Transverse Resonance Technique Research Articles

Wideband and High-Efficiency Parallel-Plate Luneburg Lens Employing All-Metal Metamaterial for Multibeam Antenna Applications

A parallel-plate Luneburg lens (LL) based on all-metal metamaterial is presented in this paper. To achieve the required refractive index distribution of the LL, an all-metal unit cell with a separated cuboid is proposed, whose height is related to its refractive index. This inserted cuboid is attached to neither the top plate nor the bottom plate of the parallel plate. Compared with traditional bed of nail design, the proposed metamaterial unit cell exhibits a wider bandwidth. The operation principle of such a unit cell is investigated using the transverse resonance technique. To construct the all-metal metamaterial LL into one body, a cruciform cuboid is added to each unit cell such that adjacent unit cells can connect to each other. Based on the designed metamaterial LL, a multibeam antenna is developed by providing seven inputs, which can generate seven predefined beams. Several parts of the prototype are separately fabricated and assembled, and good agreement is observed between simulation and measurement. The designed LL based multibeam antenna has several advantages, including wide bandwidth, high aperture efficiency, and high radiation efficiency.

A Compact, Single-Layer, Index-Modulated Microstrip Antenna With Stable Customized Tilted Beam Over a Wide Bandwidth

A compact, single-layer, wideband, tilted-beam microstrip antenna with customized tilt angle is presented. The antenna is comprised by one subwavelength driven patch and several subwavelength parasitic patches. The tilt angle of the antenna is determined by the index distributions of those subwavelength patches. The detailed index-modulation principle is developed from the generalized law of refraction, wherein the reflection phase is mapped to the index by utilizing the equivalent transmission-line theory and the transverse resonance technique. As a result, the tilt angle could be customized by allocating patch cells following specific index distributions. On top of that, as a new degree of freedom in design, one could choose subwavelength patches with low dispersion characteristics as unit cells to further enhance the operational bandwidth and improve the stability of radiation pattern. For demonstration, two types of I-shaped patch units with different dispersion characteristics have been utilized to configure tilted-beam antennas that follow the same index distributions. In addition, the effectiveness of the developed tilted-beam antenna for array application has been proven. Experiments have been carried out to verify their performance.

Tunable Multibeam Holographic Metasurface Antenna

A metasurface beam-steering antenna at microwaves is proposed in this letter, which is designed according to holographic theory and has the ability to create multibeam radiation patterns with independent control of the individual beam direction. The holographic design approach of the modulated impedance surface follows the methodology of linear superposition of individual field patterns for each beam. The unit cell of the proposed antenna is tuned with a low-loss varactor diode, and its dispersion diagram is obtained with a transverse resonance technique. A novel multibeam antenna fed by a single source is designed with independent beam steering of each beam at around 7.2 GHz. The dual-beam antenna exhibits an average of 11.6 dBi of realized gain for each independent beam.

Design Method for Modulated Metasurface Antennas Composed of Anisotropic Elements Based on Generalized Boundary Conditions

A novel and efficient design method for modulated metasurface antennas composed of anisotropic elements is proposed in this letter, based on generalized boundary conditions. An analytical model of surface impedance is derived with the effective surface susceptibilities of the patch layer, an equivalent circuit model of the element, and the transverse resonance technique. The analysis method of elements is then utilized to design modulated metasurface antennas with desired radiation patterns. A linearly polarized antenna prototype with a circular aperture of 180 mm in diameter is designed and measured to demonstrate the effectiveness of this approach. The prototype shows good radiation characteristics at 9.75 GHz with the measured gain of 21.77 dB and the aperture efficiency of 44.5%.

The microstrop step discontinuity analysis by transverse resonance technique: method of boundary value problem algebraization

The two-dimensional eigenfunctions of the magnetic and electric vector potentials are constructed in the form of their expansion in series of Chebyshev orthogonal polynomials of 1st and 2nd kind to describe the current density in a strip transmission line with a step discontinuity of finite length. The solving boundary value problems algorithms for the resonant frequencies of a symmetric microstrip resonator with a capacitive section in it are developed and investigated on convergence. The account of the field behavior on thin edge in a nonuniform strip line provides the fast convergence of algorithm and small orders of solvable linear algebraic equations system. As examples of application, the transverse resonance method was used to calculate the scattering characteristics on 2-plane symmetric discontinuities consisting of a capacitive section of a microstrip line and slot resonators of complex shape in its ground plane.

