Permittivity Gradient Research Articles

Columnar vortices induced by dielectrophoretic force in a stationary cylindrical annulus filled with a dielectric liquid

Abstract

Reduced dimensionality optimizer for efficient design of wideband millimeter‐wave 3D metamaterial GRIN lenses

AbstractIn this article we present a method for the rapid design of wideband, high efficiency metamaterial GRIN lenses with rotational symmetry. The method achieves rapid optimization by reducing the number of optimized parameters while maintaining wideband impedance matching for high aperture efficiency. For rotationally symmetric lenses with isotropic GRIN media it is sufficient to design a two‐dimensional (2D) cross section. By using intrinsically matched unit‐cells which prescribe a permittivity gradient along the axis of beam propagation the optimizer only needs to define the transverse permittivity gradient along a line, reducing the design domain from three dimensions (3D) to a single dimension (1D). At each step of the optimizer a 2D finite‐difference‐time‐domain code rapidly solves each realization of the GRIN lens cross‐section across a wide bandwidth. We demonstrate the proposed method by optimizing and fabricating a 4‐inch GRIN lens which achieves 60%–65% measured aperture efficiency from 26 to 40 GHz. The prototype lens provides a high‐efficiency aperture for Ka‐band satcom and 5G millimeter‐wave bands and the approach is suitable for higher future millimeter‐wave bands in 6G and beyond networks.

Analytical model for the transient permittivity of uncured TiO 2 whisker/liquid silicone rubber composites under an AC electric field

The electric field grading of dielectric permittivity gradient devices is an effective way of enhancing their insulation properties. The in-situ electric field-driven assembly is an advanced method for the fabrication of insulation devices with adaptive permittivity gradients, however, there is no theoretical guidance for design. In this work, an analytical model with a time constant is developed to determine the transient permittivity of uncured composites under an applied AC electric field. This model is based on optical image and dielectric permittivity monitoring, which avoids the direct processing of complex electrodynamics. For a composite with given components, the increased filler content and electric field strength can accelerate the transient process. Compared with the finite element method (FEM) based on differential equations, this statistical model is simple but efficient, and can be applied to any low-viscosity uncured composites, which may contain multiple fillers. More importantly, when a voltage is applied to an uncured composite insulating device, the proposed model can be used to analyse the spatiotemporal permittivity characteristics of this device and optimise its permittivity gradient for electric field grading.

Normal vector approach to Fourier modal scattering from planar periodic photonic structures

Fourier modal expansion techniques are very well suited for electromagnetic (EM) scattering in planar periodic stratified media. These techniques expand the transverse EM fields in Bloch modes in each strata unit-cell, but do not rigorously enforce EM boundary conditions at interior material interfaces which gives rise to slow convergence of the polarized S-matrix values with increasing Fourier series truncation order. We present a normal vector (NV) Fourier modal scattering approach that uses the gradient of the real permittivity in the unit-cell to generate a local NV resulting in anisotropic eigenmodes of Maxwell's equations that satisfy interior boundary conditions. The convergence of this expansion method is examine numerically for our analytic NV derived from planar primitive geometry elements for various example structures. The Fourier modal NV method is then derived for the planar cavity boundary value problem and the cavity eigenmodes and density of states is determined from the analytic continuation of the secular determinant. A complete scattering method for highly dispersive materials and sub-wavelength structures has been presented that is adaptable to planar EM cavity problems using fluctuation electrodynamics formalism.

A Ground Penetrating Radar Imaging Approach for a Heterogeneous Subsoil With a Vertical Permittivity Gradient

The article presents an imaging approach for ground penetrating radar prospecting over a heterogeneous background soil characterized by a dielectric permittivity variation along depth. The proposed approach is based on a linear model of the electromagnetic scattering phenomenon, where the soil inhomogeneity in the reference scenario is accounted for by introducing an equivalent permittivity function. Such a function notably simplifies the computation of the kernel of the relevant linear integral equation to be inverted. Then, the data inversion is carried out in a regularized way by resorting to the truncated singular value decomposition scheme. A procedure for estimating the equivalent permittivity function, typically unknown in practical situations, is also proposed. Reconstruction results achieved from full-wave simulated data and real data collected in a controlled test site are provided to demonstrate the effectiveness and the reliability of the proposed imaging approach.

