Dielectric Half-space Research Articles

Potential distribution and field intensity for a hyperboloidal probe in a uniform field

The scalar potential and electric field distributions in the gap region of a probe-substrate system are calculated. The probe, modeled as a dielectric medium with the geometry of a one sheeted hyperboloid of revolution, is located above a charged substrate surface which is modeled as a dielectric half space interfaced with a uniform surface charge density. The potential and field distributions are then calculated as functions of the dielectric constant of the medium filling the space between the tip and the surface, and as functions of the hyperboloidal shape parameter. Comparisons are made with the case of a dielectric spheroidal body. The analytical results attained can be used to study other related quantities such as energy density or Coulomb interaction in the neighborhood of the nanometer sized apex region without resorting to numerical methods. This investigation allows for tip shape related field variation in various dielectric media to be studied. Application of this approach to modeling probe tip-sample (probe tip-substrate) interaction in scanning probe microscopy, or to modeling dielectric breakdown processes, are examples of the potential use of the method.

Multifrequency reconstruction of moderately rough interfaces via quasi-ray Gaussian beams

In this paper, we present a new technique for determining the surface profile of a moderately rough interface between air and a homogeneous dielectric half-space. Based on sparsely sampled step-frequency ground penetrating radar measurements, the proposed inversion scheme uses a quasi-ray Gaussian beam fast forward model, coupled with a low-order parameterization of the surface profile in terms of B-splines. The profile estimation problem is posed as a parameter optimization problem, which is solved using a multiresolution continuation method via frequency hopping. Numerical experiments establish that the algorithm is efficient and yields accurate reconstructions throughout most of the illuminated region even in noisy environments, losing accuracy only in regions with very weak illumination.

Electrostatic force density for a scanned probe above a charged surface

The Coulomb interaction of a dielectric probe tip with a uniform field existing above a semi-infinite, homogeneous dielectric substrate is studied. The induced polarization surface charge density and the field distribution at the bounding surface of the dielectric medium with the geometry of half of a two sheeted hyperboloid of revolution located above the dielectric half space interfaced with a uniform surface charge density is calculated. The force density on the hyperboloidal probe medium is calculated as a function of the probe tip shape. The calculation is based on solving Laplace’s equation and employing a newly derived integral expansion for the vanishing dielectric limit of the potential. The involved numerical simulations comprise the evaluation of infinite double integrals involving conical functions.

Complex natural resonances of conducting planar objects buried in a dielectric half-space

A scheme is presented to incorporate a mixed potential integral equation (MPIE) using Michalski's formulation C with the method of moments (MoM) for analyzing the scattering of a plane wave from conducting planar objects buried in a dielectric half-space. The robust complex image method with a two-level approximation is used for the calculation of the Green's functions for the half-space. To further speed up the computation, an interpolation technique for filling the matrix is employed. While the induced current distributions on the object's surface are obtained in the frequency domain, the corresponding time domain responses are calculated via the inverse fast Fourier transform (FFT). The complex natural resonances of targets are then extracted from the late time response using the generalized pencil-of-function (GPOF) method. The authors investigate the pole trajectories as they vary the distance between strips and the depth and orientation of single, buried strips. The variation from the pole position of a single strip in a homogeneous dielectric medium was only a few percent for most of these parameter variations.

