Eigenmode Simulations Research Articles

Small-signal model for inhomogeneous helix traveling-wave tubes using transfer matrices

We introduce a practical method for modeling the small-signal behavior of frequency-dispersive and inhomogeneous helix-type traveling-wave tube (TWT) amplifiers based on a generalization of the one-dimensional (1D) Pierce model. Our model is applicable to both single-stage and multi-stage TWTs. Like the Pierce model, we assume that electrons flow linearly in one direction, parallel and in proximity to a slow-wave structure (SWS) that guides a single dominant electromagnetic mode. Realistic helix TWTs are modeled with position-dependent and frequency-dependent SWS characteristics, such as loss, phase velocity, plasma frequency reduction factor, interaction impedance, and the coupling factor that relates the SWS modal characteristic impedance to the interaction impedance. For the multi-stage helix TWTs, we provide a simple lumped element circuit model for combining the stages separated by a sever, or gap, which attenuates the guided circuit mode while allowing the space-charge wave on the beam to pass freely to the next stage. The dispersive SWS characteristics are accounted for using full-wave eigenmode simulations for a realistic helix SWS supported by dielectric rods in a metal barrel, all of which contribute to the distributed circuit loss. We compare our computed gain vs frequency, computed using transfer matrices, to results found through particle-in-cell simulations and the 1D TWT code LATTE to demonstrate the accuracy of our model. Furthermore, we demonstrate the ability of our model to reproduce gain ripple due to mismatches at the input and output ports of the TWT.

Research on a 220-GHz modified staggered double corrugated waveguide backward wave oscillator

The output power of a backward wave oscillator (BWO) is limited by the low interaction impedance of a slow wave structure (SWS) when the frequency is in the THz band. A BWO based on modified staggered double corrugated waveguide (MSDCW) SWS is researched as a high-power source operating at THz band to break through the coupling impedance limitation in this paper. The MSDCW-SWS designed for BWO with wide electronic tunable band is optimized by numerical Eigenmode simulation to obtain higher coupling impedance. The simulation results show that the coupling impedance of MSDCW-SWS at 211.5 GHz is 42% higher than that of the original staggered double corrugated waveguide (SDCW) SWS when the dispersion conditions are the same for both SWSs. The sheet beam MSDCW-BWO with a broadband output structure is designed to operate under voltage between 23 and 49 kV and an electron beam current of 160 mA. The 3-D interaction simulation results reveal that more than 80.6 W of average output power can be produced from 210 to 238 GHz and the highest electron efficiency of 2.5% can be obtained at 211.5 GHz. The MSDCW-BWO can be considered a promising high-power THz source.

Cryogenic Thermo-Optical Coefficient of SU-8 Measured Using a Racetrack Resonator at 850 nm

SU-8 is an emerging polymer material for integrated optical circuits that has demonstrated good structural properties in a cryogenic environment. In this article, we investigate the thermo-optical properties of SU-8 for a wavelength λ = 850 nm, from room temperature to cryogenic temperature down to 14 K. To measure the material properties, we designed and fabricated SU-8 racetrack resonators via electron beam lithography. While cooling the device in a closed-cycle cryostat, we measured the resonance spectrum as a function of the temperature from which we determined the temperature-induced variations of the group and effective indices of the waveguide. With the aid of waveguide eigenmode simulations, we used these data to derive the temperature dependence of the SU-8 refractive index nSU−8 (T). At room temperature (T~295 K), the thermo-optic coefficient dnSU−8/dT = −5.3 ± 0.2 × 10−5 K−1. At low temperature (T~14 K), dnSU−8/dT = −1.27 ± 0.05 × 10−4 K−1. Our research shows the potential of SU-8 photonics in a cryogenic environment, suitable for the integration with quantum light sources emitting in the near infrared (NIR).

