Inhomogeneous Dielectrics Research Articles

Corrections to “EM Field Induced in Inhomogeneous Dielectric Spheres by External Sources” [Nov 07 3178-3190

Corrections to “EM Field Induced in Inhomogeneous Dielectric Spheres by External Sources” [Nov 07 3178-3190

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches.

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

Effect of substrate dielectric inhomogeneity in the dispersion characteristics of a microstrip line

In this article, we apply the spectral domain method of moments to calculate the dispersion characteristics of a microstrip line, which is located on top of a grounded dielectric substrate. The dielectric substrate is a one-dimensional inhomogeneous material whose permittivity varies continuously in the direction normal to the ground plane. To make the spectral domain analysis applicable to a general inhomogeneous profile, we propose an accurate numerical algorithm to calculate the spectral domain transverse dyadic Green's function for an inhomogeneous substrate with an arbitrarily varying permittivity. The method is then used to obtain the dispersion curves for several inhomogeneous profiles and the results are compared with those of Ansoft HFSS simulator to verify the validity and accuracy of the proposed method. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1819–1822, 2014

Enhanced field emission properties of PECVD synthesized chlorine doped diamond like carbon thin films

Chlorine doped diamond like carbon (DLC) has been deposited for the first time on both Si and glass substrate by plasma enhanced chemical vapor deposition using acetylene and carbon tetrachloride as the source for carbon and chlorine respectively. The Chlorine concentration is varied from 0% to 3.63% as confirmed by X-Ray Photoelectron Spectroscopy. The pure and doped samples were characterized by Atomic Force Microscopy, UV–vis–NIR spectroscopy and FTIR spectroscopy. The electron field emission properties of all the pure and doped samples have been studied in high vacuum field emission set up and it is seen that the field emission properties of the DLC sample have been considerably improved after chlorine was added to it. The doped sample shows good field emission stability with turn on field as low as 4.75V/μm for highest Chlorine concentration. The dependence of field electron emission on inter-electrode distances was studied for three different inter-electrode distances. The enhanced field emission characteristics have been explained in terms of dielectric inhomogeneity induced field enhancement in sp2–sp3 bonded mixed carbon network.

The cavity electromagnetic field within the polarizable continuum model of solvation.

Cavity field effects can be defined as the consequences of the solvent polarization induced by the probing electromagnetic field upon spectroscopies of molecules in solution, and enter in the definitions of solute response properties. The polarizable continuum model of solvation (PCM) has been extended in the past years to address the cavity-field issue through the definition of an effective dipole moment that couples to the external electromagnetic field. We present here a rigorous derivation of such cavity-field treatment within the PCM starting from the general radiation-matter Hamiltonian within inhomogeneous dielectrics and recasting the interaction term to a dipolar form within the long wavelength approximation. To this aim we generalize the Göppert-Mayer and Power-Zienau-Woolley gauge transformations, usually applied in vacuo, to the case of a cavity vector potential. Our derivation also allows extending the cavity-field correction in the long-wavelength limit to the velocity gauge through the definition of an effective linear momentum operator. Furthermore, this work sets the basis for the general PCM treatment of the electromagnetic cavity field, capable to describe the radiation-matter interaction in dielectric media beyond the long-wavelength limit, providing also a tool to investigate spectroscopic properties of more complex systems such as molecules close to large nanoparticles.

An Efficient Phase Field Model for Electrostatics in Complex Dielectric Heterostructures

At the microstructural level, dielectric inhomogeneity is ubiquitous in common ceramic, polymer and composite materials. If the characteristic length scale of the dielectric heterostructure is critical to the problem of interest the position dependent dielectric constant needs to be explicitly considered. Such examples include dielectric performance of a composite, ionic transport in metal oxides containing precipitates, micropores and/or cracks (e.g., during high temperature metal oxidation), and dielectrophoresis of small particles. A bound-charge phase field model is developed to address the dielectric heterogeneity problem. The model solves electrostatic problems by using a fast-converging iteration algorithm and Fast Fourier Transform. Excellent efficiency of the model is observed that demonstrates its potential for many practical applications.

