The method of lines analysis of asymmetric optical waveguides

Abstract

The starting point of any optical waveguide analysis is normally either Maxwell’s equations or the vector wave equation. Usually very few exact analytical solutions can be obtained due to the complexity of these equations, which typically involve coupling of the three scalar components of both the electric and the magnetic field vectors. However, The slight variation in index is most helpful as it permits the vector wave equation to be replaced by a scalar equation in which the electric field is represented by one vector component. To solve such wave equation for the asymmetric optical waveguide structure, a numerical model based on the method of lines has been developed. A suitable form of the method of lines is presented in Cartesian coordinate, and absorbing boundary conditions based on the third-order rational series approximation are derived. A comparison with exact solution is also presented. It is found that the method of lines can be used as good approximation for an optical waveguide simulation.