155 GHz Dual-Polarized Fabry–Perot Cavity Antenna Using LTCC-Based Feeding Source and Phase-Shifting Surface

This communication introduces a design of a dual-polarized Fabry-Perot cavity (FPC) antenna operated at the D-band. A novel phase-shifting surface (PSS) made of a single dielectric material based on the low-temperature cofired ceramic (LTCC) technology is applied to this antenna. The proposed PSS functions as a partially reflective surface (PRS) with a transverse permittivity gradient (TPG), contributing to a directive beam radiation. A dual-polarized LTCC-based feeding source with bandwidth enhancement is designed to feed the cavity. For verification, a dual-polarized LTCC FPC antenna prototype operating at 155 GHz was designed, fabricated, and measured. It consists of the feeding source, the PSS, and a 3-D printed supporter. The measured peak gains of the horizontal and vertical polarizations are 17.5 and 17.1 dBi, respectively. The overlapped impedance bandwidth for both the polarizations is 10.4%. These performances ensure that the proposed dual-polarized LTCC antenna is a promising candidate for D-band applications.

Permittivity Gradient Induced Depolarization: Electromagnetic Propagation With the Maxwell Vector Wave Equation

Recent interest in 3-D vectorial sensors requires the development of vectorial propagation methods, rather than scalar wave equation approaches. We derive a vector wave equation from Maxwell’s equations for a medium which has an inhomogeneous dielectric permittivity dominated by variation along one dimension. It is well known that the electric field components decouple for homogeneous media. However, 1-D permittivity variations yield an upper triangular system of scalar wave equations with the wave polarization component parallel to the inhomogeneous direction/axis acting as a forcing term for the orthogonal components. The main implication is that waves with polarization oriented parallel to the permittivity gradient will act as a forcing term and excite other polarization components and, thus, induce depolarization. Contemporary studies treat the permittivity as a constant when deriving a wave equation or paraxial approximation, and then re-introduce via inhomogeneous wave speed, variable permittivity, thus missing important terms and physical mechanisms in their resulting equations. Contemporary studies neglect the term in the Maxwell vector wave equation responsible for this effect. Application of the electromagnetic propagation depolarization effect is demonstrated numerically for an air–sea interface evaporation duct with a 500 MHz source.

Effects of dielectric gradients‐mediated ions partitioning on the electrophoresis of composite soft particles: An analytical theory

AbstractIn this work, we report original analytical expressions defining the electrophoretic mobility of composite soft particles comprising an inner core and a surrounding polymer shell with differentiated permeabilities to ions from aqueous background electrolyte and to fluid flow developed under applied DC field conditions. The existence of dielectric permittivity gradients operational at the core/shell and shell/solution interfaces is accounted for within the Debye–Hückel approximation and flat plate configuration valid in the thin double layer regime. The proposed electrophoretic mobility expressions, applicable to weakly to moderately charged particles with size well exceeding the Debye layer thickness, involve the relevant parameters describing the particle core/shell structure and the electrohydrodynamic features of the core and shell particle components. It is shown that the analytical expressions reported so far in literature for the mobility of hard (impermeable) or porous particles correspond to asymptotic limits of the more generic results detailed here. The impacts of dielectric‐mediated effects of ions partitioning between bulk solution and particle body on the electrophoretic response are further discussed. The obtained expressions pave the way for a refined quantitative, analytical interpretation of electrophoretic mobility data collected on soft (nano)particles (e.g., functionalized dendrimers and multilayered polyelectrolytic particles) or biological cells (e.g., viruses) for which the classical hard core‐soft shell representation is not appropriate.

