Towards the characteristic dispersion relation for step-index hyperbolic waveguide with conducting helical winding

摘要

A study is presented of the light wave propagation in a new type of dielectric optical waveguide with hyperbolic kind of cross-section. 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.