Double-scale homogenized impedance models for periodically modulated metasurfaces

This paper investigates the accuracy of homogenized impedance models for the description of periodically modulated metasurfaces (MTSs) realized by printing subwavelength patches on a grounded dielectric slab. The problem is relevant to surface-wave based MTS antennas. The homogenized models are based on the local impedance synthesis of the subwavelength patch elements on the basis of a micro-periodicity assumption (that is, with a subwavelength period); the homogenized impedance is successively used in a macro-periodically modulated problem; that is, a periodic homogenized problem with a period which includes several micro-periods. Two different homogenized impedance models are compared. A first model is based on an anisotropic “impenetrable” impedance, defined by boundary conditions (BCs) at the MTS-air interface, while the second one uses a “penetrable” impedance sheet describing the homogenized BCs imposed by the metallic cladding on the grounded metallic slab. Although the presence of the grounded slab is considered in both models, they provide different results when the homogenized impedance is used to describe the macro-modulation. It is shown, through comparison with a full-wave analysis, that both the homogenized models can provide consistent results, but the penetrable impedance model is more accurate in the prediction of both the complex propagation constant and the current distribution. This is due to its capability to correctly account for the spatial dispersivity of the MTS

Flat optics for leaky-waves on modulated metasurfaces: Adiabatic floquet-wave analysis

4noreservedThis 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 $alpha$ and the MTS modulation index. Concerning the latter point, a closed-form formula for $alpha$ 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.mixedMinatti, Gabriele; Caminita, Francesco; Martini, Enrica; Maci, StefanoMinatti, Gabriele; Caminita, Francesco; Martini, Enrica; Maci, Stefan

Efficient method of moments analysis of metasurface antennas

This paper presents an efficient approach for the method of moments (MoM) analysis of metasurface (MTS) antennas. Instead of simulating the actual structure, made of several thousands of subwavelength patches, the presence of the MTS is accounted for using an impedance boundary condition in the integral equation. Then, when the MTS antenna exhibits rotational symmetry, the integral equation can be efficiently solved adopting a formulation for bodies of revolution. On the other hand, a novel type of basis functions can also be applied to the analysis of planar MTSs without any particular symmetry. The advantages of such basis, in both the space and spectral-domain, are outlined. Indeed, their closed-form spectrum allows one to efficiently compute the MoM impedance matrix using the spectral-domain approach. More importantly, these basis functions represent the global evolution of the surface current density in an effective manner. In both approaches, one obtains a drastic reduction in the number of unknowns, with respect to the cases in which the actual structure has been meshed with sub-entire domain basis

Synthesis of modulated-metasurface antennas with amplitude, phase, and polarization control

5noreservedAn 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.mixedMinatti, Gabriele; Caminita, Francesco; Martini, Enrica; Sabbadini, Marco; Maci, StefanoMinatti, Gabriele; Caminita, Francesco; Martini, Enrica; Sabbadini, Marco; Maci, Stefan

Green's function for grounded anisotropic liquid crystal substrate

In this paper, a procedure to calculate the dyadic impedance (or admittance) Green's function for a grounded layer of LCs is briefly presented. To validate the theoretical procedure, an example of dispersion calculation of a grounded layer of LCs is presented, showing excellent agreement with the simulations made with a commercial software

Electronically scanning antennas based on reconfigurable metasurfaces

This contribution addresses the use of reconfigurable modulated metasurfaces (MTSs) for the realization of electronically scanning antennas without the use of phase shifters. Different approaches can be used to electronically control the average equivalent impedance or the modulation period of the modulated MTS

Efficient design of transformation optics devices based on anisotropic metasurfaces

Transformation Optics (TO) is a systematic approach that makes use of coordinate transformations to design devices capable of controlling the propagation of electromagnetic waves [1]. This control is achieved on the basis of macroscopic equivalent constitutive tensors of a volumetric anisotropic material. In practice, TO-based devices can be implemented by using metamaterials, which can be engineered to achieve electromagnetic behaviors which can not be found in nature [2]. Metamaterials can be realized by periodically arranging many small inclusions in a dielectric host environment and their use offers promising opportunities for the practical implementation of TO-based devices; there are, however, technological difficulties in controlling the variation of the macroscopic constitutive tensors of volumetric metamaterials, as well as in realizing anisotropic and extreme parameters. A significant technological simplification can be obtained by using metasurfaces (MTS) [3] instead of volumetric metamaterials. MTSs are thin metamaterial layers constituted by a periodic lattice of sub-wavelength elements. Due to the small periodicity in terms of a wavelength, they can be characterized in terms of an equivalent impedance providing the relationship between the average tangential components of the electric and magnetic fields. Indeed, effects similar to addressing waves in volumetric media may be obtained by modulating the properties of an impedance surface supporting surface waves (SW) [4-6]

Surface wave dispersion for a tunable grounded liquid crystal substrate without and with metasurface on top

The surface wave dispersion of a grounded layer of liquid crystals (LCs) is investigated by taking into account the inherent electrical reconfigurability of such a material. The spectral dyadic impedance Green's function of the tunable LC grounded slab is calculated and the dispersion curve of the fundamental mode supported by the structure is presented, showing that the orientation of the optical axis of the LCs modifies the surface wave dispersion curve significantly enough to be applied for surface wave propagation control. Furthermore, it is demonstrated that the presence of an inductive metasurface on top of the LC layer impressively reduces the resonance frequency and increases the sensitivity to the continuous voltage biasing