This paper presents design and analysis methods for planar antennas based on modulated metasurfaces (MTSs). These antennas operate on an interaction between a cylindrical surface-wave (SW) excited by an isotropic TM radiator, and an MTS having a spatially modulated equivalent impedance. The MTS is realized by using sub-wavelength patches printed on a grounded slab, thus resulting in a structure with light weight and compact volume. Both features are appealing characteristics for space applications. This paper introduces for the first time an impedance-based amplitude synthesis of the aperture field distribution and shows several new examples of antennas for space applications obtained in recent research projects financed by the European Space Agency.

An effective synthesis procedure for planar antennas realized with nonuniform metasurfaces (MTSs) excited by a point source is presented. This synthesis potentiates previous formulations by introducing a control of the amplitude of the aperture field while improving the polarization and phase performances. The class of MTS antennas we are dealing with is realized by using subwavelength patches of different dimensions printed on a grounded slab, illuminated by a transverse magnetic point source. These antennas are based on the interaction between a cylindrical surface-wave and the periodic modulation of the MTS, which leads to radiation through a leaky-wave (LW) effect. This new design method permits a systematic and simple synthesis of amplitude, phase, and polarization of the aperture field by designing the boundary conditions imposed by the MTS. The polarization control is based on the local value of the MTS anisotropy, the phase is controlled by the shape and periodicity of the modulation, and the amplitude is controlled by the local leakage attenuation parameter of the LW. The synthesis is based on analytical formulas derived by an adiabatic Floquet-wave expansion of currents and fields over the surface, which are simultaneously published in this journal issue. The effectiveness of the procedure is tested through several numerical examples involving realistic structures.

This paper presents a new theory for analyzing the leaky-wave (LW) mechanism supported by planar metasurfaces (MTSs) described by continuous, anisotropic, nonuniform, locally periodic boundary conditions (BCs), and excited by a vertical dipole at the interface. These BCs well represent a dense distribution of subwavelength metal patches of infinitesimal thickness, printed on a grounded slab. We denote succinctly this theoretical formulation as flat optics for LWs. This formulation is based on an adiabatic, asymptotic form of the Floquet theorem, introduced here for the first time. The adiabatic Floquet-wave analysis allows for: 1) describing the mechanism of global interaction between the cylindrical surface wave (SW) launched by the dipole and the modulated MTS; 2) introducing a generalized curvilinear-wavefront LW field that can be used for controlling the radiation-pattern shaping; 3) describing the local and global transfer of energy from SW to LW; 4) establishing an analytical relationship between the aperture field polarization and the anisotropic parameters of the MTS and 5) between the leakage parameter α and the MTS modulation index. Concerning the latter point, a closed-form formula for α is introduced, which allows for unprecedented control of the aperture field amplitude. The theoretical results are successfully validated by comparison with a full-wave analysis, showing impressive accuracy. In a companion paper published in this Journal issue, the present theory is used for the synthesis of a large class of planar aperture antennas.

Different types of efficiencies are introduced for metasurface (MTS) antennas based on single point-source excitation: 1) the feed efficiency ε _feed is the power delivered by the feed to surface wave (SW) over the input power; 2) the tapering efficiency ε _tap quantifies the deviation with respect to a uniform illumination; 3) the conversion efficiency ε _conv defines the capability of the MTS to transform the SW power into leaky-wave power; and 4) the ohmic efficiency ε _Ω accounts for the antenna losses. The product of all of these factors provides the overall efficiency of the antenna. New, quite general analytical formulas are suggested to estimate any individual efficiency. In particular, it is seen that ε _feed can reach also 90% by using planar or quasiplanar circularly symmetric sources. It is also proven that the product ε _conv ε _tap cannot be larger than 58% for a uniform modulation; however, by using a nonuniform modulation, it can be increased to reach ε _conv ε _tap ≈ a/λ/(a/λ + 2), where a/λ is the antenna radius in free-space wavelengths. A new closedform formula for estimating the losses is given. In accordance with the prescription given here, one can reach 75% of global efficiency, including losses, until a radius of 20 wavelengths with commercially available substrates.

Metasurfaces are thin metamaterial layers characterized by unusual dispersion properties of surface/guided wave and/or reflection properties of otherwise incident plane waves. At the scales intervening in their design, metasurfaces can be described through a surface impedance boundary condition. The impedance, possibly tensorial, is often “modulated,” i.e., it can vary from place to place on the surface (by design). We investigate on different integral equation formulations of the problem, with special attention to the stability properties of the resulting system matrix.

This paper presents an effective approach for the derivation of the two-dimensional (2-D) frequency-wavenumber dispersion surface of anisotropic metasurfaces (MTSs) consisting of elliptical patches printed over a grounded slab. These MTSs are important in the design of leaky-wave antennas and transformation optics (TO) surface-wave based devices. The formulation resorts to an analytical expression of the currents excited on the element of the periodic texture to define a reduced spectral method of moments (MoM) procedure with only three basis functions. An exact compact formula, which links the MoM matrix to the homogenized equivalent anisotropic impedance of the MTS, is derived. The formulation presented here has been found accurate and useful for designing MTS antennas and TO devices.