Low-frequency Dispersion Research Articles

TCAD Modeling of GaN HEMT Output Admittance Dispersion through Trap Rate Equation Green’s Functions

We present a novel and numerically efficient approach to analyse the sensitivity of AC parameters to variations of traps in GaN HEMTs. The approach exploits an in-house TCAD simulator implementing the drift-diffusion model self-consistently coupled with trap rate equations, solved in dynamic conditions with the Harmonic Balance algorithm. The capability of the model is demonstrated studying the low-frequency dispersion of a 150 nm gate-length AlGaN/GaN HEMT output admittance YDD as a function of the trap energy of Fe-induced buffer traps. The real part of YDD exhibits strong frequency dispersion and an important degradation of the output resistance at high frequency. The imaginary part is characterized by a peak at a frequency decreasing with trap energy deeper in the gap, in agreement with experimental data on similar structures. Distributed local sources show that YDD is most sensitive to trap energy variations localized in the buffer region under the gate, peaking under the unsaturated portion of channel towards the source. Trap variations affect the output admittance when localized in depth into the buffer up to a 100 nm distance from the channel.

Trap-assisted enhancement of the responsivity in asymmetric planar GaN-based nanodiodes at low temperature

The microwave detection capability of GaN-based asymmetric planar nanodiodes (so-called Self-Switching Diode, SSD, due to its non-linearity) has been characterized in a wide temperature range, from 70 K up to 300 K. At low temperature, microwave measurements reveal an enhancement of the responsivity at frequencies below 1 GHz, which, together with a pronounced hysteresis in the DC curves, indicate a significant influence of the surface states. This leads to a significant variability and non-repeatability which needs to be reduced since it degrades the accuracy of the detection. For this sake, the RF characterization was repeated after applying a positive/negative voltage able to fill/empty the surface states in order to have a well-established preconditioned state. As a consequence of the positive pre-soak bias, a significant enhancement of the measured responsivity, with a × 10 increase at low temperature. The RF detection measurements after such preconditioning contains a time dependence induced by the slow discharge mechanism of the traps, so that the improved responsivity remains even after 100s of seconds. On the other hand, a negative voltage pre-soak benefits the discharge process, thus suppressing the low frequency dispersion and the important variability of the detection without the pre-conditioning step. We also show that the relation between the voltage and current responsivities in each case allows to explain the impact of the surface charges in terms of the device impedance.

Dodecyltrimethylammonium bromide-styrene microemulsion dielectric investigation in aqueous media

In this paper, we report the complex permittivity of aqueous microemulsions of N-dodecyltrimethylammonium bromide and styrene. The studies were carried out at 298.15 K while varying the styrene to surfactant concentration ratio, S0 (0.16 ≤ S0 ≤ 0.71) and the surfactant concentration, c (0.1032 ≤ c (mol·dm−3) ≤ 0.7806). The frequencies ranged from 100 MHz to 89 GHz. An analysis of a particular solution is conducted over the temperature range of 278.15–328.15 K to calculate the energy of the activation parameters. At 298.15 K, the spectra are fitted to a total of five Debye processes for concentration dependency series and three Debye processes for temperature dependence series. Br− surface and bulk diffusion surrounding the micelles best describes the two low-frequency dispersions, at 100 MHz and 0.8 GHz, respectively. These mechanisms were examined using Grosse theory. The Maxwell–Wagner relaxation process is equivalent to high-frequency micelle dispersion at 0.8 GHz. The thickness of the conducting shell of the micelle is determined by using the electrical conductivity of the particles and parameters taken from the Grosse theory, and the results are comparable to those from an examination of the Pauly and Schwan model. The Grosse model and solvent dispersion analysis were used to calculate the volume fractions of micelles. Both approaches were in agreement. The surfactant head group non-rotationally hydrates almost ∼7 ± 1 water molecules. Styrene addition allows for the non-rotationally bound accommodation of an additional ∼7 ± 1 water molecules.