Mode‐matching analysis of a spit‐circular cavity resonator for measurement of the dielectric constant for film on a substrate

In this paper, we apply the mode‐matching technique (eigenmode expansion) to formulate an analytical model for a split cylindrical cavity resonator with a thick ceramic film layer sandwiched between two‐layer alumina substrates. We then compute the resonant frequencies with the TE011 mode with an eigenvalue problem approach using the model formula. The quality factor (Q‐factor) of the resonator is also calculated by applying the perturbation method to the analytical model. The validity of the proposed analytical technique is confirmed by applying this method to the estimation of permittivity of thick films as an inverse problem. Ceramic films (2 µm thickness) were synthesized using a chemical solution method onto 200‐µm‐thick, 50‐mm‐diameter alumina substrates. The complex permittivity of the films was then determined using the TE011 mode split cylindrical cavity resonator in the 10‐GHz band. The extent of the edge effect at a sample insertion space was evaluated by comparing the estimated results through TE wave analysis using the mode‐matching method when the transverse resonance technique and the perturbation method were applied to calculate the resonant frequency and the dielectric Q‐factor. The results obtained indicate that a difference of 0.153% in the permittivity of the alumina substrate causes differences of 6.10 and 3.75% in the measured permittivity and loss tangent, respectively, of 2‐µm‐thick ceramic film with a permittivity of ∼50. Differences in permittivity and loss tangent were more pronounced with thinner films. It was also confirmed that the estimated results for permittivity and the loss tangent values of these ceramic films were affected by the estimated permittivity value of the alumina substrate. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Theoretical anisotropic transverse resonance technique for the design of low‐profile wideband antennas

The authors derive an anisotropic transverse resonance technique enabling the design of a low profile, wideband radiating rectangular cavity. They calculate a tapered geometry that preserves an effective half wavelength resonance within a cavity partially loaded with an anisotropic medium. This design results in an antenna profile of λ o/24, with 1.4 octaves of bandwidth, and a realised gain of 3.3–7.2 dB from 210 to 505 MHz. Using an adaption of a coaxial line to waveguide transition, which utilises two flat rectangular probes as a two-port matching network, as well as an external 180° hybrid coupler as a phase splitter, they achieve a voltage standing wave ratio of better than 2:1 across the whole band.

Periodic Collinear-Slotted Leaky Wave Antenna With Open Stopband Elimination

A low cross-polarization periodic-slotted ridged substrate-integrated waveguide (RSIW) leaky wave antenna (LWA) array is presented. Parametric constraints of the structure were investigated to realize a periodic leaky wave antenna (PLWA) with the ability of scanning from backward endfire into the forward quadrant. An appropriate multimode transverse equivalent network (TEN) is presented for the proposed antenna and values of leakage rate and phase constant for different parameters of the structure were extracted using the transverse resonance technique (TRT). The obtained results were compared to those achieved from HFSS software simulations. The open stopband in the broadside is eliminated using certain dimensions for the structure. By simultaneously manipulating a number of parameters, a variable {\alpha} and constant \b{eta} are resulted so that the desired sidelobe level (SLL) can be realized. The proposed structure was simulated and then manufactured. Simulation results show good agreement with measurement results.

Arbitrary Beam Shaping Using 1-D Impedance Surfaces Supporting Leaky Waves

A technique for generating an arbitrary, prescribed radiation pattern from a 1-D leaky-wave antenna is presented. The technique is applied to leaky-wave impedance surfaces. A homogenized model for an impedance surface is used so that the work is not limited to particular geometries. The model consists of a grounded, uniaxial dielectric substrate topped by a reactance sheet. To synthesize prescribed aperture fields, the leakage constant α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> and phase constant β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> along the antenna are tailored. The aperture field is determined by adapting the Orchard-Elliott method used in array synthesis to continuous line sources. The aperture field is related to α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> and β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> using a well-known approach, then the transverse resonance technique is employed to analytically relate α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> and β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> to the electrical parameters of the impedance surface. Specifically, the extraordinary index and sheet reactance are used to control α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> and β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub> . The designs presented demonstrate the synthesis of a variety of far-field patterns. Full-wave simulations show an improvement over previous beam synthesis techniques based on geometrical optics. Moreover, the numerical techniques demonstrate an efficient, gradient search method as an alternative to the iterative FFT methods explored previously, which have not generated radiation patterns with such high accuracy.