Green's function for a spherical dielectric discontinuity and its application to simulation.

We present rapidly convergent expressions for the Green's function of the Poisson equation for spherically symmetric systems where the dielectric constant varies discontinuously in the radial direction. These expressions are used in Monte Carlo simulations of various electrolyte systems, and their efficiency is assessed. With only the leading term of the expansion included, a precision of the polarization energy of 0.01kJmol(-1) or better was achieved, which is smaller than the statistical uncertainty of a typical simulation. The inclusion of the dielectric inhomogeneity leads to a 2.5-fold increase of the computational effort, which is modest for this type of model. The simulations are performed on six types of systems having either (i) a uniform surface charge distribution, (ii) a uniform volume charge distribution, or (iii) mobile ions, which were neutralized by mobile counterions. The ion density distributions are investigated for different dielectric conditions. These spatial distributions are discussed in terms of the importance of (i) the direct mean-field Coulomb interaction, (ii) the surface charge polarization at the dielectric discontinuity, and/or (iii) the change in the attractive Coulomb correlations.

PROPERTIES OF MUSIC-TYPE ALGORITHM FOR IMAGING OF THIN DIELECTRIC INHOMOGENEITY IN LIMITED-VIEW INVERSE SCATTERING PROBLEM

It is well known that a Multiple Signal Classification (MUSIC)-type algorithm yields good results in the imaging of thin dielectric inhomogeneity for full-view inverse scattering problems. In contrast, it yields a poor result in limited-view inverse scattering problems. In this paper, we verify the reason for the above by establishing a relationship between a MUSIC-type imaging function and the Bessel functions of the integer order of the first kind. This verification is based on the asymptotic expansion formula for thin dielectric inhomogeneity. Various numerical examples are discussed for confirming our verification.

A New Volume Integral Formulation for Broadband 3-D Circuit Extraction in Inhomogeneous Materials With and Without External Electromagnetic Fields

A new first-principles-based volume integral equation (VIE) formulation is developed for the broadband full-wave extraction of general 3-D circuits, containing arbitrarily shaped lossy conductors with inhomogeneous dielectrics. The proposed formulation accentuates all the advantages of the VIE formulation traditionally developed for solving wave-related problems, while allowing for the extraction of multiport circuit parameters such as impedance Z-, admittance Y-, and scattering S-parameters at ports located anywhere in the physical structure of a circuit. Its first-principles-based formulation without circuit-based simplifications and approximations can also be utilized to analyze the performance of a circuit in adverse ambient conditions, such as the exposure to strong external electromagnetic fields. In addition, the magneto-quasi-static and electro-magneto-quasi-static counterparts of the proposed full-wave formulation are also given for low-frequency applications. Numerical experiments have validated the accuracy and capability of the proposed new VIE formulation.

Inverse Analysis for Inhomogeneous Dielectric Coefficient of Pavement Material Based on Genetic Algorithm

The key of ground penetrating radars application lies in the calculation of dielectric coefficient. The pavement materials are inhomogeneous medium in fact, the particle surface can induce the scatter and diffraction of electromagnetic wave. The inhomogeneous dielectricity can change the characteristics of reflected wave. It may even cause background noise of reflected signal, which will lead to mistakes in signal interpretation. Therefore it is necessary to analyze the inhomogeneous dielectric coefficients by GPR. This paper proposes the solutions of inverse analysis for inhomogeneous dielectric coefficients of pavement materials used GPR data. Two examples are given to assess the validity of genetic algorithms in inversion of pavement materials inhomogeneous dielectricity. The results show that genetic algorithm can converge into true solutions well. The backcalculated inhomogeneous dielectric coefficients can help to evaluate pavement properties further.

