Modal Analysis of a Doubly Clad Optical Waveguide Having a Cross-section of the Shape of a Lemniscate

Abstract

In this paper, we choose a simple analytical method based on scalar wave approximation to study the modal behaviour of an unconventional doubly clad optical waveguide having a cross section of the shape of a lemniscate. 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. An attempt has been made to estimate how the modal behaviour changes when a single cladded waveguide having a lemniscates of Bernoulli type core cross-section is changed to a waveguide having double cladded shape of a lemniscate. It is noted that the double cladded waveguide provides an additional degree of freedom to control the cutoff frequencies on our choice.