Static van der Waals interactions in electrolytes

Using a field-theoretic formalism, we calculate the static contribution to the van der Waals interaction between two dielectric semi-infinite half-spaces in the presence of mobile salt ions. The ions can be located in the slab, in one, or in both half-spaces. We include an excess polarizability of the salt ions, i.e., each (spherical) ion has a dielectric constant which in general is different from the surrounding medium. This leads to a modification of the effective dielectric constant of the medium hosting the ions. This shift can be large for high salt concentrations and therefore influences the Hamaker constant decisively. Salt ions in the slab screen the static van der Waals interaction, as was shown by Davies and Ninham. The salt-modified van der Waals interaction also contains salt-confinement and salt-correlation effects. This is clearly demonstrated by the fact that the interaction is non-zero even in the case when the dielectric constant is homogeneous throughout the system, in which case salt correlations are solely responsible for the interaction. If the salt ions are in one or both of the two half-spaces (and no ions in the slab), the van der Waals interaction is not screened but the effective Hamaker constant approaches a universal value for large slab thickness which is different from the value in the absence of salt ions and which is independent of the salt concentration and of the effective electrolyte dielectric constant. If both half-spaces contain salt, the asymptotic value of the Hamaker constant for large separation between the half-spaces is the one obtained for the interaction between two metallic half-spaces through an arbitrary dielectric medium, which is given by A≃ - 1.20. As is explicitly demonstrated, ion enrichment or depletion at the interfaces due to image-charge effects is already included on the one-loop level and therefore does not lead to a change of the screened van der Waals interaction as given by Davies and Ninham. For positive and negative ions with different valencies or different excess polarizabilities, we obtain different adsorbed surface excesses of positive and negative ions, leading to a non-vanishing surface potential, which is computed explicitly. All of these results are obtained on the linear one-loop level. For a special case we extend the calculation of the dispersion interaction to the two-loop level. We find the corrections to the one-loop results to be quite large for high salt concentrations or multivalent ions.

Efficient evaluation of the half‐space Green's function for fast‐multipole scattering models

AbstractThere has recently been significant interest in the method‐of‐moments (MoM) and fast multipole method (FMM) for the analysis of scattering from targets in the presence of a lossy dielectric half space (soil). It is desirable to make the analysis of scattering from such a target consistent with use of the free‐space Green's function, to exploit previously developed free‐space scattering models, and for compatibility with the FMM. In this paper, we present a new and simple formulation for Green's‐function evaluation, which is shown to yield efficient and highly accurate scattering results. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 388–392, 2001.

Electromagnetic analysis of an antenna embedded in a composite environment

This paper addresses the problem of an antenna embedded in a hole dug in the ground. The composite medium configuration consists of a half-space dielectric (representing the Earth-air interface) containing a cylindrical hole filled with a different dielectric medium. The wire antenna resides within this hole, on the axis. The solution strategy is based on decomposing the problem into simpler subproblems, which are treated sequentially. First we calculate a numerical dyadic Green's function for the composite medium by solving an integral equation formulated over a background consisting of the unperturbed dielectric half space (for which the Green's functions are known in a spectral integral form). This integral equation is solved via the fictitious currents method, which is a special case of the method of moments. We then solve the integral equation for the antenna currents using this numerical Green's function and determine the input impedance and radiation pattern.

Optical interconnects realizable with thin–film helicoidal bianisotropic mediums

Parallel–plate waveguides consisting of a thin–film helicoidal bianisotropic medium (TFHBM) layer bounded by dielectric half–spaces are shown to support guided wave propagation with guide wavenumbers dependent on the direction of signal propagation. Thus, the TFHBM interconnect behaves as a space–guide . The modal fields and power transmission distributions, as determined by the time-averaged Poynting vector, are investigated and a scheme classifying each guided wave mode as either hybrid electric or hybrid magnetic is presented.

Scattering from lossy dielectric objects buried beneath randomly rough ground: validating the semi-analytic mode matching algorithm with 2-D FDFD

A new semi-analytic mode matching (SAMM) algorithm is verified by two-dimensional (2-D) finite difference frequency domain (FDFD) simulations of scattering resulting from uniform plane waves incident on randomly rough dielectric half-spaces containing buried dielectric targets. The SAMM algorithm uses moderately low-order modal superpositions of cylindrical waves, each of which satisfies the 2-D-Helmholtz equation in its appropriate region (air, ground, or mine) and then matches all nonzero electric and magnetic field components at each interface by inverting a highly overconstrained dense linear matrix equation by singular value decomposition. That is, the set of cylindrical mode coefficients is found which best fits the boundary conditions in a least squares sense. For smooth ground, coordinate scattering centers (CSCs) are chosen at the mine center and at its image above the plane to model scattering. For randomly rough ground, additional CSCs are located within the rough boundary layer. Excellent agreement between 2-D-FDFD and the 2-D version of SAMM is observed, with 2-D-SAMM being at least an order of magnitude faster. 3-D-SAMM is estimated to be four orders of magnitude faster than 3-D-FDFD, with drastically reduced memory requirements.

