Metal-Clad Multilayer Waveguide: Circle-Chain Convergent Method and Two Perturbation Methods


Computer modeling studies for the calculation of the propagation constants and attenuation coefficients of TE mode in an asymmetric metal/ dielectric/dielectric layers structure are presented. Two different perturbation methods, circle chain convergent method and Downhill method are used. The last two methods can be used easily for the waveguides consist of any number of layers with complex refractive index due to gain and loss. The developed programs were run on a personal computer and numerical results are presented.

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  1. 1.

    S. X. She, Metal-Clad Multilayer Dielectric Waveguide: Accurate Perturbation Analysis, J. Opt. Soc. Amer. A, vol. 7, no. 9, pp. 1582–1590, 1990.

    Google Scholar 

  2. 2.

    S.X. She, Characteristics Analysis of Metal-Clad and Absorptive Dielectric Waveguides by a Simple and Accurate Perturbation Method, Opt. Quantum Electron., vol. 23, pp. 1045–1054, 1991.

    Google Scholar 

  3. 3.

    L. Sun and M.E. Marhic, Numerical Study of Attenuation in Multilayer Infrared Waveguides by The Circle-Chain Convergent Method, J. Opt. Soc. Amer. A, vol. 8, pp. 478–483, 1991.

    Google Scholar 

  4. 4.

    H. Bach, On The Downhill Method, Commun. Ass, Comput., Mach., vol. 12, pp. 675–677, 1969.

    Google Scholar 

  5. 5.

    K.H. Schlereth and M. Tacke, The Complex propagation Constant of Multilayer Waveguides: An Algorithm for a Personal Computer, IEEE Jornal of Quantum Electron., vol. 26, no. 4, pp. 627–630, 1990.

    Google Scholar 

  6. 6.

    L.V. Ahlfore, Complex Analysis, 2nd ed. McGraw-Hill, New York, 1966.

    Google Scholar 

  7. 7.

    R.V. Churchill and J.W. Brown, Complex Variable and Applications, McGraw-Hill, New York, 1984.

    Google Scholar 

  8. 8.

    C. Ma and S. Liu, Optical Characteristics Analysis and TE Mode Selection for Asymmetric Metal-Clad Waveguide, Opt. Quantum Electron., vol. 20, pp. 323–328, 1988.

    Google Scholar 

  9. 9.

    NAG FORTRAN Library Manual Mark 6, Numerical Algorithm Group, Downers, Group, III, 1977.

  10. 10.

    IMSL Library Reference Manual, 7th ed. International Mathematical Libraries, Houston, Tex, 1979.

  11. 11.

    F. Tokdemir, Programing with Fortran 77, Middle East Technical University, 1990.

  12. 12.

    MINPACK Documenucation Applide Mathematical Division Argonne National Library, Argonne, III, 1979.

  13. 13.

    S. D. Cont, and C. D. Boor, Elementary Numerical Analysis, McGraw-HILL kogakusha, Ltd, 1972.

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Shabat, M.M., Abd-El naby, M.A., Barakat, N.M. et al. Metal-Clad Multilayer Waveguide: Circle-Chain Convergent Method and Two Perturbation Methods. International Journal of Infrared and Millimeter Waves 20, 1425–1440 (1999).

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  • Attenuation
  • Refractive Index
  • Computer Modeling
  • Personal Computer
  • Layer Structure