Analytical Multimodal Network Approach for 2-D Arrays of Planar Patches/Apertures Embedded in a Layered Medium

A fully analytical multimodal equivalent circuit is presented for the modeling of the scattering of an obliquely incident plane wave by a two-dimensional (2-D) periodic array of metallic patches (or apertures in a metallic screen) embedded in a layered medium. The topology of the equivalent network is rigorously derived in the analysis and all the network parameters are given in closed form. In contrast with the previously reported explicit circuit models, the proposed approach accounts for dynamical effects over a very wide frequency range, which enables the application of the model to a great variety of situations. The key advantages of the reported multimodal network representation are its analytical nature, its extremely low-computational cost and that the physical phenomena involved in the scattering can be easily understood in terms of transmission line and lumped circuital reasonings.

I. Introduction

The study of the electromagnetic properties of one dimensional (1-D) and two-dimensional (2-D) periodic distributions of planar metallic scatterers (or their complementary structures consisting of apertures in thin metal screens) embedded in layered dielectric media (see Fig. 1) is a classical topic in the microwave/antenna [1]–[5] and infrared [6]–[8] literature. In fact, this is the generic description of the widely used spatial filtering structures called frequency-selective surfaces (FSS) [9]–[13]. The study of other related devices such as reflectarrays [14], [15], artificial impedance surfaces [16], or resonant cavity antennas [17] would also benefit from the modeling of the class of structures considered in this paper. The study of this kind of problems also has a long tradition in the optics and physics communities. Indeed, in recent years, a lot of attention has been paid to 1-D and 2-D metallic periodic structures in connection with the huge interest raised by extraordinary transmission, metasurfaces, and related problems [18]–[23]. A good review of the combined interest of physicists and engineers on this topic can be found in [24].