The propagation characteristics of an elliptical step-index fiber with a conducting helical winding on the core-cladding boundary are investigated analytically and compared with those of a circular step index fiber with a conducting radial winding. Our optical waveguides are unconventional: in view of the existence of helical conducting windings on the core-cladding boundaries. Appropriate coordinate systems, circular cylindrical and elliptic cylindrical, are chosen for the circular and elliptical fibers. Applying the boundary conditions as modified by the presence of conducting helical windings, the characteristic equations are obtained for both the fibers. Dispersion curves are also obtained for two special values of the helical pitch angle ψ, namely, for ψ = 0º and ψ = π/2 for each fiber and the results have been compared. It is found that the introduction of the helical winding has two main effects on the characteristics of both types of fibers. These are: (1) The helix introduces band gaps and (2) has the effect of splitting a mode into a pair of adjacent modes In the case of the elliptical helically clad waveguide we find two band gaps for V < 30 whereas for circular guide we have only one band gap in the same range of V-values, V being the normalized frequency parameter.
Onkar Singh II,
"Elliptical and Circular Step-Index Fibers with Conducting Helical Windings on the Core-Cladding Boundaries for Different Winding Pitch Angles - a Comparative Modal Dispersion Analysis," ,
Vol. 52, 1-21, 2005. doi:10.2528/PIER04052002
8. Chu, L. J., "Electromagnetic waves in elliptic hollow pipes of metal," J. Appl. Phy., Vol. 9, 583-591, 1938. doi:10.1063/1.1710459
9. Dyott, R. B. and J. R. Stern, "Group delay in glass fiber waveguides," Electronics Letters, Vol. 7, 82-84, 1971.
10. Singh, U. N., O. N. Singh II, P. Khastgir, and K. K. Dey, "Dispersion characteristics of a helically cIadded step-index optical filber analytical study," J. Opt. Soc. Am. B, 1273-1278, 1995.
11. Kumar, D. and O. N. Singh II, "Modal characteristics equation and dispersion curves for an elliptical step-index fiber with a conducting helical winding on the core-cladding boundary An analytical study," IEEE Journal of Light Wave Technology, Vol. 20, No. 8, 1416-1424, 2002. doi:10.1109/JLT.2002.800799
12. 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 An analytical treatment," Optik, Vol. 112, No. 12, 561-566, 2001.
13. Kumar, D. and O. N. Singh II, "An analytical study of the modal characteristics of annular step-index waveguide of elliptical cross-section with two conducting helical windings on the two boundary surfaces between the guiding and the non-guiding regions," Optik, Vol. 113, No. 5, 193-196, 2002.
14. Watkins, D. A., Topics in Electromagnetic Theory, John Wiley and Sons Inc., NY, 1958.
15. McLachlan, N. W., Theory and Application of Mathieu Functions, Oxford University Press, 1947.
16. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 1965.
17. Tai, C.-T., Generalized Vector and Dyadic Analysis, IEEE Press, 1992.