A homogenization technique for obtaining generalized sheet transition conditions for an arbitrarily shaped coated wire grating

Abstract

Using a multiple‐scale homogenization method, we derive generalized sheet transition conditions (GSTCs) for an arbitrarily shaped coated wire grating. The parameters in these GSTCs are interpreted as effective electric and magnetic surface susceptibilities and surface porosities of the wire grating. We give expressions for determining these surface parameters for any arbitrarily shaped grating. We show that these GSTCs are a generalized form of the boundary conditions derived earlier by Wainstein and Sivov, who analyzed the case of symmetric, uncoated wire gratings. This work is also a first step in developing GSTCs for more general types of structures such as metasurfaces, metafilms, and metascreens.

Generalized Sheet Transition Conditions for a Metascreen—A Fishnet Metasurface

“…Some of the derivation of the desired GSTCs are analogous to that used in [12], [15] and [21]- [23], as such, we will not show some of the details when they can be found in these citations. In this section, we first expands the fields in powers of k 0 p (where p is the period of the array, k 0 = ω √ µ 0 ǫ 0 is the free-space wavenumber and ω is the angular frequency corresponding to an assumed exp(jωt) time dependence).…”

“…These two spatial length scales results in the fields having a multiplescale type variation that is associated with the macroscopic and microscopic structures of the problem. Similar to [12], [15] and [21]- [23], Maxwell's equations are expressed as:…”

“…The two BCs for the sum of the E x and E z fields [eqs. (76) and (78)] have the same functional form as the BC needed for an arbitrarily shaped wire-grating (a metagrating) [12]. The wire-grating is a similar structure in that a BC for the sum of the E-field parallel to the wires is required, and is given in terms of surface porosities [12].…”

“…where the superscripts A and B correspond to the regions above and below the reference plane of the metascreen, respectively. We add that these types of GSTCs on both the jump in, and the average of, the E-field at the interface have also appeared in the analysis of a wire grating (or metagrating) [12]. In this paper we present a systematic multiple-scale homogenization approach to fully characterize the field interaction at the surface of the periodic metascreen shown in Fig.…”

“…There are other types Manuscript received October 24, 2017. of meta-structures that lie somewhere between a metafilm and a metascreen. For example, a grating of parallel coated wires (a metagrating) behaves like a metafilm to electric fields perpendicular to the wire axes and like a metascreen for electric fields parallel to the wire axis [12]. In this paper we discuss the behavior of metascreens.…”