Dipole Arms Research Articles

Using a metasurface to enhance the radiation efficiency of subterahertz antennas printed on thick substrates

This study investigates the possibility of increasing the radiation efficiency of printed antennas and arrays by suppressing their inherent surface waves using a metasurface made of quad-split rings (QSR). A symmetrical resonant microstrip dipole and a four-element series-fed dipole array printed on an infinite grounded dielectric layer (layer thickness: 0.2 mm; relative permittivity: 9.4; tanδ: 0.0005) were simulated with FEKO 2022 software. Conducted at 100–116 GHz, the numerical results revealed extremely low radiation efficiencies of approximately 31% and 40% for the studied dipole and dipole array, respectively, which resulted from the presence of surface waves in the dielectric. However, placing only one QSR near each dipole arm triggered an increase in radiation efficiency by 2.5 times (up to 75%). The use of a metasurface in the form of two small QSR arrays triggered a pronounced improvement in radiation efficiency, reaching 93.6% and 95.8% for the studied dipole and dipole array, respectively. Analysis of the electric field distribution images showed that this enhancement resulted from surface wave suppression.

Off-the-shelf UHF RFID-based sensors for corrosion characterization of coated steel

The application of the UHF RFID technique in non-destructive testing (NDT) and structural health monitoring (SHM) has gained increasing attention due to its wireless, battery-less, and cost-effective attributes. It offers a promising approach for SHM and the Internet of Things (IoTs). This paper reports commercial off-the-shelf (COTS) flexible UHF RFID tag-based sensors for corrosion characterization on coated mild steel. Two types of COTS flexible UHF RFID tags with different bends are fabricated as sensors. The received signal strength indicator (RSSI) measurement is implemented to characterize the corrosion. Three parts (T-match area, dipole arms, and dipole loadings) of the two tags are tested for sensing purposes, and comparison and discussion of sensitivity, read range, and results are provided. This study successfully validates the feasibility of the proposed tag-bent method for corrosion characterization undercoating. It can be concluded that the dipole arm part of the applied COTS tags is the most sensitive area.

Study on the Conductivity Effect on the Characteristics of a Wideband Printed Dipole Antenna Implemented with Silver Nanoparticle Ink

This study examined a flexible composite wideband dipole antenna implemented with conductive silver nanoparticle ink having different conductivities. Two identical split ring resonators (SRRs) were designed to encompass each arm of a dipole element, and each dipole arm and its coupled SRR were printed on the top and bottom sides of a dielectric substrate. The overall dimensions of the compact antenna were 10 mm × 74.8 mm × 0.254 mm (0.053λo × 0.399λo × 0.0014λo at 1.6 GHz). The characteristics of the antenna with different conductivities were numerically investigated and experimentally confirmed. Our investigation aimed to ascertain the proposed antenna's response to different conductivity values and to determine the range of conductivity values that generates major changes in the antenna's performance characteristics in terms of impedance bandwidth, gain, and radiation efficiency. At conductivity values less than approximately 6.0 × 104 S/m, the number of generated resonances changed from three to two, and the antenna experienced a nearly 3-dB gain reduction when the conductivity approached 5.8 × 104 S/m.

A Wideband Circularly Polarized Dipole Antenna with Compact Size and Low-Pass Filtering Response.

This paper presents a compact wideband circularly polarized cross-dipole antenna with a low-pass filter response. It consists of two pairs of folded cross-dipole arms printed separately on both sides of the top substrate, and the two dipole arms on the same surface are connected by an annular phase-shifting delay line to generate circular polarization. A bent metal square ring and four small metal square rings around the cross-dipoles are employed to introduce new resonant frequencies, effectively extending the impedance and axial-ratio bandwidth. Four square patches printed on the middle substrate are connected to the ground plane by the vertical metal plates in order to reduce the antenna height. Thus, a compact wideband circularly polarized antenna is realized. In addition, a transmission zero can be introduced at the upper frequency stopband by the bent metal square rings, without using extra filter circuits. For verification, the proposed model is implemented and tested. The overall size of the model is 90mm×90mm×33mm (0.37λ0×0.37λ0×0.14λ0; λ0 denotes the center operating frequency). The measured impedance bandwidth and 3 dB axial-ratio (AR) bandwidth are 53.3% and 41%, respectively. An upper-band radiation suppression level greater than 15 dB is realized, indicating a good low-pass filter response.

