Inhomogeneous Dielectrics Research Articles

Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics

The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described macroscopically by a position-dependent dielectric function and the atoms as microscopic harmonic oscillators. We identify and discuss the role of several types of Green tensors that describe the spatio-temporal propagation of field operators. After integrating out the atomic degrees of freedom, a multiple-scattering formalism emerges in which an exact Lippmann-Schwinger equation for the electric field operator plays a central role. The equation describes atoms as point sources and point scatterers for light. First, single-atom properties are calculated such as position-dependent spontaneous-emission rates as well as differential cross sections for elastic scattering and for resonance fluorescence. Secondly, multiatom processes are studied. It is shown that the medium modifies both the resonant and the static parts of the dipole-dipole interactions. These interatomic interactions may cause the atoms to scatter and emit light cooperatively. Unlike in free space, differences in position-dependent emission rates and radiative line shifts influence cooperative decay in the dielectric. As a generic example, it is shown that near a partially reflecting plane there is a sharp transition from two-atom superradiance to single-atom emission as the atomic positions are varied.

Noncontact Temperature Measurement on Dielectrics and Semiconductors, Part 1

A review is presented of the spectral and temperature dependence of optical properties for homogeneous and inhomogeneous dielectrics and semiconductors, including organic substances and polymers. Emphasis is placed on the surface pyrometry of homogeneous dielectrics in their opaque region, as well as on the pyrometry of a uniform-temperature plane homogeneous dielectric layer.

Sensitivity of Homogeneity Mapping of Semiconducting Wafer Using Millimeter Waves

The homogeneity mapping by measuring the phase or the amplitude of millimeter wave reflected from or transmitted through the semiconducting wafer is considered. The sensitivity of the conductivity homogeneity mapping is determined and conditions at which conductivity inhomogeneities can be distinguished from dielectric constant inhomogeneities are established.

Field quantization in inhomogeneous absorptive dielectrics

The quantization of the electromagnetic field in a three-dimensional inhomogeneous dielectric medium with losses is carried out in the framework of a damped-polariton model with an arbitrary spatial dependence of its parameters. The equations of motion for the canonical variables are solved explicitly by means of Laplace transformations for both positive and negative time. The dielectric susceptibility and the quantum noise-current density are identified in terms of the dynamical variables and parameters of the model. The operators that diagonalize the Hamiltonian are found as linear combinations of the canonical variables, with coefficients depending on the electric susceptibility and the dielectric Green function. The complete time dependence of the electromagnetic field and of the dielectric polarization is determined. Our results provide a microscopic justification of the phenomenological quantization scheme for the electromagnetic field in inhomogeneous dielectrics.

Multilevel Fast Multipole Method Solution of Volume Integral Equations Using Parametric Geometry Modeling

We present a multilevel fast multipole method (MLFMM) solution for volume integral equations dealing with scattering from arbitrarily shaped inhomogeneous dielectrics. The solution accuracy, convergence, computer time and memory savings of the method are demonstrated. Previous works have employed the MLFMM for impenetrable targets. In this paper, we integrate the MLFMM with the volume integral equation method for scattering by inhomogeneous targets. Of particular importance is the use of curvilinear elements for better volume representation and the use of simple basis functions for ease of parallelization.

Boundary layer techniques for solving the Helmholtz equation in the presence of small inhomogeneities

We consider solutions to the Helmholtz equation in two and three dimensions. Based on layer potential techniques we provide for such solutions a rigorous systematic derivation of complete asymptotic expansions of perturbations resulting from the presence of diametrically small inhomogeneities with constitutive parameters different from those of the background medium. It is expected that our results will find important applications for developing effective algorithms for reconstructing small dielectric inhomogeneities from boundary measurements.

Computing induced charges in inhomogeneous dielectric media: application in a Monte Carlo simulation of complex ionic systems.

The efficient calculation of induced charges in an inhomogeneous dielectric is important in simulations and coarse-grained models in molecular biology, chemical physics, and electrochemistry. We present the induced charge computation (ICC) method for the calculation of the polarization charges based on the variational formulation of Allen et al. [Phys. Chem. Chem. Phys. 3, 4177 (2001)]. We give a different solution for their extremum condition that produces a matrix formulation. The induced charges are directly calculated by solving the linear matrix equation Ah=c, where h contains the discretized induced charge density, c depends only on the source charges-the ions moved in the simulation-and the matrix A depends on the geometry of dielectrics, which is assumed to be unchanged during the simulation. Thus, the matrix need be inverted only once at the beginning of the simulation. We verify the efficiency and accuracy of the method by means of Monte Carlo simulations for two special cases. In the simplest case, a single sharp planar dielectric boundary is present, which allows comparison with exact results calculated using the method of electrostatic images. The other special case is a particularly simple case where the matrix A is not diagonal: a slab with two parallel flat boundaries. Our results for electrolyte solutions in these special cases show that the ICC method is both accurate and efficient.

