Numerical Method for Analysis of Waveguide Modes in Planar Gradient Waveguides

This paper presents a numerical method developed to find propagation constants of planar waveguide localized modes. The method is based on both the Fourier transform application and the wave equation solution in a frequency domain. As a result, integral equation is obtained where integral is replaced by sum. Finally, a task to find propagation constants and field Fourier transforms in a discrete form is led to the eigenvalue/eigenvector problem. This method provides high accuracy subject to the conditions of the Whittaker-Shannon sampling theorem, and it is characterized by high numerical stability. The method is tested on many examples.