Analysis of Doubly Periodic Inhomogeneous Dielectric Structures by a Hybrid Projective Method

The problem of plane electromagnetic wave scattering by doubly periodic structures with both homogeneous and inhomogeneous dielectric elements arranged on a homogeneous dielectric substrate is considered. A hybrid projective method involving the method of coupled waves, method of projective matching of fields on the boundaries of partial regions, and one-dimensional finite elements method, is proposed. The method avoids using excessive number of unknown coefficients of expansion taking place in the previous versions. The effectiveness of the method is validated by a few tests including convergence of the results with increasing the number the expansion coefficients and comparison with appropriate data available in literature. The capabilities of homogeneous lossless matching dielectric elements of various shape and some properties of ultra-wideband absorbing structures with pyramidal elements are studied. The potential advantage of using inhomogeneous absorbing elements is also demonstrated.

Phase transitions and domain structures of ferroelectric nanoparticles: Phase field model incorporating strong elastic and dielectric inhomogeneity

An efficient numerical algorithm based on a Fourier spectral iterative perturbation method is proposed to accurately compute the electrostatic fields in three-dimensional (3D) microstructures with arbitrary dielectric inhomogeneity and anisotropy. The method can be conveniently implemented in phase field modeling of microstructure evolution in systems with inhomogeneous dielectric constants as well as inhomogeneous polarization and charge distributions. It is employed to determine the temperature–shape (aspect ratio) phase diagram, domain structures, and domain switching of PbTiO3 nanoparticles using phase field simulations. It is shown that the Curie temperature is enhanced for nanowires and nanorods and reduced for nanodots. The critical sizes below which the ferroelectricity disappears for the nanowire and thin film are estimated to be around 1.4nm. Vortex domain structures are found in nanorods, nanodots, and nanodisks. Results are in general agreement with existing experimental observations and first principle calculations.

Broadband All‐Dielectric Magnifying Lens for Far‐Field High‐Resolution Imaging

A transformation-optics magnifying lens is reported in the microwave frequency, which is made of inhomogeneous but isotropic dielectrics to reach impedance matching. The authors demonstrate the broadband subwavelength imaging performance and magnification factor experimentally from the far-field radiation patterns.

Surface and bulk scattering by magnetic and dielectric inhomogeneities: a first-order method

The scattering of a magnetodielectric multilayer has been studied by a first-order method. The model reported in this manuscript relies on the equivalence between heterogeneities of the medium and fictitious electric and magnetic sources. Types of inhomogeneities considered are roughness and bulk inhomogeneities and concern both permittivity and permeability. The numerical results are compared to those given in previous papers for optical scattering. It is shown in the microwave spectra that angle-resolved scattering allows identification of the scattering origins (permittivity or permeability spectra). The cases of isotropic films and metamaterials are presented and discussed.

Casimir forces for inhomogeneous planar media

Casimir forces arise from vacuum fluctuations. They are fully understood only for simple models, and are important in nano- and microtechnologies. We report our experience of computer algebra calculations towards the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases confidence in any results obtained, and use this methodology to demonstrate that the analytic derivation of scalar Green's functions is at the boundary of current computer algebra technology. We further demonstrate that Lifshitz theory of electromagnetic vacuum energy can not be directly applied to calculate the Casimir stress for models of this type, and produce results that have led to alternative regularisations. Using a combination of our new computational framework and the new theory based on our results, we provide specific calculations of Casimir forces for planar dielectrics having permittivity that declines exponentially. We discuss the relative strengths and weaknesses of computer algebra systems when applied to this type of problem, and describe a combined numerical and symbolic computational framework for calculating Casimir forces for arbitrary planar models.

Accelerated Direct Solution of the Method-of-Moments Linear System

This paper addresses the direct (noniterative) solution of the method-of-moments (MoM) linear system, accelerated through block-wise compression of the MoM impedance matrix. Efficient matrix block compression is achieved using the adaptive cross-approximation (ACA) algorithm and the truncated singular value decomposition (SVD) postcompression. Subsequently, a matrix decomposition is applied that preserves the compression and allows for fast solution by backsubstitution. Although not as fast as some iterative methods for very large problems, accelerated direct solution has several desirable features, including: few problem-dependent parameters; fixed time solution avoiding convergence problems; and high efficiency for multiple excitation problems [e.g., monostatic radar cross section (RCS)]. Emphasis in this paper is on the multiscale compressed block decomposition (MS-CBD) algorithm, introduced by Heldring , which is numerically compared to alternative fast direct methods. A new concise proof is given for the N2 computational complexity of the MS-CBD. Some numerical results are presented, in particular, a monostatic RCS computation involving 1 043 577 unknowns and 1000 incident field directions, and an application of the MS-CBD to the volume integral equation (VIE) for inhomogeneous dielectrics.

