This paper presents a rigorous approach for the propagation of electromagnetic (EM) fields along a helical waveguide with slab and rectangular dielectric profiles in the rectangular cross section. The main objective is to develop a numerical method for the calculation of the output fields, for an arbitrary step's angle and the radius of the cylinder of the helical waveguide. The other objectives are to present the technique to calculate the dielectric profiles and their transverse derivatives in the cross-section and to demonstrate the ability of the model to solve practical problems with slab and rectangular dielectric profiles in the rectangular cross section of the helical waveguide. 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 helical waveguides with slab and rectangular dielectric profiles in the metallic helical waveguides in the microwave and the millimeter-wave regimes. 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.
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. Cochran, J. A. and R. G. Pecina, "Mode propagation in continuously curved waveguides," Radio Science, Vol. 1, 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. Microwave Theory 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. Microwave Theory Tech., Vol. 47, 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, 1976.
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 F. S. Barnes, "Reduction of radiation loss in a curved dielectric slab waveguide," Sci. Rept. 2 AFOSR-72-2417, 1973.
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. 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.
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.
13. Mahmut, A., D. Begum, and K. Yamamoto, "Flow through a helical pipe with rectangular cross-section," Journal of Naval Architecture and Marine Engineering, Vol. 99, No. 110, 2007.
14. Seshadri, R., S. Ghosh, A. Bhansiwal, S. Kamath, and P. K. Jain, "A simple analysis of helical slow-wave structure loaded by dielectric embedded metal segments for wideband traveling-wave tubes," Progress In Electromagnetics Research B, Vol. 20, 303-320, 2010.
15. Ghosh, S., A. K. Sinha, R. K. Gupta, S. N. Joshi, P. K. Jain, and B. N. Basu, "Space-harmonic effects in helical slow-wave structure-An equivalent circuit analysis," Progress In Electromagnetics Research, Vol. 30, 85-104, 2001.
16. Lewin, L., D. C. Chang, and E. F. Kuester, Electromagnetic Waves and Curved Structures, 95-113, Chap. 8, Peter Peregrinus Ltd., 1977.
17. 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.
18. Menachem, Z., "Wave propagation in a curved waveguide with arbitrary dielectric transverse profiles," Progress In Electromagnetics Research, Vol. 42, 173-192, 2003.
19. Menachem, Z. and M. Haridim, "Propagation in a helical waveguide with inhomogeneous dielectric profiles in rectangular cross section," Progress In Electromagnetics Research B, Vol. 16, 155-188, 2009.
20. Menachem, Z., N. Croitoru, and J. Aboudi, "Improved mode model for infrared wave propagation in a toroidal dielectric waveguide and applications," Opt. Eng., Vol. 41, 2169-2180, 2002.
21. 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.
22. Menachem, Z., "Flexible hollow waveguide with two bendings for small values of step angles, and applications," Progress In Electromagnetics Research B, Vol. 21, 347-383, 2010.
23. Menachem, Z. and S. Tapuchi, "Helical waveguide with two bendings, and applications," Progress In Electromagnetics Research B, Vol. 26, 115-147, 2010.
24. 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.
25. Salzer, H. E., "Additional formulas and tables for orthogonal polynomials originating from inversion integrals," J. Math. Phys., Vol. 39, 72-86, 1961.
26. The Numerical Algorithms Group (NAG) Ltd., Wilkinson House, Oxford, UK.
27. Collin, R. E., Foundation for Microwave Engineering, McGraw-Hill, New York, 1996.
28. Vladimirov, V., Equations of Mathematical Physics, 1971.