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The editorial in the journal "Applications of Mathematics" is dedicated to Professor Ivo Babuška, the founder of the journal, who made significant contributions to applied mathematics, numerical analysis, and computational mechanics. The issue includes papers on topics such as superconvergence in the finite element method, finite element solutions of the Poisson equation, a posteriori error estimation for parabolic problems, and interpolation of physical quantities on spheres. The papers also cover the study of acoustic waveguides, regularity of solutions of the Poisson equation in polygonal domains, and approximation properties of Deep Neural Networks in relation to finite element spaces. [Extracted from the article]

The European DEMO (EU-DEMO) reactor studies within EUROfusion aim to develop a fusion power plant concept. The large tokamak device needs an auxiliary heating power which, at the present stage, is provided by the Electron Cyclotron (EC) heating system with up to 130 MW foreseen to reach different regions of plasma for heating, suppression of instabilities and the possibility to support ramp-up and ramp-down phases. The present conceptual design of the system is based on 2 MW coaxial-cavity gyrotron sources, a transmission line (TL) using both circular corrugated waveguides and quasi-optical evacuated multi-beam TLs, and mirror antennas located in the Equatorial Port. In order to create a modular system, the sources are grouped in 'clusters', whose powers are combined in the quasi-optical TL, up to the tokamak building, where they are split and routed as single waveguides. In the launcher, they are combined together again on the launching mirrors, to save space for the apertures in the Breeding Blanket. The present EC heating system has a certain flexibility to adapt to changing design guidelines. The development status of the system is presented. [ABSTRACT FROM AUTHOR]

This paper presents the transmission characteristics of flexible solid circular dielectric waveguides in the terahertz frequency band. In this paper, we measured the electrical properties of certain polymers within 325–500 GHz. Through simulation and measurement, the transmission loss, bending loss, and electric field distribution of solid-core polymer dielectric waveguides were analyzed and discussed. Additionally, we considered the surrounding cladding of the dielectric waveguide, the signal-feeding mode transmitter, and the interconnection of the dielectric waveguide. Ultimately, in the operating frequency range of 325–500 GHz, we selected PTFE rods with diameters of 0.5 mm and 1 mm as the dielectric waveguides, with measured transmission loss of less than 30 dB/m and 33 dB/m, respectively, and bending loss of less than 1 dB/m. The described dielectric waveguide has engineering significance for short-distance connections in complex geometric environments and provides a reference for subsequent research. [ABSTRACT FROM AUTHOR]

The possibility of using a circular waveguide with radial ridges and ring-shaped segments of finite thickness as resonant diaphragms in the synthesis of bandpass cylindrical waveguide filters is shown. The analysis of the electrodynamic parameters dependences on diaphragms geometrical dimensions has been carried out. Filters were synthesized and compared with experimental data. [ABSTRACT FROM AUTHOR]

This paper investigates a novel waveguide component design with dual functionality of mode conversion and power splitting. Because of its complex internal geometry which conventional fabrication methods cannot realize, additive manufacturing was explored, specifically selective laser melting. The end-to-end process of design, simulation, fabrication, and measurement will be discussed in detail. The said waveguide component converts between 4 rectangular waveguide TE10 mode and 1 circular waveguide TM01 mode. The 1 to 4 splitter was done while achieving low power splitting losses and mode conversion losses with low return losses. This allows for waveguide connections to be made between circular waveguides and rectangular waveguides at X-Band, which can be used for radars or satellite communication applications. The novelty of this component design comes from impedance matching between 4 rectangular waveguides operating in the fundamental mode and 1 single highly over-moded circular waveguide by means of coaxial rod and matching fins. All these are done while keeping the overall size small, compact, and lightweight. [ABSTRACT FROM AUTHOR]

The quasi-magnetostatic (briefly, magnetostatic) microwave propagation in a long, circular cross section waveguide having a metallic wall that is filled with an anisotropic uniaxial magnetic medium (here, a metamaterial consisting of split-ring resonators) is studied. Such waves do not exist in the case of a hollow metallic waveguide or a metallic waveguide filled with an isotropic medium. Physically, the present magnetostatic waves owe their existence to the anisotropic property of the system, where in the absence of this property, these magnetostatic waves disappear. A theoretical analysis is carried out and characteristics of these magnetostatic microwaves in circular metallic waveguides filled with uniaxial negative permeability media are determined. The presented results include the dispersion relation of magnetostatic waves and their corresponding cutoff frequencies, group velocities, transverse modal field distributions, power flows, and stored energies. [ABSTRACT FROM AUTHOR]

This paper describes the principles behind the radio-frequency (RF) sensing of bacterial biofilms in pipes and heat exchangers in a dairy processing plant using an electromagnetic simulation. Biofilm formation in dairy processing plants is a common issue where the absence of timely detection and subsequent cleaning can cause serious illness. Biofilms are known for causing health issues and cleaning requires a large volume of water and harsh chemicals. In this work, milk transportation pipes are considered circular waveguides, and pasteurizers/heat exchangers are considered resonant cavities. Simulations were carried out using the CST studio suite high-frequency solver to determine the effectiveness of the real-time RF sensing. The respective dielectric constants and loss tangents were applied to milk and biofilm. In our simulation, it was observed that a 1 µm thick layer of biofilm in a milk-filled pipe shifted the reflection coefficient of a 10.16 cm diameter stainless steel circular waveguide from 0.229 GHz to 0.19 GHz. Further sensitivity analysis revealed a shift in frequency from 0.8 GHz to 1.2 GHz for a film thickness of 5 µm to 10 µm with the highest wave reflection (S11) peak of ≈−120 dB for a 6 µm thick biofilm. A dielectric patch antenna to launch the waves into the waveguide through a dielectric window was also designed and simulated. Simulation using the antenna demonstrated a similar S11 response, where a shift in reflection coefficient from 0.229 GHz to 0.19 GHz was observed for a 1 µm thick biofilm. For the case of the resonant cavity, the same antenna approach was used to excite the modes in a 0.751 m × 0.321 m × 170 m rectangular cavity with heat exchange fins and filled with milk and biofilm. The simulated resonance frequency shifted from 1.52 GHz to 1.54 GHz, for a film thickness varying from 1 µm to 10 µm. This result demonstrated the sensitivity of the microwave detection method. Overall, these results suggest that microwave sensing has promise in the rapid, non-invasive, and real-time detection of biofilm formation in dairy processing plants. [ABSTRACT FROM AUTHOR]