Impedance-Frequency Response of Closed Electrolytic Cells

The electric AC response of electrolytic cells with DC bias is analyzed solving numerically the Poisson-Nernst-Planck equations and avoiding the commonly used infinite solution approximation. The results show the presence of an additional low-frequency dispersion process associated with the finite spacing of the electrodes. Moreover, we find that the condition of fixed ionic content inside the electrolytic cell has a strong bearing on both the steady-state and the frequency response. For example: the characteristic frequency of the high-frequency dispersion decreases when the DC potential increases and/or the electrode spacing decreases in the closed cell case, while it remains essentially insensitive on these changes for open cells. Finally, approximate analytic expressions for the dependences of the main parameters of both dispersion processes are also presented.

Investigation of conduction mechanism and UV light response of vertically grown ZnO nanorods on an interdigitated electrode substrate.

Vertically aligned zinc oxide nanorod (ZnO-NR) growth was achieved through a wet chemical route over a comb-shaped working area of an interdigitated Ag-Pd alloy signal electrode. Field-emission scanning electron microscopy images confirmed the formation of homogeneous ZnO-NRs grown uniformly over the working area. X-ray diffraction revealed single-phase formation of ZnO-NRs, further confirmed by energy-dispersive X-ray spectroscopy analysis. Temperature-dependent impedance and modulus formalisms showed semiconductor-type behavior of ZnO-NRs. Two electro-active regions i.e., grain and grain boundary, were investigated which have activation energy ∼0.11 eV and ∼0.17 eV, respectively. The conduction mechanism was investigated in both regions using temperature-dependent AC conductivity analysis. In the low-frequency dispersion region, the dominant conduction is due to small polarons, which is attributed to the grain boundary response. At the same time, the correlated barrier hopping mechanism is a possible conduction mechanism in the high dispersion region attributed to the bulk/grain response. Moreover, substantial photoconductivity under UV light illumination was achieved which can be attributed to the high surface-to-volume ratio of zinc oxide nanorods as they provide high density of trap states which causes an increase in the carrier injection and movement leading to persistent photoconductivity. This photoconductivity was also facilitated by the frequency sweep applied to the sample which suggests the investigated ZnO nanorods based IDE devices can be useful for the application of efficient UV detectors. Experimental values of field lowering coefficient (βexp) matched well with the theoretical value of βS which suggests that the possible operating conduction mechanism in ZnO nanorods is Schottky type. I-V characteristics showed that the significantly high photoconductivity of ZnO-NRs as a result of UV light illumination is owing to the increase in number of free charge carriers as a result of generation of electron-hole pairs by absorption of UV light photons.

Post-annealing optimization of the heteroepitaxial La-doped SrSnO3 integrated on silicon via ALD.

Wide band gap (WBG) alkaline-earth stannate transparent oxide semiconductors (TOSs) have attracted increasing attention in recent years for their high carrier mobility and outstanding optoelectronic properties, and have been applied widely in various devices, such as flat-panel displays. Most alkaline-earth stannates are grown by molecular beam epitaxy (MBE); there are some intractable issues with the tin source including the volatility with SnO and Sn sources and the decomposition of the SnO2 source. In contrast, atomic layer deposition (ALD) serves as an ideal technique for the growth of complex stannate perovskites with precise stoichiometry control and tunable thickness at the atomic scale. Herein, we report the La-SrSnO3/BaTiO3 perovskite heterostructure heterogeneously integrated on Si (001), which uses ALD-grown La-doped SrSnO3 (LSSO) as a channel material and MBE-grown BaTiO3 (BTO) as a dielectric material. The reflective high-energy electron diffraction and X-ray diffraction results indicate the crystallinity of each epitaxial layer with a full width at half maximum (FWHM) of 0.62°. In situ X-ray photoelectron spectroscopy results confirm that there was no Sn0 state in ALD-deposited LSSO. Besides, we report a strategy for the post-treatment of LSSO/BTO perovskite heterostructures by controlling the oxygen annealing temperature and time, with a maximum oxide capacitance Cox of 0.31 μF cm-2 and a minimum low-frequency dispersion for the devices with 7 h oxygen annealing at 400 °C. The enhancement of capacitance properties is primarily attributed to a decrease of oxygen vacancies in the films and interface defects in the heterostructure interfaces during an additional ex situ excess oxygen annealing. This work expands current optimization methods for reducing defects in epitaxial LSSO/BTO perovskite heterostructures and shows that excess oxygen annealing is a powerful tool for enhancing the capacitance properties of LSSO/BTO heterostructures.

