Dielectric Half-space Research Articles

An electromagnetic scattering model for multiple tree trunks above a tilted rough ground plane

An efficient and complete electromagnetic scattering model for multiple tree trunks above the ground is presented. The individual trunks are modeled by finite-length stratified cylinders, with an external corrugated bark layer. The ground is modeled by a dielectric half space underneath the cylinders, with a slightly rough interface. The spatial distribution of the cylinders is random over an elliptic illuminated area, and their lengths follow a Gaussian distribution. Moreover, cylinders are randomly oriented with a variable degree of noncolinearity, and the ground can have an arbitrary orientation. The scattering results provided in this paper consider the summation of all scattered fields from the trunk-ground sets as a response to the incident field. Results have been computed for the mean square error of the bistatic scattering pattern, by means of a Monte Carlo simulation. The computed patterns are highly dependent on the geometry of the problem (lengths and radii of the trunks, tilting, surface roughness, incidence, and observation angles). The variability of the involved random parameters produces softening effects and an increased cross-polarized signal. Moreover, results are very sensitive to the dielectric characteristics of the trunks. As a result, the method can be useful in the interpretation of remote-sensing measurements from vegetation and in the development of classification schemes.

Multimode solution for the reflection properties of an open-ended rectangular waveguide radiating into a dielectric half-space: the forward and inverse problems

Open-ended rectangular waveguides are extensively used in nondestructive dielectric material evaluation. The dielectric properties of an infinite-half space of a material are calculated from the measured reflection properties referenced to the waveguide aperture. This calculation relies on a theoretical and numerical derivation of the reflection coefficient likewise referenced to the waveguide aperture. Most of these derivations assume the dominant mode field distribution across the waveguide aperture. However, when dealing with low permittivity and low loss dielectric materials, there may exist significant errors when calculating the dielectric properties from the measured reflection coefficient. These errors have also shown to be more significant in the upper frequency portion of a waveguide band. More accurate results are obtained when higher order modes are considered in addition to the dominant waveguide mode. However, most studies incorporating higher-order modes have used various approximations when calculating the reflection properties and have not provided a full discussion on the influences of dielectric properties of the infinite-half space and the frequency of operation. This paper gives a rigorous and exact formulation in which the dominant mode and the evanescent higher-order modes are used as basis functions to obtain the solution for the reflection coefficient at the waveguide aperture. The analytic formulation uses Fourier analysis in addition to the forcing of the necessary boundary conditions at the waveguide aperture. The solution also readily accounts for the complex contributions of both TE and TM higher-order modes. Finally, the influences of the dielectric properties of the infinite-half space and the frequency of operation are investigated.

The electromagnetic field near a dielectric half-space

We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform non-dispersive dielectric. This gives predictions for the Casimir-Polder force on an atom in the `retarded' regime near a dielectric. We also find a positive energy density due to the electromagnetic field. This would lead, in the case of two parallel dielectric half-spaces, to a positive, separation-independent contribution to the energy density, besides the negative, separation-dependent Casimir energy. Rough estimates suggest that for a very wide range of cases, perhaps including all realizable ones, the total energy density between the half-spaces is positive.

Green's function for the boundary-value problem of wave scattering by a dielectric halfspace at small grazing angles

Green's function for the boundary-value problem of wave scattering by a dielectric halfspace at small grazing angles

Transfer Relations for Electromagnetic Wave Scattering From Periodic Dielectric One-Dimensional Interface: Te Polarization

Some general statements for theory of wave multiple scattering in a three-dimensional inhomogeneous layered dielectric medium are established using the composition rule of the scattering (T-matrix) operators to show that the problem of wave scattering from dielectric interface may be studied similar to the problem of volume wave scattering. The medium is thought as being a stack of n layers, each of them is confined by perpendicular to the z axis planes and consists of a three-dimensional discrete or continuous inhomogeneous medium. The layers do not intersect between them and are embedded into a homogeneous background. A result of the paper is a mixed system of exact operator equations (transfer relations) for the operator wave reflection and transmission coefficients of the medium and the operator wave amplitudes of waves in splits between layers. It is shown that the transfer relations lead to a separate recurrent system of operator equations, which describe the incremental change of the operator wave reflection and transmission coefficients of stack of n - 1 layers upon attachment of a n's layer to the stack. We derive from this recurrent equations a generalized Riccati equation for the operator wave reflection coefficient of the medium and an corresponding equation for the operator wave transmission coefficient of the medium, the coefficients of the Riccati equation and the corresponding equation being expressed in terms of the operator wave reflection and transmission coefficients of a thin slice of the medium and embedding parameter being taken along the z axis. The derived Riccati equation is applied to the problem of electromagnetic wave reflection from a periodic one-dimensional interface of two dielectric half-spaces, the interface being varied in the x axis direction and the wave electric field vector being parallel to the y axis. A solution to the Riccati equation for this problem is found numerically, taking into account with the aid of the Bloch (Floquet) theorem both the propagating and evanescent waves and not invoking the Rayleigh hypothesis. A resonant effect related to the Wood anomalies is discussed.

