Effective Surface Impedance Research Articles

Scattering suppression and wideband tunability of a flexible mantle cloak for finite-length conducting rods

A simple, thin, flexible mantle cloak for conducting rods based on scattering cancellation is analyzed, designed and experimentally realized. We show strong scattering suppression at all angles of incidence, for both far-field plane-wave and near-field Gaussian excitations. The required effective shunt surface impedance is realized by a subwavelength patch array, targeting the suppression of the dominant omnidirectional scattering contribution of a conductive rod. Full-wave simulations predict a total radar cross-section reduction better than 14 dB in the lossless case and nearly 8 dB when considering a lossy substrate in the cover. Measurements of the realized cloak are consistent and validate these numerical predictions. The proposed geometry is also shown to be an ideal platform for monolithic integration of varactor diodes, allowing real-time tuning of the effective surface capacitance of the cloak. We show with numerical simulations the possibility of tunable scattering suppression over 1 GHz of bandwidth by seamlessly integrating varactor diodes in our mantle cloak design.

Causality and passivity properties of effective parameters of electromagnetic multilayered structures

Effective properties of periodic structures are investigated at all frequencies. It is shown that a simple dielectric multilayer with arbitrary low contrast can display artificial magnetoelectric coupling and magnetism. Effective parameters, as functions of the complex frequency, possess all the analytic properties required by the causality principle. The theoretical expression of the effective index and surface impedance are numerically tested; the former is shown to reduce to the mean refractive index at infinite frequency, just like the refractive index in the x-ray regime. We stress that periodic multilayers, with frequency-independent (noncausal) dielectric constants, make effective media with artificial causality.

An Asymptotic Solution for Surface Fields on a Dielectric-Coated Circular Cylinder With an Effective Impedance Boundary Condition

An effective surface impedance approach is introduced for determining surface fields on an electrically large dielectric-coated metallic circular cylinder. Differences in analysis of rigorously-treated coated metallic cylinders and cylinders with an impedance boundary condition (IBC) are discussed. While for the impedance cylinder case a single constant surface impedance is considered, for the coated metallic cylinder case two surface impedances are derived. These are associated with the TM and TE creeping wave modes excited on a cylinder and depend on observation and source positions and orientations. With this in mind, a uniform theory of diffraction (UTD) based method with IBC is derived for the surface fields by taking into account the surface impedance variation. The asymptotic expansion is performed, via the Watson transformation, over the appropriate series representation of the Green's functions, thus avoiding higher-order derivatives of Fock-type integrals, and yielding a fast and an accurate solution. Numerical examples reveal a very good accuracy for large cylinders when the separation between the observation and the source point is large. Thus, this solution could be efficiently applied in mutual coupling analysis, along with the method of moments (MoM), of large conformal microstrip array antennas.

Effective surface impedance of a high temperature superconductor

In this work, we will investigate theoretically the effective surface impedance of a high temperature superconducting thin film in the microwave range. This investigation will be according to varying the thickness of the superconducting thin film and the operating temperature, based on means of impedance transformations. The microwave surface impedance is related to the fundamental properties of high-Tc superconductors. The study of surface impedance has two important aspects. The first one is the real part of the surface impedance; the surface resistance determines the electromagnetic power dissipation through the superconductor thin film. The second is the imaginary part of the surface impedance; the surface reactance is proportional to the magnetic-field penetration depth.

Effective Surface Impedance of a Printed-Circuit Tensor Impedance Surface (PCTIS)

The surface impedance and dispersion equation of a printed-circuit tensor impedance surface (PCTIS) are derived using a modified transverse resonance technique. A PCTIS consists of a subwavelength-patterned metallic cladding over a grounded dielectric substrate. The metallic cladding is analytically modeled as a tensor impedance sheet. An explicit expression is derived for the effective surface impedance of the PCTIS using a transmission-line approach. First, the surface-impedance expression is found for a printed-circuit scalar impedance surface using the transverse resonance technique. Next, a modified transverse resonance technique is applied to an idealized tensor impedance boundary condition (TIBC) to find its dispersion equation. Finally, the analysis of the printed-circuit scalar impedance is combined with that of the idealized TIBC to find the tensor surface impedance and dispersion equation of a PCTIS. A discussion of the principal axes and the propagation of TM and TE waves is provided. The special case of electrically thin PCTISs is also analyzed and discussed.

