Modal characteristic equation and dispersion curves for an elliptical step-index fiber with a conducting helical winding on the core-cladding boundary - an analytical study

A special type of elliptical step-index fiber with a conducting helical winding on the core-cladding boundary is proposed and investigated theoretically. Using elliptic cylindrical coordinates, boundary conditions are derived and longitudinal field components for the even and odd modes are obtained. The characteristic equation for the waveguide to be studied is determined by solving the fourth-order determinantal equation, which also contains complex quantities. In order to study the fundamental mode, the modal index ν is put as ν=1. The equations obtained involve modified Mathieu functions of the first order and their derivatives. Applying approximations, cutoff conditions are obtained. Numerical computations are made. Dispersion curves are obtained for different pitch angles of the helical winding.