Buried depressed-cladding waveguides were fabricated in 0.7-at.% Nd:Ca3Li0.275Nb1.775Ga2.95O12 (Nd:CLNGG) and 7.28-at.% Yb:CLNGG disordered laser crystals grown by Czochralski method. Circular waveguides with 100 μm diameters were inscribed in both crystals with picosecond (ps) laser pulses at 532 nm of 0.15 μJ energy at 500 kHz repetition rate. A line-by-line writing technique at 1 mm/s scanning speed was used. Laser emission at 1.06 μm (with 0.35 mJ pulse energy) and at 1.03 μm (with 0.16 mJ pulse energy) was obtained from the waveguide inscribed in Nd:CLNGG and Yb:CLNGG, respectively, employing quasi-continuous wave pumping with fiber-coupled diode lasers. The waveguide realized in RE3+-doped CLNGG crystals using ps-laser pulses at high repetition rates could provide Q-switched or mode-locked miniaturized lasers for a large number of photonic applications. [ABSTRACT FROM AUTHOR]

Examples of the application of the confluent hypergeometric functions in miscellaneous areas of the theoretical physics are presented. It is suggested these functions to be utilized as a universal means for solution of a large number of problems, leading to: cylindrical, incomplete gamma, Coulomb wave, Airy, Kelvin, Bateman, Weber's parabolic cylinder, logarithmic-integral and exponential integral functions, generalized Laguerre, Poisson-Charlier and Hermit polynomials, integral sine and cosine, Fresnel and probability integrals, etc. (whose complete list is given), which are their special cases. The employment of such an approach would permit to develop general methods for integration of these tasks, to generalize results of different directions of physics and to find the common features of various phenomena, governed by equations, pertaining to the same family. Emphasis is placed here on the use of the Kummer function in the field of microwaves: the cases of normal and slow rotationally symmetric TE modes propagation in the azimuthally magnetized circular ferrite waveguide are considered. Lemmas on the properties of the argument, real and imaginary parts, and positive purely imaginary (real) zeros of the function mentioned in the complex (real) domain, of importance in the solution of boundary-value problem stated for normal (slow) waves, are substantiated analytically or numerically. A theorem for the identity of positive purely imaginary and real zeros of the complex respectively real Kummer function for certain parameters, is proved numerically. Tables and graphs support the results established. The terms for wave transmission are obtained as four bilaterally open intervals of variation of the quantities, specifying the fields. It turns out that the normal (slow) modes may exist in one (two) region(s). The theoretically predicted phase curves for the first waves of the two TE sets examined show that the structure explored is suitable for ferrite control components design. [ABSTRACT FROM AUTHOR]

The complex permittivity of 8-mol yttria-stabilized zirconia (8-YSZ) in powder and sintered (i.e., solid) forms were measured from 32 to 40 GHz using a circular waveguide probe. This probe is suitable for measuring both the powder and solid forms of materials. Comparative completely filled rectangular waveguide measurements of the powder were performed at three frequency bands to verify these results and also to extend the measured complex permittivity estimation frequency range. The results indicated good agreement between the two different measurement techniques. The complex permittivity of the 8-YSZ powder was measured to be $(\epsilon _{r} = 2.45 - j0.04)$ . Conductor-backed solid 8-YSZ, representative of an in-service ceramic coating, was also measured using the circular waveguide probe. Complex permittivity was measured to be significantly higher $(\epsilon _{r} = 29.28 - j0.07)$ when the 8-YSZ was sintered into a solid form. This was attributed to densification and other effects occurring during the sintering process.

In this article, an exact formulation is derived for the mode reflection coefficient (and in general, the full S-parameter matrix) for a circular waveguide radiating into a multilayered structure and when excited with any combination of axially symmetric modes (i.e., modes of the form TE0m and TM0m, where $\mathbf {m}$ is a positive integer). This formulation solves for the fields in the waveguide, including fields resulting from higher-order evanescent modes, using Fourier analysis. This leads to an accurate calculation of the mode S-parameter matrix, which includes the reflection coefficient of each excited mode. The derived formulations were validated through comparison to those computed using full-wave 3-D electromagnetic simulations. Additional simulations demonstrated the effect of considering higher-order modes on the results. The effect of having a finite flange and sample size on the complex reflection coefficient was also shown through 3-D simulations, indicating the relative insensitivity of the TE01 probe to edge effects. Reflection coefficient measurements, using a circular waveguide probe with the TE01 mode, were performed to experimentally verify the accuracy of the formulations. Forward-iterative optimization (i.e., optimal curve fitting) techniques were then performed on the reflection coefficient measurements to demonstrate the efficacy of this method for accurately estimating the thickness and complex permittivity of thin dielectric layers.