Quantum electrodynamics of an atom in front of a non–dispersive dielectric half–space. II. Effects of finite temperature

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Wu Shin-Tza and Eberlein Claudia 2000Quantum electrodynamics of an atom in front of a non–dispersive dielectric half–space. II. Effects of finite temperatureProc. R. Soc. Lond. A.4561931–1951http://doi.org/10.1098/rspa.2000.0595SectionRestricted accessQuantum electrodynamics of an atom in front of a non–dispersive dielectric half–space. II. Effects of finite temperature Shin-Tza Wu Shin-Tza Wu Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK Google Scholar Find this author on PubMed Search for more papers by this author and Claudia Eberlein Claudia Eberlein Sussex Centre for Optical and Atomic Physics, University of Sussex, Falmer, Brighton BN1 9QH, UK Google Scholar Find this author on PubMed Search for more papers by this author Shin-Tza Wu Shin-Tza Wu Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK Google Scholar Find this author on PubMed Search for more papers by this author and Claudia Eberlein Claudia Eberlein Sussex Centre for Optical and Atomic Physics, University of Sussex, Falmer, Brighton BN1 9QH, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 August 2000https://doi.org/10.1098/rspa.2000.0595AbstractThe energy–level shifts of an atom located at a distance Z outside a dielectric half–space are calculated at finite temperatures. The refractive index of the medium is real and frequency independent; the limiting case of perfect reflectors is also considered. The analytic expressions for the energy–level shifts are analysed in various regimes of temperature and of the distance of the atom from the surface. The significance of thermal corrections in comparison with zero–temperature effects is analysed in each regime and discussed for recent experiments. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Haug T, Buhmann S and Bennett R (2019) Casimir-Polder potential in the presence of a Fock state, Physical Review A, 10.1103/PhysRevA.99.012508, 99:1 Zhou W and Yu H (2018) Boundarylike behaviors of the resonance interatomic energy in a cosmic string spacetime, Physical Review D, 10.1103/PhysRevD.97.045007, 97:4 Bimonte G and Emig T (2015) Interplay of curvature and temperature in the Casimir–Polder interaction, Journal of Physics: Condensed Matter, 10.1088/0953-8984/27/21/214018, 27:21, (214018), Online publication date: 3-Jun-2015. Sernelius B (2014) Electromagnetic normal modes and Casimir effects in layered structures, Physical Review B, 10.1103/PhysRevB.90.155457, 90:15 Wu P and Yu H (2014) Thermal dispersion potential of a diamagnetic atom, Physical Review A, 10.1103/PhysRevA.90.032502, 90:3 Zhou W and Yu H (2014) Energy shift and Casimir-Polder force for an atom out of thermal equilibrium near a dielectric substrate, Physical Review A, 10.1103/PhysRevA.90.032501, 90:3 Zhu Z, Yu H and Wang B (2012) Temperature-dependent Casimir-Polder forces on polarizable molecules, Physical Review A, 10.1103/PhysRevA.86.052508, 86:5 Ellingsen S, Buhmann S and Scheel S (2012) Casimir-Polder energy-level shifts of an out-of-equilibrium particle near a microsphere, Physical Review A, 10.1103/PhysRevA.85.022503, 85:2 Buhmann S (2012) Introduction: Dispersion Forces Dispersion Forces I, 10.1007/978-3-642-32484-0_1, (1-43), . Buhmann S (2012) Thermal Casimir–Polder Forces Dispersion Forces II, 10.1007/978-3-642-32466-6_7, (213-262), . Ellingsen S, Buhmann S and Scheel S (2010) Casimir-Polder potential and transition rate in resonating cylindrical cavities, Physical Review A, 10.1103/PhysRevA.82.032516, 82:3 Ellingsen S, Buhmann S and Scheel S (2010) Temperature-Independent Casimir-Polder Forces Despite Large Thermal Photon Numbers, Physical Review Letters, 10.1103/PhysRevLett.104.223003, 104:22 Ellingsen S, Buhmann S and Scheel S (2009) Enhancement of thermal Casimir-Polder potentials of ground-state polar molecules in a planar cavity, Physical Review A, 10.1103/PhysRevA.80.022901, 80:2 Zhu Z and Yu H (2009) Modification of energy shifts of atoms by the presence of a boundary in a thermal bath and the Casimir-Polder force, Physical Review A, 10.1103/PhysRevA.79.032902, 79:3 Rosenblit M, Japha Y, Horak P and Folman R (2006) Simultaneous optical trapping and detection of atoms by microdisk resonators, Physical Review A, 10.1103/PhysRevA.73.063805, 73:6 Eberlein C and Wu S (2003) Methods of asymptotic analysis in cavity quantum electrodynamics, Physical Review A, 10.1103/PhysRevA.68.033813, 68:3 Henkel C, Joulain K, Mulet J and Greffet J (2002) Radiation forces on small particles in thermal near fields, Journal of Optics A: Pure and Applied Optics, 10.1088/1464-4258/4/5/356, 4:5, (S109-S114), Online publication date: 1-Sep-2002. This Issue08 August 2000Volume 456Issue 2000 Article InformationDOI:https://doi.org/10.1098/rspa.2000.0595Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/08/2000Published in print08/08/2000 License: Citations and impact Keywordsenergy-level shiftsfinite temperaturecavity quantum electrodynamicsCasimir{Polder effectLamb shifts