Analysis of Loaded Substrate Integrated Waveguides and Attenuators

This letter provides an approximate analysis of a slotted substrate integrated waveguide with periodic loading elements using the transverse resonance technique. The technique is used to design a travelling wave attenuator whereby pin diodes are capacitively coupled to the waveguide slot. By changing the bias, and therefore loading resistance, a very constant, variable attenuation is produced over the waveguide band.

Rapid Surface-Wave Dispersion and Plane-Wave Reflection Analyses of Planar Corrugated Surfaces by Asymptotic Corrugations Boundary Conditions Even for Oblique Azimuth Planes

The asymptotic corrugations boundary condition (ACBC) is used together with classical theory of vector potentials to analyze planar corrugations. A transcendental characteristic equation is derived, from which the dispersion diagram can be obtained, thereby conveying surface wave passband and stopband properties, even for propagation within oblique azimuth planes as well as both principal TE and TM polarizations. From the formulation, field distributions for the regions within the grooves and above the corrugations can also be generated. When compared with the dispersion graphs obtained from characteristic equations derived by the classical transverse resonance technique (TRT), the newly presented ACBC method provides superior accuracy. Explicit formulas for the complex reflection coefficient (amplitude and phase) for both TE and TM polarized plane-wave incidences are also derived as closed-form analytic functions of all parameters (especially the azimuth phi angle of incidence) using a novel concept of unusual transversely phased plane-waves. These proposed approaches are massively more efficient than full-wave solvers, providing unparalleled speedup of computation by thousands of times. The surface-wave and reflection properties of planar corrugations are thus herein analyzed in a unified, complete, and elegant manner that is also highly efficient but yet accurate. This thorough work is thus a great boost to the continued use of corrugated surfaces as artificial magnetic conductors (AMC), electromagnetic bandgap (EBG) structures, and soft/hard surfaces in all walks of antenna design, especially in terms of speed and accuracy.

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.

Moment method analysis of plane wave scattering from planar corrugated surfaces using parallel‐plate cavity Green's functions and derivation of analytic reflection‐phase formulas for both polarizations and oblique azimuth planes

A rigorous but yet highly accurate and efficient numerical treatment of plane wave scattering by T‐shaped planar corrugations through full‐wave modal analysis is first presented in this paper, which entails the moment method using parallel‐plate waveguide cavity Green's functions and a numerical spectral‐domain Green's function for planar stratified media. Investigations in terms ofbothreflection‐phase and dispersion diagrams are conducted. After validating with the commercial software package: CST Microwave Studio, this moment‐method is in turn used to verify a formula derived by the transverse resonance technique (TRT) for the surface‐wave propagation constant of corrugations in terms of the dispersion diagram. Correspondences between the reflection‐phase and dispersion diagrams are then established by relating the high and low impedance frequencies in the former with the pass and stop bands of the latter. With the abovementioned formula, the way is paved for a novel derivation of explicit formulas for the reflection‐phase of an incident plane wave impingent on the corrugations as closed‐form analytic functions of the various parameters, even for oblique azimuth planes of incidence and for both TE and TM polarizations. Doing so, the high or low surface‐impedance (AMC or AEC) properties of such corrugations can virtually be acquired instantly, thus providing incomparable speedup of the process of thorough reflection‐phase characterization of AMC or high‐impedance surfaces and soft surfaces, thus affording rapid designs of antennas and microwave devices that make use of them.

Analysis of coupled slot resonators of complex shape in metalization plane of a micro-strip transmission line using the transversal resonance techniques

The transverse resonance techniques is developed for analyzing three-layer planar structures based on micro-strip transmission line with slot resonators of complex shape in the grounding plane. Development of the techniques consists in considering higher space harmonics of current density in the strip line and mutual coupling between the slots in the grounding plane when numerically solving the boundary problem. In order to verify the techniques we conduct analysis of structures that consist of two coupled U- and symmetrical H-shaped slot resonators in the grounding plane of the micro-strip transmission line.

Low-Frequency Dominant-Mode Propagation in Spatially Dispersive Graphene Nanowaveguides

Dispersion properties of the dominant modes supported by different 2-D graphene-based nanowaveguides are studied by means of an exact approach based on the transverse-resonance technique and using an equivalent-circuit representation of graphene sheets which also takes into account the spatially dispersive nature of the graphene conductivity: it is quantitatively shown that neglecting spatial-dispersion effects can cause errors in the determination of the modal properties of extremely slow surface waves, also well below the terahertz regime. The modal features of graphene nanowaveguides are thus investigated in detail showing their potential in future nanoelectromagnetic and nanophotonic applications.

