Analytical circuit model for stacked slit gratings

Abstract

This work presents a rigorous circuit model to compute the transmission/reflection properties of a finite number of stacked slit gratings printed on dielectric slabs of arbitrary thickness. A key aspect of the present approach is that the circuit model itself leads us to find fully analytical expressions for the finite stacked-grating structure. An analytical model to obtain the Brillouin diagram for the fully periodic structure (infinite number of identical unit cells) is also provided. Index Terms-Bloch waves, equivalent circuit modeling, metal gratings, periodic structures. I. I NTRODUCTIONPeriodic structures consisting of planar periodic distribu tions of metallic scatterers printed on one or more dielectric substrates have been studied for decades in the microwaves and optics literature [1], [2]. The simplest case corresponds to an infinite 1D periodic array of slits made in a thin metal plate printed on a dielectric slab [3]- [5]. Nowadays, the analysis of this kind of structures is mostly carried out using commercial software, although recently a lot of attention is being paid in the literature to the development of circuit-like models [6], [7]. These models provide closed-form analytical expressions for the transmission, reflection and absorption properties of that kind of geometries; see, for instance, the quasi-heuristic approaches for 2D arrays of slots in [8], for 2D arrays of patches in [9] or for strip/slit-like structures in [10], as well as the rigorous circuit-model derivation in [11] for 1D arrays of strips/slits. It should be noted that all the above mentioned papers only consider the case of a single structured periodic metallic surface (the periodicity is assumed to be in the transverse directions). The extension of the circuit-like models to the case of cascaded (stacked) structured surfaces is of great interest [see Fig. l(a)]. Thus, for instance, controlled transmission and rejection bands appear associated with the quasi-periodic nature of the system along the propagation direction of the wave when C l = C2 = ... = CN and d1 = d2 = ... = d N. This extension is relatively simple when the distance between the structured metal surfaces is large enough to preclude high-order mode interaction (i.e., when the interaction between metallic surfaces is due to the fundamental TEM propagating mode) [12]. However, interaction through the first few high-order modes drastically modifies the physics of the problem and makes the analysis much more compli cated. The purpose of the present contribution is to present a simple and efficient procedure to extend the analysis reported in [11] in order to account for the electromagnetic properties of a densely packaged set of slit-like structures consisting of a finite (or infinite) number of screens [ Fig. 1 (a)]. To the authors' knowledge, a closed-form solution to this problem is here reported for the first time.

Wideband equivalent circuit for non-aligned 1-D periodic metal strips coupled gratings

“…Two 1D periodic arrays of conducting strips having the same lattice parameter (period p in the figure) are printed at both sides of a dielectric substrate. The case corresponding to h = 0 and w 1 = w 2 has already been considered in [15] and [17]. In contrast to that case, our new problem does not have a vertical symmetry plane, thus precluding the use of the even/odd excitation method employed in the above mentioned references.…”

“…Since a magnetic wall boundary condition (instead of a grounded metal) at the non-metallized side of the dielectric substrate can be easily incorporated in the model, this method also allows for the analysis of closely spaced identical gratings by means of a superposition of even and odd excitations. Moreover, this strategy makes it possible to solve analytically the problem posed by stacked slit gratings based on identical metallic patterns separated by arbitrary dielectric layers [17]. However, if the slits in both gratings have different width and/or the gratings are shifted with respect to each other (non-aligned gratings), as it is required in some interesting situations [18], the method in [15] cannot be directly applied due to the lack of a symmetry plane.…”

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

“…Although this strategy is useful in many situations, our aim here is to derive the appropriate circuit topology in a rigorous way from first principles and to give the values of the circuit parameters in closed form. This standpoint has been used in the past by some of the authors of the present work to model other periodic structures [35], [49]- [51], and it is now extended to stacked 2D geometries so that the problem under study (multilayer fishnets) can be covered.…”

“…In [51] it was shown that the key aspect that makes it possible to easily obtain an equivalent network for the problem of N stacked metallic slit gratings (1D version of the problem of interest in that paper) comes from the decomposition of the two-coupled metallic screens problem into "internal" and "external" sub-problems as a consequence of the Equivalence Theorem [52]. The extension of this idea to a pair of coupled aperture-type frequency selective surfaces (FSS's) (the most basic form of fishnet structure) is immediate as long as the FSS's are of slot-type nature too (the procedure is not directly applicable to patch-based FSS's).…”

“…The extension of this idea to a pair of coupled aperture-type frequency selective surfaces (FSS's) (the most basic form of fishnet structure) is immediate as long as the FSS's are of slot-type nature too (the procedure is not directly applicable to patch-based FSS's). Thus, following [51], the problem of the two-coupled aperture-type FSS's shown in Fig. 2(a) has the equivalent π network shown in Fig.…”