Reduction of beam-divergence fluctuation for KTN optical beam deflector

We report a new technique to suppress beam-divergence fluctuations in a DC-biased KTa1-xNbxO3 (KTN) optical beam deflector. In our new configuration, we introduced a temperature gradient in the direction of the electric field applied to the KTN crystal, to produce a permittivity gradient in the direction required to cancel out the effect of the asymmetry of the electron injection. We demonstrated experimentally that this temperature gradient successfully reduced the beam-divergence fluctuation.

Flexoelectricity in polycrystalline TiO2 thin films

The flexoelectric effect describes the electromechanical coupling of a strain gradient to a polarization and vice versa. This effect scales linearly with permittivity and strain gradients can get very high for dimensions on the micro and nanoscale. Even though the flexoelectric effect can be best exploited within micro or nanoelectromechanical systems (M/NEMS) applications, it has not been established in today`s M/NEMS device architectures as other transducer principles, like piezoelectricity. In this work, values of the converse flexoelectric coefficient for one of the most promising flexoelectric materials, titanium dioxide (TiO2) are provided. The experimental results are based on a carefull characterization of IrO2/TiO2/IrO2 cantilevers. Besides CMOS compatiblity TiO2 is selected as functional thin film material as it offers a very high permittivity and shows no hysteresis or saturation effects as it is neither ferro- nor paraelectric. Additionally, it guarantees a low cost, lead-free realization and can be directly integrated in a standard silicon MEMS fabrication process by sputter deposition. In order to correctly determine the flexoelectric coefficient, other electromechanical coupling effects are considered and assessed. The flexoelectric coefficient is shown to be µeff = 1.78 ± 0.16 nC m−1 at 10 kHz. The flexoelectric coupling constant with a value of 2.75 V is in good agreement with that theoretically predicted by Kogan`s estimate of 3.14 V.

Programmable field localization and enhancement effects on a non-structured planar surface with a permittivity gradient.

We demonstrate electromagnetic field localization and enhancement effects on the non-structured planar surface of a two-dimensional gradient permittivity material. Surface plasmons are excited by a normally-incident Gaussian illumination beam and are confined to subwavelength rings on the surface of the gradient permittivity material. The performance of the surface is programmable by adjusting the permittivity distribution of the material and polarization of incident light. We show that field localization and enhancement effects can be realized at mid-infrared frequencies by conventional semiconductor materials with designed doping distributions. This demonstration suggests a compact and readily accessible platform for materials characterizations with spatially controlled illumination, providing a convenient approach to explore nanospectroscopy and light-matter interactions of nanomaterials, such as quantum dots, nanowires, and organic molecules.

Flexoelectricity in Polycrystalline Tio <sub>2</sub> Thin Films

The flexoelectric effect describes the electromechanical coupling of a strain gradient to a polarization and vice versa. This effect scales linearly with permittivity and strain gradients can get very high for dimensions on the micro and nanoscale. Even though the flexoelectric effect can be best exploited within micro or nanoelectromechanical systems (M/NEMS) applications, it has not been established in today`s M/NEMS device architectures as other transducer principles, like piezoelectricity. In this work, values of the converse flexoelectric coefficient for one of the most promising flexoelectric materials, titanium dioxide (TiO2) are provided. The experimental results are based on a carefull characterization of IrO2/TiO2/IrO2 cantilevers. Besides CMOS compatiblity TiO2 is selected as functional thin film material as it offers a very high permittivity and shows no hysteresis or saturation effects as it is neither ferro- nor paraelectric. Additionally, it guarantees a low cost, lead-free realization and can be directly integrated in a standard silicon MEMS fabrication process by sputter deposition. In order to correctly determine the flexoelectric coefficient, other electromechanical coupling effects are considered and assessed. The flexoelectric coefficient is shown to be μ eff= 1.78 ± 0.16 nC m-1 at 10 kHz. The flexoelectric coupling constant with a value of 2.75 V is in good agreement with that theoretically predicted by Kogan`s estimate of 3.14 V.