In this study, a dual-mode waveguide circularly polarized antenna for TC&R (telemetry, command, and ranging) was proposed for the communication between a low-orbit satellite and a ground station. The proposed antenna required both a wide -10 dB bandwidth and axial ratio bandwidth of 7.1-7.3 GHz and 8.0-8.4 GHz. The antenna was designed with a stepped septum inside a square waveguide to obtain circular polarization and the axial ratio wide bandwidth. Next, a dual-mode synthesis method was adopted for link budgeting by combining square and circular waveguides. The requirement was that the co-polarization level with a symmetric -3 dB beamwidth of 39° must be -5 dBic or higher at ±76.5°, and the cross-polarization level must average -15 dBic or lower at ±76.5°. Finally, the corrugate structure attached to the outside of the extended circular waveguide was offset in multiple steps to suppress the back lobe of the cross-polarization As a result, the axial ratio maintained an average of 1.8 dB at 0° within each band of the required frequency. In addition, the co-polarization obtained an average of -4.52 dBic in the 7.2 GHz band and -5.31 dBic in the 8.2 GHz band at ±76.5°. Finally, in the case of the cross-polarization pattern, the back lobe level was suppressed by 9.89 dB at 7.2 GHz by the corrugate structure, and an average value of -19.9 dBic or less was obtained at ±76.5°. The proposed antenna was confirmed to be effective as a Korean low-orbit satellite TC&R antenna with a radiation pattern of a symmetric beamwidth. [ABSTRACT FROM AUTHOR]

The presence of π gauge flux enabled by positive and negative hopping amplitude can lead to Möbius bands, which was recently demonstrated in both realistic acoustic and photonic lattices, twisted at k = π. Here, we show that the artificial gauge flux configuration can be achieved by exploiting the interactions between photonic s and p orbital-like fundamental modes in circular and peanut-shaped waveguides, respectively. By manipulating the interplay between the gauge fields and the crystal symmetry, we show that breaking the primitive translation symmetry through lattice site dimerization and deformation can cause the original Dirac semimetal phase, characterized by a four-fold Dirac point at the Brillouin zone center, to transform into various topological phases. The designed photonic waveguide array supports topological phases such as Möbius insulator and Weyl-like semimetal phases. Noticeably different to the existing cases, we explicitly show that the twisting Möbius bands cross each other at k = 0 due to the lattice gauging with alternating sign, which results in distinct beam dynamics excitation. We also present Weyl-like flat-band edge states in such photonics waveguide arrays. Our results suggest that such s − p hybridized photonic waveguide array servers as a convenient and flexible platform for studying topological physics, particularly in simulating the effects of gauge field in alternative configuration. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method to generate Vector Vortex Modes (VVM) inside a metallic cylindrical waveguide at microwave frequencies and demonstrate the experimental validation of the concept. Vector vortex modes of EM waves can carry both spin and orbital angular momentum as they propagate within a tubular medium. The existence of such waves in tubular media can be beneficial to wireless communication in such structures. These waves can carry different orbital angular momentum and spin angular momentum, and therefore, they feature the ability to carry multiple orthogonal modes at the same frequency due to spatial structure of the phase and polarization. In essence, high data rate channels can be developed using such waves. In free space, Orbital Angular Momentum carrying vortex waves have beam divergence issues and a central field-minima, which makes these waves unfavorable for free space communication. But vector vortex mode waves in guided structures do not suffer from these drawbacks. This prospect of enhancement of communication spectrum in waveguides provides the background for the study of vortex wave in circular waveguides. In this work, new feed structures and a radial array of monopoles are designed to generate the VVM carrying waves inside the waveguide. The experimental findings on the distribution of the amplitude and phase of the electromagnetic fields inside the waveguide are presented and the relationship between the waveguide fundamental modes and VVMs are discussed for the first time. The paper also presents methods for varying the cutoff frequency of the VVMs by introducing dielectric materials in the waveguide. [ABSTRACT FROM AUTHOR]

With the help of the original mathematical method for solving Maxwell's equations, it is shown that in dielectric waveguides along with usual waveguides and quasi-normal modes, there are perfect invisibility modes or perfect non-scattering modes. In contrast to the usual waveguide modes, at eigenfrequencies of the perfect invisibility modes, light can propagate in free space. The properties of the invisibility modes in waveguides of circular and elliptical cross-sections are analyzed in detail. It is shown that at the eigenfrequencies of the perfect invisibility modes, the power of the light scattered from the waveguide tends to zero and the optical fiber becomes invisible. The found modes can be used to create highly sensitive nanosensors and other optical nanodevices, where radiation and scattering losses should be minimal. [ABSTRACT FROM AUTHOR]

The dispersion properties of surface-type electromagnetic waves propagating along azimuthal angles in circular metal waveguides entirely filled by two layers of plasma in an axial static magnetic field are studied. The three-component structure models plasma radial inhomogeneity and generalizes two research which was two researches which were accomplished earlier. One is a circular metal waveguide entirely filled by cold plasma in an axial static magnetic field. The other is a coaxial metal waveguide entirely filled by plasma. Introducing the additional interface between the plasma column and coaxial plasma layer causes arising of the additional root of the dispersion relation which can be of interest for practical applications. The disappearance of additional wave branches with decreasing the difference in the plasma particle densities is carefully investigated. The wave dispersion properties are demonstrated to be mostly determined by the plasma with smaller particle density. [ABSTRACT FROM AUTHOR]

In this paper, we present the design and implementation methods of quarter-wavelength resonators accommodating Beltrami standing waves with parallel electric and magnetic (E‖H) fields. The resonator is bounded by the quarter-wavelength longitudinal electromagnetic conductor (LEMC), the circumferential electromagnetic conductor (CMEC), and the radial electromagnetic conductor (REMC). The LEMC, CEMC, and REMC boundaries are artificially implemented by the circumferentially aligned corrugation, concentrically aligned circular fins, and axisymmetrically aligned radial fins, respectively. The coupling control methods by introducing slots in the CEMC and REMC with the external TM01 and TE01 circular waveguides are presented. We design the quarter-wavelength resonators with the implemented LEMC, CEMC, and REMC boundaries with controlled external couplings and numerically demonstrate their E‖H properties, which confirms the validity of the proposed design method. [ABSTRACT FROM AUTHOR]

The method of successive approximations is applied to solve the Maxwell equations in cylindrical plasma waveguide geometry for electromagnetic waves with arbitrary azimuthal wave index and small axial wavenumber. The theory of surface flute waves is used as zeroth approximation. This study generalizes previous investigations whose results are utilized for verification of newly obtained conclusions. The influences of several plasma waveguide parameters such as magnitude and sign of the azimuthal wave index, the width of the dielectric layer between a plasma and a waveguide wall and the magnitude of its dielectric constant, the radii of the plasma column and the metal wall, and the external axial static magnetic field on the wave dispersion properties are analyzed. [ABSTRACT FROM AUTHOR]

