Non-uniform Electric Field Distribution Research Articles

Simulation analysis of microwave sintering of recycled building bricks based on three-phase porous medium model

The visualization and quantification characteristics of numerical simulation can overcome many obstacles caused by experimental conditions and contribute to the development of the microwave sintering mechanism of recycled building bricks (RBB). However, existing research has paid little attention to the numerical simulation of the microwave sintering of RBB. This study considers the phase transition and mass transfer of three-phase porous media, and establishes a fully coupled model of electromagnetic, heat transfer, and three-phase porous media to study the thermal behavior of RBB under microwave irradiation. The results indicate that the electric field inside the cavity exists in a non-uniform form with high and low energy regions. The addition of RBB will see a redistribution of the electric field in the cavity. The non-uniform distribution of electric field and the selective heating of microwaves result in the appearance of hot and cold regions inside RBB during sintering. Phase transition and mass transfer are beneficial for improving the uniformity of temperature field. The geometric size and position of RBB will affect the uniformity of the temperature field of RBB, and adding SiC board can be effective to improve the uniformity.

Characterization of migration behavior of organic electric-field regulator in polyethylene composite based on the synchronous spectra of space charge and polarization current

Organic electric-field regulator has the ability to suppress the space charge accumulation in the composite due to its electric-field and filler-content enhanced conductivity. Moreover, it can also migrate towards the high electric field region under the electric field gradient force, which further homogenizes the non-uniform electric field distribution. To characterize the migration behavior of the organic electric-field regulator in the composite under electric field, a distributed equivalent circuit model is firstly introduced, and it is solved to obtain the space-time distribution of conductivity in composite based on the synchronous spectra of space charge and polarization current. Combining the mathematical relationship between the direct current (DC) conductivity and electric field as well as regulator content, the space-time distribution of organic electric-field regulator in the composite is then settled. The allyloxy polyethylene glycol (APEG) is used as an example organic electric-field regulator and is filled into low-density polyethylene (LDPE) matrix to prepare composites. The DC conductivity and the synchronous spectra of space charge and polarization current are measured, respectively. The composites show noticeable electric-field and regulator-content enhanced conductivities. The space charge distribution shows that the APEG is capable of suppressing the space charge and homogenizing the electric field distribution compared with pure LDPE. The space-time distribution of regulator content in the 0.5 wt% composite is determined by the proposed method, and the regulator content near the electrodes is much higher than in the bulk, which is consistent with the infrared microscope images. The higher filler content means a higher DC conductivity, which lowers the high electric field near the electrodes and contributes to more uniform electric field distribution in the composite. The proposed method experimentally characterizes the migration behavior of the organic electric-field regulator in the polymer composite for the first time, and provides an effective way to study the migration mechanism of organic molecules (e.g. organic electric-field regulator) in the polymer composite.

A closed-form expression of electric polarizability for elliptical apertures excited by nonuniform electric field

It is well known that electric field penetration through a small aperture in a perfectly conducting plane behaviors like an electric dipole. When excited by uniform electric field, the dipole moment has analytical solution for elliptical apertures and numerical/experimental values for other shapes. In this paper, for the case of nonuniform field excitation, based on the electrostatic reciprocity theorem, the closed-form expression of electric dipole moment is derived for elliptical apertures. This expression is in integral form, and its integrand is the product of the nonuniform electric field distribution and the potential distribution when excited by uniform field in the aperture plane. Taking a point charge located on the aperture plane as an example of nonuniform field excitation, the dipole moment is calculated using the proposed closed-form expression. The validation is verified by comparisons with exact integral solution for circular apertures and with finite element simulations for elliptical apertures.

