Surface Impedance Tensor Research Articles

Method for extracting the surface impedance of a generic reflective metasurface

We develop a method for the extraction of the surface impedance tensor of a generic reflective metasurface using an analytic relation between the tensorial surface impedance and the four polarisation-dependent reflection coefficients. We apply this technique to experimental data obtained from a metasurface with a rhomboidal unit cell in the 16–26 GHz range, but note that it could be applied to reflective metasurfaces in any frequency regime. The extraction method can also be applied to model data to facilitate the design process of spatially graded tensorial metasurfaces that allow for full control of the form of the scattered field.

Design and Tensor Impedance Analysis of 4×4 Isotropic Homogeneous Metasurface-Backed Slotted Dual-Layered Bio-Superstrate-Loaded MPA

A 4×4 Isotropic Homogeneous Metasurface (IHM) backed, rectangular slotted dual-layered triband microstrip patch antenna (MPA) is proposed in this article. A detailed mathematical way to analyze the tensor surface impedance matrix (TSIM) of the proposed 4×4 IHM and slotted patch is demonstrated. The proposed IHM-backed MPA has a triband even-mode resonance at fr0=2.45 GHz, 2fr0=5.4 GHz, and 4fr0=7.7 GHz. A better and more accurate estimation of bio-superstrate loading effect for triband resonance is employed using the human skin (εr=52.79, σs=1.39) and blood (εr=52.8, σs=1.23) layer on the top of dual-layered metasurface-backed slotted MPA. TSIM characterization is observed for both blood- and skin layer-loaded dual-layered metasurface-backed slotted MPA. Chicken breast (εr=55.2, σs=1.49, and tanδ=0.325) with blood (εr=58.2, σs=2.59, and tanδ=0.364) is loaded onto fabricated dual-layered structure to verify numerically modeled estimation. A closed form triband, even-order resonance mode (i.e., fr0, 2fr0, and 4fr0) estimation based on dielectric superstrate thickness (Hs) is numerically established using MATLAB solver. Complete measurement setup with simulated vs. measured results is compared in this article.

Tensor-Free Holographic Metasurface Leaky-Wave Multi-Beam Antennas with Tailorable Gain and Polarization.

Recently, the community has seen a rise in interest and development regarding holographic antennas. The planar hologram is made of subwavelength metal patches printed on a grounded dielectric board, constituting flat metasurfaces. When a known reference wave is launched, the hologram produces a pencil beam towards a prescribed direction. Most earlier works on such antennas have considered only a single beam. For the few later ones that studied multiple beams, they were achieved either by having each beam taken care of by a distinct frequency or by partitioning the hologram, thereby depriving each beam of the directivity it could have had it not shared the holographic aperture with other beams. There have been recent studies related to the use of tensor surface impedance concepts for the synthesis of holograms which have attained control over the polarizations and intensities of the beams. However, this approach is complicated, tedious, and time-consuming. In this paper, we present a method for designing a planar holographic leaky-wave multi-beam metasurface antenna, of which each simultaneous beam radiating at the same frequency towards any designated direction has a tailorable amplitude, phase, and polarization, all without hologram partitioning. Most importantly, this antenna is exempted from the need for the cumbersome technique of tensor impedance. Such features of beam configurability are useful in selective multiple-target applications that require differential gain and polarization control among the various beams. Only a single source is needed, which is another benefit. In addition, effective methods to mitigate sidelobes are also proposed here. Designs by simulations according to the method are herein validated with measurements performed on fabricated prototypes.

Reflection and Transmission Analysis of Surface Acoustic Wave Devices.

This paper presents a study of the propagation of surface acoustic waves in a single and periodic array of metal strip overlays on the surface of layered substrates. Responses of reflected and transmitted surface acoustic waves due to various geometric design parameters of the grating arrays are investigated. An eight-dimensional matrix formulation based on Stroh formalism is adopted to analyze wave propagation in piezoelectric layered media. The dispersion curves for aluminum-zinc oxide films on glass substrates are determined using the surface impedance tensor method. A transfer matrix in terms of the state vectors in cooperation with continuity conditions on the edges of the grating array is used to determine the reflectivity and transmittance of the horizontally propagating surface acoustic waves. The analysis and simulation results show that when the surface acoustic wave is obliquely incident on an array of gratings and the strip width is equal to the gap between strips, the constructive interference of the reflected wave occurs at odd multiples of the strip width to a wavelength ratio of 0.25. When the strip width is unequal to the gap, the constructive interference of the reflected wave is an odd multiple of the strip width to a wavelength ratio of 0.5. An increase in the number of strips concentrates the reflectivity's extreme frequencies, and an increase in the strip height increases the bandwidth of the extreme frequencies. Both of these increases strengthen the reflected wave's constructive interferences.

