On the Brillouin Zones of Glide-Symmetric Structures

In this work, we investigate the appropriate definitions of the Brillouin zones and unit cells for glide-symmetric structures. In addition to translational periodicity, such structures possess glide symmetry; that is, invariance after a translation and a mirroring. Starting from basic concepts, we show that defining glide-symmetric structures only by their translational periodicity leads to dispersion diagrams that are less clear and practical, similar to the effect observed when unnecessarily large periods are employed. In particular, we observe that the anisotropy of the structure is incorrectly assessed when following the definitions commonly adopted in the existing literature. Therefore, we introduce a modeling technique utilizing the multi-modal transfer matrix method. This method can incorporate glide-periodicity effectively, leading to an efficient solution as it operates with a reduced computational domain. It also leads to the demonstration of the effects of misleading definitions on various commonly used geometric configurations in the literature. The framework described here is applicable to any glide-symmetric structure and facilitates the comparison of different types of unit cells.