Structural, dielectric, magnetic and magnetoelectric studies of (1-x) BaFe12O19-x BiFeO3 composites

The synthesis of multiferroic (1-x) BaFe12O19-x BiFeO3; (x = 0.05, 0.08, 0.10) composites was carried out with solid state reaction. The XRD data confirmed the formation of the composites with phases of both compounds. The low values of Rietveld refinement parameters along with modified lattice parameters of both hexaferrite and multiferroic phase reconfirmed the amalgamation of phases. FESEM with EDX were utilized for morphological study and elemental compositional analysis in the composites. The dielectric constant and tanδ both parameters showed typical low frequency dispersion. A mild anomaly in dielectric constant and tangent loss is quite noticeable near to magnetic transition temperature (TN) of BiFeO3 suggests the possible occurrence of magnetoelectric effect in prepared composite system. The fitting of AC conductivity data suggested the OLPT (overlapping large polaron tunneling) conduction process in the composite system. The saturation magnetization (Ms) showed a decreasing trend with increment of BiFeO3 content in composites owing to substituted Fe3+ ion in spin-up state. Coercivity (Hc) found in good agreement with magnetocrystalline anisotropy of hexaferrite phase. The improvements in magnetoelectric coupling coefficient of barium hexaferrite were clearly noticeable with the introduction of BiFeO3 phase owing to piezoelectric coefficient and magnetostriction of ferroelectric and ferrite phases respectively.

Analysis of High-Temperature Wideband Dielectric Properties of ATH-Filled Silicone Rubber Used for On-Site Insulation of Bare Overhead Conductors

Due to its excellent electrical and mechanical properties, and easy to cure at room temperature, room temperature vulcanizing silicone rubber is currently used in the on-site insulation of bare overhead conductors in the distribution system. The dielectric properties of silicone rubber materials have a great impact on power loss, which is vital to the transmission lines. Therefore, in this article, the dielectric properties of silicone rubber with the addition of different aluminum hydroxide contents are investigated by broadband dielectric spectroscopy in wide broadband range and wide temperature ranges, and the influence of aluminum hydroxide filler on the dielectric response is analyzed using a modified Cole–Cole model which takes the low-frequency dispersion process into account. It is found that the relationship of the dc conductivity and the low-frequency dispersion strength with temperature follows the Arrhenius equation law. The low-frequency dielectric response is influenced by dipoles’ polarization and electrode polarization. Moreover, the relaxation time decreases with the increase in temperature, and its mechanism can be revealed by the double-well model. The characteristic parameters obtained in this article can provide a reference for on-site insulating of bare overhead conductors.

Temperature- and Degradation-Dependent Maximum Electric Field Stress in Wire-Bonding Power Modules Under PWM Waves

Electric field stress concentration is one of the causes of partial discharge (PD) in power modules, which threatens the power modules’ safe operation. Herein, this article investigates the influences of temperature (from 150 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$250~^{\circ }\text{C}$ </tex-math></inline-formula> ) and operation duration on the maximum electric field stress at the triple point (silicone elastomers, ceramic, and copper). It reveals that the maximum electric field stress rises with the increase in temperature, while the maximum electric field first increases but then decreases along the operation duration, especially under low temperature. Both the influences of temperature and the operation duration are related to the permittivity (dominated by the relaxation of Si–O bonds), low-frequency dispersion (LFD) phenomenon, and dc conductivities of silicone elastomers, which can be manipulated to suppress electric field stress concentration. This article provides a method to accurately calculate the electric field. The results are also critical to evaluation and improvement of power modules’ insulation.