Numerical simulation of electric field distribution inside streamer zones of positive and negative lightning leaders

It is widely known that there is an asymmetry in development modes of positive and negative leaders. Negative leaders in air always propagate in a step-wise manner, while positive ones can grow either continuously (at least optically) or via steps (restrikes). The step-formation mechanism in negative and especially positive leaders is poorly understood. In particular, it is still unknown how space stems, precursors of space leaders, form inside and/or at the boundary of the streamer corona, where an expected electric field is sufficiently smaller than the dielectric strength of air. The study presents numerical simulation of electrostatic conditions inside streamer zones of positive and negative lightning leaders. It is shown that, regardless of polarity, streamer coronas are characterized by highly nonuniform electric field distribution. Moreover, it appears that they always contain the areas of locally increased electric fields sometimes exceeding the breakdown level that can be the potential places of space stems origin. Due to the well-known asymmetry between propagation threshold fields of positive and negative streamers, the number of such zones and the magnitudes of electric fields inside them are sufficiently bigger for negative leaders. A significant factor influencing the level of electric field amplification is found to be the share of streamer zone channels that deviate from an expected direction of growth. The role of the streamer corona fractal dimension and the leader channel sheath line charge density is also analyzed. The model predicts that the space stem formation conditions worsen with increasing altitude above the mean sea level and get better with rising humidity which is in line with observations. The study is helpful for further development of the theory of propagation mechanisms of positive and negative leaders.

Modeling of radio frequency heating of packed fluid foods moving on a conveyor belt: A case study for tomato puree

Computer simulation models were used to study radiofrequency heating of liquid foods moving on a conveyor belt between staggered-through field electrodes of non-uniform electric field distribution. Voltage across the electrodes was estimated using a finite-element model and a one-dimensional model, and these were utilized to simulate heating of tomato puree mixtures of varying dielectric and thermal properties, at various nominal voltages and electrode gaps. The experimental results for volume average temperatures showed good agreement with the outcome of both simulation models. Although the temperature profiles indicate a concentration of heat at the bottom and edges of the bottle, natural convection and the shape of the container helped mitigate heat localization. It was determined that, while simple models could provide accurate volume average temperatures, incorporating convectively enhanced conductivity was necessary to accurately predict temperature distribution. The heating rate was found to decrease with an increase in salt concentration. Industrial relevanceIn-package tunnel pasteurization is preferred over continuous-flow pasteurization for certain commercial products such as carbonated beverages or semi-solid foods of high viscosity. Dielectric heating can be applied in these cases with much lower requirements of floor space, water, and energy, while reducing heat losses and localized overheating. However, the radiofrequency heating of liquid foods has not been extensively studied, especially for in-package thermal treatments. A better understanding of the effect of various processing parameters on temperature distribution and heating rates could support a wider adoption of this technology in industrial processes.

New Insight Into Total-Ionizing-Dose Effect-Induced Breakdown Voltage Degradation for SOI LDMOS: Irradiation Charge Field Modulation

In this article, the concept of irradiation charge field ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}_{\text {rc}}$ </tex-math></inline-formula> ) is proposed to provide a new insight into total-ionizing-dose (TID) effect-induced breakdown voltage (BV) degradation for high-voltage silicon-on-insulator (SOI) lateral double-diffused metal–oxide-silicon (LDMOS). A unified explanation on TID-induced BV degradation is given that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}_{\text {rc}}$ </tex-math></inline-formula> exerts modulation on net electric field, changing the relationship between lateral BV (BVL) and vertical BV (BVV). <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}_{\text {rc}}$ </tex-math></inline-formula> would weaken electric field at silicon side of silicon/buried oxide interface and enhance that at oxide side, resulting in BVV increasing monotonously. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}_{\text {rc}}$ </tex-math></inline-formula> would also weaken surface electric field at drain side and enhance that at source side, resulting in BVL changing with two potential trends: monotonic descent and nonmonotonic descent, corresponding to different initial surface breakdown points. Eventual BV degradation is determined by the combined result of BVV and BVL changing. Based on the new insight, a radiation hardening design strategy is proposed. Nonuniform initial surface electric field distribution with single drain peak is pursued, breaking the conventional optimization principle. Nonmonotonic descent of BV is achieved to enhance TID tolerance and verified by the developed 80-V SOI LDMOS with the proposed radiation hardening strategy.

Dual-Function Smart Windows Using Polymer Stabilized Cholesteric Liquid Crystal Driven with Interdigitated Electrodes.