Scattering of Electromagnetic Waves by Rough Interfaces and Inhomogeneous Layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

AXISYMMETRIC CHARGE DISTRIBUTIONS ON AN ELASTIC DIELECTRIC HALF SPACE

The solution of the axisymmetric boundary value problem of an isotropic elastic dielectric half space subjected to charge distribution on its rigid polarization free surface is constructed by Hankel transforms. For the problem of an electric point dipole applied at origin, exact expressions for the components of displacement and polarization vectors and the potential fields are obtained in terms of Bessel function and fundamental solutions 1/R and e-mR/R, R being the distance from the source point. The electric field is determined both inside and outside the polarized region. In the particular case of a continuous electric charge distribution with density of the form l/(r2+h2)1/2, the mechanical and electric stresses on the surface of the semi-space are derived. The MathematicsTM software is used to present the numerical results on graphs depicting the variation of surface stresses for the particular charge distributions.

Electromagnetic fields in air of traveling-wave currents above the earth

The problem of the electromagnetic field created by a thin, straight conductor of infinite length carrying a forward traveling-wave current with a complex propagation constant γ above a homogeneous and isotropic planar earth of wave number k1 is formulated in terms of contour integrals. In the limit where γ becomes equal to the free-space wave number k0, the component of the magnetic field in air normal to both conductor and interface is evaluated in closed form in terms of known special functions while the remaining components of the field in air are expressed as series expansions in δ=k02(k14−k04)−1/2 via the application of a contour integration technique. The new analytical formulas involve familiar transcendental functions and are valid at any distance from the source. The analysis sheds light on the intricate nature of low-frequency electromagnetic fields generated by transmission lines in the presence of a conducting or a dielectric half-space.

Quantum radiation from moving dielectrics in two, three, and more spatial dimensions

Quantum radiation from a moving dielectric semi-infinite half-space is investigated in a scalar model in two, three, and arbitrary integer spatial dimensions. The dielectric medium is non-dispersive and non-absorbing. The Hamiltonian describing the field in the presence of the moving dielectric body is obtained from considerations of Lorentz invariance. The field is quantized by an expansion into photon eigenmodes that are composed of incoming, reflected, and transmitted plane waves. The treatment includes total internal reflection and evanescent modes which are specific to dimensions . The Schrodinger equation for the state of the field is solved to first order in the velocity of the dielectric by a generalized adiabatic approximation. Non-uniform motion is found to lead to the emission of photon pairs whose spectrum and angular distribution are analysed in detail. The radiated energy and the radiation-reaction force are studied with particular emphasis to their dependence on the dimension of the system. In addition, the energy is worked out for several test trajectories.

Spontaneous emission from a dielectric slab

The electromagnetic field in a dielectric slab bounded by two dielectric half spaces with arbitrary refractive indices is quantized by computing the complete set of orthonormal electromagnetic modes. The zero-point fluctuations of the electromagnetic field are determined as a function of position. The dependence of the rate of spontaneous emission of thin dielectric films on the thicknesses of the films and the refractive index of the substrate is studied and compared with experimental results.

Theoretical analysis of coupling and cross polarization of perpendicular slot antennas on a dielectric half-space

In this paper, design curves are given for minimizing the coupling between two perpendicular slot antennas on a dielectric half space. Such antennas may be utilized in polarimetric receivers in which coupling must be minimized to ensure polarization purity and in polarization diplexed quasi-optical receivers in which the local oscillator (LO) is received in a polarization perpendicular to that of the RF signal. For this analysis, Galerkin's method in the spectral domain is applied along the length of the slots and point matching across their widths. At the second resonance, for equal length slots and for constant width/length (w/L) of the slots, there is a decrease of about 2-dB coupling for a factor of three increase in dielectric constant (/spl epsiv//sub 1/=1.0/spl rarr/3.8 and /spl epsiv//sub 1/=3.8/spl rarr/12.8). For fixed dielectric constant there is a 1-2-dB increase in coupling for a factor of two increase in w/L. For slots of unequal length (L/sub 2/=L/sub 1//2), the changes are even smaller. Design curves are shown for various relative positions of the slots in two dimensions. A strong correlation between coupling levels and peak cross-polarization levels is found.

Analytic expression for triple-point electron emission from an ideal edge

The electric field in the vicinity of a metallic edge attached to a dielectric half-space is calculated analytically. The resulting electric field is used to evaluate the current emitted from the edge using the Fowler-Nordheim formula. It is shown analytically that the emitted current is proportional to the dielectric coefficient of the material.

