Numerical Modelling of Higher-Symmetric Periodic Structures with Hexagonal Lattice

This paper presents the development of the multi-modal transfer matrix method (MMTMM) to deal with periodic structures with hexagonal unit cells and higher symmetries. The method is able to calculate complex modal solutions, including the attenuation in the stopband. A key feature is the reformulation of the MMTMM into an eigenvalue problem whose eigensolutions in the complex plane can be systematically obtained for the boundaries of the irreducible Brillouin zone, where the phase-shift conditions are linearly dependent. The obtained phase-shift dispersion diagrams are verified against a commercial software, while the attenuation constant is validated with a developed method of moments. A glide-symmetric structure and a mirror half-turn structure are investigated. The latter is found to possess a highly isotropic stopband with a fractional bandwidth of 94.9%, wider than previously reported for holey structures. Finally, the operation of the unit cell is demonstrated with a practical implementation for preventing leakage in a waveguide flange.