Modal analysis and waveguide dispersion of an optical waveguide having a cross-section of the shape of a cardioid

In this paper, we choose a simple and practical analytical method based on scalar wave approximation to study the modal behaviour, cutoff condition of an unconventional optical waveguide having a cross section of the shape of a cardioid. We take the appropriate orthogonal coordinates for the proposed structure and impose the boundary conditions under the weak guidance approximation to get the modal eigen value equation. Using this equation we obtain numerical results in the form of dispersion curves and cutoff frequencies. Also the dependence, d(Vb')/dV on V has been obtained and shown graphically, where V stands for normalized frequency parameter and b' stands for normalized propagation constant. An attempt has been made to estimate how the modal behaviour and waveguide dispersion change as circular shape is changed to the shape of a cardioid.