Periodic structures eigenanalysis incorporating the Floquet Field Expansion

The current work elaborates on the study of periodic structures loaded either with anisotropic or isotropic media. An eigenanalysis methodology is adopted using Finite Difference in Frequency Domain (FDFD) in order to evaluate the Floquet wavenumbers. An eigenvalue problem is addressed and solved with Arnoldi iterative Algorithm. The periodicity of the structure is accounted in two alternative approaches. Initially Periodic Boundary Conditions (PBCs) are imposed on the periodic surfaces whose results found to be in a very good agreement with analytical ones. However, there is a deviation when the phase difference between periodic surfaces rise above 150 degrees. In order to get more accurate results, a Floquet Field Expansion is incorporated into the FDFD formulation. Also, adaptive meshing is employed for the accurate study of very fine discontinuities. In turn certain periodic structures loaded with anisotropic media are simulated in order to reveal the so-called Frozen Modes.