Resonant cavity method based on RF measurement and simulation for measuring complex permittivity or permeability of RF absorbing materials

Accurate measurement of complex permittivity and/or permeability of radio-frequency (RF) absorbing materials is essential to predict the performances of higher-order-mode damping in damped accelerating cavities or in vacuum chambers. We propose an improved resonant cavity method that can be used as a complement to the widely used Nicolson–Ross–Weir method for measuring the RF characteristics of materials. The conventional resonant cavity method is based on the cavity perturbation theory. However, the measurements are inaccurate when losses in the materials are large. The improved method we propose determines the complex permittivity or permeability of materials from the measured resonant frequencies and Q factors based on eigenmode simulations. Because the reliability on the eigenmode calculation for RF cavities with lossy materials has become sufficiently reliable, determination of complex permittivity and permeability can be achieved using such a simulation software. We demonstrate this method using ferrite HF70 (TDK Corp.), which is useful for RF absorbers in damped accelerating cavities or in vacuum chambers.

Conceptual design of a high reactive-power ferroelectric fast reactive tuner

We present a novel design of a ferroelectric fast reactive tuner (FE-FRT) capable of modulating mega-VAR reactive power on a submicrosecond timescale. The high reactive power capability of our design extends the range of applications of reactive tuners to numerous applications. We present a detailed analytical model of the performance of a megawatt-class reactive power device and benchmark it against finite-element method eigenmode and frequency domain electromagnetic simulations. We introduce new features, including an annulus design for the ferroelectric capacitors and capacitive window coupling to the cavity. We consider thermal design issues and nonlinear effects in the ferroelectric. The model covers several configurations, allowing control of the frequency of superconducting and normal-conducting cavities in a variety of applications and frequencies. We calculate that the FE-FRT designed should be capable of handling around 0.45 MVAR of reactive power with around 3 kW of resistive losses, providing a frequency tuning range of 8 kHz in an example of 400 MHz cavity geometry. Published by the American Physical Society 2024

Systematic Analysis of Rotated Dual-Split Elliptical SRR with Band-Stop Characteristics

In this research article, a novel double-split elliptical split ring resonator (DS-ESRR) is proposed to achieve frequency-notching behavior of ultrawideband filtenna, where the semimajor and minor axes of the ellipse are taken as a bivariate random variable and expressed in Ramanujan’s correction coefficient so that more degree of freedom is available for choosing degenerated impedance and thus for variable frequency-notching applications. To verify this hypothetical method, finite sets of variables for DS-ESRR are presented in this proposed work, and a mathematical expression is formulated to estimate the resonant frequency of the DS-ESRR, such that for practical applications, frequency-notching parameters can be easily estimated accurately rather than previously used SRR like circular or square-shaped geometry. DS-ESRR is deployed at the back of a CPW-fed ultrawideband antenna for notching filter application, and the computed data is compared with the eigen mode simulation results which reveal good agreement with each other.

Reduced Loss and Prevention of Substrate Modes with a Novel Coplanar Waveguide Based on Gap Waveguide Technology

The Gap Waveguide technology utilizes an Artificial Magnetic Conductor (AMC) to prevent the propagation of electromagnetic (EM) waves under certain conditions, resulting in various gap waveguide configurations. In this study, a novel combination of Gap Waveguide technology and the traditional coplanar waveguide (CPW) transmission line is introduced, analyzed, and demonstrated experimentally for the first time. This new line is referred to as GapCPW. Closed-form expressions for its characteristic impedance and effective permittivity are derived using traditional conformal mapping techniques. Eigenmode simulations using finite-element analysis are then performed to assess its low dispersion and loss characteristics. The proposed line demonstrates an effective suppression of the substrate modes in fractional bandwidths up to 90%. In addition, simulations show that a reduction of up to 20% of the dielectric loss can be achieved with respect to the traditional CPW. These features depend on the dimensions of the line. The paper concludes with the fabrication of a prototype and validation of the simulation results in the W band (75-110 GHz).

Measurement Method for the Dispersion Curves of a Spoof SPP Transmission Line Using a Single Sample

Research works on spoof surface plasmon polariton (SPP) transmission lines (TLs) have been carried out toward the goal of achieving flexible control of dispersion. The existing measurement methods for the dispersion of the spoof SPPs require two SPP TL samples with different numbers of units and transition structures, which makes the process more difficult and expensive. This work proposes a new approach for measuring the dispersion curve of a spoof SPP TL by using experimental near-field data. A mathematical model is presented to describe the relation between the wavenumber <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> and the near-field data by considering the presence of reflected waves. The high efficiency and accuracy of this method are verified by the good agreement obtained between the measured dispersion curve and the eigenmode simulation result for a typical spoof SPP TL. Hence, the proposed method makes it possible to measure the dispersion curve of a spoof SPP TL based on a single sample, providing significant progress toward decreasing testing error and cost.