Atomistic investigation of the interaction between an edge dislocation and 1/2 interstitial dislocation loops in irradiated tungsten

By impeding dislocation motion, the irradiation-induced dislocation loops cause irradiation hardening and further embrittlement of plasma-facing tungsten in fusion reactors, leading to its performance degradation. But fundamental questions regarding the mechanisms remain to be clarified and predictive model for loop hardening remains to be built. In this paper, interactions between gliding edge dislocations and interstitial dislocation loops (with Burger vector bL = ½<111>) are studied using atomistic simulations. The influences of bL orientations, dislocation-loop intersection positions, loop sizes, and loading conditions (temperature and strain rate) on the interactions are systematically calculated and analyzed. Results show a large variety of interaction mechanisms, depending mainly on the relative orientations of bL to dislocation slip plane, while slightly affected by loading conditions. Although loops with bL parallel to the plane can be easily swept away by gliding dislocations, loops with bL inclined to dislocation slip plane can strongly pin the gliding dislocation by forming a sessile 〈100〉 segment, which would bend the dislocation line into a screw dipole. Thus, high stress is required for the dislocation line to break away from the inclined loops by cross-slip of each individual arm of the screw dipole coupled with glide of the 〈100〉 segment. On the other hand, increasing temperature and/or decreasing strain rate hardly change the above mechanisms, but monotonically reduce the obstruction by these loops. Simplifying the complex motion of the edge dislocation pinned by the inclined loops as a thermally-activated process of a 1/2[111] edge dislocation overcoming barriers, a hardening model for the inclined loops is proposed. This model well describes the dependence of loop strength on loop sizes, temperatures and strain rates. The model is then applied to predict irradiation hardening at experimental strain rates, and it shows reasonable agreement with experimental results.

Dual-band ends-fed dipole-like driver for dual-band antenna arrays

The article addresses the problem of dual-band structure designs based on the quasi-Yagi arrangements. The reported dual-band dipole antenna comprises the out-of-phase power divider, whose outputs excite the corresponding dipole arms to produce appropriate surface current distribution on them. The topology of the antenna itself is designed the way to provide high matching (the realized input reflection coefficient is not exceed minus 25 dB) at both central working frequencies. The low-band dipole is meandered to fit the substrate size. In addition, both the dipoles are excited on their remote terminals, which allows the more efficiently use of the circuit body space. The low profile implementation contributes to meeting the high demands of today and future wireless communications. The fundamental properties of linear dipole antennas, such as the Yagi, of being relatively simple in design, pure linearly polarized, having almost omnidirectional patterns made them of the great interest among researches. In addition, the Yagi arrangement itself allows building on its base even more complex antenna structures, comprised a number of linear dipoles, maintained along one of orthogonal axis. When centrally fed, the classical single-band Yagi antenna suffers from narrow band characteristics, becoming a kind of challenge, which has successfully been addressed by a number of researches in the past. At the same time, on the base of Yagi and quasi-Yagi designs it is possible to combine a number of radiating elements, producing, therefore, multi-band or wideband characteristics. This approach is highly efficient when designing multipurpose devices with different transmitting rates. In this project the novel approach for dual-band dipole antennas design is presented. The driven elements are excited from their remote terminals, forming the quasi-Yagi arrangement with untraditional excitation. The balancing scheme is formed by an out-of-phase power divider, whose outputs are connected to the dipoles arms. The topology of the antenna itself is designed to provide high matching (input reflection coefficient does not exceed minus 25 dB) at both center operating frequencies. When integrating a dual band balancing unit with the radiating elements it is crucial to provide low interference for better radiation characteristics. Besides, the surface currents on the ground plane, should not affect those on the radiating elements for better matching.