Fast computation of Green's functions for a lossy dielectric half-space

Dyadic Green's functions for a dielectric half-space, based on Formulation C, are computed by a fast algorithm using the discrete complex image method with a two-level approximation. The results show ver god agreement with those calculated by direct numerical integration. It is expected to be used for the analysis of radiation and scattering from targets buried underground. (C) 2000 John Wiley & Sons, Inc.

Corrections to "asymptotic solutions for the scattered fields of plane wave by a cylindrical obstacle buried in a dielectric half-space"

Corrections to "asymptotic solutions for the scattered fields of plane wave by a cylindrical obstacle buried in a dielectric half-space"

Efficient and accurate computation of an annular slot on a dielectric half-space

An efficient and accurate method of analysis for an annular slot radiating on a dielectric half-space is presented. The result involves neither singularity nor any numerical integration and, therefore, is computationally very efficient and easy to implement numerically. The method is very rigorous and general and should find applications in other related configurations.

Electromagnetic scattering from a layer of periodically distributed cylinders

An electromagnetic scattering model, which accounts for multiple scattering up to the second order, for a layer of periodically distributed cylinders over a dielectric half space is developed. This is based on the second-order analytical solutions for two adjacent cylinders. By applying the Monte Carlo simulation technique, the results show that the periodic distribution may have great effects on the scattering properties. A layer of cylinders over a ground plane can be used to model some vegetation canopies, and therefore, it is necessary to take the periodic effect into account for the theoretical scattering model of a vegetation canopy. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 24: 367–370, 2000.

Scattering of Electromagnetic Waves from a Deeply Buried Circular Cylinder

Utilizing an approximate induced current distribution, the far-zone scattered fields from a perfectly conducting, circular cylinder, which is deeply buried in a dielectric half-space are evaluated. Interpretation of these scattered fields is presented in terms of ray optics. Important scattering parameters, i.e., far-zone field patterns, 3dB beamwidth, scattering width and total scattered power are evaluated. It is found that monostatic scattering width of circular cylinder, which is deeply buried in a dielectric half-space configuration, is related to monostatic scattering width of circular cylinder in a homogeneous medium via dielectric constant times the fourth power of Fresnel transmission coefficient. Behaviour of the total scattered power as a function of depth is found to be oscillatory around a mean value which is the total power scattered from a cylinder in homogeneous medium.