Tensor surface impedance modelling of metasurfaces with printed elements

AbstractTwo methods for extraction of the effective tensor surface impedance representing metasurfaces with printed elements and arbitrary geometry are presented. The surface impedance can be modelled as a shunt admittance on a transmission line. The extracted surface impedance combined with transmission line theory enables to compute easily and efficiently the transmission coefficient through a multilayer metasurface structure. The metasurface modelling as a shunt admittance enables to conduct a multi‐parameter study on the transmission and reflection performance through the metasurface structure. The results of the proposed methods are compared, and very good agreement was obtained up to 30° incident angle. Beyond 30° it is suggested to recalibrate the model or upgrade it. For model validation purposes, a 2D flat lens antenna with patch elements loaded with capacitors was designed, fabricated, and measured. Simulation and experimental results of the lens near and far‐field are presented.

Off-Diagonal Magnetoimpedance in Annealed Amorphous Microwires with Positive Magnetostriction: Effect of External Stresses

It was observed recently that the giant magnetoimpedance (GMI) effect in Fe-rich glass-coated amorphous microwires with positive magnetostriction can be improved significantly by means of post-annealing. The increase in the GMI is attributed to the induced helical magnetic anisotropy in the surface layer of the microwire, which appears after the annealing. The application of external stresses to the microwire may result in changes in its magnetic structure and affect the GMI response. In this work, we study theoretically the influence of the tensile and torsional stresses on the off-diagonal magnetoimpedance in annealed amorphous microwires with positive magnetostriction. The static magnetization distribution is analyzed in terms of the core–shell magnetic structure. The surface impedance tensor is obtained taking into account the magnetoelastic anisotropy induced by the external stresses. It is shown that the off-diagonal magnetoimpedance response exhibits strong sensitivity to the magnitude of the applied stress. The obtained results may be useful for sensor applications of amorphous microwires.

Microwave Hall effect measurement for materials in the skin depth region

We developed a new microwave Hall effect measurement method for materials in the skin depth region at low temperatures using a cross-shaped bimodal cavity. We analytically calculated electromagnetic fields in the cross-shaped cavity and the response of the cavity including the sample, whose property is represented by the surface impedance tensor; furthermore, we constructed the method to obtain the Hall component of the surface impedance tensor in terms of the change in resonance characteristics. To confirm the validity of the new method, we applied our method to measure the Hall effect in metallic Bi single crystals at low temperatures, and we confirmed that the microwave Hall angles coincide with the DC Hall angle. Thus, it becomes clear that the Hall angle measurement under cryogenic conditions becomes possible without any complicated tuning mechanisms, and our bimodal cavity method can be used to measure the microwave Hall effect on materials in the skin depth region. The result opens a new approach to discuss the Hall effect in condensed matter physics such as the microwave flux-flow Hall effect in superconductors.

Возбуждение анизотропной импедансной метаповерхности в виде эллиптического цилиндра.

The problem of arbitrary excitation of waves by a system of external sources near an anisotropic metasurface in the form of an elliptical cylinder with a surface homogenized impedance tensor of general form is solved. The solution to the problem is written as a superposition of E- and H-waves in elliptical coordinates. The partial reflection coefficients of waves were found from the boundary conditions using the orthogonality of the Mathieu angular functions. For these coefficients, four coupled infinite systems of linear algebraic equations of the second kind are obtained. The conditions under which the solution of the excitation problem by the method of eigenfunctions is obtained in an explicit form are found and analyzed. It is shown that for this, the surface impedance tensor of a uniform metasurface must belong to a class of deviators (have zero diagonal elements). In the particular case of a mutual (most easily realized) metasurface, its impedance tensor should only be reactance. In another special case, the impedance tensor of a set of deviators describes a class of anisotropic nonreciprocal metasurfaces with the so-called perfect electromagnetic conductivity (PEMC).