Dielectric and electrical properties of nematic liquid crystals 6CB doped with iron oxide nanoparticles. The combined effect of nanodopant concentration and cell thickness

Dispersing nanomaterials in liquid crystals has emerged as a very promising non-synthetic way to produce advanced multifunctional and tunable materials. As a rule, dielectric and electrical characterization of such materials is performed using cells of single thickness. As a result, the published reports vary even for similar systems. Confusion still exists as to the effects of nanodopants and cell thickness on the dielectric and electrical properties of liquid crystals. This factor hinders a widespread use of liquid crystals - nanoparticles systems in modern tech products. In this paper, we report systematic experimental studies of the combined effect of the cell thickness and iron oxide nanoparticle concentration on the electrical and dielectric properties of nematic liquid crystals 6CB. The measured dielectric spectra can be divided into three distinct regions corresponding to a low frequency (<10 Hz) dispersion, dispersion free range (102 – 104 Hz (electrical conductivity) and 102 – 105 (dielectric permittivity)), and high frequency dispersion (104 – 106 Hz (electrical conductivity) and 105-106 Hz (dielectric permittivity)). The real part of the dielectric permittivity is not affected by the cell thickness and its value can be tuned by changing the concentration of nanoparticles. At the same time, the electrical conductivity depends on both cell thickness and nanoparticle concentration. At intermediate frequencies (102 – 104 Hz) the electrical conductivity obeys the Jonscher power law and is dependent on the cell thickness because of ion-releasing and ion-capturing effects caused by nanoparticles and substrates of the cell. In addition, its value is affected by the electronic conductivity due to iron oxide nanoparticles and their nanoclusters. At higher frequencies (104 – 106 Hz) the electrical conductivity follows a super linear power law and is nearly independent of the cell thickness and nanoparticle concentration.

Broadband Dielectric Characterization of High-Permittivity Rogers Substrates via Terahertz Time-Domain Spectroscopy in Reflection Mode

We report the dielectric characterization of three commercially available, high-permittivity Rogers laminates in the sub-terahertz range, by means of terahertz time-domain spectroscopy measurements in reflection mode. A transmission-line model is developed to obtain the reflectance spectra as a function of the frequency-dispersive complex relative permittivity of the substrates. The latter is fitted through optimization to a single Lorentzian term, which is shown to accurately reproduce the measured reflectance spectra. The substrates RO3010 and RT/duroid 6010.2LM exhibit significant frequency dispersion of both their relative permittivity and loss tangent. Conversely, the thermoset microwave laminate TMM10i is characterized by both a lower frequency dispersion and overall dielectric losses, thus making it a promising candidate for the design of low-profile and broadband components for novel terahertz applications. Owing to the simple Lorentzian dispersion model used for the description of the relative permittivity, the presented results can serve as a reference, and they can be directly introduced in design and optimization workflows for novel devices in emerging terahertz applications.

Optical properties, dielectric relaxor behavior, impedance and modulus spectroscopy of 0.8BiFeO3-0.2CaTiO3 composite

0.8BiFeO3-0.2CaTiO3 (0.8BFO-0.2CTO) was synthesized by the sol-gel route. Structural characterization was performed by X-ray diffraction which confirms the rhombohedral structure. FESEM analysis reveals the irregular grains that are inhomogenous and slightly dense. Temperature-dependent dielectric permittivity shows a dielectric anomaly near the magnetic phase transition temperature (TN) of BiFeO3 as well as relaxor-type ferroelectric properties. The PE loop confirms the presence of ferroelectricity in the sample. Frequency-dependent ac conductivity exhibits low frequency dispersion and was well explained by Jonscher power law. The obtained fitting parameters A (pre-exponential factor that indicates polarizability) and n (dimensionless frequency exponent) show maxima and minima at the transition temperature. The electrical properties were further analysed by impedance and modulus spectroscopy. According to these analysis, the relaxation time was distributed and does not follow the Debye type behaviour. Nyquist plots had been used to estimate grain and grain boundary contributions. A typical negative temperature coefficient of resistance (NTCR) behaviour was apparent due to the decrement in bulk and grain boundary resistances as the temperature increases. The temperature-dependent relaxation time revealed Arrhenius's behaviour. 0.8BFO-0.2CTO exhibits absorption and shows a transmittance of 40–44% in the visible region of spectra. The obtained value of Eg was ∼2.26 eV, which implies the application in ultrafast optoelectronic devices. The good ability of absorption in visible region, high transmittance, the increase of extinction coefficient with wavelength, and low band gap makes 0.8BFO-0.2CTO an extraordinary material for optical devices application. The sample also shows a decrease in magneto-capacitance and increase in magneto-impedance which reflects the presence of strong magneto dielectric coupling in 0.8BFO-0.2CTO at room temperature.

