This paper presents a rigorous approach for the propagation of electromagnetic (EM) fields along a helical waveguide with arbitrary profiles in the rectangular cross section. The main objective is to develop a mode model to provide a numerical tool for the calculation of the output fields, output power density, and output power transmission for an arbitrary step's angle and the radius of the cylinder of the helical waveguide. 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. Laplace transform is necessary to obtain the comfortable and simple input-output connections of the fields. 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. The output power transmission and the output power density are improved by increasing the step's angle or the radius of the cylinder of the helical waveguide, especially in the cases of space curved waveguides.
"Propagation in a Helical Waveguide with Inhomogeneous Dielectric Profiles in Rectangular Cross Section," Progress In Electromagnetics Research B,
Vol. 16, 155-188, 2009. doi:10.2528/PIERB09022202
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. 11, 75-83, 1975. Correction, Ibid., Vol. 12, 313, 1976. doi:10.1109/JQE.1975.1068563
4. Kawakami, S., M. Miyagi, and S. Nishida, "Bending losses of dielectric slab optical waveguide with double or multiple claddings," Appl. Optics, Vol. 14, 588-2597, 1975. Correction, Ibid., Vol. 15, 1681, 1976..
5. Chang, D. C. and F. S. Barnes, "Reduction of radiation loss in a curved dielectric slab waveguide," Sci. Rept. 2 AFOSR-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, 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. doi:10.1049/el:19870383
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. 40, No. 12, 2200-2206, 1992. doi:10.1109/22.179881
10. Cornet, P., R. Dusseaux, and J. Chandezon, "Wave propagation in curved waveguides of rectangular cross section," IEEE Trans. Microwave Theory Tech., Vol. 47, 965-972, 1999. doi:10.1109/22.775427
11. Ghosh, S., P. K. Jain, and B. N. Basu, "Fast-wave analysis of an inhomogeneously-loaded helix enclosed in a cylindrical waveguide," Progress In Electromagnetics Research, Vol. 18, 19-43, 1998. doi:10.2528/PIER97032900
12. Kumar, D. and O. N. Singh II, "Elliptical and circular step-index with conducting helical windings on the core-cladding boundaries for the different winding pitch angles --- A comparative modal dispersion analysis," Progress In Electromagnetics Research, Vol. 52, 1-21, 2005. doi:10.2528/PIER04052002
13. Lewin, L., D. C. Chang, and E. F. Kuester, Electromagnetic Waves and Curved Structures, 95-113, Chap. 8, Peter Peregrinus Ltd., 1977.
14. Trang, N. T. and R. Mittra, "Field profile in a single-mode curved dielectric waveguide of rectangular cross section," IEEE Trans. Microwave Theory Tech., Vol. 29, 1315-1318, 1981. doi:10.1109/TMTT.1981.1130558
15. Menachem, Z., "Wave propagation in a curved waveguide with arbitrary dielectric transverse profiles," Progress In Electromagnetics Research, Vol. 42, 173-192, 2003. doi:10.2528/PIER03012303
16. 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. 46, 975-982, 1998. doi:10.1109/22.701451
17. 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.
18. Menachem, Z. and M. Mond, "Infrared wave propagation in a helical waveguide with inhomogeneous cross section and applications," Progress In Electromagnetics Research, Vol. 61, 159-192, 2006. doi:10.2528/PIER06020205
19. Salzer, H. E., "Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms," Math. Tables and Other Aids to Comut., Vol. 9, 164-177, 1955. doi:10.2307/2002053
20. Salzer, H. E., "Additional formulas and tables for orthogonal polynomials originating from inversion integrals," J. Math. Phys., Vol. 39, 72-86, 1961.
21. The Numerical Algorithms Group (NAG) Ltd., , Wilkinson House, Oxford, UK.
22. Collin, R. E., Foundation for Microwave Engineering, McGraw-Hill, New York, 1996.
23. Vladimirov, V., Equations of Mathematical Physics, 1971.