Low-Profile Differentially-Fed Tightly-Coupled Dipole Array

Introduction. Tightly coupled dipoles currently belong to one of the most popular types of antenna arrays. Their main advantages include an electrically low-profile height, the ability to scan the beam across a wide sector of angles without the onset of scan blindness, and a low level of cross-polarization. In recent years, the number of publications on the topic of antenna arrays of this type has increased significantly. The authors have paid sufficient attention to baluns included in the antenna array elements. However, the possibility of implementing a differentially-fed scheme in antenna arrays of this type remains poorly studied. This makes the study of this subject especially relevant in the development of radio devices where such feed technique is preferable.Aim. Differentially-fed tightly-coupled dipole array design and study.Materials and methods. The following materials were used to create the prototype: copper sheet, ceramic glass substrate ST-50-1, dielectric RO3003. A numerical study of the characteristics was carried out in the ANSYS HFSS environment; an experimental study of the prototype was carried out in an anechoic chamber using an automated measuring complex and a vector network analyzer.Results. The results of designing a planar antenna array of tightly-coupled dipoles for the X-band are presented. In the antenna array, each of the dipole arms is fed using a separate coaxial cable, while the two arms of one dipole are fed out-of-phase. The results of a numerical study of the characteristics of an 8 × 8 antenna array made from the developed elements are presented. Across the range from 6.5 to 12.25 GHz, the average active VSWR does not exceed 3, while the gain varies from 21.5 to 25.7 dBi. The possibility of beam scanning in a sector of angles up to ±45° is shown. The results of an experimental study of the radiation characteristics and matching of the prototype of a single element are presented.Conclusion. The importance of taking into account the effects that arise at the edges of finite antenna arrays during simulations is shown. The feasibility of manufacturing and measuring antenna array prototypes with a large number of elements is experimentally confirmed. The proposed element design demonstrates the possibility of implementing the differentially-fed scheme in tightly coupled antenna arrays.

Graphene-Tuned, Tightly Coupled Hybrid Plasmonic Meta-Atoms.

Tightly coupled meta-atoms (TCMAs) are densely packed metamaterials with unnatural refractive indexes. Actively modulated TCMAs with tunable optical properties have found many applications in beam shaping, holography, and enhanced light-matter interactions. Typically, TCMAs are studied in the classic Bloch theory. Here, tightly coupled H-shaped meta-atoms are proposed with an ultra-high permittivity of ~6000, and their active modulation with graphene is designed by using the tightly coupled dipole array (TCDA) theory. The H-shaped meta-atoms are used as dipole arms, and the graphene strips function as the dipole loads. By tuning the chemical potential of graphene, the resonant amplitude, frequency, and permittivity are dynamically modulated. The simulations indicate that the real and imaginary parts of permittivity change from 6854 to 1522 and from 7356 to 2870, respectively. The experimental validation demonstrates a modulation depth of 11.6% in the resonant frequency, i.e., from 219.4 to 195 GHz, and a substantial 52.5% modulation depth in transmittance under a bias voltage of less than 1.5 V.

Wide-Angle Scanning and High Isolation Dual-Polarized Base Station Antennas for Sub-6 GHz Applications

This paper presents a wide-angle scanning and high isolation base station antenna array. The antenna element employs a compact dual-polarized umbrella-shaped printed dipole with a small size of 0.23λ0 × 0.23λ0 × 0.26λ0, which provides the possibility for a small element spacing array. The antenna element possesses wide 3 dB beamwidth of 84.6∘ benefiting from the pulling down of the dipole arms. Then, a dual-layer metal superstrate structure and metal wall is adopted to mitigate different kinds of mutual coupling between the dual-polarized antenna elements in the array. Owing to the wide beamwidth of the element and the low mutual coupling between the elements, the final 4×6 antenna array can achieve a good beam-scanning capability with maximum scanning angle up to ±55∘ and a small gain variation of less than 3 dB over the operation band 3.3-3.8 GHz. The fabricated array shows the measured isolation between all ports of the antennas is increased to more than 20 dB. Scanning characteristics also agree well with the simulated results. With the merits of wideband, low-cost (simple design and easy fabrication), wide-angle beam-scanning capacity, and good radiation performance, the proposed design has potential for application in 5G base stationsystems.