Comparative Study of Optimization Algorithms on the Design of Broadband Antennas

Broadband antennas find many applications in modern communication systems, such as Wi-Fi, 5G, and SatCom. Multiple competing optimization methods are available for the application to antenna design, while it would be preferable to know in advance if any method is superior. Here, an application of the cross-entropy method, along with particle swarm optimization and covariance matrix adaptation evolutionary strategy, to the design of broadband antennas is presented. The first example is an aperture-coupled microstrip patch antenna that has 9.5 dBi peak directivity and 53% bandwidth after optimization. It is then used as a feed in a high-gain broadband resonant cavity antenna. Using an all-dielectric superstrate with a transverse permittivity gradient, a compact thin resonant cavity antenna with a peak directivity of 19 dBi and 40% 3-dB bandwidth was designed. A comparative analysis of the cross-entropy method, particle swarm optimization, and covariance matrix adaptation evolutionary strategy applied to these two problems was carried out to provide the basis for further optimization of antennas in radio frequency and microwave frequency bands. We found that although all three methods reached a similar solution, the cross-entropy method has a speed advantage. It improves our ability to optimize existing designs and has wider applicability beyond antenna engineering.

Comparison of permittivity gradient in resin injected and simulated cone-shaped spacers

Functionally graded materials are at the cutting edge of material technology. They will enable high efficiency and downsizing of apparatus leading to energy conservation in the power sector. Spacers with graded relative permittivity enable a decrease in the diameter of gas-insulated switchgears. Distribution of epoxy-based composite materials (resins) with different permittivities dominate the permittivity gradient in spacers. This paper compares resin injected spacers with simulation. High-permittivity resins, mixtures of high/low-permittivity resins at various mixing ratios, and low-permittivity resins were continuously injected to form spacers. In these spacers, both experiment and simulation showed similar tendencies of resin distribution and demonstrated permittivity gradients. Moreover, the high-permittivity resins were localized on the outlet sides rather than the inlet sides in both experimental and in simulation, and the simulation showed a stronger localization behavior than in the experiment.

Resin injection behavior in process of manufacturing insulation spacer with permittivity gradient using computational fluid dynamics

The advent of new technology for designing insulation materials with desired properties stimulates our interest in development of insulation spacers in gas-insulated switchgear (GIS). Tailoring of two kinds of epoxy-based composite materials (resins) with different relative permittivities enables development of insulation spacers with graded permittivity that decrease the diameter of a GIS tank. Computational fluid dynamics for the resin injection process based on the properties of resin mixtures at various mixing ratios between two resins with high/low relative permittivity enables us to estimate the injection behavior and distribution of resins in the manufacturing of insulation spacers. Simulation results demonstrated the gradient of resins in the insulation spacers by this resin injection method using two resins. In particular, the insulation spacer formed by two or four injection inlets have a more favorable distribution of resins than that achieved by one injection inlet.

A Stripline-Based Planar Wideband Feed for High-Gain Antennas with Partially Reflecting Superstructure.

This paper presents a new planar feeding structure for wideband resonant-cavity antennas (RCAs). The feeding structure consists of two stacked dielectric slabs with an air-gap in between. A U-shaped slot, etched in the top metal-cladding over the upper dielectric slab, is fed by a planar stripline printed on the back side of the dielectric slab. The lower dielectric slab backed by a ground plane, is used to reduce back radiation. To validate the wideband performance of the new structure, in an RCA configuration, it was integrated with a wideband all-dielectric single-layer partially reflecting superstructure (PRS) with a transverse permittivity gradient (TPG). The single-layer RCA fed by the U-slot feeding structure demonstrated a peak directivity of 18.5 dBi with a 3 dB directivity bandwidth of 32%. An RCA prototype was fabricated and experimental results are presented.

