On the dispersion curves of a circularly deformed planar waveguide

Abstract

A mathematical formulation has been made of a planar waveguide under a state of small circular deformation in transverse direction of the electromagnetic wave propagation. The scalar wave equation and the weak guidance approximation are used for the analysis, and the eigenvalue equation for the guide has been derived. A mode designation scheme, which is not conventional, is employed to present the dispersion curves for such a waveguide. It is found that these dispersion curves exhibit a partial resemblance with the existing curves for the various structures analyzed by other investigators. It is noticed that for higher order modes, the curves show the expected regular behaviour, while a curious and unusual behaviour is seen for the lower order modes.