This article presents a dual-circularly polarized array antenna based on gap waveguide technology operating at E-band. Double-grooved circular waveguide polarizers that utilize two annulus grooves placed at 45° and 135° offset from both excitation ports are used in this work. The operating principles of the polarizer are analyzed. Multilayer design using gap waveguide is implemented on the basis of the polarizer. The antenna consists of six layers, including three layers for the feeding networks, one layer for the polarizer, one layer of back cavity, and another layer of radiating grid. A 2 $\times $ 2 unit cell is proposed first and employed to realize an 8 $\times $ 8 planar array. Corporate feeding networks that use compact E-plane T-junctions and H-plane T-junctions are proposed. The antenna has been fabricated and verified by measurements. The measured results of S-parameters agree well with the simulation and show that reflection coefficients are better than −10 dB for both circular polarizations (CPs) from 76 to 81 GHz. The measured isolation between the input ports is larger than 25 dB in the operating band. The far-field measurements show that the antenna has realized gain larger than 24 dBi and axial ratios less than 1.5 dB from 76 to 81 GHz at boresight direction. [ABSTRACT FROM AUTHOR]

The quantum state transfer of a system of N coupled waveguides in a ring geometry, where the last waveguide is coupled to the first one is considered. The coupling parameters are chosen not to be equal, but to vary according to the position of the waveguides. We examine the fidelity between different waveguides in order to check if it is possible to achieve a perfect state transfer (PST). We focused our analysis on the single-photon Fock state and the two-photon N 00 N state. Very high values of fidelity (> 95%) were found for both cases, but the PST was only observed for the single-photon Fock state. • Perfect State Transfer (PST) and high fidelities are achieved in circular lattices with non-uniform couplings. • Analytical expressions are provided for the quantum state transfer of Fock and N00N states. • Fidelity values above 50% are observed for systems with five and six coupled waveguides. [ABSTRACT FROM AUTHOR]

A panoramic ultra-high resolution photonic integrated circuit spectrometer is under development by the authors. The architecture comprises a tunable ring resonator (RR) stage and an AWG stage. The resolution defines the bandwidth of the RR, determined by the cross-coupled power and hence the gap between the access and ring waveguides. The AWG channel frequency spacing determines the required free-spectral range (FSR) and hence the perimeter of the ring resonator. The specified <1 GHz resolution combined with an FSR of 50 GHz renders accurate simulation difficult, obstructing the design process. In this report, a simplified design rule to determine the minimum gap between straight access waveguides and a circular ring waveguide is proposed. Realistic assumptions such as the existence of local bisymmetry and adiabatic mode evolution throughout the coupling region permit a simple mode solver to determine the relationship between the cross-coupled power and the minimum gap size. A parameter extraction method is also formulated for add-drop rings equipped with two nominally identical couplers that disentangles the loss and coupling ring parameters from intensity-only transmission measurements. The proposed rule is applied to the design of ring resonators fabricated on a Si3N4 platform. The parameter extraction method is used to analyze the measured characterization data of the ring resonators. The results show good agreement within ~43 nm between the design rule and the gaps size determined by the parameters extracted from the measured data and provide experimental confirmation of the technological viability of the ring resonators required by the spectrometer. [ABSTRACT FROM AUTHOR]

In this article, two wideband choke flanges (Flange 1 and Flange 2) are designed to reduce the passive intermodulation (PIM) level of the orthmode transducer (OMT). Since flange connections are important sources of PIM, circular Flange 1 introduces a choke groove and achieves a power suppression level of 41.95 dB. To meet the requirement of miniaturization and lightweight, Flange 2 with rectangular structure and rectangular choke groove is proposed for reducing height waveguide. Compared with conventional circular choke flange for reduced height waveguide, it has a smaller cross area and better power suppression level (39.92 dB). To evaluate the PIM performance of the proposed OMT with two flanges, temperature circulation test is executed. It is proved that the third-order PIM level is about −135 dBm from measurement results. Therefore, the proposed flanges can be utilized in large-scale multibeam array for low PIM satellite communication applications. [ABSTRACT FROM AUTHOR]

A perturbation method is developed for the analysis of anisotropic circular waveguides partially filled with eccentric cylinders. The method allows to compute axial wavenumbers and field patterns for hybrid modes supported in waveguides with small eccentricities via a perturbation series. The proposed method is validated against analytical results and numerical results based on the finite-element method (FEM) and the finite-integration technique (FIT) in different configurations. The results show that the presented approach can solve, for example, the longitudinal wavenumbers of anisotropic waveguides with an eccentricity of 23% with a relative error less than 1.78% at a much lower computational cost when compared to numerical techniques. [ABSTRACT FROM AUTHOR]

We present a resonant leaky-wave lens antenna, fed by a circular waveguide with annular corrugations in the ground plane. The proposed leaky-wave feed reduces the impact of the spurious TM0 leaky-wave mode in all planes over a wide bandwidth while reducing assembly complexity compared to previous methods. The proposed leaky-wave antenna has an aperture efficiency above 80%, a return loss below −15 dB, and a cross-polarization level below −20 dB over a bandwidth from 110–220 GHz (2:1). We have fabricated and measured a WR-5 band (140–220 GHz) antenna prototype with a lens diameter of 3 cm that achieves excellent agreement between measurement and simulation in terms of return loss, directivity, and gain. [ABSTRACT FROM AUTHOR]

In this article, we present a numerically stable formulation for the electromagnetic analysis of lossy circular waveguides. The associated boundary value problem is solved analytically via an appropriate set of scaled cylindrical functions. A new numerically stable characteristic equation that simplifies the application of Cauchy’s argument principle is introduced. Numerical results are presented and show that the proposed approach can solve modal fields even in extreme lossy scenarios. [ABSTRACT FROM AUTHOR]

