Astudy is presented of the light wave propagation in a new type of dielectric optical waveguide with hyperbolic kind of crosssection. Further, the waveguide is assumed to have a conducting helical winding. The analysis essentially requires the use of elliptical coordinate system, which finally results into Mathieu and modified Mathieu functions as the representatives of the electromagnetic fields within the lightguide. Field components in the different sections of the guide are deduced, and the characteristic dispersion equation for the system is derived. The preliminary investigation on such type of waveguide throws the idea that the presence of helix pitch angle (which serves the purpose of additional controlling parameter for the guide) in the dispersion relation would greatly affect the propagation characteristics of the guide, and this can be of great practical importance.
2. Ikuno, H. and K. Nakashima, "Numerical analysis of ellipticallycored optical fiber," Res. Rep. Inst. Elect. Eng. (Jpn.), Vol. EMT83-4, 83-4, 1983.
3. Kumar, A. and R. K. Varshney, "Propagation characteristics of highly elliptical core optical waveguides: Ap erturbation approach," Opt. Quantum Electron., Vol. 16, 349-354, 1984.
4. Dyott, R. B., "Cutoff of the first order modes in elliptical dielectric waveguide: an experimental approach," Electron. Lett., Vol. 26, 1721-1723, 1990.
5. Lim, M. H., S. C. Yeow, P. K. Choudhury, and D. Kumar, "On the dispersion characteristics of tapered core dielectric optical fibers," J. Electromag. Waves and Appl., Vol. 20, 1597-1609, 2006.
6. Goell, J. E., "Acircular-harmonic computer analysis of rectangular dielectric waveguides," Bell Syst. Tech. J., Vol. 48, 2133-2160, 1969.
7. Goell, J. E., "Slab-coupled waveguides," Bell. Syst. Tech. J., Vol. 53, 645-674, 1974.
8. Borland, W. C., D. E. Zelmon, C. J. Radens, J. T. Boyd, and H. E. Jackson, "Properties of four-layer planar optical waveguides near cutoff," IEEE J. Quantum Electron., Vol. QE-23, 1172-1179, 1978.
9. Kumar, A., K. Thyagarajan, and A. K. Ghatak, "Analysis of rectangular core dielectric waveguides: an accurate perturbation approach," Opt. Lett., Vol. 8, 63-65, 1983.
10. Choudhury, P. K., "On the modal behaviour of rectangular and deformed planar waveguides," Microw. and Opt. Tech. Lett., Vol. 10, 333-335, 1995.
11. James, J. R. and I. N. L. Gallett, Modal analysis of triangularcored glass-fiber waveguides, Proc. IEE, Vol. 120, 1362-1370, 1973.
12. Dyott, R. B., "Glass-fiber waveguide with triangular core," Electron. Lett., Vol. 9, 288-290, 1973.
13. Ojha, S. P., P. K. Choudhury, and P. Khastgir, Glass fibers of triangular cross-sections with metal-loading on one or more sides â€” Acomparativ e modal study, Proc. SPIE, Vol. 1580, 278-287, 1991.
14. Shukla, P. K., P. K. Choudhury, P. Khastgir, and S. P. Ojha, "Comparative aspects of a metal-loaded triangular waveguide with uniform and non-uniform distribution of Goell's matching points," J. Inst. Electron. & Telecommun. Engg., Vol. 41, 217-220, 1995.
15. Choudhury, P. K., P. Khastgir, S. P. Ojha, and L. K. Singh, "Analysis of the guidance of electromagnetic waves by a deformed planar waveguide with parabolic cylindrical boundaries," J. Appl. Phys., Vol. 71, 5685-5688, 1992.
16. Choudhury, P. K., P. Khastgir, and S. P. Ojha, "Amathematically rigorous cutoff analysis of parabolic cylindrical waveguides," J. Phys. Soc. Jpn., Vol. 61, 3874-3877, 1992.
17. Choudhury, P. K., P. Khastgir, S. P. Ojha, and K. S. Ramesh, "An exact analytical treatment of parabolically deformed planar waveguides near cutoff," Optik, Vol. 95, 147-151, 1994.
18. Choudhury, P. K. and R. A. Lessard, "Parabolic cylindrical waveguides: revisited," Optik, Vol. 112, 358-361, 2001.
19. Misra, V., P. K. Choudhury, P. Khastgir, and S. P. Ojha, "Modal propagation analysis of a waveguide with a regular pentagonal cross-section with conducting and non-conducting boundaries," Microw. and Opt. Tech. Lett., Vol. 8, 280-282, 1995.
20. Choudhury, P. K., "On the preliminary study of a dielectric guide having a Piet Hein geometry," Ind. J. Phys., Vol. 71B, 191-196, 1997.
21. Misra, V., P. K. Choudhury, P. Khastgir, and S. P. Ojha, "Electromagnetic wave propagation through a dielectric guide having Piet Hein cross-sectional geometry," Microw. and Opt. Tech. Lett., Vol. 12, 250-254, 1996.
22. Choudhury, P. K. and O. N. Singh, "Some multilayered and other unconventional lightguides," Electromagnetic Fields in Unconventional Structures and Materials, 289-357, 2000.
23. Kumar, D., "Apreliminary ground work for the study of the characteristic dispersion equation for a slightly elliptical sheath helix slow-wave structure," J. Electromag. Waves and Appl., Vol. 18, 1033-1044, 2004.
24. Kumar, D. and O. N. Singh II, "Analysis of the propagation characteristics of a step-index waveguide of annular circular crosssection with conducting helical windings on the inner and outer boundary surfaces between the guiding and the non guiding regions," J. Electromag. Waves and Appl., Vol. 18, 1655-1669, 2004.
25. Watkins, D. A., Topics in Electromagnetic Theory, 39-62, 39-62, Wiley, USA, 1958.
26. Brillouin, L., Wave Propagation in Periodic Structures, Dover Publications, Inc., New York, 1953.
27. Kornhauser, E. T., "Radiation field of helical antennas with sinusoidal current," J. Appl. Phys., Vol. 22, 887-891, 1951.
28. Mathers, G. W. C. and G. S. Kino, "Some properties of a sheath helix with a center conductor or External shield," Report No. 65, No. '' Report 65, 1953.
29. Kumar, D. and O. N. Singh II, "Some special cases of propagation characteristics of an elliptical step-index fiber with a conducting helical winding on the core-cladding boundary â€” An analytical treatment," Optik, Vol. 112, 561-566, 2001.
30. Kumar, D. and O. N. Singh II, "Modal characteristic equation and dispersion curves for an elliptical step-index fiber with a conducting helical winding on the core-cladding boundary â€” An analytical study," J. Light. Tech., Vol. 20, 1416-1424, 2002.
31. Kumar, D. and O. N. Singh II, "Elliptical and circular step-index fibers with conducting helical windings on the core-cladding boundaries for different winding pitch angles â€” Acomparativ e modal dispersion analysis," Progress In Electromagnetics Research, Vol. 52, 1-21, 2005.
32. Verma, K. K. and D. Kumar, The Elements of Vector Calculus, AITBS Publisher and Distributor, New Delhi, India, 2005.