International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 560403, 8 pages

http://dx.doi.org/10.1155/2015/560403

## Suppression of Specular Reflections by Metasurface with Engineered Nonuniform Distribution of Reflection Phase

^{1}School of Electronics and Information Engineering, Soochow University, Suzhou 215006, China^{2}State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China^{3}Electronic Countermeasure Laboratory, Air Force Early Warning Academy, Wuhan 430019, China

Received 9 November 2014; Accepted 8 January 2015

Academic Editor: Sanming Hu

Copyright © 2015 Xin Mi Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We make preliminary investigations on a new approach to reducing radar cross section (RCS) of conducting objects. This approach employs novel planar metasurfaces characterizing nonuniform distribution of reflection phase. The operation principle of this approach and the design rule of the associated metasurfaces are explained using a simplified theoretical model. We then present a design example of such metasurfaces, in which three-layer stacked square patches with variable sizes are utilized as the reflecting elements. The proposed RCS-reduction approach is verified by both numerical simulations and measurements on the example, under the assumption of normal plane wave incidence. It is observed that, in a fairly wide frequency band (from 3.6 to 5.5 GHz), the presented example is capable of suppressing the specular reflections of conducting plates significantly (by more than 7 dB) for two orthogonal incident polarizations.

#### 1. Introduction

Reduction of target radar cross section (RCS) for military or civilian applications has been a subject of extensive studies in both scientific and engineering communities for decades. The existing RCS-reduction strategies can be classified into two categories. One is decreasing or even canceling the scattered energy and the other is reshaping the scattering pattern. Traditionally, the radar absorbing material (RAM) is adopted for the first category while the second category is usually achieved through shaping of target [1–4]. Recently, great efforts have been made for the sake of improving the traditional RAM technology. For instance, reduced RAM thickness has been achieved by employing artificial magnetic conductor (AMC) or reactive impedance ground as the backing panel of RAM [5–7]. It is worth mentioning that the rapidly growing research field of metamaterials has contributed a completely new strategy called invisibility cloak [8, 9], which can be grouped into the first category. The invisibility cloak is a kind of inhomogeneous wrappage that could steer the incoming electromagnetic waves smoothly around the hidden object and return them to their original trajectory, making the object almost invisible (i.e., have no scattered field). New ideas have emerged regarding the second category of RCS-reduction techniques these years as well [10–14]. For example, it was proposed by Paquay et al. that, by combining AMC and perfect electrical conductor (PEC) cells in a chessboard-like configuration, the cancelation of reflections from these two kinds of cells would effectively reduce the specular reflections and hence the RCS of planar conducting plate [10]. In addition, some researchers have paid attention to metamaterial coatings with randomly distributed refractive indices or gradients of refractive index [11–13]. Such coatings are capable of suppressing remarkable lobes of conducting plates by creating diffuse reflections in front of these plates. In 2014, Wang et al. proposed a design of broadband and broad-angle low-scattering metasurface based on a hybrid optimization algorithm [14].

In this paper, we make further investigations on RCS-reduction schemes characterizing redistribution of scattered energy, by making use of novel metasurfaces with nonuniformly distributed reflection phase. The rest of the paper is organized as follows. In Section 2, a theoretical model for analyzing the backscattering performance of such metasurfaces is given and a fundamental design rule of the relevant nonuniform distribution of reflection phase is promoted for RCS-reduction in the specular direction. Section 3 introduces a practical implementation scheme of such metasurfaces through an example. Finally, Section 4 presents both the simulation and measurement results of the example, which confirms that metasurfaces with properly designed nonuniform phase distribution have the potential of suppressing specular reflections of planar conducting plates under normal incidence.

#### 2. Theory

Metasurface with nonuniformly distributed reflection phase, which is referred to as nonuniform surface below for brevity, is artificial composite constituted by reflecting elements each of which reflects local incident ray back into space with certain phase shift. One or several geometrical parameters of these elements vary along the surface such that the reflection phase is nonuniformly distributed with respect to incident plane waves.

It is well known that directive radiation is closely related to equiphase surface perpendicular to the radiation direction. For planar conducting plate which has uniform reflection phase, the reflected field possesses a planar equiphase surface with respect to incident plane wave and hence the reflected energy is focused in specific direction (i.e., the specular direction). If the conducting plate is covered with certain composite structure to form a nonuniform surface, the equiphase surface will be no doubt disturbed and the incident plane wave will be reflected or scattered irregularly. Moreover, it is possible that the directional reradiation in the specular direction is remarkably suppressed or even eliminated, provided that the distribution of reflection phase is appropriately chosen.

For simplicity, consider the problem geometry shown in Figure 1, where a planar nonuniform surface is divided into squares with lattice constant denoted by . Each square represents a reflecting element which is assumed to totally reflect its local incident beam. The origin of coordinate is situated at the center of the plane defined by the surface. An infinite -polarized plane wave is normally incident on the nonuniform surface and is given bywhere is the wave number in free space. The local reflected field at each element can be estimated using the infinitely periodic array model and is supposed to be dominated by the fundamental copolarized Floquet mode (in this model, each element is analyzed by assuming local periodicity; i.e., each element is considered in an array environment with all the elements identical). Hence, the reflected electric field at the element numbered as , can be written aswhere is the reflection phase of the corresponding element. By applying the second principle of equivalence, the angular spectrum of plane waves for scattered field in the half-space can be expressed by the following Fourier transform [15]:where is the tangential component of the scattered electric field along the surface (i.e., the plane of ) and , are variables related to the spherical coordinates by and . Note that the double integral in (3) is limited in the region of metasurface, because is assumed to be zero outside of the surface. This assumption implies that the edge diffraction is ignored. Associating with (2), the spectral function is further derived asIn the above formula,where , representing sample function.