Diffraction assisted rough ground effect: Models and data

The destructive interferences observed in Excess Attenuation (EA) spectra over periodically and randomly spaced roughness elements with different cross-sectional profiles (semicylindrical, rectangular and wedge-shaped strips) have been investigated. If the roughness is spaced periodically, then two or three destructive interference maxima are observed in the same frequency range as the one or two observed with randomly distributed roughness. Roughness-induced surface waves are investigated also. Their amplitudes and the frequencies at which they occur are found to depend on the roughness height, mean center-to-center spacing and the extent to which the roughness is periodic. A semianalytical Multiple Scattering Theory and a numerical method (the Boundary Element Method) have been used to make predictions of the EA spectra which are compared with measurements. In addition it is found that the effective surface impedance spectra deduced from complex EA measurements over rough surfaces exhibit resonances similar to those observed for a hard-backed porous layer. On this basis a heuristic effective impedance model for rough hard surfaces is developed and the corresponding predictions of EA spectra are compared with data.

Propagation effect of a fractal rough ground boundary on the lightning-radiated vertical electric field

A two-dimension fractional Brown motion (fBm) model is presented for describing the nature rough ground surface. By using an effective surface impedance algorithm derived by Barrick reference, the propagation effects of a fractal rough ground surface on the vertical electric field generated by lightning return strokes are analyzed. The results show that the extra field attenuation increment caused by the roughness decreases with the decrease of the ground conductivity, when the ground conductivity is less than 0.001S/m, the propagation effect of the rough ground surface with a mean square height of less than 10m is nearly as same as that of the smooth and finitely conducting ground. However, when the ground conductivity is larger than 0.1S/m (wet earth), the frequencies higher than about 2MHz are attenuated significantly by a rough ground surface with a mean square height of 10m. For the derivative of the vertical electric field in time domain, the field attenuation caused by a rough ground is significant, while for the peak of the vertical electric field, there is no obvious attenuation.

Enhancing the Dual-Band Guiding Capabilities of Coaxial Spoof Plasmons via use of Transmission Line Concepts

We derive closed analytical forms for the response of coaxial spoof plasmons, aided by transmission line concepts under the effective complex surface impedance framework. This constitutes a powerful platform to improve as well as to elucidate designs with enhanced performances. In particular, we propose a dual-band spoof plasmon waveguiding geometry with the higher order slow-wave mode operating well below the regime governed by dispersion of periodic guides (Bragg reflections at Brillouin zone boundaries), that is, diffraction. The analysis is supported by eigen mode numerical calculations. As an example in a waveguide device context, we demonstrate the dual-band planar routing ability of elliptical–coaxial cable-based spoof plasmons along a straight chain as well as a Y-splitter.

MICROWAVE PROPERTIES OF A HIGH-TEMPERATURE SUPERCONDUCTOR AND FERROMAGNETIC BILAYER STRUCTURE

Microwave properties for a bilayer structure made of the high-temperature superconducting and the ferromagnetic materials are theoretically investigated. The properties are explored through the effective surface impedance calculated by using the enhanced twofluid model for high-temperature superconductors together with the transmission line theory. The calculated effective surface impedance will be numerically analyzed as a function of the frequency, the temperature, and the thicknesses of the constituent layers. It is found that, for a thinner superconducting film, the effective surface resistance is a strong function of the frequency, and the effective surface reactance exhibits a peak and a dip in the frequency-domain. In the study of the effect of thickness in ferromagnetic substrate, there is a peak frequency in the surface reactance for a thinner substrate. There is also a threshold thickness for the ferromagnetic substrate such that it behaves like a bulk substrate when its thickness is larger than this threshold value. In the temperature dependence of surface reactance, the peak near critical temperature is shifted to lower temperature and broadened as the film thickness decreases. Received 13 November 2010, Accepted 15 December 2010, Scheduled 19 December 2010 Corresponding author: Chien-Jang Wu (jasperwu@ntnu.edu.tw).