Platelets corrugated horn is a promising technology for its scalability to a large corrugated horn array. In this communication, we present the design, fabrication, measurement, and uncertainty analysis of a wideband 170–320 GHz platelet corrugated horn that features with low sidelobe across the band (<−30 dB). We also propose an accurate and universal method to analyze the axial misalignment of the platelets for the first time. It is based on the mode matching (MM) method with a closed-form solution to off-axis circular waveguide discontinuities obtained by using Graf addition theorem for the Bessel functions. The uncertainties introduced in the fabrication have been quantitatively analyzed using the Monte Carlo method. The analysis shows that the cross-polarization of the corrugated horn degrades significantly with the axial misalignment. It well explains the discrepancy between the designed and the measured cross-polarization of platelets corrugated horn fabricated in the THz band. The method can be used to determine the fabrication tolerance needed for other THz corrugated horns and evaluate the impact of the corrugated horn for astronomical observations. [ABSTRACT FROM AUTHOR]

Abstract A novel design for a TE10‐mode rectangular waveguide to a TE11‐mode circular waveguide mode converter based on the use of an intermediate one‐step double‐cruciform section is proposed. The converter achieves compactness and broadband by employing the one‐step double‐cruciform transition instead of the conventional multi‐step transitions or smooth transitions. Due to the one‐step structure, the converter achieves an extremely short‐length (around 0.3λ, where λ is the wavelength at the centre frequency), which makes it suitable for highly compact systems. For verification purpose, a back‐to‐back connection rectangular‐to‐circular mode converter was fabricated and measured. The measured results show that the return loss is around 15 dB and the insertion loss is around 0.4 dB in the operating frequency band. Thus, we can infer that the return loss and insertion loss of a single mode converter are around 19 and 0.2 dB, respectively. The experimental results reasonably agree with the simulated results.

Waveguide-like transmission line (WLTL) structures, including rectangular waveguides, circular waveguides, and coaxial lines, have been widely used in microwave engineering. Determining how to efficiently model WLTLs has become vital for the design of various WLTL-based devices. In this paper, a circuit-based wave port boundary condition (CWPBC) is developed and applied in the discontinuous Galerkin time-domain (DGTD) method to accurately simulate these structures for the first time. In the CWPBC, modal voltages and currents of a WLTL are defined, and circuits based on modal voltages and currents are introduced. By co-simulating the modal circuit and the WLTL modeled using the DGTD method, various modal fields can be excited in the WLTL, and at the same time, the WLTL can be terminated without reflections. No extra costs or approximations are used in the proposed CWPBC, and there is no requirement of either the extension of the computational domains widely used in perfectly matched layer (PML) termination or the longitudinal field continuity used in the reported DGTD method. The proposed method can easily obtain the postprocessing parameters, including S-parameters and port power. Numerical results, including rectangular waveguide filters, circular waveguide horns, and coaxial-fed electromagnetic bandgaps (EBG), are given to validate the effectiveness of the proposed CWPBC. [ABSTRACT FROM AUTHOR]

A novel methodology to perform mode conversion from rectangular fundamental TE10 mode to circular TE $_{n1}$ ($n $ = 2, 3, $4, \ldots $)/TE $_{0p}$ ($p $ = 1, 2, $3, \ldots $)/TE $_{1q} (q $ = 2, 3, $4, \ldots $) modes with similar topologies is presented in this article. The mode converter consists of two sections: a novel H-plane T-junction-based rectangular TE $_{m0}$ ($m $ = 2, 3, $4, \ldots $) mode launcher and a rectangular TE $_{m0}$ -circular TE $_{n1}$ /TE $_{0p}$ /TE $_{1q}$ mode converter. This kind of mode converter possesses good comprehensive performance and is highlighted by three primary advantages: 1) it is flexible to produce various circular TE modes and rectangular TE $_{m\mathrm {0}}$ modes; 2) the mode converter has a relatively simple and easy-to-fabricate geometry, making it especially suitable for the terahertz-band operation; and 3) it possesses a high mode conversion efficiency over a wide bandwidth, which is adequate to satisfy most of the application requirements. The analysis of mode conversion principle, numerical simulations, microfabrication, and experimental measurement of two H-band (220–325 GHz) prototypes are described. Back-to-back measurement results exhibited good agreement with simulation predictions having considered the conductor loss. A 3-dB transmission bandwidth of 56.7 GHz (231.4–288.1 GHz)/42.1 GHz (244.0–286.1 GHz) was experimentally obtained for the ${\mathrm {TE}}^{\square}_{10}-{\mathrm {TE}}_{01}^{\circ}/{\mathrm {TE}}_{31}^{\circ}$ mode converter. [ABSTRACT FROM AUTHOR]

It has been technically challenging to efficiently couple external radio frequency (RF) power to cylindrical dielectric-loaded accelerating (DLA) structures, especially when the DLA structure has a high dielectric constant. This article presents a novel design of matching section for coupling the RF power from a circular waveguide to an $X$ -band DLA structure with a dielectric constant $\varepsilon _{\text {r}}=16.66$ and a loss tangent $\tan \delta =3.43\times {10}^{-5}$. It consists of a compact dielectric disk with a width of 2.035 mm and a base angle of 60°, resulting in a broadband coupling at a low RF field, which has the potential to survive in the high-power environment. To prevent a sharp dielectric corner break, a 45° chamfer is also added. A microscale vacuum gap, caused by metallic clamping between the thin coating and the outer thick copper jacket, is also studied in detail. Through optimization, most of RF power is coupled into the DLA structure, with no enhancement of peak electromagnetic fields above those of the structure itself. Tolerance studies on the geometrical parameters and mechanical design of the full-assembly structure are also carried out as a reference for fabrication. [ABSTRACT FROM AUTHOR]

