A solution of the wave equation for planar gradient waveguides in a frequency domain

摘要

Possibilities of a numerical method for solving the wave equation of gradient planar waveguides are studied. The method is based on both the Fourier transform application and the wave equation solution in a frequency domain. Finally, a task to find propagation constants and field Fourier transforms in a discrete form is led to the eigenvalue/eigenvector problem. The new method provides high accuracy subject to the conditions of the Whittaker-Shannon sampling theorem, and it is characterized by high numerical stability.