A Core–Shell Model for Magnetoimpedance in Stress-Annealed Fe-Rich Amorphous Microwires

The magnetoimpedance effect in a stress-annealed Fe-rich amorphous microwire with induced magnetic anisotropy in a surface region is studied theoretically. The static magnetization distribution within the microwire is described in the framework of the core–shell magnetic structure. It is assumed that the microwire has an axial magnetic anisotropy in the inner core and a helical anisotropy in the external shell appearing due to the stress-annealing. Both the diagonal and off-diagonal magnetoimpedance responses are found in terms of the surface impedance tensor. The influence of the bias current on the magnetoimpedance is analyzed. The obtained theoretical dependences are shown to be in a qualitative agreement with the results of recent experimental studies of the magnetoimpedance effect in stress-annealed Fe-rich glass–coated amorphous microwires.

Superscattering from Subwavelength Corrugated Cylinders

Wave scattering from a cylinder with a tensor impedance surface is investigated based on the Lorentz-Mie theory. A practical example of such a cylinder is a subwavelength metallic rod with helical dielectric-filled corrugations. The investigation is performed with the aim to maximize scattering cross-section by tailoring the surface impedance of cylindrical scatterers. For the normally incident TEz and TMz waves the required surface impedance of a subwavelength cylinder can be produced by longitudinal (axial) and transverse (circumferential) corrugations, respectively. It is shown that such corrugations induce superscattering at multiple frequencies, which can be widely tuned with either or both the size and permittivity of dielectric-filled corrugations. In the microwave band, this effect is demonstrated to be robust to material losses and is validated against the full-wave simulations and experiment. For the TEz waves the enhanced scattering from the cylinder is found to have a broad frequency bandwidth, provided that the relative permittivity of corrugations is low or equal unity. In the latter case, the corrugated cylinder acts as an all-metal superscatterer. For such cylinders the near-field measurements are implemented and provide the first experimental evidence of the superscattering phenomenon for all-metal objects. In addition to multifrequency superscattering, the dielectric-filled corrugations are shown to provide multifrequency cloaking of the cylinder under the incidence of the TMz waves. Simultaneous superscattering and cloaking at multiple frequencies distinguishes corrugated cylinders from other known practicable scatterers for potential applications in antenna designing, sensing, and energy harvesting.

Analytical study of surface wave multiple refraction in boundary of a scalar impedance surface with a tensor impedance surface

In this paper, the multiple refraction phenomenon is investigated on the boundary of a scalar impedance surface (SIS) and a tensor impedance surface (TIS). When a surface wave (SW) propagates on the SIS and radiates to the boundary of the TIS, the propagation direction of it is changed and the refraction phenomenon is accrued. The method that is proposed in this paper can predict the multiple refraction for the SW. Moreover, another analytical method is introduced for designing the proposed structure which the double refraction (DR) occurs at arbitrary angles on it. Using it, a sample of the structure is designed by printed circuits in 15.2GHz and the results are verified by the full-wave simulation and measurement. The results are shown that in the structure, DR is occurred in 2° and 22° as predicted. The proposed method can provide many applications such as design of SW power dividers based on the TISs, impedance surface based waveguides, holographic antennas, and feeding of array antennas.

Design and Experimental Demonstration of Impedance-Matched Circular-Polarization-Selective Surfaces with Spin-Selective Phase Modulations

We present the design and experimental demonstration of an impedance-matched circular-polarization-selective surface that also offers spin-selective phase modulations at microwave frequencies. We achieve this by leveraging the theory of Pancharatnam-Berry phase shift and cascading four tensor impedance layers, each comprising an array of crossed meander lines. These meander lines are precisely tuned and rotated to implement particular tensor surface impedance values to satisfy the impedance-matching condition for the transmitted right-handed circularly polarized field while inducing Pancharatnam-Berry phase shift for only the reflected left-handed circularly polarized field. We present a detailed numerical synthesis technique to obtain the required impedance values to satisfy the impedance-matching condition, and demonstrate spin-selective phase modulations based on Pancharatnam-Berry phase shifts. To verify the proposed idea, we experimentally demonstrate nearly reflectionless transmission of right-handed circular polarization at broadside and reflection of left-handed circular polarization at ${33}^{\ensuremath{\circ}}$ off broadside at 12 GHz. For this purpose, a free-space quasioptical setup and a near-field measurement system are used to measure the transmitted and reflected circularly polarized fields, respectively.