Analysis of Laterally Open Periodic Waveguides by Means of a Generalized Transverse Resonance Approach

The combination of the generalized transverse resonance technique, a field-matching method, and the generalized scattering matrix (GSM) concept is proposed in this paper as an efficient, versatile, and accurate method for the analysis of laterally open periodic waveguides. The proposed method accounts for both open and periodic boundary conditions without any approximation. Its only drawback is its restriction to the analysis of structures that can be segmented in the Cartesian coordinate system. How ever, a staircase approach has been successfully applied to over come this basic limitation. The segmentation of the waveguides, the field expansions for TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p,q</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sup> Bloch modes in each partition, and a modification of the well-known GSM cascading procedure for the analysis of a particular type of structure are detailed. In order to demonstrate the capabilities of the proposed approach, four structures, similar to the substrate integrated waveguide, have been analyzed, built, and measured. These examples include single-row square-post and circular-post waveguides, and displaced-row and multiple-row square-post waveguides. The computations and measurements confirm the efficiency, accuracy, and great versatility of this method.

Periodic Structure on the Slot Resonators in Microstrip Transmission Line

In this paper, scattering and phase-shift characteristics of 1-D periodic structures based on slot resonators in a ground plane of a microstrip line were studied. The scattering matrix of a slot resonator in a microstrip line ground plane was calculated by the two methods: using from scattering matrix of microstrip-slotline transition, and rigorous calculation of slot resonator in microstrip line. Both matrices were obtained by a transverse resonance technique. Amplitude characteristics and phase shift on period were studied for one-, two-, and three-stages periodic structures. As an example of possible application, the high-order harmonics filter based on a three-stage periodic structure was designed, which has a phase of a reflection coefficient equal to 0 and pi on the second and third harmonic, respectively. Such values of the phase find application in the output network of inverse class <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> power amplifiers.

Accurate Analysis of Meanderline Polarizers With Finite Thicknesses Using Mode Matching

Most of the existing methods for the analysis of meanderline polarizer assume that the embedded metallic grids are infinitely thin. A modal procedure is presented here for treating meanderline grids with finite thicknesses. The space between the metallic grids in a unit cell is considered as a meanderline waveguide with a stepped cross-section and length given by the grid thickness. The modes of this guide are obtained using the transverse resonance technique. A generalized scattering matrix characterization of the grid is obtained by field matching of the modes of the meanderline guide and the free space Floquet guide. The accuracy of this approach is verified by the very good agreement obtained between predicted and measured transmission phases of polarizer grids.

Leaky wave phenomena of a conductor‐back dielectric slab covered with a two‐dimensionally electromagnetic band gap superstrate

This paper presents the leaky wave phenomena associated with a waveguide structure that consists of a conductor‐back dielectric slab covered with a superstrate made up of a two‐dimensionally (2‐D) electromagnetic band gap (EBG) structure. A guided wave has its energy bounced back and forth between the metallic ground plane and the EBG structure that is taken as a frequency‐selective reflection mirror. Because of the finite thickness of the 2‐D EBG superstrate, the guided wave will leak or radiate some of its energy into the air region above the waveguide structure to become a leaky wave. By the mode‐matching method and the transverse resonance technique, the overall waveguide structure is formulated as a rigorous electromagnetic boundary value problem to yield an exact dispersion relation of the waveguide so that the complex propagation constant of a guided mode can be accurately determined, including the phase and attenuation constants. Additionally, the electric field distribution inside the waveguide and the far‐field radiation pattern were also calculated to demonstrate the leaky wave phenomena of this waveguide from a microscopic point of view. On the basis of the excitation of leaky waves, the phenomenology concerning a class of directive antennas with EBG structure as superstrate was clarified in this research.

A Simple, Fast and Accurate Method for Calculating Cutoff Wavelengths for the Dominant Mode in Elliptical Waveguide

In this paper, the transverse resonance technique is employed to calculate the cutoff wavelength of the dominant mode in elliptical waveguide for the first time. Numerical results are given and verified for various eccentricities. The impact of the number of step junctions for the approximation of the elliptical boundary line is discussed. Compared with other methods involving Mathieu functions, the technique is simple, fast, accurate and easy to understand. The method can also be applied to other guide structures and field modes with slight modifications.