Transient excitation of a layered dielectric medium by a pulsed electric dipole

We consider the transient excitation by a pulsed vertical or horizontal dipole of a continuously layered lossy dielectric slab embedded in between two dielectric half-spaces. The focus of the paper is on finding a highly efficient numerical implementation. To this end, we choose all spatial approximations independent of frequency. In the first place, this concerns the inverse spatial Fourier transformation in the Sommerfeld representation of the fields. A suitable quadrature rule is obtained by introducing a normalized wave number, and identifying the result in terms of dual analytic signals. In the second place, this concerns the spectral fields for which a new integral equation is derived with a degenerate kernel. This integral equation is solved by a fully recursive procedure. Representative results are presented and discussed that can be understood from physical intuition.

Transient analysis of two coupled horizontal wires over a real ground

Transient behaviour of two coupled wires immersed in a two-media configuration is analysed. The active wire is excited by a time-dependent voltage source. As the wires are identical, the symmetry of the configuration is expoited, and two coupled wires are considered as two single-wire problems. Each mode is represented by the corresponding space–time integral equation of the Hallen type. The effect of real ground is taken into account by the space–time reflection coefficient appearing within integral-equation kernels. The set of decomposed Hallen integral equations is solved by the direct time-domain finite-element technique, and the corresponding transient response is obtained. The computed numerical results are compared with the time-domain data obtained by solving the frequency-domain electric field integral equation for thin wires and with the aid of the Fourier transform approach. The mathematical model is applicable to an arbitrary ground, and numerical implementation and calculations are presented for lossless cases. Illustrative numerical results for transient current along the active and the parasitic wire are shown for the case of a perfectly conducting half-space and a dielectric half-space.

Iterative Step-Like Reconstruction of Stratified Dielectric Media from Multifrequency Reflected-Field Data

We describe in this paper a frequency domain microwave method to reconstruct the permittivity profile of layered dielectric half-space. The inversion algorithm is based on the iterative Newton–Kantorovitch procedure applied to the Riccati nonlinear differential equation. To obtain a correction term to the initial profile, the integral equation relating to a small change of the profile function and corresponding change of the reflection coefficient is solved twice, with different systems of expanding functions for the unknown profile. The first set of functions is utilized to determine positions of the reflecting interfaces between layers. The second set represented by the Heaviside step functions provides the profile correction term completing the iteration. The proposed approach is valid for the essentially band-limited input data, that is, when both low- and high-frequency information is not available. This alleviates practical implementation especially from the viewpoint of antenna design, dielectric rods fed by TEM horns are used as transmitting/receiving antennas. Some numerical and experimental examples are presented for the input data in the frequency range of 1–4GHz, which demonstrate validity and robustness of the method for the complicated highly contrasted dielectric profiles.

Quantum electrodynamics of an atom in front of a non–dispersive dielectric half–space

The energy–level shifts and the change in the rate of spontaneous emission are calculated for an atom located at a distance Z from a dielectric half–space. The dielectric is a non–dispersive and non–absorbing medium characterized by a constant real refractive index n . The explicit analytic formulae derived are applicable for arbitrary values of n . All results are analysed in the non-retarded and retarded limits, which apply to the atom being close to or far from the interface, respectively, i.e. to Z being small or large on the scale of a wavelength of a typical atomic transition. For ground-state atoms, the energy–level shift varies as 1/ Z 3 in the non–retarded regime and as 1/ Z 4 in the retarded regime, which agrees with the Casimir–Polder result for the limit n →α. For excited–state atoms, the energy–level shifts receive additional contributions that oscillate with the distance Z from the interface.

Fast multipole method for scattering from 3-D PEC targets situated in a half-space environment

The fast multipole method (FMM) is extended to the problem of an arbitrary, three-dimensional perfect conductor situated above or below a lossy, dielectric half space. The interactions between basis and testing functions within an FMM cluster, and for nearby clusters, are handled via the rigorous dyadic Green's function, with the latter evaluated efficiently using the complex-image technique. Intercluster interactions are modeled as in the free-space FMM, with the dyadic Green's function approximated via real images and equivalent reflection coefficients; these approximations have proven to be highly accurate. Example results are presented for a large trihedral fiducial target, in free space and above a lossy, dispersive half space, with comparisons presented between the FMM and a rigorous method-of-moments (MoM) solution. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21: 399–405, 1999.