging in a homogeneous three-dimensional region // Optics Express. 2006. V. 14. № 21. P. 9627−9635.
June 24, 2020
May 29, 2020

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio