This paper presents the technique to solve inhomogeneous profiles in the cross section of the helical rectangular waveguide. We present the technique to solve inhomogeneous dielectric profiles and the relation to the method of the propagation of electromagnetic fields along a helical waveguide with a rectangular cross section. The inhomogeneous examples will introduce for a dielectric slab, for a rectangular dielectric profile, and for a circular dielectric profile, in a rectangular metallic waveguide, in the cross section of the helical waveguide. This model is useful to improve the output results of the output power transmission in the cases of space helical waveguides, by increasing the step's angle or the radius of the cylinder. The application is useful for space helical waveguides in the microwave and the millimeter-wave regimes.
2. Trang, N. T. and R. Mittra, "Field profile in a single-mode curved dielectric waveguide of rectangular cross section," IEEE Trans. on Microwave Theory and Tech., Vol. 29, 1315-1318, 1981.
3. Cochran, J. A. and R. G. Pecina, "Mode propagation in continuously curved waveguides," Radio Science, Vol. 1 (new series), No. 6, 679-696, 1966.
4. 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.
5. Weisshaar, A., S. M. Goodnick, and V. K. Tripathi, "A rigorous and efficient method of moments solution for curved waveguide bends," IEEE Trans. on Microwave Theory and Tech., Vol. 40, No. 12, 2200-2206, 1992.
6. Cornet, P., R. Duss'eaux, and J. Chandezon, "Wave propagation in curved waveguides of rectangular cross section," IEEE Trans. on Microwave Theory and Tech., Vol. 47, No. 7, 965-972, 1999.
7. 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, 1975.
8. Kawakami, S., M. Miyagi, and S. Nishida, "Bending losses of dielectric slab optical waveguide with double or multiple claddings," Appl. Optics, Vol. 14, 2588-2597, 1975. Correction, ibid., Vol. 15, 1681, 1976.
9. Chang, D. C. and E. F. Kuester, "Radiation and propagation of a surface-wave mode on a curved open waveguide of arbitrary cross section," Radio Science, 449-457, 1976.
10. 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.
11. Lewin, L., D. C. Chang, and E. F. Kuester, Electromagnetic Waves and Curved Structures, Chap. 8, 95-113, Peter Peregrinus Ltd., 1977.
12. 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.
13. 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.
14. Kuester, E. F. and D. C. Chang, "Surface wave radiation loss from curved dielectric slabs and fibers," J. Quantum Electron., Vol. 11, 903-907, 1975.
15. Mahmoud, S. F. and J. R. Wait, "Guided electromagnetic waves in a curved rectangular mine tunnel," Radio Science, Vol. 9, 567-572, 1974.
16. Abbas, Z., R. D. Pollard, and R. W. Kelsall, "A rectangular dielectric waveguide technique for determination of permittivity of materials at W-band," IEEE Trans. on Microwave Theory and Tech., Vol. 46, No. 21, 2011-2015, 1998.
17. Wolfson, B. J. and S. M. Wentworth, "Complex permittivity and permeability measurement using a rectangular waveguide," Microwave and Optical Technology Letters, Vol. 27, No. 3, 433-452, 2000.
18. Yamamoto, T. and M. Koshiba, "Analysis of propagation characteristics of whispering gallery modes in a dielectric disk or a curved rectangular dielectric waveguide," Journal of Lightwave Technology, Vol. 11, 400-404, 1993.
19. Menachem, Z., "Wave propagation in a curved waveguide with arbitrary dielectric transverse profiles - Abstract," Journal of Electromagnetic Waves and Aplications, Vol. 17, No. 10, 1423-1424, 2003.
20. Menachem, Z., "Wave propagation in a curved waveguide with arbitrary dielectric transverse profiles," Progress In Electromagnetics Research, Vol. 42, 173-192, 2003.
21. Menachem, Z. and S. Tapuchi, "Wave propagation in a helical waveguide with slab and rectangular dielectric profiles and applications," Progress In Electromagnetics Research B, Vol. 34, 77-102, 2011.
22. 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.
23. Salzer, H. E., "Additional formulas and tables for orthogonal polynomials originating from inversion integrals," J. Math. Phys., Vol. 39, 72-86, 1961.
24. Vladimirov, V., Equations of Mathematical Physics, 1971.