A compact wideband circularly polarized dipole antenna with wide beamwidth

AbstractA wideband circularly polarized (CP) dipole antenna with compact size and wide beamwidth is proposed. To achieve a wide half‐power beamwidth (HPBW), the dipole is designed to be a folded bowtie, and four rotationally symmetric vertical metal plates are placed on the square ground plane. A circular parasitic patch above the dipole arms improves the impedance bandwidth. By using a 3‐dB coupler, the proposed antenna achieves wideband CP performance. The measured results show that an impedance bandwidth for VSWR ≤ 2 and a 3‐dB axial‐ratio (AR) bandwidth are from 0.76 to 2.1 GHz (93.7%). Moreover, a bandwidth of HPBW ≥ 102° is from 0.76 to 1.8 GHz (81.2%).

A low‐profile dual‐wideband magnetoelectric dipole antenna with stable gain

AbstractA dual‐wideband magnetoelectric dipole antenna is proposed. The magnetoelectric dipole is fed by a hook‐shaped metal sheet. To increase the gain at the upper band, the radiation arm of the electric dipole is designed in stepped shape. To widen the impedance bandwidth of the lower band, stepped‐shaped metal walls are employed and placed along the edges of the ground plane. To further improve and stabilize the higher band gain, four parasitic umbrella‐shaped metals are utilized. By using this novel scheme, a magnetoelectric dipole antenna with dual‐wideband operation is designed. It introduces two wide bandwidths of 35.3% (0.698–1 GHz) for the lower band and 63% (1.52–2.9 GHz) for the upper band. The lower‐band gain is stabilized within 7.3 ± 0.6 dBi, while the upper‐band gain is stabilized within 9.2 ± 0.8 dBi. The antenna dimension is only 0.41λL × 0.41λL × 0.1λL (λL denotes the wavelength at 0.698 GHz in vacuum).

A frequency‐ and polarization‐reconfigurable cross dipole antenna using liquid metal

AbstractA frequency and polarization reconfigurable wideband cross‐dipole antenna is proposed. A /4 phase‐shifted ring structure is used to design a reconfigurable frequency and polarization wideband antenna, which is connected to the dipole arm with the liquid metal as a parasitic branch. The antenna consists of a pair of rectangular dipoles, a pair of curved phase‐shifted rings, and a square ring. Two mutually perpendicular rectangular dipole arms are connected by a phase‐shifted ring, which is printed on the upper and lower surfaces. The left‐hand circular polarization and right‐hand circular polarization can be switched by loading liquid metal at different positions of the antenna, and the frequency can be reconstructed by adjusting the length of liquid metal at corresponding positions. The total 3 dB axial ratio bandwidth are 41.27% (1.50–2.28 GHz) and 43.57% (1.49–2.32 GHz), and eight adjustable circularly polarized frequency bands can be obtained at the same time. To verify the proposed design, a reconfigurable antenna is fabricated and measured. The measured results are in good agreement with the simulated results.

A Ku/K‐band wideband crossed dipole circularly polarized array with low profile

AbstractA low‐profile Ku/K band circularly polarized phased array antenna based on crossed dipole and four parasitic elements is presented. Four parasitic patches and the outline of dipole arms which are designed as an exponentially gradual curve are intended to broaden impedance bandwidth. For better integrated design, the plated through holes at the bottom of substrate replaces the metal cavity, aiming to enhance the radiation characteristics of the positive direction. The small angle sequential ro0tation tech is adopted to further increase the axial ratio (AR) bandwidth. The 8 × 8 antenna array is operated from 15.5 to 23.5 GHz (41%), with the size of 56 mm × 56 mm × 2.54 mm. In the operating frequency, the array demonstrates an average peak realized gain of 24.3 dBic and has a 3‐dB AR beamwidth with scanning angle from −60° to 60° in the plane of ɸ = 0° and ɸ = 90°.

An Ultrathin Low-Profile Tightly Coupled Dipole Array Fed by Compact Zigzagging Baluns

In this paper, we propose for the first time a novel feed approach to a tightly coupled dipole array (TCDA). Firstly, compact zigzagging microstrip feedlines are utilized as baluns to feed our array elements to obtain wideband impedance-matching characteristics. Secondly, this array is designed on ultrathin substrates aiming at obtaining ultra-tight coupling between the dipole arms of two neighboring elements. Some irreplaceable parasitic pads are developed and added to the radiating arms to improve both the impedance and radiation characteristics of the TCDA. With these technologies, a 12 × 12 TCDA prototype is designed, fabricated and measured for verification. The array achieves an impressive impedance bandwidth spanning of 4–18 GHz for S11&lt;−10 dB. Its radiation patterns and realized gain are measured to verify its stable electromagnetic characteristics. Its realized gain is from 15 dB to 25 dB within the operating frequency band. Its efficiency is around 91%. Its measured results show good agreement with simulations.

