Theoretically obtained dispersion characteristics of an annular waveguide with a guiding region cross section bounded by two hypocycloidal loops

This article presents a theoretical analysis of the modal dispersion curves of an annular waveguide with a core cross section bounded by two hypocycloids. This cross section can be conceived as having the shape of a distorted annular square and leads to a tolerance study of deformation in an annular square waveguide. We take a new and appropriate coordinate system (ξ, η, z) for the proposed geometry and impose boundary conditions under the weak guidance approximation. The characteristic equation is then derived analytically. Finally, we show some numerical results in the form of modal dispersion curves.