2D optical confinement in an etchless stratified trench waveguide.

We demonstrate novel trapezoidal and rectangular stratified trench optical waveguide designs that feature low-loss two-dimensional confinement of guided optical modes that can be realized in continuous polymer thin film layers formed in a trench mold. The design is based on geometrical bends in a thin film core to enable two-dimensional confinement of light in the transverse plane, without any variation in the core thickness. Incidentally, the waveguide design would completely obviate the need for etching the waveguide core, avoiding the scattering loss due to the etched sidewall roughness. This new design exhibits an intrinsic leakage loss due to coupling of light out of the trench, which can be minimized by choosing an appropriate waveguide geometry. Finite-difference eigenmode simulation demonstrates a low intrinsic leakage loss of less than 0.15 dB/cm. We discuss the principle of operation of these stratified trench waveguides and present the design and numerical simulations of a specific realization of this waveguide geometry. The design considerations and tradeoffs in propagation loss and confinement compared with traditional ridge waveguides are discussed.

Hybrid-gyrokinetic simulations of low-n toroidal Alfvén eigenmodes using gKPSP

We report a benchmark study of toroidal Alfvén eigenmode (TAE) simulation using the hybrid-gyrokinetic code GyroKinetic Plasma Simulation Program (gKPSP). A simulation capability for energetic particles based on the gyrokinetic δf method has been newly implemented in the gKPSP code. Benchmark simulations have been performed in both circular and realistic tokamak geometries. Good agreement has been found with previously reported results, demonstrating the new capability of the gKPSP code. We have investigated the effects of the distribution function on TAE stability by examining both isotropic and anisotropic slowing-down distributions of energetic particles. The slowing-down distribution produces a higher linear growth rate than a Maxwellian distribution, while a growth rate scan with the anisotropy shows an opposite trend. This can be attributed to competition between Landau damping and the linear drive, which are correlated with the fraction of resonant passing particles and their distribution in phase space.

Clarifying duplicated electromagnetic characteristics for 220-GHz two-beam extended interaction oscillator

In this paper, we clarify the duplicated electromagnetic characteristics between the proposed two-beam overmoded multi-gap structure published in the paper titled “Tractable resonant structure with two nonuniform beams for a high-power 0.22-THz extended interaction oscillator” [Bi et al., IEEE Electron Device Lett. 42(6), 931–934 (2021)] and conventional multi-gap structures from the physical concept point of view. The replacement of the TE10 mode by the TE30 mode used in the interaction gaps provides the basis for the duplicated electromagnetic field distributions and frequencies between the two structures. The concept of magnetic coupling is proposed to support the resonant condition that supports duplication of the TE30 field and the frequency of the single-gap structure into the periodic standing-wave field of the multi-gap structure. With this concept, the perturbation of different axial phase shifts across one period to the standing-wave field of the TE30-0 mode is analyzed to clarify the profiles of the dispersion curves of the TE30 mode in the overmoded structure and the TE10 mode in the conventional structure. To demonstrate the profiles, a 220-GHz overmoded and conventional structure with nine gaps is designed, and their dispersion curves are obtained by using eigenmode simulations. In addition, the effect of the difference in the boundary conditions of the geometries of these two structures on the magnetic field distribution is analyzed to demonstrate the duplication of the ohmic losses between the two structures. The physical analysis in the duplicated electromagnetic characteristics lays a foundation for the promising design of the overmoded structure with two beams for high frequency extended interaction oscillators.

Metamaterial Liner for MRI Excitation—Part 1: Theory, Modeling and Design

This work details the practical and theoretical concepts underlying the design of a metamaterial (MM) liner for magnetic resonance imaging (MRI) radio frequency (RF) excitation. The Part 2 companion to this paper details the practical design and performance comparison to a conventional birdcage coil. The operation of the MM liner relies on specifically engineered effective permittivity and permeability of a thin liner on the inner surface of the MRI bore, to enable the propagation of electromagnetic (EM) waves at frequencies below the natural-cutoff of the bore itself. Here, the effective anisotropic EM properties of the MM liner structure are calculated by a combined circuit- and effective-medium model, and the analytical dispersion characteristics are compared to full-wave eigenmode simulations. The results of the effective medium model representation of the MM liner agree fundamentally with simulation. The model may thus assist the design and tuning of the liner to achieve a standing-wave resonance with field distribution and mode spacing suitable for MRI RF excitation. The transmission properties and EM fields of a full-scale MM lined bore for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{B}_{0}=4.7$ </tex-math></inline-formula> T MRI are simulated including realistic losses. These methods enable robust design of thin MM liners for arbitrary bore sizes and B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> field strengths.

