## 1. Introduction

[2] The relative benefits of conventional microstrip antennas, possessing a conducting strip printed on a grounded microwave substrate, as well as their attractive resonance and radiation characteristics have been meticulously documented in the literature [see, e.g., *Pozar and Schaubert*, 1995; *Wong*, 1999; *Nasimuddin*, 2011; *Gao et al.*, 2001; *Bzeih et al.*, 2007; *Rubelj et al.*, 1997]. More precisely, the microstrip antennas offer light-weight, ease of fabrication, conformability to planar and non-planar surfaces, integrability with microwave and millimeter-wave circuits, as well as mechanical robustness. Microstrip antennas have been widely utilized in communication systems, radars, sensors, radio frequency identifications etc. The progress in wireless communications has further increased the demand for microstrip antennas, capable to be embedded in portable, hand-held, and wireless network devices [*Nasimuddin*, 2011]. Moreover, the remarkable electromagnetic properties of various types of metamaterials paved the way for the incorporation of similar substances materials as substrates or superstrates of microstrip antennas in order to achieve features, such as high directivity and increased gain [*Xu et al.*, 2008; *Attia et al.*, 2009].

[3] On the other hand, diminishing the electromagnetic interaction of a device or component is a topic that has attracted considerable attention from both a theoretical as well as from an experimental point of view. The general idea of cloaking a sensor, without affecting its capability to receive signals proportional to the measured quantity, is analyzed by *Alù and Engheta* [2009], where a system design is proposed whose presence is not perceived by the surrounding. An alternative materialization of the aforementioned concept, based on optics transformation, is presented by *Greenleaf et al.* [2011], where a sensor effect that breaks the strong connection between cloaking and shielding, allowing the former without the latter, is thoroughly described. Scattering cancelation mechanisms by means of isotropic and homogeneous thin covers in both electromagnetic and acoustic domains have been recently investigated [*Guild et al.*, 2011], which could be employed in achieving low profile for receiving structures.

[4] In this work, motivated by the above considerations, we consider a two-dimensional (2-D) infinite planar microstrip antenna, excited by an incident plane wave, and propose its potential capability of operating as a low-profile receiving antenna, after incorporating a suitable cloaking superstrate. The aforementioned problem is indeed an inherently difficult and challenging problem to achieve a low profile, due to the facts that the microstrip structure is considered to be infinite, while the incident plane wave constitutes also an excitation with infinite wavefront. In particular, the under consideration 2-D planar microstrip antenna is comprised of a perfect electric conductor (PEC) plane, a slab substrate, a thin rectangular PEC strip, and a slab superstrate. The goal of the analysis lies in the determination of the influence of the superstrate on the scattering features of the microstrip. Additionally we aim at achieving a low profile for the receiving antenna by choosing appropriately the thickness*h* and material parameters *ϵ*_{2} and *μ*_{2}of the superstrate. We note that the utilization of the terminology “cloaking” in the present context does not concern that electromagnetic waves get around the object to be cloaked but more likely refers to a “carpet-cloaking” in the sense of concealing the presence of the strip from its environment; for carpet-cloaking see*Li and Pendry* [2008].

[5] We implement a semi-analytic integral equation method to determine the scattering characteristics of the receiving microstrip antenna (for a discussion on analysis methodologies of microstrip antennas see*Tsitsas and Valagiannopoulos* [2011] and *Valagiannopoulos and Tsitsas* [2008] and of scattering by strips embedded in homogeneous or layered media see *Gürel and Chew* [1992], *Cangellaris* [1991], and *Gürel and Aksun* [1996]; aspects of optimal modeling of microstrip antennas are discussed by *Kolundžija and Bajic* [2002]). First, we determine analytically the Green's function as well as the primary induced fields on the homogeneous (strip-free) layered structure. Then, we apply a methodology based on the radiation integral to compute the scattered field by the microstrip antenna. In particular, we consider the integral representation of the scattered electric field due to the presence of the PEC strip, incorporating the unknown surface current induced on the strip. To this end, we decompose the PEC strip into a suitably large number of thin cylindrical wires, in each one of which flows a different but constant filamentary current. By imposing the boundary condition on the wires, we result to a linear system the solution of which provides the unknown current coefficients. Having determined these coefficients, we compute the total field in the vacuum region (above the antenna) and subsequently the antenna's far-field response. Furthermore, in order to investigate the regulating effect of the superstrate on the scattered field generated by the overall structure and then seek to reduce considerably the field generated by the actual antenna with respect to that by the superstrate-free antenna, we define two quantities of interest: the*cloaking* (or *low-profile*) *factor*, and the *antenna's reaction.*The former provides a measure of the reduction of the mean value of the far-field radiated over all directions under the presence of the superstrate compared to the superstrate-free case. The latter expresses the normalized far-field over the primary excitation for specific scattering angles. Also, in order to show that the possible reduction of the radiated field by the microstrip antenna is accompanied by a maintenance of the antenna's sensible received signal, we define the received*equivalent current* induced on the strip.

[6] Numerical simulations are presented dealing with the achieved low-profile features of the receiving microstrip antenna by choosing suitably the parameters*ϵ*_{2}, *μ*_{2}, and *h* of the cloaking superstrate. It is demonstrated that for a specific neighborhood of material parameters *ϵ*_{2} and *μ*_{2}the scattered field from the microstrip antenna is considerably reduced, while the received equivalent current on the strip is maintained at sensible levels. In fact, we show that for those parameter values the cloaking factors may be decreased to nearly 25%, meaning that the field generated by the microstrip is nearly one quarter of the field generated by the superstrate-free microstrip. Also, we indicate that the values of*ϵ*_{2} and *μ*_{2}for which this far-field reduction is achieved, correspond to a superstrate composed of an*ϵ*-near-zero (ENZ) material [*Silveirinha and Engheta*, 2006; *Alù et al.*, 2007] or a low-index metamaterial (LIM) [*Lovat et al.*, 2006; *Valagiannopoulos*, 2007a]. Numerical results are also presented concerning the cloaking factors reductions versus the superstrate thickness *h*, the operating frequency *f*, and the incidence angle *ϕ*^{i}. Finally, we depict the variations of the device reaction for various superstrate parameters and conclude that, for no superstrate and for an arbitrary superstrate, the values of the device reaction are very close, while in the case that the superstrate's parameters are optimized, then the device reaction values are significantly reduced, while at certain distinct scattering angles these values even approach zero.