Semi-Analytical Method for the Analysis of Bound and Leaky Modes in Woodpile Dielectric Structures

An efficient semi-analytical method to study modes with real and complex wavenumbers in three-dimensional woodpile bandgap structures, that consist of layered periodic arrays of circular dielectric cylinders, is proposed. The reflection and transmission matrices of the woodpile structure are rigorously calculated using the transition-matrix approach combined with the lattice sums technique and the recurrence formulae for the layered structure. A dispersion equation is rigorously derived taking into account proper and improper determinations of each space-harmonic. Two different configurations of the woodpile cavity structures are investigated. The dispersion characteristics of bound and complex modes, in the closed stopband region, and of hybrid TE and TM leaky modes, propagating at arbitrary angles within the open woodpile cavity waveguide, are numerically calculated. The results are compared with those obtained by fully independent commercial software simulations. Suitable post-processing and radiation patterns based on leaky-wave theory are used for validation of the proposed method, and very good agreement between theoretical and full-wave results are obtained.