In this study, we present an electrically switchable window that can dynamically transmit both visible light and infrared (IR) light. The window is based on polymer stabilized cholesteric liquid crystals (PSCLCs), which are placed between a top plate electrode substrate and a bottom interdigitated electrode substrate. By applying a vertical alternating current electric field between the top and bottom substrates, the transmittance of the entire visible light can be adjusted. The cholesteric liquid crystals (CLC) texture will switch to a scattering focal conic state. The corresponding transmittance decreases from 90% to less than 15% in the whole visible region. The reflection bandwidth in the IR region can be tuned by applying an in-plane interdigital direct current (DC) electric field. The non-uniform distribution of the in-plane electric field will lead to helix pitch distortion of the CLC, resulting in a broadband reflection. The IR reflection bandwidth can be dynamically adjusted from 158 to 478 nm. The electric field strength can be varied to regulate both the transmittance in the visible range and the IR reflection bandwidth. After removing the electric field, both features can be restored to their initial states. This appealing feature of the window enables on-demand indoor light and heat management, making it a promising addition to the current smart windows available. This technology has considerable potential for practical applications in green buildings and automobiles.

Corona Discharge Behaviors with Presence of Floating Electrode in Air Insulation using Numerical Model Analysis

This paper deals with numerical analysis method for analyzing the partial discharge behaviors in terms of corona discharge in the presence of a floating electrode under lightning impulse voltage. To analyze the corona discharge behaviors at 0.5 mm short electrode gap system as basic research work between main conductor and floating electrode, we considered fully coupled numerical model based on the charge continuity equations for positively charged ion, negatively charged ion and free electrons. Poisson’s equation is coupled with hydro-dynamic drift-diffusion equations derived from the three kinds of charge continuity equation. Fowler-Nordheim field emission is assumed that the electron emission by electric field is used as boundary conditions for main conductor and floating electrode. As a results, it is found that the floating electrode creates a non-uniform electric field distribution with a large field enhancement, causing ionization to initiate corona discharge. In other words, floating electrode is early corona discharge inception by collecting the induced charge developed by high voltage electrode. This result is expected to be applicable to various corona discharge generating systems as well as insulation design of power apparatus with presence defects such as a floating metal particle under lightning impulse voltage.

Electric Field Analysis on the Corona Discharge Phenomenon According to the Variable Air Space between the Ionizer and Ground Current Collector

In this paper, we present the optimized air space of the lightning protection rod (SK-AOR380) with the function of a charge transfer system (CTS). For evaluation of CTS in the laboratory setting, some studies have focused on the modification of the structure and shape of the CTS; the air space is designed (&gt;2 mm) as an empirical design without quantitative data. However, in this paper, we have focused on the air space between the ionizer conductor and current collector to control the inception and occurrence position of corona discharge in air insulation. This is because the performance, such as the initial corona discharge inception of CTS, is determined by the air space. The simulation analysis was performed in a narrow, micro-sized air space as a first step, where the air space was reduced to the extent possible for simulation. To evaluate the performance of SK-AOR380 according to the narrow air space, we considered the numerical analysis method. The fundamental equations consist of Poisson’s equation and the charge continuity equation. Poisson’s equation for electric fields is a fully coupled numerical model based on the charge continuity equations for a positively charged ion, negatively charged ion, and free electron. Fowler–Nordheim electron emission was employed for the boundary condition at the surface of the ionizer conductor. To simulate the corona discharge behavior under standard lightning impulse voltage, we used a source of lightning voltage with 1.2/50 μs based on a double exponential equation; the corona discharge behaviors (electric field distribution, free electron density, positive and negative ion density) were investigated dependent on each time step (0.5, 1 and 1.2 μs) until 3.5 μs. The results revealed that the characteristics graph of free electron density, positive and negative ion density showed similar trends, with lightning impulse voltage increasing with increasing time steps until 1.2 μs and each density resulted in a decreasing trend from 1.2 μs to 3.5 μs. The SK-AOR380 is improved with a decreasing air space in terms of electric field distribution, electron, and ion density. In other words, the 0.0005 mm air space created a non-uniform electric field distribution with a large field enhancement, causing ionization to initiate corona discharge. In addition, in the case of a 0.0005 mm air space, the electric field and electron density are increased by 1.3 and 1.9 times, respectively, than that of 0.001 mm. However, there was no longer a significant difference under 0.0005 mm in the simulation results. To improve the CTS, we suggest the air space between the ionizer conductor and current collector should be less than 2 mm than that of conventional CTS from our research work.

Buffer Traps Effect on GaN-on-Si High-Electron-Mobility Transistor at Different Substrate Voltages.