Scattering From a Layer of Vertical Cylinders Over a Dielectric Half Space

An electromagnetic scattering model for a layer of randomly distributed vertical long cylinders over a dielectric half space is developed in this paper, which takes into account multiple scattering terms up to second order. Closed-form expressions for the second-order scattering fields are derived for two adjacent cylinders in the near field of each other based on the reciprocity theorem and are validated by comparison with numerical results based on the moment method. By applying the Monte-Carlo simulation technique, the backscattering properties of a layer of conducting cylinders above a conducting ground plane and a layer of dielectric cylinders above a dielectric ground plane are studied. The simulation results show that the HH polarization solution is dominated by single scattering for the layer of cylinders whose diameters are fairly small and lengths are much long compared with the excitation wavelength. The secondary scattering shows great effect on the VV polarization results in the vicinity of the Brewster angle of dielectric cylinders. The simulation results are compared with those obtained by the radiative transfer (RT) method which is based on the addition of intensities and the comparison shows that the RT solutions could not give correct results for the medium composed of vertical long cylinders.

Influence of Losses in a Dielectric Half-Space on the Characteristics of a Reflected Three-Dimensional Pulsed Beam

Influence of Losses in a Dielectric Half-Space on the Characteristics of a Reflected Three-Dimensional Pulsed Beam

Square spiral antenna on dielectric half-space: Analysis using an electric field equation formulated by a finite–difference technique

A tangential electric field equation for a wire antenna on a dielectric half-space of relative permittivity ɛr is formulated using a finite-difference technique. This equation involves only single-integral calculations and is used to obtain the current distribution of a square spiral antenna. The validity of the current obtained is checked by FD-TD analysis. Based on the current distribution obtained, the radiation characteristics of the spiral are evaluated. It is found that the gain in the dielectric material is larger than that in free space, with a ratio of ɛr1.5 in the broadside directions. As ɛr increases, the circularly polarised radiation region bounded by the critical angles in the dielectric becomes narrower and the resistance value of the input impedance becomes lower.

Green's function refinement as an approach to radar backscatter: general theory and applications to LGA scattering from the ocean

We present a new approach to the computation of radar returns from dielectric bodies whose boundary is the deformation of a plane surface. The method relies on combining a systematic improvement in the Green's function with a good approximate choice of local boundary condition. In this paper, the general theory is presented together with a simple application where the Green's function is that for a lossy dielectric half-space. We derive the root radar cross section (RCS) for a statistical surface and the mean backscatter RCS for a rough surface. We explore the applications to low-grazing-angle (LGA) scattering from statistical surfaces with an ocean-like spectrum and demonstrate that such a model explains some of the previously unexplained LGA phenomena, such as the absolute and relative levels of the vertical (VV) and horizontal (HH) channel RCS measurements.

Te Scattering By a Cylindrical Dielectric Obstacle Buried in a Half-Space: a H-Field-Based Solution Method

Scattering of a transverse electric (TE) wavefield by an inhomogeneous lossy dielectric cylindrical obstacle embedded in a lossy dielectric half-space is investigated. The cylinder is of arbitrary cross-section, and its axis lies parallel to the interface. The formulation involves a domain integral equation of the field obtained by applying the Green's theorem to the appropriate Helmholtz wave equations. The convolution-correlation structure of the formulation is such that the discretized counterpart of the integral equation (provided by the application of a Method of Moments where the obstacle is divided into triangular patches and where the contrast and the H-field are expanded using two different basis functions) can be efficiently handled using a FFT-based conjugate gradient solver. The validity of the approach is illustrated by comparison with results found in the literature.

Transient Response of Resistively Loaded Straight Thin Wire in Half-Space Configuration

The transient behaviour of the resistively loaded wire antenna radiating in the presence of a lossy half-space is analyzed in the time domain. The mathematical model is based on a corresponding time domain Hallen integral equation. The influence of a lossy half-space is taken into account via the Fresnel space-time reflection coefficient appearing in the integral equation kernel. The resulting integral equation is then solved by the space-time finite element procedure. Numerical results for the current distribution along the wire are obtained for the case of dielectric half-space.

Distinctive features of a pulsed beam scattering on a plane surface (two-dimensional case)

A two-dimensional problem of scattering of pulsed beams having arbitrary time and spatial form on a plane surface of a lossy dielectric halfspace is solved. A pulsed beam has been modeled by letting an E- or H-polarized plane pulse with homogeneous front pass through a space filter. The reflected pulse is found using an expansion of the incident pulsed beam over time-harmonic plane waves.

Electrostatic image method for the anisotropic half space

Electrostatic image theory, well known for a point charge in front of an isotropic dielectric half space, is generalised to the case where the half space may be anisotropic, characterised by a symmetric and positive-definite permittivity dyadic. The theory is derived through Heaviside operational calculus involving manipulations with pseudodifferential operators. As a result, the image of a point charge is seen to consist of a point charge at the mirror image point plus a continuous distribution of surface charge filling an angular sector the apex of which lies at the image point. The surface charge is shown to obey a simple analytic law. The angle of the image sector depends on the amount of transverse anisotropy of the half space. For decreasing anisotropy, the angle becomes small and the angular image can be approximated by a quadrifilar line charge coinciding with the result recently obtained by these authors for the case of small anisotropy. Numerical tests confirm the validity of the image expression. The result can be readily applied to a wide variety of electrostatic problems involving sources and obstacles in front of an anisotropic half space, making a numerical development of a Green function for the anisotropic half space obsolete.