PEEC Model Based on a Novel Quasi-Static Green's Function for Two-Dimensional Periodic Structures

A quasi-static periodic Green's function (PGF) is proposed for modeling and designing metasurfaces in the form of two-dimensional (2D) periodic structures. By introducing a novel quasi-static approximation on the full-wave PGF in the spectrum domain, the quasi-static PGF is derived that can retain the contribution from propagating and evanescent modes below resonant frequency by a second-order polynomial of frequency. Unlike full-wave PGF, the proposed quasi-static PGF polynomial coefficients are frequency-invariant. Consequently, it can save the modeling time significantly by calculating the coefficients only once for a frequency band of interest. Moreover, a quasi-static PEEC model is developed from the proposed quasi-static PGF. It circumvents the breakdown problem around near-zero frequencies since the singularity in PGF is separated in the quasi-static PGF and eliminated analytically in model development. Therefore, both the time- and frequency-domain analysis can be conducted easily using a SPICE-like solver on the PEEC model. Two examples are given, one of which validates the accuracy of the proposed quasi-static PGF in a 2D periodic unit cell working at 0–12 GHz; the other demonstrates the superior performance in terms of model efficiency and stability by a Jerusalem-cross frequency selective surface (FSS) working at 0–20 GHz. The numerical results show that the proposed method is accurate and efficient in a wide band for metasurfaces made of two-dimensional periodic structures.