Engineering the next generation of large-area displays: prospects and pitfalls.

Considerable effort is currently expounded on the development and improvement of the myriad display technologies that have come to the market place. In this paper, several key questions are addressed in the development of the future generation of large-area field-emission-based displays based on semiconducting amorphous carbon thin films and carbon nanotubes (CNTs). The development of carbon-based cathodes has to date proceeded along empirical lines, with attempts to correlate the variation of field-emission characteristics with changes in deposition or post-deposition processing parameters, often without a full explanation being forthcoming. In addition, there have been incidents of incorrect interpretation of some of the results, due to a lack of appreciation of the significant differences between the different types of amorphous carbon film that exist. It is only recently that a fuller understanding of the different electron-emission mechanisms has begun to emerge through an understanding of the roles played by the electrical and structural inhomogeneity at nanometre level. This 'intrinsic dielectric inhomogeneity' is shown to possess some remarkable electronic properties, which also have important consequences for extrinsic inhomogeneous nanometre systems such as CNT and CNT-polymer-composite-based displays. The future outlook for broad-area displays based on amorphous carbon and CNTs is also addressed.

Broadband nonreflecting properties of thin inhomogeneous coatings for arbitrarily polarized electromagnetic waves in a wide range of angles of incidence

In the electrodynamics of inhomogeneous dielectrics, a new model that allows an exact solution is proposed. The fields of s-and p-polarized waves are determined for the case of their propagation through a layer with a monotonic distribution of the dielectric constant, as well as with a nonmonotonic distribution characterized by two free parameters. Inhomogeneous coatings of this kind are shown to exhibit nonreflecting properties under arbitrarily polarized waves incident at arbitrary angles.

Quantum approach to electromagnetic energy transfer between two dielectric bodies

The problem of radiative heat transfer between two dielectric bodies is analyzed from the point of view of elementary quantum electrodynamics. The dielectric properties of the bodies are assumed to be linear, but dispersion and losses are allowed. Quantization of the electromagnetic field in inhomogeneous, dispersive, and lossy dielectrics is performed with the help of the Huttner-Barnett procedure. The electromagnetic energy flux is expressed through the expectation value of the Poynting vector. In order to compute the Poynting vector, two techniques suitable for nonequilibrium processes are employed: the Heisenberg equations of motion and the diagrammatic Keldysh procedure. They are shown to give identical final results. These quantum-mechanical calculations provide a solid basis for the further, mainly numerical, development of the theory of thermal scanning microscopy.

Brownian dynamics simulations of ion atmospheres around polyalanine and B-DNA: effects of biomolecular dielectric.

We have extended an earlier Brownian dynamics simulation algorithm for simulating the structural dynamics of ions around biomolecules to accommodate dielectric inhomogeneity. The electrostatic environment of a biomolecule immersed in water was obtained by numerically solving the Poisson equation with the biomolecule treated as a low dielectric region and the solvent treated as a high dielectric region. Instead of using the mean-field type approximations of ion interactions as in the Poisson-Boltzmann model, the ions were treated explicitly by allowing them to evolve dynamically under the electrostatic field of the biomolecule. This model thus accounts for ion-ion correlations and the finite-size effects of the ions. For a 13-residue alpha-helical polyalanine and a 12-base-pair bp B-form DNA, we found that the choice of the dielectric constant of the biomolecule has much larger effects on the mean ionic structure around the biomolecule than on the fluctuational and dynamical properties of the ions surrounding the biomolecule.

Role of nanostructure on electron field emission from amorphous carbon thin films

The mechanism of electron field emission from different forms of amorphous carbon (a-C) thin films is discussed. We show that it is possible to explain electron emission from a variety of amorphous carbon films by understanding the nature of electron states near the Fermi level. The films can be described as consisting of conductive sp2 C clusters lying within a more insulating sp3 C matrix. We show that the trend in the threshold field for emission can be explained in terms of improvements in the connectivity between these sp2 clusters and that cluster concentration and size can be in turn controlled by the choice of deposition conditions. The presence of the dielectric inhomogeneity between the two regions of sp2 clusters and sp3 C matrix is also shown to be very important in understanding the apparently low barrier heights that appear in the analysis of the current-voltage emission characteristics using the Fowler–Nordheim theory. This article attempts to set the framework for a unified model for electron emission from carbon films.

Electromagnetic scattering by small dielectric inhomogeneities

In this work we carefully derive accurate asymptotic expansions of the electric and magnetic fields, the resonant frequencies, and the scattering amplitude in the practically interesting situation, where a number of dielectric objects of small diameter and with different material characteristics are imbedded in an otherwise smooth medium.