Modeling Proteins and Small Molecules with Inhomogeneous Dielectric Function: Implementation in Delphi

Most implicit solvent models treat bio-molecules as homogeneous dielectric medium inside high dielectric water phase. However, the dielectric distribution inside biological macromolecules is non-homogeneous, which depends on various factors, such as amino acid composition, structure, packing and flexibility. Many approaches have been developed to model the inhomogeneous dielectric distribution in biomolecules, including amino acid specific dielectric constant, using non-typical probe radius in finite-difference algorithm or delivering the dielectric constant from Gaussian distribution of atomic densities. Here, in DelPhi program, we developed an inhomogeneous dielectric method based on Gaussian smooth function. We tested this new method on calculating the solvation energies of 504 small molecules and the results show the method achieves better accuracy of the solvation energy calculation than homogeneous dielectric methods. Other tests on real proteins demonstrate that our inhomogeneous dielectric method is more reliable than homogeneous dielectric method for pKa and electrostatic potential calculations.

Analysis of Arrays of Printed Strip Dipole Antennas and Broadband Antennas of Six Series Fed Strip Dipoles

Dipole antennas are suitable in wireless multi-band technology, because they are simple to design and have excellent radiation properties. Also, it is well known that analysis of series-fed strip dipoles antennas are very hard to do because of the presence of dielectric inhomogeneity. In addition, the strip dipoles are closely spaced and connected through transmission lines that are integral part of the antenna. Therefore, an analysis method that takes into account the presence of dielectric substrate and the effect of connecting lines is presented to accurately design these antennas. In this paper, arrays of printed strip dipoles antennas are analyzed based on moment method in the spectral domain. The double-sided configuration has been selected because it offers several practical advantages. In this paper, further we will complicate the analysis by taking into account broadband antennas comprised of six series fed strip dipoles.

Effects of dielectric inhomogeneity in polyelectrolyte solutions

We illustrate the effects of dielectric inhomogeneity on the statistical properties of polyelectrolytes in solution, by a lattice Monte Carlo simulation that combines the bond fluctuation model with a local algorithm for computing the electrostatic interactions. Our model accounts for the difference in the dielectric properties between the polymer backbone and the solvent. Taking the coil–globule transition of a single polyelectrolyte chain in solvent as an example, we show that the chain conformation and the degree of counterion condensation are substantially affected by the dielectric contrast.

Far field model for time reversal and application to selective focusing on small dielectric inhomogeneities

Based on the time-harmonic far field model for small dielectric inclusionsin $3$D, we study the so-called DORT method (DORT is the French acronymfor ``Diagonalization of the Time Reversal Operator'').The main observation is to relate the eigenfunctions of thetime-reversal operator to the location of small scattering inclusions.For non penetrable sound-soft acoustic scatterers, this observation has been rigorouslyproved for $2$ and $3$ dimensions by Hazard and Ramdani in [21] for small scatterers.In this work, we consider the case of small dielectric inclusions with far field measurements.The main difference with the acoustic case is related to the magnetic permeability and the related polarization tensors. We show that in the regime $kd\rightarrow \infty$ ($k$ denotes here the wavenumber and $d$ the minimal distance between the scatterers), each inhomogeneity gives rise to -at most- 4 distinct eigenvalues (one due to the electric contrast and three to the magnetic one) while each corresponding eigenfunction generates an incident wave focusing selectively on one of the scatterers. The method has connections to the MUSIC algorithm known in Signal Processing and the Factorization Method of Kirsch.