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

Abstract

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.

Annular Apertures in Metallic Screens as Extraordinary Transmission and Frequency Selective Surface Structures

“…Other works relied on multimodal equivalent networks in order to characterize planar strip gratings [18]- [20]. Recently, fully analytical ECAs have been derived by some of the authors of this work for one-dimensional (1D) and two-dimensional (2D) periodic metallic screens printed on dielectric slabs [21], [22], stacked fishnet structures [23] or T-shaped corrugated surfaces [24]. A great number of papers dealing with equivalent circuits applied to FSS structures can be found elsewhere; see, for instance, the review presented in [25] and references therein.…”

Accurate Circuit Modeling of Fishnet Structures for Negative-Index-Medium Applications

“…In particular, for rectangular apertures and for the type of illumination considered in this paper, we have employed the spatial profile suggested in [53] (see the Appendix). Here it is important to point out that the above approximation turns out to be quite accurate up to frequencies close to the second self-resonance of the individual aperture that is compatible with the impinging wave [50]. In practice, this means that the aperture has not F o r P e e r R e v i e w to be sub-wavelength for the circuit approach to be applied with reliability.…”

“…4. The analysis of this much simpler structure will follow some of the guidelines reported in [35], [50]. When this analysis is carried out, the final results for the equivalent admittance corresponding to the incident TM plane wave (electric field directed along the y direction) are the following [see Fig.…”

“…However, in this paper, it will only be considered incidence along principal planes; i.e., ϕ will be allowed to take only the values 0 o and 90 o . The general case of conical incidence could be treated using the method reported in [50]. It is worth mentioning that the given expression for Y (e/o) eq accounts for all the high-order harmonics excited at the discontinuity.…”

“…In practice, this means that the aperture has not F o r P e e r R e v i e w to be sub-wavelength for the circuit approach to be applied with reliability. Actually, for normal incidence, the size of the apertures can be even greater than a wavelength [50]. It is also noteworthy that A TE 0m = 0 ∀m and also that A TM n0 = 0 ∀n = 0.…”