Tailored acoustic metamaterials. Part II. Extremely thick-walled Helmholtz resonator arrays.

We present a solution method which combines the technique of matched asymptotic expansions with the method of multipole expansions to determine the band structure of cylindrical Helmholtz resonator arrays in two dimensions. The resonator geometry is considered in the limit as the wall thickness becomes very large compared with the aperture width (the extremely thick-walled limit). In this regime, the existing treatment in Part I (Smith & Abrahams, 2022 Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays), with updated parameters, is found to return spurious spectral behaviour. We derive a regularized system which overcomes this issue and also derive compact asymptotic descriptions for the low-frequency dispersion equation in this setting. We find that the matched-asymptotic system is able to recover the first few bands over the entire Brillouin zone with ease, when suitably truncated. A homogenization treatment is outlined for describing the effective bulk modulus and effective density tensor of the resonator array for all wall thicknesses. We demonstrate that extremely thick-walled resonators are able to achieve exceptionally low Helmholtz resonant frequencies, and present closed-form expressions for determining these explicitly. We anticipate that the analytical expressions and the formulation outlined here may prove useful in designing metamaterials for industrial and other applications.

Topological Engineering of the Iso-Frequency Contours in Connection-Type Metamaterials

The topology of isofrequency surface governs the electromagnetic wave propagation and light–matter interaction in metamaterials. For most metamaterials with local medium description, the low-frequency isosurfaces are typical spheres or ellipsoids centered at zero momentum, which, to some extent, limits our manipulation ability on low-frequency wave. In this work, based on connection-type wire metamaterials, we propose a scheme to engineer the shapes of isofrequency surfaces. An equivalent circuit model is developed to analyze the low-frequency dispersion of connection-type metamaterials. It implies that the shape of index ellipsoids at quasistatic limit is determined by the equivalent inductances and capacitances of the metallic meshes. By adjusting these equivalent circuit parameters, we can achieve the isotropic or anisotropic index ellipsoids at quasistatic limit and, hence, a cruciform or bowtie-shaped isofrequency contours for the lowest-frequency band. Our results demonstrate a feasible platform for topological engineering of isofrequency surfaces, which may pave the way to novel devices for manipulating long-wavelength electromagnetic wave.

Flexible multi-walled carbon nanotubes/polyvinylidene fluoride membranous composites with weakly negative permittivity and low frequency dispersion

Flexible composites with negative permittivity have great potentials in flexible electronics and wearable devices. To improve their working performance, it is critical to search for such materials that possess weakly and stable negative permittivity in a wide frequency range. In this work, the polyvinylidene fluoride (PVDF) was selected as the flexible matrix and the modified multi-walled carbon nanotubes (MWCNTs) were used as functional fillers to prepare MWCNTs/PVDF membranous composites with a weakly negative permittivity. When the content of MWCNTs exceeded 13 wt%, the negative permittivity conforming to Drude model appeared. The absolute value of negative permittivity can be as low as approximately 10 in the whole test frequency range, presenting a low frequency dispersive behavior. It demonstrated that the weakly negative permittivity was ascribed to the dilution of electrons in the resulting composites, and the high electron mobility in MWCNTs was responsible for the low frequency dispersion. The MWCNTs/PVDF membranous metacomposites with a twisted and foldable flexibility can contribute to the development of flexible metamaterials and enrich their significant applications.

