volume | PIER Journals

Abstract

A rigorous approach is derived for the analysis of electromagnetic (EM) wave propagation in dielectric waveguides with arbitrary profiles, situated inside rectangular metal tubes, and along a curved dielectric waveguide. The first objective is to develop a mode model in order to provide a numerical tool for the calculation of the output fields for radius of curvature 0.1 m â‰¤ R â‰¤ âˆž. Therefore we take into account all the terms in the calculations, without neglecting the terms of the bending. Another objective is to demonstrate the ability of the model to solve practical problems with inhomogeneous dielectric profiles. The method is based on Fourier coefficients of the transverse dielectric profile and those of the input wave profile. These improvements contribute to the application of the model for inhomogeneous dielectric profiles with single or multiple maxima in the transverse plane. This model is useful for the analysis of dielectric waveguides in the microwave and the millimeter-wave regimes, for diffused optical waveguides in integrated optics, and for IR regimes.

1. Riess, K., "Electromagnetic waves in a bent pipe of rectangular cross-section," Q. Appl. Math., Vol. 1, 328-333, 1944.

2. Rice, S. O., "Reflections from circular bends in a rectangular wave guides-matrix theory," Bell Syst. Tech. J., Vol. 27, 305-349, 1948.

3. Heiblum, M. and J. H. Harris, "Analysis of curved optical waveguides by conformal transformation," IEEE J. Quantum Electron., Vol. 12, 75-83, 1976.

4. Kawakami, S., M. Miyagi, and S. Nishida, "Bending losses of dielectric slab optical waveguide with double or multiple claddings," Appl. Optics, Vol. 15, 2588-2597, 1976.

5. Chang, D. C. and F. S. Barnes, "Reduction of radiation loss in a curved dielectric slab waveguide," Sci.Rept.2AFOSR-72-2417, 72-2417, 1973.

6. Marcatily, E. A. J. and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J., Vol. 43, 1783-1809, 1964.

7. Cochran, J. A. and R. G. Pecina, "Mode propagation in continuously curved waveguides," Radio Science, Vol. 1 (new series), No. 6, 679-696, 1966.

8. Carle, P. L., "New accurate and simple equivalent circuit for circular E-plane bends in rectangular waveguide," Electronics Letters, Vol. 23, No. 10, 531-532, 1987.

9. Weisshaar, A., S. M. Goodnick, and V. K. Tripathi, "A rigorous and efficient method of moments solution for curved waveguide bends," IEEE Trans. Microwave Theory Tech., Vol. MTT-40, No. 12, 2200-2206, 1992.
doi:10.1109/22.179881

10. Cornet, P., R. Duss'eaux, and J. Chandezon, "Wave propagation in curved waveguides of rectangular cross section," IEEE Trans. Microwave Theory Tech., Vol. MTT-47, 965-972, 1999.
doi:10.1109/22.775427

11. Lewin, L., D. C. Chang, and E. F. Kuester, Electromagnetic Waves andCurve dStructur es, 95-113, Chap. 8, 1977.

12. Menachem, Z. and E. Jerby, "Transfer matrix function (TMF) for wave propagation in dielectric waveguides with arbitrary transverse profiles," IEEE Trans. Microwave Theory Tech., Vol. MTT-46, 975-982, 1998.
doi:10.1109/22.701451

13. Menachem, Z., N. Croitoru, and J. Aboudi, "Improved mode model for IR wave propagation in a toroidal dielectric waveguide and applications," Opt. Eng., Vol. 41, 2002.
doi:10.1117/1.1496490

14. Salzer, H. E., "Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms," Math. Tables andOther Aids to Comut., Vol. 9, 164-177, 1955.
doi:10.2307/2002053

15. Salzer, H. E., "Additional formulas and tables for orthogonal polynomials originating from inversion integrals," J. Math. Phys., Vol. 39, 72-86, 1961.

16. The Numerical Algorithms Group (NAG) Ltd., Wilkinson House, Wilkinson House, Oxford.

17. Croitoru, N.D. Mendlovic, J. Dror, S. Ruschin, and E. Goldenberg, "Improved metallic tube infrared waveguides with inside dielectric coating," Proc. Soc. Photo-Opt. Instrum. Eng., Vol. 713, 6-11, 1986.

Dr. Zion Menachem