A Symmetry-Based Multimodal Transfer-Matrix Method for the Analysis of 2D-Periodic Structures

We propose a systematic and efficient extension of the multimodal transfer-matrix method to obtain the dispersion diagram of structures with 2-D periodicity specifically targeted to primitive unit cells that possess internal symmetries. When symmetry planes can be applied, the study of the unit cell can be simplified to a number of 1D-periodic scenarios that depend on the boundary conditions imposed by the symmetry planes. The study of these 1D-periodic scenarios is simpler, more accurate, and requires less computational cost. The proposed methodology has been validated with different examples of periodic structures with different lattices (squared, rectangular, and hexagonal), symmetries, and motifs. Furthermore, this approach brings about a deeper understanding of the study of the Brillouin zone (BZ) and the relationship between phase shift and paths on its irreducible Brillouin zone (IBZ).