Enhanced dielectric stability and coercivity of band gap tuned Ba–Al Co-doped bismuth ferrite: An experimental and DFT+U investigation

Employing a modified sol-gel combustion technique, BiFeO3 and Bi0.85Ba0.15Fe1-xAlxO3 (x = 0, 0.025 and 0.050) nanoparticles were synthesized, and the effects of these dopants were investigated analyzing the experimental findings and adopting the DFT + U approach. Rietveld analysis of XRD revealed a deformed perovskite rhombohedral structure for all the Ba–Al co-doped nanoparticles, which was also validated by theoretical study. Suppression of the low-frequency dispersion promoting outstanding dielectric stability was observed due to Al3+ doping, and the least dielectric constant along with the highest resistivity was reported for BBFAO-2.5. The band gap of co-doped nanoparticles (x = 2.5 & 5) decreased to 1.95 eV and 1.98 eV, respectively, compared to 2.06 eV, and 2.09 eV for BBFAO-0 and pure BFO. The average particle size of all the co-doped nanoparticles was below the repeat length of the cycloid structure, which is favorable for improved magnetic properties. Remanent magnetization, coercivity, and squareness increased as the motion of domain walls is inhibited by the smaller-sized nanoparticles. DFT + U study further endorses the findings of the experimental study. Analysis of DOS revealed the emergence of shallow impurity states around VBM due to doping, which can operate as active trap centers and impede carrier recombination. Thus, it can be inferred that, Ba–Al co-doped nanoceramics with intriguing dielectric, optical, and magnetic properties are a promising candidate for high-frequency microwave devices, magnetic memory and storage devices, near UV-detector, and solar photocatalysis applications.

Homogenization of the wave equation with non-uniformly oscillating coefficients

The focus of our work is a dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g., functionally graded) media endowed with periodic microstructure. For this class of quasi-periodic medium variations, we pursue homogenization of the scalar wave equation in , , within the framework of multiple scales expansion. When either or , this model problem bears direct relevance to the description of (anti-plane) shear waves in elastic solids. By adopting the lengthscale of microscopic medium fluctuations as the perturbation parameter, we synthesize the germane low-frequency behavior via a fourth-order differential equation (with smoothly varying coefficients) governing the mean wave motion in the medium, where the effect of microscopic heterogeneities is upscaled by way of the so-called cell functions. In an effort to demonstrate the relevance of our analysis toward solving boundary value problems (deemed to be the ultimate goal of most homogenization studies), we also develop effective boundary conditions, up to the second order of asymptotic approximation, applicable to one-dimensional (1D) shear wave motion in a macroscopically heterogeneous solid with periodic microstructure. We illustrate the analysis numerically in one dimension by considering (i) low-frequency wave dispersion, (ii) mean-field homogenized description of the shear waves propagating in a finite domain, and (iii) full-field homogenized description thereof. In contrast to (i) where the overall wave dispersion appears to be fairly well described by the leading-order model, the results in (ii) and (iii) demonstrate the critical role that higher-order corrections may have in approximating the actual waveforms in quasi-periodic media.

Study of electrical properties of Al/Si3N4/n-GaAs MIS capacitors deposited at low and high frequency PECVD

As for silicon, surface passivation of GaAs and III-V semiconductors using silicon nitride (Si3N4) deposited by plasma enhanced chemical deposition (PECVD) is widely used to improve devices and circuits stability, reliability and for encapsulation. In this work, the effect of plasma excitation frequency in the PECVD reactor on the surface passivation efficiency of GaAs during Si3N4 deposition was investigated. Metal-Insulator-Semiconductor (Al/Si3N4/n-GaAs) capacitors are fabricated and characterized using capacitance–voltage (C–V), and conductance–voltage (G–V) to compare electronic properties of GaAs/Si3N4 interfaces depending on the use of a high frequency PECVD (HF-PECVD) or low frequency (LF-PECVD) process. The drastic advantage of using the LF-PECVD technique for the passivation of GaAs is clearly demonstrated on the characteristic C–V at 1 MHz where a good surface potential was observed, while a quasi-pinned surface Fermi level was found when HF-PECVD was used. To unpin Fermi level, a sulfur pre-treatment prior before HF-PECVD deposition and post-metallisation annealing were necessary. A lower frequency dispersion and a lower hysteresis indicating low densities of slow traps were observed for MIS devices fabricated by LF-PECVD. The advantage of having an efficient passivation without sulfur treatment is important since ammonium sulfide used for this purpose is corrosive and difficult to adapt in industrial environment. The better electronic properties of GaAs/Si3N4 interface were found for silicon nitride layers using LF-PECVD deposition. This can probably be associated with the high-level injection of H+ ions on the semiconductor surface reducing thus the native oxides during the initial steps of dielectric deposition.

