부산대학교 도서관

Periodic structures are widely used in the design of microwave devices, such as filters and lenses [1, 2]. By altering the periodic element arrangements or their geometric parameters, the wave propagation properties through the structure can be manipulated to realize different functions. The dispersion diagram, which describes the relationship between wavevector components and frequency, is commonly employed to analyze the behavior of the phase/group velocities in periodic structures. In the engineering community, two-dimensional periodic structures have received significant attention, and structures arranged in rectangular and non-rectangular lattices have been investigated [3]. Additionally, three-dimensional (3D) periodic structures arranged in a simple cubic lattice have been studied, but limited efforts have been invested into other lattice arrangements possible in 3D periodic structures. In this contribution, we investigate the dispersion properties of 3D periodic structures with different lattice arrangements and provide detailed analysis steps. Specifically, the simple cubic, body-centered cubic, and face-centered cubic lattices are taken as examples to demonstrate our proposed analysis. Figure 1 illustrates these lattices and their respective smallest geometrical unit cells [4]. The setting of lattice points represents the underlying geometry of periodic structures. In this study, the connection between the lattices in the real and wavevector space is also shown. The smallest unit cell in the wavevector space that describes the full symmetry of the lattice is known as the Brillouin zone (BZ). By considering the symmetry of the smallest unit cell and the real periodic element, the BZ can be reduced further to the irreducible BZ to simplify the analysis. The dispersion properties of periodic structures can then be analyzed by checking the dispersion diagrams within the irreducible BZ, or even solely along its boundaries. We further compare the dispersion diagrams of the different periodic structures to illustrate some interesting properties of the structures. The extension of this study to more complex lattices is also discussed. The analysis and results shown here facilitate the study of 3D periodic structures and can be used in the antenna design process.