Substrate voltage (VSUB) effects on GaN-on-Si high electron mobility transistors (HEMTs) power application performance with superlattice transition layer structure was investigated. The 2DEG conductivity and buffer stack charge redistribution can be affected by neutral/ionized donor and acceptor traps. As the donor/acceptor traps are excessively ionized or de-ionized by applying VSUB, the depletion region between the unintentionally doped (UID)/Carbon-doped (C-doped) GaN layer may exhibit a behavior similar to the p-n junction. An applied negative VSUB increases the concentration of both the ionized donor and acceptor traps, which increases the breakdown voltage (BV) by alleviating the non-uniform distribution of the vertical electric field. On the other hand, an applied positive VSUB causes the energy band bending flattener to refill the ionized traps and slightly improves the dynamic Ron degradation. Moreover, the amount of electrons injected into the buffer stack layer from the front side (2DEG channel/Ohmic contact) and the back side (AlN nucleation layer/superlattice transition layer) are asymmetric. Therefore, different VSUB can affect the conductivity of 2DEG through the field effect, buffer trapping effect, and charge redistribution, which can change the electrical performance of the device.

A combined experimental and modeling study of Microwave-assisted methane dehydroaromatization process

The challenges in direct methane conversion to higher-value chemicals include rapid catalyst deactivation and comparatively low single-pass conversion. The most important step in direct methane conversion is the activation of strong C–H bonds. In this paper, we integrated microwave irradiation with heterogeneous catalysis to enable a higher methane conversion to C2 and aromatics at low temperature. The results showed that the methane conversion can reach 18% at 550 °C under microwave irradiation, while a temperature higher than 800 °C was required to achieve the same level of methane conversion in a traditional fixed-bed reactor. The microwave irradiation may facilitate this heterogeneous catalysis process both thermally and non-thermally. Thermal effect, as known as “hot spots”, can be characterized experimentally. The results indicated the “hot spot” temperature can reach as high as 800 °C while the bulk temperature stayed at 550 °C. However, the non-thermal effect is difficult to characterize due to the limitations of existing in-situ instrumentations. Finite-element modeling can be a powerful engineering tool to simulate and understand complex physic fields. The simulation results show that between spherical catalyst particles the electric field on the catalyst bed was at a level of 104 V/m and the non-uniform electric field distribution on the catalyst bed. Under this level of external electric field, methane activation on the catalyst surface was possible. These field distributions can explain the non-thermal effects of microwave-assisted catalytic chemical reactions, supported by the observation of benzene hydrogenolysis side reaction. With the thermal and non-thermal effects from microwave irradiation, microwave-assisted heterogeneous catalytic process can be an attractive solution to activate stable feedstock molecules and can be applied to direct methane conversion process.

A novel method for high‐gain and high‐aperture efficiency Fabry‐Perot resonator antenna design

Due to the nonuniform electric field distribution over its aperture, the Fabry-Perot resonator antenna (FPRA) is normally with high gain but relatively low-aperture efficiency. In this paper, a novel nonuniform superstrate design method is proposed to improve the gain and aperture efficiency of the FPRA. The reflection amplitude design formula of the superstrate for uniform electric field distribution is derived. Based on this formula, a nonuniform superstrate with different reflection amplitudes and a fixed reflection phase is designed to uniformize the aperture electric field distribution and maximize the aperture efficiency of the FPRA. As a verification of this design method, a FPRA working at 10 GHz with the aperture size of 3.5 × 3.5 λ is designed, fabricated and measured. The simulated gain of the nonuniform FPRA is 21.6 dBi at 10 GHz with the aperture efficiency as high as 93.9%.

Wave-like emission propagation and fine structures at the contact points of adjacent dielectric pellets in packed bed plasma reactors (PBPRs) operated in helium