Characteristic Estimation of Artificial Magnetic Conductors

This article proposes a model for estimating the phase of reflection coefficient and the resonant frequency of artificial magnetic conductor structures, which are composed of an array of frequency selective surface elements at the interface of a grounded dielectric slab. This model is based on the microstrip coupled-line theory and the effective surface impedance model. The reflection phase and resonant frequency resulting from the proposed model are thoroughly verified by full-wave simulations and measurements, and they are also compared with available data in the open literature resulting from different methods.

Effective Surface Impedance of a High-Temperature Superconducting Film in Semiconductor Plasma Substrate at Mid-infrared Frequency

The effective surface impedance of a high-temperature superconducting thin film on a semiconductor plasma substrate is calculated. Two possible configurations are considered. The first one is a superconducting film deposited on a semi-infinite semiconductor substrate. It is seen that there exists a critical film thickness for the superconductor such that a minimum effective surface resistance is attained. The effective surface resistance is strongly dependent on the high-frequency permittivity of semiconductor plasma. The second will be limited to the more practical case, that is, the semiconductor substrate is of finite thickness. The investigation of substrate resonance in the effective surface resistance shows some fundamental distinctions when a semiconductor plasma substrate is introduced.

Terahertz Intrinsic and Effective Surface Impedances of High-Temperature Superconducting Thin Films

Terahertz wave properties of high-temperature superconducting thin films are theoretically investigated based on the calculated surface impedances. The surface impedances for three model structures are considered in this work. We first treat the intrinsic bulk surface impedance for a superconductor occupying the half space. Second, the intrinsic film surface impedance of a superconducting film of finite thickness is calculated. Third, we calculate the effective surface impedance for a superconductor-dielectric layered structure, i.e., a superconducting film on the dielectric substrate of finite thickness. All calculations that will be made are based on the two-fluid model of superconductors together with the transmission line theory.

Electromagnetic Properties of a Nearly Ferroelectric Superconductor in Layered Structure

Electromagnetic microwave properties of a superconducting bilayer structure made of a high-temperature superconductor (HTSC) and a nearly ferroelectric superconductor (NFE SC) are investigated. Microwave properties are analyzed by the effective surface impedance calculated by using the impedance transform method. It is found that the anomalous resonant peaks in the surface resistance appearing in an NFE SC slab are greatly affected by the presence of the HTSC film. In the case where the HTSC is in front of the NFE SC, the resonant peaks are shifted to higher frequencies and the peak heights are strongly suppressed as well. However, if the HTSC is at the backside of the NFE SC, the peak heights are strongly enhanced in addition to shifting to higher frequencies.

Effective magnetic penetration depth in superconducting cylinders and spheres with highly anisotropic electrodynamics

Effective magnetic penetration depth and microwave surface impedance are derived for anisotropic layered superconductors in the shape of spheres and long cylinders, where the external magnetic field is applied in the plane of the highly conducting layers to induce out-of-plane screening currents. We show how the results can be extended by analytical continuation to highly anisotropic conductors and to lossy superconductors at high frequency. The electrodynamics for the general case of a superconductor or metal with arbitrary anisotropy are presented. The treatment is then specialized to layered materials with uniaxial anisotropy, in which the penetration depth for currents flowing perpendicular to the layers, ${\ensuremath{\lambda}}_{c}$, is much greater than that for in-plane currents, ${\ensuremath{\lambda}}_{a}$. Exact solutions are found in the limit ${\ensuremath{\lambda}}_{a}\ensuremath{\rightarrow}0$ and are expected to provide an accurate representation of many experiments on cuprates and other layered superconductors, particularly on grain-aligned powders.

Effective Surface Impedance for a Superconductor-Semiconductor Superlattice at Mid-Infrared Frequency

The effective surface impedance for a superconductor-semiconductor superlattice at mid-infrared frequency is calculated based on the transfer matrix method together with the enhanced two-fluid model for the high-temperature superconductor. We first investigate the effective surface resistance and surface reactance in the case of normal incidence. We find that there is a critical thickness for superconductor film such that a minimum loss is attained. We next study the effective surface impedance under the oblique incidence. The calculated effective surface impedance indicates that the angle-dependent feature is only seen for the single period. However, it does not rely on the number of periods when the period is greater than two and, in the meantime, the surface resistance is nearly unchanged as a function of the angle of incidence.

