Evaluation of Eigenmodes of Dielectric Waveguides by a Numerical Method Based on the BPM

For weakly guiding dielectric waveguides, the eigenmode field distributions are calculated numerically with a simple algorithm. In this numerical method, the transverse sampling space can be chosen arbitrarily, and hence a narrow waveguide can be analyzed. The field satisfying scalar wave equation is expressed by the discrete Fourier transform and the mode eigenvalues and eigenfunctions are calculated by solving an eigenvalue equation numerically. The validity of this method is checked for 2-D waveguides having step and parabolic or square index distributions. It is found that for the well guided TE modes of the slab waveguide, the accuracy of this method is remarkably good, but some discrepancies are found if the mode is near cut off. In the problems where the normalized guide index b is small, caution should be taken in applying the results of this numerical method.