Ultra-Thin Metasurface-Based Absorber of Low-Frequency Sound With Bandwidth Optimization

We report, both theoretically and experimentally, a type of ultra-thin metasurface-based low-frequency sound absorber with bandwidth optimization. Such a metasurface unit consists of an ultrathin resonator (thickness∼1/90 wavelength) with a circular hole on the upper panel and four narrow slits inside a multiple-cavity structure. Eigenmode simulations of the unit show rich artificial Mie resonances, in which a type of monopolar Mie resonance mode can be obtained at 238.4 Hz. Based on the excitation of the monopolar mode, we can realize the near-perfect low-frequency sound absorption with the maximum absorption coefficient and fractional bandwidth of 0.97 and 12.9%, respectively, which mainly arises from the high thermal-viscous loss around the circular hole and four narrow slits of the unit. More interestingly, by combining 4 units with different diameters of the circular hole, we further enhance the fractional bandwidth of the compound unit to 18.7%. Our work provides a route to design ultra-thin broadband sound absorbers by artificial Mie resonances, showing great potential in practical applications of low-frequency noise control and architectural acoustics.

A G-Band High Output Power and Wide Bandwidth Sheet Beam Extended Interaction Klystron Design Operating at TM31 with 2π Mode

In this paper, we propose a high-order mode sheet beam extended interaction klystron (EIK) operating at G-band. Through the study of electric field distribution, we choose TM31 2π mode as the operating mode. The eigenmode simulation shows that the resonant frequency of the modes adjacent to the operating mode is far away from the central frequency, so there is almost no mode competition in our high mode EIK. In addition, by studying the sensitivity of the related geometry parameters, we conclude that the height of the coupling cavity has a great influence on the effective characteristic impedance, and the width of the gap mainly affects the working frequency. Therefore, it is necessary to strictly control the fabrication tolerance within 2 μm. Finally, the RF circuit using six barbell multi-gap cavities is determined, with five gaps for the input cavity and idler cavities and seven gaps for the output cavity. To expand the bandwidth, the stagger tuning method is adopted. Under the conditions of a voltage of 16.5 kV, current of 0.5 A and input power of 0.2 W, the peak output power of 650 W and a 3-dB bandwidth of 700 MHz are achieved without any self-oscillation.

Modeling Graphene-Based Plasmonic Waveguides by Mixed FEM With Surface Current Boundary Condition

In this letter, the mixed finite element method (Mixed FEM) incorporating with the surface current boundary condition (SCBC) is firstly proposed to perform eigenmode numerical simulations of graphene-based plasmonic waveguides. The SCBC which is based on modeling graphene as the zero-thickness conductive sheet, is introduced to reduce the extremely fine discretization of graphene at the atomic scale. Thus, enormous unknowns and computational resources are significantly decreased in the proposed new method. Numerical examples of some typical graphene-based waveguides are presented to verify numerical accuracy and computational efficiency of the new method.

Compact, Wide Stopband, Shielded Hybrid Filter Based on Quarter-Mode Substrate Integrated Waveguide and Microstrip Line Resonators

A novel miniaturized bandpass filter (BPF) with high stopband rejection based on a hybrid structure is proposed with shielded quarter-mode substrate integrated waveguide (QMSIW) and microstrip technologies. The shielded QMSIW cavity provides a high-quality ( $Q$ ) factor with substantial size reduction. This filter exhibits flexible response with four poles and two controllable transmission zeros (TZs) by incorporating two quarter-wavelength microstrip resonators into two back-to-back QMSIW resonators. The working principles for higher order mode suppression and filter coupling topology are carefully illustrated by eigen-mode simulation, coupling matrix, and field distribution analysis, respectively. Compared with the reported works, the proposed four-order BPF demonstrates advantageous features in terms of a compact size of $0.62\,\,\lambda _{0}\times 0.62 \,\,\lambda _{0}$ , a low insertion loss of 1.2 dB, a wide passband (22.7%), and a high stopband rejection (better than 36 dB).