Microwave vortex dynamics in Tl-2212 thin films

We present measurements of the effective surface impedance changes due to a static magnetic field, ΔZ(H,T)=ΔR(H,T)+iΔX(H,T), in a Tl-2212 thin film with Tc>103K, grown on a CeO2 buffered sapphire substrate. Measurements were performed through a dielectric resonator operating at 47.7GHz, for temperatures 60K⩽T<Tc and magnetic fields μ0H⩽0.8T. We observe exceptionally large field induced variations and pronounced super-linear field dependencies in both ΔR(H)andΔX(H) with ΔX(H)>ΔR(H) in almost the whole (H,T) range explored. A careful analysis of the data allows for an interpretation of these results as dominated by vortex dynamics. In the intermediate-to-high field range we extract the main vortex parameters by resorting to standard high frequency model and by taking into proper account the creep contribution. The pinning constant shows a marked decrease with the field which can be interpreted in terms of flux lines softening associated to an incipient layer decoupling. Small vortex viscosity, by an order of magnitude lower than in Y-123 are found. Some speculations about these findings are provided.

SPM NUMERICAL RESULTS FROM AN EFFECTIVE SURFACE IMPEDANCE FOR A ONE-DIMENSIONAL PERFECTLY-CONDUCTING ROUGH SEA SURFACE

From the analytical theory of rough surface Green's function based on the extension of the diagram method of Bass, Fuks and Ito, with the smoothing approximation, numerical results are presented for Gaussian and sea spectra and compared with a benchmark method by considering a one-dimensional perfectly conducting Gaussian rough surface. The effects of multiple scattering due to the surface roughness are incorporated systematically into the solutions through an effective surface impedance, which can be iterated up to the second-order. In addition, comparisons of the bistatic scattering coefficients are presented with the first- and second- orders conventional small perturbation method. This study will be useful for remote sensing of the ocean surface, especially when the transmitter is close to the surface.

Calculation of effective permittivity, permeability, and surface impedance of negative-refraction photonic crystals

We consider the eigen-fields of a two-dimensional negative-refraction photonic crystal and obtain negative effective permittivity and negative effective permeability. Effective permittivity, permeability, and surface impedance are calculated by averaging the eigen-fields. The value of the surface impedance is shown to be location-dependent and is validated by finite-difference time-domain simulations. The unique power propagation mechanism in the photonic crystal is demonstrated through time-evolution of eigen-fields.

Substrate Contribution to the Surface Impedance of HTS Films on Si

We study the effects of semiconductor substrates on the surface impedance of high-T c Superconductor (HTS) YBa2Cu3O7−δ (YBCO) films. The characteristic impedance of silicon (Si) (for different doping levels and for different charge carrier scattering times) is evaluated. In particular, the most relevant features of Si electrodynamics are highlighted by the introduction of suitable normalized quantities. The effective surface impedance of the YBCO films on Si substrates is then calculated and discussed for different temperatures and frequencies in the microwave range, comparing the obtained results to their limiting expressions for bulk and thin-film HTS. Our analysis shows how the widely used thin-film approximation for the surface impedance can fail, critically highlighting the conditions it requires to be correctly used. We show that substrate contributions can heavily influence the overall response.

Dielectric Resonators for the Measurement of Superconductor Thin Films Surface Impedance in Magnetic Fields at High Microwave Frequencies

We present the design and realization of cylindrical dielectric resonators operating in the 40–60 GHz frequency range, designed for the measurement of the surface resistance and of the surface reactance shift in High-Tc Superconductors (HTS) thin films in a dc magnetic field. The resonators are single tone, based on the TE011 mode, and multiple tone, the latter allowing in principle to exploit the simultaneous determination of the surface impedance at different frequencies. As an application example, we report the temperature and field dependencies of the effective surface impedance of some cuprate superconductors thin films. The results are compared with those obtained through the use of a standard metal cavity with a similar Q-factor and operating in the same frequency range. The comparison highlights a superior stability and a higher sensitivity, resulting in an increase of about two orders of magnitude in the resolution of the surface impedance measurement. By contrast, the dissipative part of the superconducting transition (above T/Tc = 0.97) is better studied with the metal cavity. We also present measurements in the vortex state in YBaCa2Cu3O7−δ and Tl2Ba2CaCu2O8+x that show significantly different physics.