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Rigorous Coupled Wave Analysis of Radially and Azimuthally-Inhomogeneous, Elliptical, Cylindrical Systems

By John Jarem
Progress In Electromagnetics Research, Vol. 34, 89-115, 2001
doi:10.2528/PIER01032302

Abstract

Rigorous Coupled Wave Analysis (RCWA) (used for electromagnetic (EM) analysis of planar diffraction gratings) has been applied to solve EM scattering and diffraction problems for spatially inhomogeneous, cylindrical, elliptical systems. The RCWA algorithm and an appropriate method for matching EM boundary conditions in the elliptical system are described herein. Comparisons of the eigenfunctions determined by RCWA (found in spatially homogeneous elliptical regions) and Mathieu functions are presented and shown to agree closely with one another. Numerical results of scattering from a uniform elliptical shell system (excited by an electrical surface current) obtained by using both a Mathieu function expansion method and by using the RCWA algorithm are presented and also shown to agree closely with one another. The RCWA algorithm was used to study EM scattering and diffraction from an elliptical, azimuthally inhomogeneous dielectric permittivity, step profile system. EM field matching and power conservation were shown to hold for this step profile example. A comparison of the EM fields of the step profile elliptical shell example and that of a uniform profile elliptical shell having the same excitation and bulk material parameters (permittivity and permeability) was made and significant differences of the EM fields of the two systems were observed.

Citation

 (See works that cites this article)
John Jarem, "Rigorous Coupled Wave Analysis of Radially and Azimuthally-Inhomogeneous, Elliptical, Cylindrical Systems," Progress In Electromagnetics Research, Vol. 34, 89-115, 2001.
doi:10.2528/PIER01032302
http://jpier.org/PIER/pier.php?paper=0103232

References


    1. Bhartia, P., L. Shafai, and M. Hamid, "Scattering by an imperfectly conducting conductor with a radially inhomogeneous dielectric coating," Int. J. Electron., Vol. 31, 531-535, 1971.
    doi:10.1080/00207217108938250

    2. Kishk, A. A., R. P. Parrikar, and A. Z. Elsherbeni, "Electromagnetic scattering from an eccentric multilayered circular cylinder," IEEE Trans. Antennas Propagat., Vol. 40, No. 3, 295-303, 1992.
    doi:10.1109/8.135472

    3. Elsherbeni, A. Z. and M. Hamid, "Scattering by a cylindrical dielectric shell with inhomogeneous permittivity profile," Int. J. Electronics, Vol. 58, No. 6, 949-962, 1985.
    doi:10.1080/00207218508939090

    4. Elsherbeni, A. Z. and M. Hamid, "Scattering by a cylindrical dielectric shell with radial and azimuthal permittivity profiles," Proc. 1985 Symp. of Microwave Technology in Industrial Development, (Invited), 77–80, Brazil, July 22–25, 1985.

    5. Elsherbeni, A. Z. and M. Tew, "Electromagnetic scattering from a circular cylinder of homogeneous dielectric coated by a dielectric shell with a permittivity profile in the radial and azimuthal directions-even TM case," IEEE Proceedings-1990 Southeastcon, Session 11A1, 996–1000, 1990.

    6. Jarem, J. M., "Rigorous coupled wave theory solution of phi-periodic circular cylindrical dielectric systems," Journal of Electromagnetic Waves and Applications, Vol. 11, 197-213, 1997.
    doi:10.1163/156939397X00161

    7. Jarem, J. M., "Rigorous coupled wave theory of anisotropic, azimuthally-inhomogeneous, cylindrical systems," Progress In Electromagnetics Research, Vol. 19, Chap. 4, 109–127, 1998.

    8. Jarem, J. M. and P. P. Banerjee, "Bioelectromagnetics: A rigorous coupled wave analysis of cylindrical biological tissue," Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, (METMBS 00), F. Valatar (Ed.), 467–472, Vol. II, Las Vegas, Nev., June 26–29, 2000.

    9. Moharam, M. G. and T. K. Gaylord, "Rigorous coupled-wave analysis of planar grating diffraction," J. Opt. Soc. Amer., Vol. 71, 811-818, 1981.
    doi:10.1364/JOSA.71.000811

    10. Moharam, M. G. and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Amer., Vol. 72, 1385-1392, 1982.
    doi:10.1364/JOSA.72.001385

    11. Rokushima, K. and J. Yamakita, "Analysis of anisotropic dielectric gratings," J. Opt. Soc. Amer., Vol. 73, 901-908, 1983.
    doi:10.1364/JOSA.73.000901

    12. Moharam, M. G. and T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Amer., Vol. 73, 1105-1112, 1983.
    doi:10.1364/JOSA.73.001105

    13. Glytsis, E. N. and T. K. Gaylord, "Rigorous three-dimensional coupled-wave diffraction analysis of single cascaded anisotropic gratings," J. Opt. Soc. Amer. B, Vol. 4, 2061-2080, 1987.
    doi:10.1364/JOSAA.4.002061

    14. Jarem, J. M. and P. Banerjee, "An exact, dynamical analysis of the Kukhtarev equations in photoretractive barium titanate using rigorous wave coupled wave diffraction theory," J. Opt. Soc. Amer. A, Vol. 13, No. 4, 819-831, April 1996.
    doi:10.1364/JOSAA.13.000819

    15. Jarem, J. M., "A rigorous coupled-wave theory and crosseddiffraction grating analysis of radiation and scattering from threedimensional inhomogeneous objects," IEEE Transactions on Antennas and Propagation, Vol. 5, No. 46, 740-741, May 1998.
    doi:10.1109/8.668922

    16. Jarem, J. M., "Rigorous coupled-wave-theory analysis of dipole scattering from a three-dimensional, inhomogeneous, spherical dielectric and permeable system," IEEE Microwave Theory and Techniques, Vol. 45, No. 8, 1193-1203, Aug. 1997.
    doi:10.1109/22.618407

    17. Jarem, J. M. and P. P. Banerjee, Computational Methods for Electromagnetic and Optical Systems, Marcel Dekker, Inc., 2000.
    doi:10.1201/9780203908112

    18. Bowman, J. J., T. B. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, Chap. 3. “The Elliptic Cylinder”, 129–180, Hemisphere Publishing Corp., New York, N.Y., revised printing, 1987.

    19. Sebak, A. R., "Scattering from Dielectric-Coated Impedance elliptic cylinder," IEEE Transactions on Antennas and Propagation, Vol. 48, No. 10, 1574-1580, Oct. 2000.
    doi:10.1109/8.899674

    20. Abramowitz, M. and I. Stegum, Handbook of Mathematical Functions, Chap. 20, “Mathieu Functions”, Dover publications, New York, N.Y., 1972.

    21. Zhang, S. and J. Jin, "FORTRAN routines for computation of special functions,", Programs: “MTU12,MTU0,FCOEF,CVF,CVA2” at Web Site http://irislee3.ece.uiuc.edu/˜jjin/routines/routines.html, Mar. 8, 01. (Programs associated with the book Computation of Special Functions, John Wiley and Sons. Inc.).