The method of auxiliary sources with an excitation source (MAS-ES) is a reliable method for determining the eigenvalues $k$ in hollow, 2-D waveguides. This is done using a $k$ -dependent response function $F(k)$ , defined as the mean-square value of the magnitude of the field at a number of random points within the waveguide: plotting $F(k)$ for a fine grid of $k$ yields a response curve with sharp peaks at the positions of the eigenvalues. In this work, it is shown that the eigenvalues can be determined, more simply, by means of the auxiliary currents vector norm (ACVN). We explain our method analytically for the simple problem of the circular waveguide, apply it numerically to more complicated geometries, and compare our results to those of a finite element method (FEM)-based commercial software. We introduce a Hankel-function lookup procedure, which greatly reduces computational times, and discuss the rather peculiar effect of divergence/oscillations of the auxiliary currents. [ABSTRACT FROM AUTHOR]

An omnidirectional conformal array antenna has been implemented in air-filled waveguide technology for the 37–40 GHz band. The input port of the antenna is a standard WR28 rectangular waveguide. The TE10 mode excited in the rectangular waveguide is used to generate the TE01 mode inside a circular waveguide by means of a TE10–TE01 mode converter. The circular waveguide section is progressively widened, forming a radial waveguide structure, where the TE01 mode propagates radially through several radiating apertures. Due to the rotational symmetry of the structure, an omnidirectional radiating performance with low ripple can be achieved. This structure has been three-dimentional (3-D) manufactured using the direct metal laser sintering technology. A good agreement between simulations and measurements has been found. A reflection coefficient of below −15 dB, a low-ripple omnidirectional performance in a conical cut plane, a low cross-polar radiation, and a total efficiency higher than 83% are obtained. This conformal antenna design is proposed for fifth generation (5G) New Radio indoor applications. [ABSTRACT FROM AUTHOR]

A high-efficiency W-band 12-way power combiner system based on the TM01 mode in a circular waveguide has been presented in this study. It is a radial structure composed of three elements: a circular waveguide TM01-mode transducer, an isolated 12-way radial power combiner, and amplifier modules. The measured passive combining efficiency is observed to be greater than 89.5% over the range of 85–100 GHz. The isolation between the inputs is better than 10 dB, with a maximum back-to-back return loss of 13 dB. By using 12 GaN monolithic microwave integrated circuit (MMIC) 2-W power amplifiers, the active combiner system produces a maximum power output of up to 22 W with an average combining efficiency of 81.7% within the band of 92–97 GHz. The power-added efficiency within the operating band has been measured to be up to 20.8%. [ABSTRACT FROM AUTHOR]

2.4 The first generation of THz integrated circuits on all-Si platform High-resistivity all-Si photonic crystal slabs have proven to be effective for integrating THz range components, including straight waveguides, waveguide bends, grating couplers [[89]] but also attenuators and resonators. Graph: Figure 2: THz waves in photonic crystals, (a) photonic crystal slab showing PGB effect and removable holes (purple region) to create waveguide track, (b) photonic crystal waveguide showing PBG effect and removed holes to create waveguide track, (c) illustration of TIR. Graph: Figure 6: Planar all-Si waveguide platforms and respective simulated field distribution, (a) photonic crystal waveguide with equilateral lattice [[108]], (b) photonic crystal waveguide with isosceles lattice [[108]], (c) Bragg-mirror suppressed waveguide [[34]], (d) topological waveguide [[109]], (e) EM waveguide [[24]], (f) unclad waveguide [[25]]. Keywords: communications; integration; photonic crystal; silicon photonics; terahertz; waveguide EN communications integration photonic crystal silicon photonics terahertz waveguide 1741 1759 19 05/12/22 20220401 NES 220401 1 Introduction A lot of research effort has been dedicated to the terahertz (THz) range in recent years. [Extracted from the article]

This article presents a wideband dual-circular-polarization (dual-CP) antenna with high port isolation based on a grooved-wall CP horn combined with an orthomode transducer (OMT) in the W-band. A pair of grooves on the inner wall of the horn serves as an inbuilt polarizer within the horn antenna, which is capable of generating both left-hand circular polarization (LHCP) and right-hand circular polarization (RHCP) without any septum. The continuous linearly tapered groove design also allows this multisection grooved-wall CP horn to achieve low reflection coefficients over a wide bandwidth, thereby realizing wideband dual-CP with high port isolation when it is used together with a wideband OMT. A prototype of the proposed dual-CP antenna is designed in simulation and measured in an experiment. The simulated and measured results agree very well, showing that port isolation >32.5 dB over 31.6% bandwidth from 80 to 110 GHz is achieved with axial ratio (AR) < 2.8 dB and reflection coefficient $< -20$ dB for both LHCP and RHCP. Rotationally symmetric radiation patterns over the entire operating bandwidth are also observed with a measured gain of 19.6 ± 2 dBic. [ABSTRACT FROM AUTHOR]

The generalized finite difference method (GFDM) is a meshless method that has become popular in recent years. The basic theory underlying GFDM is to expand the point cluster function value at the center node by Taylor’s formula and then obtain the best linear combinations of these function values to represent the derivative at the central node by the least square fitting technique. Subsequently, the minimized weighted error between the approximated value and the accurate value is obtained. This paper establishes the general steps for solving waveguide eigenvalue problems with GFDM. Excellent performance is shown by comparing the proposed method and other common solutions. The robustness of the proposed method is verified by calculating the cutoff wavenumbers of typical waveguides and the eccentric circular waveguide in different modes. [ABSTRACT FROM AUTHOR]

In this paper, to achieve high-quality filters, nanostructured plasmon resonators are proposed. The structure of proposed resonator is based on metal-dielectric-metal configuration and is designed in the range of 1550-nm telecommunication wavelength. To evaluate the proposed structure, finite-difference time-domain method and analytical method of coupled mode theory have been used. To obtain optimal results, the effects of the number of waveguides as well as the radius of circular and ring waveguides were investigated. The appropriate results will be obtained by considering a strong coupling between the incoming light and the surface plasmon. In addition, two transient and static wave structures have been used to evaluate the structure. The simulation results show that besides filtering behavior of the structure, it is possible to control the surface plasmon propagation speed in the proposed structure. Therefore, it is expected that the proposed structure will be used in many parts of a telecommunication link such as multiplexers. [ABSTRACT FROM AUTHOR]

