Determination of the truncation order and numerical window for modeling general dielectric waveguides by the Fourier method

The Fourier method of Henry and Verbeek, provides fast and accurate computation of the guided modes of 2- and 3-D waveguides with either homogeneous or inhomogeneous refractive index profiles. However, the accuracy and speed of the computation depends on the size of the numerical window and the number of terms (or truncation order) in the Fourier expansion of the solution to the reduced scalar wave equation. In this paper, we present a novel technique for the a priori determination of the numerical window and truncation order (of the Fourier method) by using the Wentzel-Kramers-Brillouin technique and the effective index method. This obviates the need to iteratively correct the computational parameters when using the Fourier method.