Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary condition

Abstract

The finite-element approach to the eigenmode analysis of a photonic bandgap cavity by use of an anisotropic perfectly matched layer absorbing boundary is presented. This method rigorously calculates the resonant frequency, the field pattern, and the quality factor of the resonant mode of a finite-sized cavity in free space. The validity of the approach is examined through its application to two-dimensional photonic bandgap cavities. Analyses of numerical error for the resonant frequencies and the quality factor of the cavities demonstrate the accuracy and reliability of our approach, which used nonuniform grids, higher-order elements, and the perfectly matched layer. Far-field patterns of the resonant modes were obtained by simple transformation. Because the perfectly matched layer can represent the real boundary condition well, cavities of any size and shape can be analyzed with the desired accuracy.