A circular TE0n mode content analysis technique based on the multi-mode coupler with high mode selectivity is proposed. To improve the mode selectivity, a deformed waveguide, entitled the quad-polar waveguide, which discriminates the azimuthally symmetric TE-mode on the waveguide wall, is introduced. The influence of deformation on the TE01 and TE02 modes’ field pattern, the corresponding transmission loss, and the power capacity in the quad-polar waveguide are analyzed. Based on the analysis, a dual-mode coupler of the circular TE01 and TE02 modes, consisting of an oversized deformed circular waveguide coupler and a pair of circular-to-quad-polar waveguide transitions, is designed for a high-power Ka-band gyrotron traveling-wave tube system. To verify the high mode selectivity of a quad-polar waveguide, a simple coupling with equal-radius and equal-interval holes are used. A prototype is fabricated and measured, and the results show that the coupling coefficient is −40 dB with the directivity of 27 dB for the TE01 mode, suppressing the unwanted mode TE02 mode with 53 dB. For the TE02 mode, the coupling coefficient is −40 dB with the directivity of 25 dB and suppresses the unwanted mode TE01 mode with 75 dB from 30 to 40 GHz. [ABSTRACT FROM AUTHOR]

Mode converter is one of the most important devices in the high-power microwave (HPM) applications. To conduct an in-depth research for the orthogonal mode converter, a novel 90° compact TM01-TE11 circular waveguide converter working at 9.7 GHz is proposed in this article. This design innovatively integrates the traditional mode converter with 90° bend techniques based on the mode coupling theory, which ensures a compact structure and high-power handling capacity. Calculated and simulated results illustrate that the maximum conversion efficiency of the converter at central frequency reaches 99.4% when the structure length is 535 mm, and the bandwidth reaches 680 MHz when the conversion efficiency exceeds 95%. For demonstration, a prototype is fabricated, and the corresponding experiments are investigated. According to the $S$ -parameter measurement, it has a high conversion efficiency at central frequency. Meanwhile, the high-power performance is conducted by connecting it with a relativistic backward oscillator (RBWO), and the converter works stably under a maximum output power of 4 GW. The good agreement of the theoretical analyses, simulations, and experimental results indicates the feasibility of the proposed converter. [ABSTRACT FROM AUTHOR]

A novel compact fan-shaped folded waveguide resonator (FSFWGR) is proposed in this article. The resonator can reduce the size by 87.5% compared with the waveguide cavity while retaining a high unloaded quality ($Q_{u}$) value (>1500). Due to these advantages, a high-quality (-Q) fourth-order bandpass filter centered at 6.0 GHz with a 6.67% bandwidth is designed first. Novel slots cross-coupling is presented to produce a pair of transmission zeros (TZs) while avoiding support structures that traditional metal probes often used. Then compact deformed folded antenna is designed to integrate with the filter. Compared with published works where the last resonator of the reference filter often needs to be detuned, all parameters here do not need to change by introducing a metal probe between the feeding point of the filter and antenna. Therefore, the integrating process is more straightforward. The integrated filter/antenna achieves the same filtering function as the reference filter and a high gain of 6.7 dBi. For experimental demonstration, metal 3-D printing technology was used to fabricate models with only two pieces that significantly reduced the assembly loss. The final measured results agreed well with simulated ones. [ABSTRACT FROM AUTHOR]

This article proposes a method to excite the TM11 mode in circular waveguides. The principle of synthesizing a circular TM mode is deduced based on the electric dipole moment theory first, and the output mode and its purity are analyzed theoretically. Then, a mode conversion scheme to convert the rectangular TE10 into circular TM11 mode via a pair of out-of-phase quasi-TEM mode is proposed. In order to achieve the broadband excitation in a compact size, the ridge gap waveguide is used as a medium between the rectangular and cylindrical waveguide. Simulation results present that the proposed exciter has a propagation bandwidth up to 10 GHz in Ka-band with a mode purity over 98%. A prototype is manufactured and measured, and the presence of TM11 mode and the mode purity are confirmed by a port radiation pattern measurement. The mode exciter features high mode purity, broad bandwidth, and a compact size, which provides a low-power generator for the research of novel gyrobackward-wave devices and devices in the high-power transmission line. [ABSTRACT FROM AUTHOR]

Novel sensors for ultrashort-distance measurements, with choke flanges applied at the open ends of both a WR10 waveguide and a circular waveguide, featuring a radius of 1.42 mm, are proposed. Field distributions between the sensors and a target are analyzed and explained on the basis of higher order modes of a radial line formed by the sensors and a planar reflective target. A robust equivalent circuit using a cascade of lossy waveguides is proposed and a new calibration/correction method is derived. Properties of both sensors are verified experimentally for target distances of 0–6 mm (more than one and half of wavelength). The new circular waveguide sensor operates in a frequency band of 75-76 GHz with a maximum error of measured distance $19~\mu \text{m}$. The new rectangular waveguide sensor enables to use an outstanding applicable frequency bandwidth from 76 up to 86 GHz, with best properties around 80 GHz, where the maximum error of the measured distance is 12 $\mu \text{m}$. The new sensors make possible to achieve about ten times smaller distance measurement errors in comparison with the state-of-the-art sensors. [ABSTRACT FROM AUTHOR]

A Fabry-Perot open resonator (FPOR) is a tool dedicated to broadband accurate microwave and millimeter-wave characterization of dielectric sheets. Despite the various advantages of that method, one of the major challenges limiting its applicability is unintentional coupling of Gaussian modes of interest with a particular family of parasitic higher order modes. The coupling affects the resonance frequency of the resonator loaded with the material under test, thus disturbing the extracted permittivity. It has already been shown that spectral properties of these parasitic modes can be predicted using a recently developed electromagnetic model of a FPOR based on the scattering matrix method. It is shown in this article that the systematic analysis of experimental results supplemented with accurate numerical computations allows us to suppress the impact of mode coupling on the measured permittivity. [ABSTRACT FROM AUTHOR]

