Bandwidth determination for soft and hard ground planes: a unified approach in visible and surface wave regions

This work gives a unified definition of the bandwidth for the soft and hard operations of periodic ground planes. The spectral FDTD technique is used to calculate the reflection coefficient on the entire wavenumber-frequency plane and soft and hard factors for TM and TE waves are found. It is described that the regions with infinite reflection on the wavenumber-frequency plane represents the propagation of a surface wave mode. It is generally observed that the soft operation occurs at the frequencies slightly above the surface wave mode, whereas the hard operation occurs slightly below the surface wave mode. The corrugated surface and mushroom-like EBG are analyzed, and the bandwidth for soft, hard and PMC like behavior of these surfaces are identified in the wavenumber-frequency plane.