Solution of the scalar wave equation for arbitrarily shaped dielectric waveguides by two-dimensional Fourier analysis

A method for calculating the modes of arbitrarily shaped dielectric waveguides is presented. It consists of expanding the field in a two-dimensional Fourier series. The expansion is used to convert the scalar wave equation into a matrix eigenvalue equation. To facilitate calculation of the matrix elements, the waveguide geometry is approximated by a number of rectangles of constant refractive index. The accuracy of the method is demonstrated by calculating the dominant mode of a circular optical fiber and comparing it with the exact solution. The method well-fitted the experimental data on dielectric film waveguides on silicon, including data on waveguide-to-fiber butt-coupling loss, waveguide far-field angles, and the coupling length of directional couplers.<>