Accurate Multipole Analysis for Leaky Microcavities in Two-Dimensional Photonic Crystals

A multipole method is presented to analyze leaky microcavities in finite two-dimensional photonic crystals. The eigenfrequency of a leaky mode is solved from the condition that the eigenvalue with the smallest magnitude (instead of the determinant) of the coefficient matrix is zero. Accurate solutions are obtained with a relatively small truncation order in the associated cylindrical wave expansions.