We proposed an oversized coaxial multi-beam relativistic klystron amplifier (OCMB-RKA) with a new input coupler of lesser complexity giving enhanced input microwave power absorption rate for generating high power millimeter-wave radiation in Ka-band. The high-frequency structure of the OCMB-RKA was designed, fabricated, and cold-tested for results that agreed well with the simulated results. Furthermore, using the 3D particle-in-cell (PIC) code, the beam-wave interaction of the OCMB-RKA was simulated, considering two different materials (stainless steel and copper) making the interaction structure. When a 500 kV, 3 kA electron beam, and a focusing magnetic flux intensity of 1 T were adopted in the PIC simulation, a five-cavity OCMB-RKA yielded the output power of 610 MW at 30.525 GHz with the electronic efficiency of 40.7% and the saturated gain of 55.3 dB. Experimentally, the OCMB-RKA demonstrated its capability of generating high power Ka-band radiation typically of 390 MW power with the pulse width of 27 ns. [ABSTRACT FROM AUTHOR]

This letter proposed a broadband circular waveguide rotary joint with substrate integrated coaxial line (SICL) feeder. The SICL feeder can effectively convert TEM mode in the SICL into TM210 and TM020 modes in the multi-mode substrate integrated circular cavity (SICC). The annular slot on the surface of SICC can provide strong coupling between the SICC with TM210 and TM020 modes and the circular waveguide cavity with TM010 and TM011 modes. All the modes show symmetric electric field distribution. Thus, a wide bandwidth can be obtained due to six modes and strong coupling, and stable performance can be achieved while rotating because of symmetric field distribution. Comparing with reported circular waveguide rotary joints, the proposed design has the advantages of wide bandwidth and planarization of feeder. A prototype centered at 9.35 GHz is fabricated with a 10 dB impedance matching bandwidth of 24.6% and the insertion loss between 0.82 and 1.65 dB. [ABSTRACT FROM AUTHOR]

We present an S-band high-power microwave (HPM) oscillator based on crossed-elliptical metamaterial (MTM) rings in a circular waveguide and powered by a high-power electron beam. Particle-in-cell (PIC) simulations demonstrate that when an output horn antenna of radius of 200 mm is used, an output power of 443 MW of a backward wave TE41 mode below its cutoff frequency at 2.80 GHz can be generated using a pulsed electron beam with a voltage of 990 kV and a current of 1.736 kA in a 1.8-T solenoidal magnetic field, corresponding to an electronic efficiency up to 26%. Meanwhile, another degenerate frequency of 2.80 GHz of a forward wave in the TM01 mode with an output power of 9 MW is also observed. When an output horn antenna of radius 150 mm is used, this crossed-elliptical MTM oscillator operates mainly in a forward TM01 mode at 2.80 GHz with an output power of 325 MW at an electronic efficiency of 19%, and at the same time, a backward wave TE41 mode below its cutoff frequency of 2.80 GHz with an output power of 8 MW can be observed. Simulations indicate that this slow-wave structure (SWS) consisting of a periodically crossed-elliptical MTM loaded circular waveguide can support degenerate mode operation. This result suggests that this configuration is favorable for mode switching and this work seeks to design a compact HPM source. [ABSTRACT FROM AUTHOR]

In this letter, the design and 3-D-printed manufacturing of an omnidirectional and circularly polarized dual-band antenna for telemetry/telecommand (TMTC) applications in satellite communication on space segment are described. The antenna consists of slotted arrays on the circular waveguide with radially outward metallic disks and choke structures on these disks to improve the omnidirectionality and circular polarization performances. As the main novelty of the antenna design, the structure is fed with only one rectangular waveguide; therefore, the proposed antenna can be considered as a transceiver antenna. The design and simulations of the antenna and measurement results for 3-D-printed manufacturing are given at Ku-band. A 10 dB return loss bandwidth is found to be 500 MHz both for telemetry and telecommand bands having center frequencies of 12 and 14 GHz, respectively. Besides, the maximum axial ratio and minimum gain within 65° beamwidth are obtained as 3 dB and −5 dBi, respectively, which are sufficient for the omnidirectional and circularly polarized antenna providing TMTC communication in satellite systems. [ABSTRACT FROM AUTHOR]

In circular waveguides, the TE01 mode has the lowest transmission loss, which is very suitable for long-distance transmission of high-power microwaves (HPMs). The output mode of HPM sources is mainly the TM01 mode; however, there are few research studies on mode converters of TM01-TE01. In this paper, a high efficiency HPM TM01-TE01 mode converter is designed; compared with the traditional TM01-TE01 mode converters, the structure of the mode converter is compact and easier to process. It is mainly composed of an input circular waveguide, a tapered rectangular waveguide, a 90° bent rectangular waveguide, and an output circular waveguide. A prototype with a center frequency of 2.4 GHz is fabricated and HPM experiments are carried out. The transmission efficiency of this device reaches 99.8% in the simulation, and the measured transmission efficiency is more than 98%. Additionally, the measured power handling capacity is more than 1 GW, which is consistent with simulation. This design has important reference significance for the design of long-distance power transmission devices and HPM mode converters. [ABSTRACT FROM AUTHOR]

An optimum approach for designing a TE01 mode oversized waveguide bend is proposed based on angular-deformed circular waveguide. Due to the deformation of the circular waveguide cross section, the degeneracy of the TE01 mode and the TM11 mode is removed, and the mode conversion inside the waveguide bend is weakened. Characterizations of the angular-deformed circular waveguide with different deformation and its influence on the mode spectrum, the transmission loss, and the power capacity are investigated. Based on the analysis results and the coupling-wave theory, a Ka-band broadband oversized deformed circular waveguide bend with the propagating TE01 mode is designed, fabricated, and measured. A good agreement between the calculation results and the S-parameter measurement of a prototype is achieved. The transmission efficiency is over 95% in the frequency range of 26.5–35.9 GHz (the relative band is over 30%). The near-field test results further demonstrate the high output purity of the TE01 mode in the working frequency band. [ABSTRACT FROM AUTHOR]