volume | PIER Journals

Abstract

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.

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

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

3. Cochran, J. A. and R. G. Pecina, "Mode propagation in continuously curved waveguides," Radio Science, Vol. 1, No. 6, 679-696, 1966. Google Scholar

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.
doi:10.1049/el:19870383 Google Scholar

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.
doi:10.1109/22.179881 Google Scholar

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.
doi:10.1109/22.775427 Google Scholar

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.
doi:10.1364/AO.14.002588 Google Scholar

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. Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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.
doi:10.2528/PIERB10031201 Google Scholar

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.
doi:10.2528/PIER00011001 Google Scholar

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. Google Scholar

18. 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 Google Scholar

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.
doi:10.2528/PIERB09022202 Google Scholar

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.
doi:10.1117/1.1496490 Google Scholar

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.
doi:10.2528/PIER06020205 Google Scholar

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. Google Scholar

23. Menachem, Z. and S. Tapuchi, "Helical waveguide with two bendings, and applications," Progress In Electromagnetics Research B, Vol. 26, 115-147, 2010.
doi:10.2528/PIERB10081503 Google Scholar

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.
doi:10.2307/2002053 Google Scholar

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

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

27. Collin, R. E., Foundation for Microwave Engineering, McGraw-Hill, 1996.

28. Vladimirov, V., Equations of Mathematical Physics, 1971.

Dr. Zion Menachem

Dr. Saad Tapuchi