An analytical investigation of the dispersion characteristic of a lightguide with an annular core cross section bounded by two cardioids

With the use of the scalar field approximation, an analytical study has been made of a lightguide having a cardioidically distorted annular core cross section. Using appropriate new coordinates (ξ, η, z) and with the weak guidance boundary conditions, the modal characteristic equation has been deduced analytically. From this equation, the modal characteristic curves have been obtained for some low-order modes (ν=0).