Reconfigurable dipole receive array for dynamic parallel imaging at ultra-high magnetic field.

To extend the concept of 3D dynamic parallel imaging, we developed a prototype of an electronically reconfigurable dipole array that provides sensitivity alteration along the dipole length. We developed a radiofrequency array coil consisting of eight reconfigurable elevated-end dipole antennas. The receive sensitivity profile of each dipole can be electronically shifted toward one or the other end by electrical shortening or lengthening the dipole arms using positive-intrinsic-negative-diode lump-element switching units. Based on the results of electromagnetic simulations, we built the prototype and tested it at 9.4 T on phantom and healthy volunteer. A modified 3D SENSE reconstruction was used, and geometry factor (g-factor) calculations were performed to assess the new array coil. Electromagnetic simulations showed that the new array coil was capable of alteration of its receive sensitivity profile along the dipole length. Electromagnetic and g-factor simulations showed closely agreeing predictions when compared to the measurements. The new dynamically reconfigurable dipole array provided significant improvement in geometry factor compared to static dipoles. We obtained up to 220% improvement for 3 × 2 (Ry × Rz ) acceleration compared to the static configuration case in terms of maximum g-factor and up to 54% in terms of mean g-factor for the same acceleration. We presented an 8-element prototype of a novel electronically reconfigurable dipole receive array that permits rapid sensitivity modulations along the dipole axes. Applying dynamic sensitivity modulation during image acquisition emulates two virtual rows of receive elements along the z-direction, and therefore improves parallel imaging performance for 3D acquisitions.

Radio wave propagation analysis with dominant path model using MIMO antenna element for vehicular base station application

AbstractA low-profile slant ±45° polarized antenna for a 4G/5G base station with a dominant path wave propagation model (DPM) is reported in this paper. For dual-polarization and wide impedance bandwidth, the two dipole radiators are crisscrossed and a square metallic ring is integrated with the dipole arms and screwed with the four shorting vias. The antenna operates in Band 40/41/42/43 with strong isolation and low ECC (Envelop Correlation Coefficient). Fabricated antenna results show that the predicted wideband antenna has 13.38% bandwidth in 4G, which is Band 40/41, and 29.33% bandwidth in 5G sub-6 GHz Band 42/43. The antenna has a consistent radiation pattern, a 40 dB XPD (Cross Pol Discrimination), and a beam width of 69.5° ±1.5° in the entire frequency band. Three base station sites were explored to deploy the radiation pattern of a dual-polarized antenna in the 3D EM (Electromagnetic Analysis) tool. To evaluate signal quality, strength, radio network planning, and wave propagation analysis by analyzing antenna performance in real-time scenarios with 64 and 256 QAM (Quadrature Amplitude Modulation) techniques. For the proposed four-stream MIMO (Multiple-Input-Multiple-Output) antenna arrangement at deployed cell sites for 4G/5G base station applications, the maximum downlink and uplink data rates are 3.826/2.8 Mbps and 1044/800 Mbps respectively.

A Multicompressed-High-Order Modes Dipole Antenna With Wide-Beam and High-Gain Radiations in Two Different Bands

In this letter, a multi-compressed-high-order mode dipole antenna with wide-beam coverage and high-gain radiations in two respective sub-6 GHz bands is proposed. The capacitors and inductors are loaded at the current distribution nulls of the fifth-order mode of the dipole arms. The loading brings the resonant frequencies of the third- and the seventh-order modes closer to the fifth-order mode, and thus achieves wide bandwidth. In addition, the loadings change the current distribution of the third- and the seventh-order modes, and achieve radiation patterns with wide coverage in the lower band and high gain in the higher band. To facilitate fabrication, the capacitors and inductors are replaced by narrow slits and bending lines separately. A prototype of this design is fabricated and measured. The measurement and simulation results are in good agreement. The proposed antenna achieves a wideband of 3.30 to 5.35 GHz (VSWR < 2) with an omnidirectional radiation pattern in the horizontal plane. In addition, it achieves a ±57° coverage angle over 0 dBi in the lower band and 6.41 dBi peak gain in the higher band in the vertical plane, which can be applied for 5G wireless communication.

