Equivalent-Circuit Modeling of Lossless and Lossy Bi-Periodic Scatterers by an Eigenstate Approach

The use of an eigenstate-based equivalent-circuit topology is proposed for the analysis and modeling of lossless and lossy bi-periodic scatterers. It significantly simplifies the design of this kind of surfaces, since it reduces the number of elements with respect to other general equivalent circuits. It contains at most only two admittances and one complex turns ratio. The real parts of these admittances can be assured to be nonnegative, an interesting aspect in the modeling of lossy surfaces such as those present in absorbers. Moreover, due to the capability of decomposition into the eigenexcitations of the structure, the circuit provides an important physical insight. Different cases of scatterers have been analyzed: symmetric and asymmetric, and lossy and lossless. In all these cases, modeling of the circuit admittances has been successfully achieved with a few positive and frequency-independent RLC elements. In the case of structures with symmetries, the turns ratio directly reflects the physical orientation of the scatterer eigenexcitations. Furthermore, in the case of lossy scatterers without symmetries, the resulting equivalent circuit reveals that their eigenexcitations are not linear polarizations, but elliptic polarizations whose properties are described by a complex turns ratio.