Tunneling and “ Growing Evanescent Envelopes ” in a Pair of Cascaded Sets of Frequency-Selective Surfaces in Their Band Gaps

The presence of “growing evanescent” field distributions in a suitably designed, periodically layered stacks of frequency selective surfaces (FSS) is discussed in this paper. It is shown that there are structures other than the slab of double-negative (DNG) or left-handed metamaterials that can lead to the buildup of the evanescently modulated waves inside these structures. Moreover, it is shown how an interface resonance phenomenon similar to the one present at the interface between metamaterials with oppositely signed constitutive parameters may be induced by a proper choice of the periodicities of the FSS stacks and the geometrical properties of these surfaces. The analysis is performed through an equivalent transmission-line approach, and some physical insights into this phenomenon are presented. Salient features, such as the complete wave tunneling through the pair of cascaded FSS, each operating at its bandgap, are presented and discussed. INTRODUCTION In his paper describing the idea of “perfect lens” using the slab of properly selected double-negative (DNG) media, i.e., a medium in which the real permittivity and permeability are simultaneously negative (also known as “left-handed” or “negative index” media), Pendry theoretically showed that in such a DNG slab the evanescent wave has a “growing exponential”, which contributes to the higher resolution of the image [1]. This idea has generated a lot of interests in the field of metamaterials, and many groups worldwide are studying this issue of reconstruction of the evanescent waves and its sub-wavelength focusing. A natural question may arise: “May the growing exponential happen in other classes of media or in properly designed structures, hopefully more easily realizable than DNG media? ” Some ideas have been already reported in the literature [2], [3]. We have been interested to explore the answers to this question and to explore other alternatives. Here, we show that a somewhat analogous phenomenon in the form of growth of evanescently modulated waves can occur inside suitably designed periodic arrangements of stacks of frequency-selective surfaces (FSS) within conventional (i.e., double-positive (DPS)) media. Frequency Selective Surfaces (FSS), which are constructed as planar 2-dimensional periodic arrays of metallic elements with specific geometrical shapes, or as periodic apertures in a metallic screen, have been widely studied and known for many years [4]. The transmission and reflection coefficients for these surfaces are dependent on the frequency of operation and may also depend on the polarization and angle of incidence. In this work, we show how by periodically stacking two sets of FSS with “dual” behaviors, one may achieve growing field distributions towards the interface between these two stacks, and may have complete tunneling of wave through this pair, even though each stack alone would be “under cut-off” (i.e., it is in its stop band regime), similar to what we have obtained for an incident plane wave tunneling through a pair of properly chosen single-negative (SNG) bilayers [5]. THEORETICAL ANALYSIS It is well known that an equivalent circuit model representation may be used for plane wave interaction with FSS [4]. In the transmission-line analogy, at a given frequency an FSS may be represented as a shunt load, either inductive or capacitive depending on its geometrical parameters, in a transmission line (TL) segment. A cascade of FSS with dielectric materials filling the space between them (shown in Fig. 1a) would therefore be modeled as a series of TL cells periodically loaded by shunt loads, as in Figure 1b. The distance between every FSS would correspond to the distance between the loads, and the “host” TL parameters, i.e., c Z and TL k depend on the angle of incidence, the frequency and the polarization of the incident plane wave. The values of the shunt admittances of FSS depend directly on the geometrical parameters of the FSS, in addition to the frequency, polarization, and angle of incidence of the incoming wave. Such parameters have been extensively studied and reported in the literature (see e.g., [4]). Obviously, in the limit of no loss, the values of the shunt admittances of FSS are assumed to be purely imaginary. Referring to Figure 1, therefore, the length of every single cell d equals the distance between the two