SICL-Fed Balanced Antipodal Dipole Antenna With Wideband Operation and Cross-Polarization Improvement at Millimeter-Wave Band

A substrate integrated coaxial line-fed balanced antipodal dipole antenna array is proposed for millimeter-wave (MMW) applications in this letter. Different from the traditional dual-armed dipole antenna, a balanced antipodal dipole element with three arms is proposed to improve the cross-polarization level by canceling the vertically polarized electric-field components. A cross-polarization level of less than −20 dB is achieved over the entire frequency band. Meanwhile, a gap is etched on each dipole arm to achieve dual-mode operation and broaden the impedance bandwidth of the dipole element, and an impedance bandwidth of more than 65% is obtained. By combining the proposed dipole elements with the unequal feeding network, a 1 × 8 dipole antenna array is designed, fabricated, and measured. The measured results show that the proposed dipole antenna array can achieve a wide −10 dB impedance bandwidth of more than 54% from 24.5 to 43 GHz, a sidelobe level of low than −18 dB in E-plane, and a cross-polarization level of low than −20 dB. With the merits of wide operating bandwidth, low cross-polarization level, low sidelobe level, low profile, and easy integration, the proposed antenna array is valuable to advanced MMW communication systems.

A Low-Profile Ultra-Wideband and Wide-Scanning Phased Array for UHF Applications

This article presents a novel low-profile ultra-wideband and wide-scanning array antenna using the transversely connected folded tightly coupled dipoles array (TCF-TCDA). The tightly coupled folded dipole arms are used to extend the operational frequency band with a simple feed structure. The capacitively-loaded metallic walls are adopted to move the problematic common-mode resonance out of the desired band and mitigate the bandwidth-limiting loop mode at the lower frequency, as well as reducing the weight and cost. A meta-surface-based wide angle impedance matching (MS-WAIM) layer is used to improve the beam scanning ability and lower the antenna profile, which consists of the star-shaped patches loaded on the dipole element. To demonstrate the wideband and wide scanning-range capability, a prototype is designed with an 8:1 bandwidth (0.41–3.3 GHz) at broadside, a scanning range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm \mathrm{75}^{\circ }$ </tex-math></inline-formula> from 0.5 to 3.25 GHz (6.5:1 bandwidth) in the E- and D-planes and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm \mathrm{50}^{\circ }$ </tex-math></inline-formula> from 0.6 to 3.3 GHz (5.5:1 bandwidth) in the H-plane for active VSWR < 3.6. The proposed antenna has a very low profile, which is only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.07\lambda _{\mathrm {low}}$ </tex-math></inline-formula> at the lowest operating frequency. A 16 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 16 array prototype is fabricated and measured. Experimental results show that the design and measurement results have good agreement. The proposed antenna has an ultra-wide bandwidth, a wide scanning range, a very compact size and a low cost, which is a good candidate for modern wireless system.

Miniaturized Spoof Plasmonic Antennas with Good Impedance Matching.

The ability of spoof surface plasmon polaritons (SSPPs) to confine electromagnetic fields in a subwavelength regime enables the design of miniaturized antennas. However, the impedance matching scheme for miniaturized spoof plasmonic antennas has not been studied systematically. In this paper, we propose a general method in the antenna design based on SSPPs, providing a feasible solution to impedance matching at the feeding point of miniaturized spoof plasmonic antennas. To verify the method, a prototype of a planar spoof plasmonic dipole antenna is simulated, fabricated and measured, of which the dipole arm length is reduced by 35.2% as compared with the traditional dipole antenna. A peak gain level of 4.29 dBi and the radiation efficiency of about 94.5% were measured at 6 GHz. This general method can be extended to solve the impedance matching problem in the design of other spoof plasmonic devices.