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Journal of Radio Electronics Online scientific journal · eISSN 1684-1719
2006, № 6 · ELECTRODYNAMICS

Numerical Analysis of Waveguides and Waveguide Elements in EBG Structures

S.E. Bankov1, M.D. Duplenkova1

1 Kotelnikov IRE RAS, Moscow, Russia
Full text EDN KUIBMD

Abstract

This paper presents an efficient technique for analysis of waveguides, resonators and waveguide discontinuities in two-dimensional electromagnetic bandgap (EBG) structures. Waveguides and resonators formed by elements removed from EBG array are considered. The technique includes the following key steps. The first step is a solution of problem of electromagnetic (EM) field scattering on a single element of array. Scattered field is presented as a finite series of cylindrical harmonics with coefficients depending on incident field. The second step is an introduction of a compensating source (CS) and excitation of a homogeneous EBG structure by the source. CS produces EM field in the same form of sum of cylindrical harmonics but with fixed coefficients. The last third step is analysis of EM field in waveguide or resonance structure inside EBG array. Elements forming the structure are not removed from array but instead of it CSs with unknown coefficients are placed in the elements. These coefficients are defined under condition that total field produced by the element (scattered field plus field induced by a CS) is equal to zero that is equivalent to removal of the element from array. These conditions formulated for all of removed elements give one a system of linear algebraic equations (SLAE) relatively mentioned coefficients that is simply solved numerically or analytically. Resonator, infinite waveguide, waveguide with lumped discontinuity and waveguide bends are considered in the paper.

For citation

Bankov S.E., Duplenkova M.D. Numerical Analysis of Waveguides and Waveguide Elements in EBG Structures // Journal of Radio Electronics. – 2006. – No. 6.

References

  1. Y. Rahmat-Samii and H. Mosallaei, Electromagnetic bandgap structures: Classification, characterization and applications, in Proc. 11th Int. Conf. Antennas and Propagation, Manchester, U.K., Apr. 17-20, 2001, p.p. 560-564.
  2. T.K. Wu, Frequency Selective Surface and Grid Array. New York: Wiley, 1995.
  3. B.A. Munk, Frequency Selective Surfaces: Theory and Design. New York, Wiley, 2000.
  4. J.D. Joannopopoulus, R.D. Meade and J.N. Winn, Photonic Crystals: Molding the Flow of Light. Princeton, NJ: Princeton Univ. Press, 1995.
  5. O. Painter, R.K. Lee, A. Scherer, A. Yariv, J.D. OBrien, P.D. Dapkus and I. Kim, Two-dimensional photonic bandgap defect mode laser, Science, vol. 284, p.p. 1819-1821, June 1999.
  6. A. Mekis, J.C. Chen, I. Kurland, S. Fan, P.R. Villeneuve, and J.D. Joannopopoulus, High transmission through sharp bends in photonic crystal waveguides, Phys. Rev. Lett., vol. 77, no. 18, pp. 3787-3790.
  7. H. Mosallaei and Y. Rahmat-Samii, Periodic bandgap and effective dielectric materials in electromagnetics, IEEE Trans. Antennas Propagat., vol. 51, 549-563, March, 2003.
  8. S. Datta, C.T. Chan, K.M. Ho and C.M. Soukoulis, Effective dielectric constant of periodic composite structures, Phys. Rev. B, Condens. Matter, vol. 48, no. 20, pp. 14936-14943, Nov. 1993.
  9. Bankov S.E. Waveguide and waveguide components based on sparse photonic crystals. Journal of Communications Technology and Electronics, Vol. 49, No. 11, 2004, pp. 1208-1217.
  10. Bankov S.E. Waveguide bends based on sparse two dimensional photonic crystals. Journal of Communications Technology and Electronics, Vol. 50, No. 1, 2005, pp. 23-30.
  11. Nielsen N., Hadbuch der Theorie der Cylinderfunktionen, Leipzig, 1904.
  12. A. Papoulis. The Fourier Integral and Its Applications. New York: Mc-Graw-Hill, 1962.