Effects of stress on electron emission from nanostructured carbon materials

The electron field emission properties of highly graphite like (sp2 rich) amorphous carbon films have been investigated. These films were prepared by dual ion beam-assisted deposition technique, where the assisting energies were varied from 0 to 800 eV. Threshold fields as low as 8 V/μm is observed at an assisting energy of 400 eV, which is comparable to the best threshold fields observed in high sp3 carbon films. Surface nanostructures are found on these films during growth, but are thought not to be the primary reason for the observed low threshold fields. The combination of a highly graphite-like structure with a high intrinsic compressive stress and a high local (electronic) density, obtained from x-ray photoelectron spectroscopy, is identified as the source for the field enhancement. The controllable stress is thought to modify the band structures of the graphite-like sp2 rich component in the films, which results in high dielectric inhomogeneity. This analysis is in agreement with the concept of an internal or nongeometric field enhancement from sp2 nanostructures within the carbon thin films. The effect of stress induced band structure modification can also be extended to explain the field emission behavior of carbon nanotubes under stress.

Numerical methods for locating small dielectric inhomogeneities

We present numerical simulations illustrating the reconstruction of data for electromagnetic inverse problems. Two situations are considered: prescribed electric field and measured magnetic field at the boundary of a medium with cylindrical symmetries, and the analysis of the far field pattern of a scattered field produced by the incidence of an incoming wave on a set of small inhomogeneities.

Correction of order three for the expansion of two dimensional electromagnetic fields perturbed by the presence of inhomogeneities of small diameter

The derivation of the correction of order 3 for the expansion of 2 dimensional electromagnetic fields perturbed by the presence of dielectric inhomogeneities of small diameter was completed in [3]. However previous numerical work such as that in [6] and in [14] do not corroborate the existence of these correcting terms. The inhomogeneities used in all those numerical simulations were collections of ellipses. In this paper we propose to elucidate this discrepancy. We prove that the correction of order 3 is zero for any inhomogeneity that has a center of symmetry. We present numerical experiments for asymmetric inhomogeneities. They illustrate the importance of the correction of order 3. Finally we prove that numerical schemes based on the usual quadrature for solving mixed linear integral equations on a smooth contour with smooth integration kernels and kernels involving logarithmic singularities preserve at the discrete level the fact that correcting terms of order 3 are zero for inhomogeneities that are symmetric about their center.

Enhancing the electrical conduction in amorphous carbon and prospects for device applications

The problems and possible solutions associated with producing practical electronic devices based upon amorphous carbon (a-C) thin films are discussed. The clustering of the carbon sp 2 phase is shown to be a critical aspect in understanding the current device limitations. In order to exploit the sp 2 clustering we show that the use of ion beams to deposit energy into the microstructure in a controlled manner, as opposed to conventional thermal anneal treatments, results in a delocalised electron wavefunction and an enhancement of conductivity. A barrier controlled device is demonstrated by carefully choosing the ion energy and dose. One of the consequences of ion implantation is that film can now be considered as consisting of conductive sp 2 C clusters within an insulating sp 3 C matrix. We show that the presence of this dielectric inhomogeneity between the conductive sp 2 regions and the sp 3 matrix plays an important role in understanding the field emission behaviour from a-C based materials.

Dielectric Response of Soft Modes in Ferroelectric Thin Films

The concept of effective soft mode in thin films and its role in the effective dielectric response of high-permittivity thin films is introduced. Compared to bulk soft mode response, it may be strongly influenced by stresses from the substrate and dielectric inhomogeneities like interface layers, grain boundaries and porosity. The available techniques for the determination of the effective soft-mode response (far-infrared and time-domain THz spectroscopies) are discussed. The experiments on various ferroelectric (PbTiO 3, PZT, BaTiO 3, SrBi 2 Ta 2 O 9 ), incipient ferroelectric (SrTiO 3 ), doped incipient ferroelectric (SrTiO 3 :Ba), and relaxor ferroelectric (PLZT) films are briefly reviewed and compared with the results in bulk materials.

Properties of the Generalized Polarization Tensors

Generalized polarization tensors (GPTs) are employed for the derivation of full asymptotic expansions of the perturbations in the steady-state voltage potentials that are due to the presence of dielectric inhomogeneities of small diameter. In this paper we investigate some important properties of these GPTs such as symmetry, positivity, and their relations to the Dirichlet-to-Neumann map and weighted volume. It is expected that these results will find important applications not only for developing efficient algorithms for identifying dielectric inhomogeneities of small diameter but as well for optimizing properties of dilute composite materials.

Recovery of Small Inhomogeneities from the Scattering Amplitude at a Fixed Frequency

We rigorously derive the leading order term in the asymptotic expansion of the scattering amplitude of a collection of a finite number of dielectric inhomogeneities of small diameter. We then apply this asymptotic formula for the purpose of identifying the location and certain properties of the shapes of the small inhomogeneities from scattering amplitude measurements at a fixed frequency. Our main idea is to reduce this reconstruction problem to the calculation of an inverse Fourier transform.