Lens Antenna With Planar Focal Surface for Wide-Angle Beam-Steering Application

A new lens antenna for wide-angle beam-steering application is presented. The 2-D lens permittivity profile according to Luneburg is modified using transformation optics to obtain a planar focal surface, allowing for a simple cost-effective planar feed technology. A slice of the lens is confined between two metallic surfaces forming a parallel-plate transmission line, enabling beam-steering in the plane containing the slice. Stacking up such slices result in a more focused beam and beam-steering capabilities in the perpendicular plane. As a result, full 2-D beam-steering becomes possible, with a very wide steering range of ±60° in one plane and a smaller steering range of ±15° in the orthogonal plane. The inhomogeneous dielectric slice is made of four dielectric materials with different permittivity, with a pattern of drilled holes of different diameters realizing a smooth gradient of the effective permittivity. The measured performance of the antenna prototype, operating at about 10 GHz includes 17.2 dB maximum directivity, a scan loss better than 0.8 dB, a sidelobe level better than 11 dB, and an aperture efficiency of 74%, outperforming any other reported beam steering antenna with planar focal surface.

Converse flexoelectricity with relative permittivity gradient

Flexoelectricity represents the linear relationship between the strain/electric gradient field and the induced electric polarization/mechanical stress in dielectric materials. This electro-mechanical behavior is important for prospective applications due to its size effect and other advantages. In this work, a converse flexoelectric effect is generated by the designed permittivity gradient with Ba0.67Sr0.33TiO3 ceramic powder and the substrate. The equivalent piezoelectric effect of the gradient composite is obviously increased by converse flexoelectricity. This study opens up an avenue for prospective sensing and actuating approaches for both piezoelectric and non-piezoelectric dielectric materials with relative permittivity gradients and uniform geometric structures.

Electrokinetic instabilities in co-flowing ferrofluid and buffer solutions with matched electric conductivities

Electrokinetic instabilities have been extensively studied in microchannel fluid flows with conductivity or conductivity and permittivity gradients for various microfluidic applications. This work presents an experimental and numerical investigation of the electrokinetic co-flow of ferrofluid and buffer solutions with matched electric conductivities. We find that the ferrofluid and buffer interface becomes unstable with periodic waves if the applied direct-current electric field reaches a threshold value. We develop a two-dimensional numerical model to seek a preliminary understanding of such an electrically originated flow instability. Our model indicates that the observed phenomenon is not a consequence of the electric body force acting on the permittivity gradients between the ferrofluid and buffer solutions. It is instead attributed to the diffusion-induced conductivity gradients that are formed at the ferrofluid and buffer interface due to the mismatching diffusivities of ferrofluid nanoparticles and buffer ions.

Alteration in contact line dynamics of fluid-fluid interfaces in narrow confinements through competition between thermocapillary and electrothermal effects

The paper reports the results of our numerical investigation on contact line dynamics of a thermal field assisted flow configuration of two immiscible fluids in a narrow thermofluidic pathway. The surfaces of the channel are wetted with predesigned wettabilities and interdigitated electrodes are mounted on the substrates to generate a non-uniform electric field. In this study, the interplay of thermocapillary and electrothermal forces on interfacial dynamics are considered. The former is caused by temperature-induced surface tension gradients while the latter is originated from the temperature-induced gradients in permittivity and electrical conductivity. Our investigations reveal that the relative strength of interfacial forces and electrothermal forces and their interactions can be effectively used to control the capillary filling time as well as flow dynamics. For the same strength of thermocapillary and electrothermal forces (characterized by individual dimensionless numbers), electrothermal effects dominate over thermocapillary effects. However, interfacial forces dominate over electrothermal forces at certain wettabilities (characterized by the imposed contact angle on the surfaces), and depending on the direction of the interfacial forces, the contact line travels toward the entry or exit of the channel.