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

A periodic ground plane may be built to either stop the propagation of wave or support a quasi transverse electromagnetic wave along the surface. The former is called a soft surface, and the latter is a hard surface. However, a soft or a hard surface can only be realized in certain frequency and wavenumber regions; therefore, it is important to identify the bandwidth for the surface so that it can be used efficiently. The bandwidth for soft and hard operations of a ground plane has been previously characterized by studying the reflection of normal and oblique plane waves with the real angle of incidence. The bandwidth for soft and hard operations of a periodic ground plane is defined as a wavenumber-frequency region in which the complex value of reflection coefficient is inside a circle with the radius of 1/√2 and centered at -1 or 1 for soft or hard operation, respectively. This definition gives a unified approach to characterize the bandwidth in both the visible (k_x²+k_y²0²) and surface wave (k_x²+k_y²>k₀²) regions. The paper uses a newly developed numerical technique referred to as the spectral finite-difference time-domain (FDTD) method, which is capable of calculating the reflection coefficient and impedance of the surface for any given set of wavenumber and frequency of the incident wave including the surface wave region. By using this method, the reflection coefficients and impedances of a corrugated dielectric-lined surface and a mushroom-like EBG are calculated, and the bandwidth for soft, hard, and perfect magnetic conductor like behavior are specified.