Hyperbolic Sound Propagation over Nonlocal Acoustic Metasurfaces.

Hyperbolic metasurfaces, supporting extreme anisotropy of the surface impedance tensor, have recently been explored in nanophotonic systems for robust diffractionless propagation over a surface, offering interesting opportunities for subdiffraction imaging and enhanced Purcell emission. In acoustics, due to the longitudinal nature of sound transport in fluids, these phenomena are forbidden by symmetry, requiring the acoustic surface impedance to be inherently isotropic. Here we show that nonlocalities produced by strong coupling between neighboring impedance elements enable extreme anisotropic responses for sound traveling over a surface, supporting negative phase and energy velocities, as well as hyperbolic propagation for acoustic surface waves.

Tunable mantle cloaking utilizing graphene metasurface for terahertz sensing applications.

Design of sensors which are able to probe electromagnetic radiation with larger cross section and at the same time with having negligible perturbation in measurement has attracted significant attention. For this purpose, scattering-cancellation sensors or cloaking sensors are introduced. However, tunable cloaking sensors are very challenging. In this regards, here, a metasurface based on graphene strips is proposed to cloak a dielectric cylinder under illumination of TEz and TMz polarized incident waves in terahertz range. According to the in plane effective surface impedance tensor for the considered metasurface and the required surface impedance for achieving invisibility under TE and TM polarized impinging waves, the geometrical parameters of the covering structure and characteristics of graphene are obtained. Numerical simulations show radar cross section reduction for both TE and TM polarizations. Furthermore, the introduced metasurface is able to cloak the cylinder for incoming waves with circular polarization. In addition, it is shown that by properly adjusting the chemical potential of graphene, the required surface impedance to have cloaking for the two polarizations in other frequencies can also be achieved, which results in a tunable dual polarized cloaking. The proposed structure provides 2-11 dB reduction in scattering strength relative to the uncloaked configuration for 0.3eV variation of graphene chemical potential.

Analytical study and experimental verification of the surface wave loss on a tensor impedance surface

AbstractIn this article, propagation loss is investigated for a surface wave (SW) when enters from a scalar impedance surface (SIS) to a tensor impedance surface (TIS). This loss has two components: (a) loss due to change in the propagation direction and mode transformation of the SW and (b) loss due to the surface impedance mismatch between the SIS and the TIS. First, two analytical methods are presented to calculate the loss and then the methods are verified by a sample structure, which is fabricated with the printed circuit technology at 15.1‐15.75 GHz frequency bandwidth. The calculated total loss for the sample structure is 8.7 dB and 5.6 dB at 15.1 and 15.7 GHz, respectively, which is in good agreement with the measured results.

Intensity and Impact of the New York Railroad Superstorm of May 1921

AbstractAnalysis is made of low‐latitude ground‐based magnetometer data recording the magnetic superstorm of May 1921. By inference, the storm was driven by a series of interplanetary coronal mass ejections, one of which produced a maximum pressure on the magnetopause of ~64.5 nPa, sufficient to compress the subsolar magnetopause radius to ~5.3 Earth radii. Over the course of the storm, low‐latitude geomagnetic disturbance exhibited extreme local time (longitude) asymmetry that can be attributed to substorm disturbance extending to low latitudes. The storm attained an estimated maximum −Dston 15 May of 907 ± 132 nT, an intensity comparable to that of the Carrington event of 1859. The May 1921 storm brought spectacular aurorae to the nighttime sky. It also interfered with and damaged telephone and telegraph systems associated with railroad systems in New York City and State. These later effects were due to a combination of three factors: the localized details of geomagnetic vector disturbance, the geographic expression of the Earth's surface impedance tensor, and the configurations and physical parameters of the electrical networks of the day.