Packed bed plasma reactors (PBPRs) inherently have complex geometries where the volume between the electrodes is filled with dielectric/catalytic pellets to form a large array of voids. While the dimension of the plasma region can be several centimeters, the size of a single void at the edges and pores of dielectrics/pellets can reach micrometer dimensions. The understanding of plasma propagation on these diverse length scales is essential for optimizing and controlling plasma processes performed in such discharges. It is known that plasmas are generated in PBPRs as multiple pulses due to cathode-directed positive streamers in the volume, surface ionization waves, or surface streamers over the dielectric surface and stationary microdischarges at the contact points of adjacent dielectrics. In this work, we have investigated the discharge formation and propagation as a function of applied voltage in simplified PBPRs with a single layer of hexagonally arranged hemispherical pellets, operated in helium, using phase and space resolved optical emission spectroscopy. Despite similar discharge conditions at multiple positions, the emission intensity during each pulse spreads like a wave from the center to the edges in the whole discharge cell. The emission due to surface ionization waves is significantly reduced compared to earlier works. These observations could be explained by possible interactions between adjacent microdischarges, already known in other arrays of microdischarges or adjacent streamers. Higher resolution images of the contact points show that the discharge has fine structures with stronger emission at the edges of the contact points; this effect is enhanced as a function of the driving voltage amplitude. This is possibly the consequence of non-uniform electric field distribution at the contact points due to the polarization of dielectrics.

Enhancing microwave heating uniformity using reconfigurable diffractive beamforming surface

AbstractConventional microwave oven suffers nonuniform electric field distribution due to standing wave inside the cavity, requiring improved heating uniformity. Multimode ovens, which are regarded as the most popular method, suffer from relatively limited accuracy and dependency on experimental validations. In this paper, a new class of microwave heating methodology is proposed to achieve heating uniformity improvements through the suppression of undesired standing waves. Microwave absorbers and focusing of electromagnetic waves using reconfigurable diffractive surface are devised, validated, and discussed. Numerical and experimental studies ascertain that the heat uniformity is improved by more than three factors compared to conventional microwave applicators, indicating its potential application and feasibilities.

Study on water treatment effect of dispersion discharge plasma based on flowing water film electrode

To improve the utilization rate of plasma active species, in this study, a closed non-uniform air gap is formed by a flowing water film electrode and a sawtooth insulating dielectric layer to realize the diffuse glow discharge in the atmosphere. Firstly, the electric field distribution characteristics of non-uniform air gap in the sawtooth dielectric layer are studied, and the influence of aspect ratio on the characteristics of diffuse discharge plasma is discussed. Subsequently, the effects of wire mesh, the inclination angle of the dielectric plate, and liquid inlet velocity on the flow characteristics of the water film electrode are analyzed. The results show that the non-uniform electric field distribution formed in the sawtooth groove can effectively inhibit the filamentous discharge, and the 1 mm flowing water film is directly used as the electrode, and high-active plasma is formed directly on the lower surface of the water film. In addition, a plasma flowing water treatment device is built to treat the methyl orange solution and observe its decolorization effect. The experimental results show that after 50 min of treatment, the decolorization rate of the methyl orange solution reaches 96%, which provides a new idea for industrial applications of wastewater treatment.

Fine-Tuning Electrokinetic Injections Considering Nonlinear Electrokinetic Effects in Insulator-Based Devices.

The manner of sample injection is critical in microscale electrokinetic (EK) separations, as the resolution of a separation greatly depends on sample quality and how the sample is introduced into the system. There is a significant wealth of knowledge on the development of EK injection methodologies that range from simple and straightforward approaches to sophisticated schemes. The present study focused on the development of optimized EK sample injection schemes for direct current insulator-based EK (DC-iEK) systems. These are microchannels that contain arrays of insulating structures; the presence of these structures creates a nonuniform electric field distribution when a potential is applied, resulting in enhanced nonlinear EK effects. Recently, it was reported that the nonlinear EK effect of electrophoresis of the second kind plays a major role in particle migration in DC-iEK systems. This study presents a methodology for designing EK sample injection schemes that consider the nonlinear EK effects exerted on the particles being injected. Mathematical modeling with COMSOL Multiphysics was employed to identify proper voltages to be used during the EK injection process. Then, a T-microchannel with insulating posts was employed to experimentally perform EK injection and separate a sample containing two types of similar polystyrene particles. The quality of the EK injections was assessed by comparing the resolution (Rs) and number of plates (N) of the experimental particle separations. The findings of this study establish the importance of considering nonlinear EK effects when planning for successful EK injection schemes.