Dirac cones with zero refractive indices in phoxonic crystals.

In this paper, simultaneous zero refractive indices (ZRIs) for both sound and light are realized on the basis of a 2D triangular lattice phoxonic crystal (PxC) with C6v symmetry. For the phononic mode, accidental phononic Dirac degeneracy at the center of Brillouin zone (BZ) occurs at a relatively high frequency which leads to the failure of the efficient medium theory; hence, it is no longer applicable to the realization of acoustic ZRI. We thus turn to a low-frequency phononic Dirac cone located at K point, the corner of the BZ, which shows in-phase pressure field oscillations in expanded unit cells. Using zone folding, we further reveal the cause for the characteristic of acoustic ZRI. For the photonic mode, a low-frequency photonic Dirac-like cone can be achieved by adjusting the geometric parameter due to the high contrast permittivity between scatterers and the matrix. When the phononic and photonic low-frequency Dirac dispersions coexist, the PxC can be mapped into a zero-index material for both sound and light at the same time. The new mechanism for simultaneously controlling sound and light helps to achieve acousto-optic synchronous cloaking and unidirectional transmission, which are numerically demonstrated.

Induced polarization signal manifestation in multi-spacing installations in offshore areas up to 100 m deep

The purpose of the work is to show the manifestation of an induced polarization signal in the transient electromagnetic signal for multi-spacing axial electrical installations depending on the spacing and sizes of the source at different depths of installation for the offshore conditions of sea depth of up to 100 m. The study uses the solution of the direct problem of a transient electromagnetic field for conducting polarizable media with a description of electrical resistivity dispersion by the Cole – Cole formula. Analysis is given to the change in the transient signal ΔU(t), final difference of the transient signal Δ2U(t) and transform P1(t) (ratio of Δ2U(t) to ΔU(t)) depending on multi-spacing installation size. The study involves installations with a source length (a source is a horizontal grounded electrical line AB) from 50 to 500 m, receiver length (receiver is represented by three-electrode electrical lines) from 50 to 500 m, and distance between the centers of the source and receiver (spacing) multiple of the source length: (3/2)·AB, 2·AB, (5/2)·AB, 3·AB, (7/2)·AB, 4·AB, (9/2)·AB, 5·AB. Comparison is given to the signals from conductive model and conductive polarizing model. A multi-spacing installation was placed inside a conductive medium with a conductive polarizing base. The conductive medium was associated with the layer of sea water in offshore areas with sea depths of up to 100 m. The conductive polarizing base was represented by a geological formation (ground) covered by a layer of water. Calculations performed as a result of conducted research works show the manifestation of various components of the transient process associated with electromagnetic field formation and manifestation of low-frequency dispersion of the electromagnetic properties of the earth caused by both galvanic and eddy currents. These components manifest themselves in different ways on multi-spacing installations at different depths. Therefore, it could be argued that the components of the transient process associated with the transient electromagnetic field, galvanically induced polarization and inductive induced polarization manifest themselves in different ways in multi-spaced installations of different sizes immersed at different depths. Induced polarization manifests itself in two ways for water area conditions as it is associated with both galvanic and eddy currents. Previously, when performing practical measurements, the manifestation of inductive induced polarization was considered as interference manifestation. But being simulated this signal can be considered as information about induced polarization. The factor influencing the manifestation character of induced polarization signal in the transient signal is the installation height above the bottom Δh and the spacing r. Δh is the distance between the installation and the seafloor, which is a polarizing base of the model. r is the distance between the centers of the source and the meter represented by a three-electrode measuring line. Depending on the installation height and spacing the induced polarization signal in the transform P1(t) can appear as an ascending branch at later times, as well as in the form of a descending branch that turns into negative values of P1.