Microstrip Ferrite Circulator Design With Control of Magnetization Distribution

This article presents a study of the impact of different external magnetic bias field (MBF) distributions on Y-junction microstrip ferrite circulator performance. By using magnetostatic, full-wave, and circuit commercial simulation tools for a circular ferrite disk, several permanent magnet (PM) configurations are investigated for unsaturated and nonuniform bias conditions. Eigenmode simulations are used to analyze the circulator bandwidth over a range of MBF intensities. We show in simulations and experiments that different bias conditions can result in an operating frequency range from 1.5 to 7GHz using the same 9.7-mm-diameter commercial ferrite disk resonator.

Electron energy-loss spectroscopy of surface plasmon activity in wrinkled gold structures.

The surface plasmon response of a cross-sectional segment of a wrinkled gold film is studied using electron energy loss spectroscopy (EELS). EELS data demonstrate that wrinkled gold structures act as a suitable substrate for surface plasmons to propagate. The intense surface variations in these structures facilitate the resonance of a wide range of surface plasmons, leading to the broadband surface plasmon response of these geometries from the near-infrared to visible wavelengths. The metallic nanoparticle boundary element method toolbox is used to simulate plasmon eigenmodes in these structures. Eigenmode simulations show how the diverse morphology of the wrinkled structure leads to its high spectral complexity. Micron-sized structural features that do not provide interactions between segments of the wrinkle have only a small effect on the surface plasmon resonance response, whereas nanofeatures strongly affect the resonant modes of the geometry. According to eigenmode calculations, different eigenenergy shifts around the sharp folds contribute to the broadband response and infrared activity of these structures; these geometrical features also support higher energy (shorter wavelength) symmetric and anti-symmetric plasmon coupling across the two sides of the folds. It is also shown that additional plasmon eigenstates are introduced from hybridization of modes across nanogaps between structural features in close proximity to each other. All of these factors contribute to the broadband response of the wrinkled gold structures.

Fabrication and characterization of deformed microdisk cavities in silicon dioxide with high Q-factor.

We demonstrate the excitation and characterization of whispering gallery modes in a deformed optical microcavity. To fabricate deformed microdisk microresonators we established a fabrication process relying on dry plasma etching tools for many degrees of freedom and a shape-accurate morphology. This approach allowed us to fabricate resonators of different sizes with a controlled sidewall angle and underetching in large quantities with reproducible properties such as a surface roughness RQ≤2nm. The excitation and characterization of these modes were achieved by using a state-of-the-art tapered fiber coupling setup with a narrow linewidth tunable laser source. The conducted measurements in shortegg resonators showed at least two modes within a spectral range of about 237 pm. The highest Q-factors measured were in the range of 105. Wave optical eigenmode and frequency domain simulations were conducted that could partially reproduce the observed behavior and therefore allow us to compare the experimental results.

Graphene oxide integrated silicon photonics for detection of vapour phase volatile organic compounds

The optical response of a graphene oxide integrated silicon micro-ring resonator (GOMRR) to a range of vapour phase Volatile Organic Compounds (VOCs) is reported. The response of the GOMRR to all but one (hexane) of the VOCs tested is significantly higher than that of the uncoated (control) silicon MRR, for the same vapour flow rate. An iterative Finite Difference Eigenmode (FDE) simulation reveals that the sensitivity of the GO integrated device (in terms of RIU/nm) is enhanced by a factor of ~2, which is coupled with a lower limit of detection. Critically, the simulations reveal that the strength of the optical response is determined by molecular specific changes in the local refractive index probed by the evanescent field of the guided optical mode in the device. Analytical modelling of the experimental data, based on Hill-Langmuir adsorption characteristics, suggests that these changes in the local refractive index are determined by the degree of molecular cooperativity, which is enhanced for molecules with a polarity that is high, relative to their kinetic diameter. We believe this reflects a molecular dependent capillary condensation within the graphene oxide interlayers, which, when combined with highly sensitive optical detection, provides a potential route for discriminating between different vapour phase VOCs.