Method for Extracting the Effective Tensor Surface Impedance Function From Nonuniform, Anisotropic, Conductive Patterns

A patterning technique known as the point shifting method has enabled the generation of smoothly varying and highly anisotropic impedance surfaces with a wide range of patch sizes and shapes. Previously, the surface impedances of different shapes of unit cells were assumed by the impedance of similar size rectangle cells. In this paper, we study an approach to calculate the surface impedances for anisotropic polygon unit cells more accurately, based on the area moment of inertia equations. We define an alternative unit cell called the equivalent rectangle, which has the same tensor impedance properties of a general polygon unit cell in the surface impedance pattern. The size of the equivalent rectangle cell is calculated by using the moment of inertia equations between the polygon and the rectangle. The extracted surface impedance from the equivalent rectangle is compared to the surface impedance of polygon in the unit cell simulation, validating our method. We also verify the method by comparing the results between PEC patterns and impedance boundary sheets to which the extracted impedances are applied. Simulations of the patterns are verified by measurements as well.

Scalar Differential Equations for Transversely Varying Thickness Modes in Doubly Rotated Quartz Crystal Sensors

For time-harmonic motions, we generalize the 2-D scalar differential equation by Stevens and Tiersten for transversely varying thickness-shear vibrations of doubly rotated quartz plate sensors to include the effects of surface acoustic loadings. Starting from the 3-D equations of piezoelectricity, the governing equations are first transferred into a new coordinate system formed by the three eigenvibration directions; then, by neglecting the terms pertaining to the third and higher order in-plane wavenumbers, which are considered to be small compared to the thickness wavenumber, a scalar differential equation for the quasi-thickness shear modes is derived. The surface impedance tensor was introduced to represent the mechanical effects of surface mass layers and viscous fluid. Both unelectroded and electroded plates are treated. For electroded plates, both free and electrically forced vibrations under a time-harmonic driving voltage are analyzed. In addition to the fast thickness variation, which was considered in conventional 1-D models such as Sauerbrey's equation and Kanazawa's equation, the new equations properly accounted for the slow transverse variation of the finite sensors. Numerical examples for partially electroded fluid viscosity sensors are presented to show practical applications of the new equations for design and analysis of quartz crystal sensors.

A unified analysis framework for tensor metasurfaces

Tensor impedance metasurfaces have attracted much attention recently due to their ability to flexibly manipulate both propagating and surface waves. So far, the analysis of tensor impedance has not been fully supported by commercial electromagnetic simulation software. Also, the representation of formulas of penetrable tensor impedance for both propagating and surface waves is limited in the literature. Hence, a unified analysis framework is proposed for this purpose. It allows the calculation of wave reflection and transmission with arbitrary incident angles, or inversely, the calculation of surface impedance tensors given the desired wave propagation properties. It also allows surface eigenmode analysis, where surface modes with novel isofrequency contours are found for penetrable tensor impedance surfaces. The relationship between penetrable and impenetrable metasurfaces is derived so that the resultant formulas are applicable in both scenarios. A finite difference method code is implemented to validate the derived formulas. The proposed unified formulas are of closed form, hence offering very fast operation for research and design of tensor impedance metasurfaces.

Dual circularly polarized broadside beam antenna based on metasurfaces

Design details of a Ku band metasurface (MTS) antenna with dual circularly polarized (CP) broadside radiation is shown in this work. By means of the surface impedance tensor modulation, synchronized propagation of two transversal magnetic (TM) and transverse electric (TE) surface waves (SWs) is ensured in the structure, which contribute to the radiation in broadside direction by the generation of a CP leaky wave. The structure is implemented by elliptical subwavelength metallic elements with a cross-shaped aperture in the center, printed on top of a thin substrate with high permittivity (AD1000 with a thickness of λ0/17). For the experimental validation, the MTS prototype has been excited employing an orthomode transducer composed by a metallic stepped septum inside an air-filled waveguide. Two orthogonal TE11 modes excited with ±90° phase shift in the feed couple with the TM and TE SWs supported by the MTS and generate RHCP or LHCP broadside beam. Experimental results are compared with the simulation predictions. Finally, conclusions are drawn.