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.

This paper presents a fully analytical model to determine the transmission and reflection properties of planar 1-D distributions of metal strips or slits made in thin metal screens. In contrast with other analytical or quasi-analytical approaches, the formulation incorporates the presence of dielectric slabs and is valid over a wide frequency band, from the long wavelength limit to the grating lobes operation. The model has been adapted to the case where two 1-D planar grids are stacked or a single grid is printed on a grounded substrate. In these cases, the model rigorously takes into account higher order mode interaction between the two stacked arrays of strips/slits or with the ground plane. Oblique incidence and both TE and TM polarizations have been considered. The analytical results show a good agreement with those computed by high-performance numerical methods, accounting for very fine details of extremely complicated transmission/reflection spectra. These results are of straightforward application to a variety of practical situations from microwaves to the terahertz regime. The present methodology can still be useful at higher frequencies provided that adequate models of the planar conductors are incorporated. In general, the model provides physical insight on the nature of the expected spectra and facilitates the design of devices based on planar metallic gratings.

In the study of electromagnetic wave propagation and scattering, researchers have always faced the dichotomy of dealing directly with Maxwell's equations (and their complicated analytical/numerical solution methods) or trying to find a simplified model (usually in terms of an equivalent circuit) that can help provide some physical insight into the involved electromagnetic phenomena. The pursuit of analytical solutions for propagation, radiation, and scattering problems does not seem to be a task currently in much demand in microwave engineering, although it was only 20 years ago that many research papers on these topics included some sort of analytic derivations.

This paper presents a quasi-analytical approach to study the classic topic of transmission/reflection of electromagnetic waves through 1-D periodic arrays of strips/slits in metal screens. The approach is based on standard waveguide discontinuity theory. Starting from field equations, it is inferred a circuit-like reduced-order model with just one parameter to be determined. The value of this parameter can be obtained from the transmission/reflection coefficient provided by any full-wave method at just one single frequency. In this way, the computation effort to obtain very wide-band responses of periodically distributed slits or strips under oblique TE/TM illumination in the presence of loading dielectric slabs is reduced to the full-wave analysis of the structure at a single frequency value. For relatively narrow strip/slit gratings, this procedure gives very accurate results even for very complicated transmission/reflection spectra. An additional advantage of the present approach is that it allows for an easy understanding of the underlying physics of the phenomena involved.

A critical discussion on the computation of the dispersion diagram of electromagnetic guiding/radiating structures with one-dimensional periodicity using general-purpose electromagnetic simulation software is presented in this work. In these methods, full-wave simulations of finite sections of the periodic structure are combined with appropriate simplifying network models. In particular, we analyze the advantages and limitations of two different combined methods, with emphasis on the determination of their range of validity. Our discussion is complemented with several selected numerical examples in order to show the most relevant aspects that a potential user of these methods should be aware of. Special attention is paid to the relevant role played by the high-order coupling between adjacent unit cells and between the two halves of unit cells exhibiting reflection, inversion, and glide symmetries.