Influence of non-uniform electric field distribution on the atmospheric pressure air dielectric barrier discharge

The dielectric barrier discharge (DBD) in air at atmospheric pressure is not suitable for industrial applications due to its randomly distributed discharge filaments. In this paper, the influence of the electric field distribution on the uniformity of DBD is theoretically analyzed and experimentally verified. It is found that a certain degree of uneven electric field distributions can control the development of electron avalanches and regulate their transition to streamers in the gap. The discharge phenomena and electrical characteristics prove that an enhanced Townsend discharge can be formed in atmospheric-pressure air with a curved-plate electrode. The spectral analysis further confirms that the gas temperature of the plasma produced by the curved-plate electrode is close to room temperature, which is beneficial for industrial applications. This paper presents the relationship between the electron avalanche transition and the formation of a uniform DBD, which can provide some references for the development and applications of the DBD in the future.

Design and development of a nozzle-free electrospinning device for the high-throughput production of biomaterial nanofibers

This technical note provides a step-by-step guide for the design and construction of a temperature-controlled nozzle-free electrospinning device. The equipment uses a rotating mandrel partially immersed within a polymer solution to produce fibers in an upward motion by inducing the formation of multiple Taylor cones and subsequently multi-jetting out of an electrified open surface. Free-surface electrospinning can overcome limitations and drawbacks associated with single and multi-nozzle spinneret configurations, such as low yield, limited production capacity, nonuniform electric field distribution, and clogging. Most importantly, this lab-scaled high-throughput device can provide an alternative economical route for needleless electrospinning research, in contrast to the high costs associated with industrially available upscaling equipment. Among the device's technical specifications, a key feature is a cryo-collector mandrel, capable of collecting fibers in sub-zero temperatures, which can induce ultra-porous nanostructures, wider pores, and subsequent in-depth penetration of cells. A multi-channel gas chamber allows the conditioning of the atmosphere, temperature, and airflow, while the chamber's design averts user exposure to the high-voltage components. All the Computer-Aided Design (CAD) files and point-by-point assembly instructions, along with a list of the materials used, are provided.

Evidence of the retardation effect on the plasmonic resonances of aluminum nanodisks in the symmetric/asymmetric environment.

A single metallic nanodisk is the simplest plasmonic nanostructure, but it is robust enough to generate a Fano resonance in the forward and backward scattering spectra by the increment of nanodisk height in the symmetric and asymmetric dielectric environment. Thanks to the phase retardation effect, the non-uniform distribution of electric field along the height of aluminum (Al) nanodisk generates the out-of-plane higher-order modes, which interfere with the dipolar mode and subsequently result in the Fano-lineshape scattering spectra. Meanwhile, the symmetry-breaking effect by the dielectric substrate and the increment of refractive index of the symmetric dielectric environment further accelerate the phase retardation effect and contribute to the appearance of out-of-plane modes. The experimental results on the periodic Al nanodisk arrays with different heights confirm the retardation-induced higher modes in the asymmetric and symmetric environment. The appearance of higher modes and blueshifted main dips in the transmission spectra prove the dominant role of out-of-plane higher modes on the plasmonic resonances of the taller Al nanodisk.

Efficient leaky-wave antennas at terahertz frequencies generating highly directional beams

Due to their frequency-dependent angular emission, leaky-wave antennas have been recently introduced in the terahertz band to tackle many of the challenges associated with THz wireless communications. Most previous works have exploited conventional leaky-wave waveguide architectures developed for the microwave region. In this paper, we study in detail the emission characteristics of leaky-wave antennas at THz frequencies. We show that, at these high frequencies, the wavelength-scale interaction with the aperture causes a nonuniform electric field distribution at the slot interface, which is a unique regime that is not typically encountered at lower frequencies. This effect is even more pronounced as the slot width increases to a point where the sides of the slot act as secondary leaking structures, and the well-known frequency–angle relationship is not obeyed as the energy at a given frequency is radiated in a broad range of angles. Therefore, to exploit the phase matching condition, which couples frequency to emission angle, one must use very thin rectangular slots d≪λ, at the expense of device efficiency. To address this problem, we explore an alternate slot aperture design, in which the slot width increases linearly along its length (i.e., a trapezoidal shape). We show that this preserves the phase-matching constraint while allowing higher output coupling efficiencies. Moreover, since a wider effective aperture is used, the radiated beam is narrow in both angular directions, allowing the generation of true pencil-like THz beams.