Dielectric Half-space Research Articles

A new integral equation method for direct electromagnetic scattering in homogeneous media and its numerical confirmation

In this paper, we derive a new integral equation method for direct electromagnetic scattering in homogeneous media and present a numerical confirmation of the new method via a computer simulation. The new integral equation method is based on a paper written by DeSanto [1], originally for scattering from an infinite rough surface separating homogeneous dielectric half-spaces. Here, it is applied to a bounded scatterer, which can be an ohmic conductor or a dielectric, with some simplification of the continuity conditions for the fields. The new integral equation method is developed by choosing the electric field and its normal derivative as boundary unknowns, which are not the usual boundary unknowns. The new integral equation method may provide significant computational advantages over the standard Stratton–Chu method [2] because it leads to a 50% sparse, rather than 100% dense, impedance (collocation) matrix. Our theoretical development of the new integral equation method is exact.

Direct-write electron-beam lithography of an IR antenna-coupled microbolometer onto the surface of a hemispherical lens

This article describes a method for performing direct-write lithography of an IR antenna-coupled microbolometer onto the surface of a hemispherical lens. Antennas on a dielectric half-space receive power more efficiently from the substrate side than from the air side. The use of a hemispherical lens facilitates reception through the substrate as well as elimination of trapped surface waves that would normally occur in the substrate. Using direct-write lithography onto the surface of the hemispherical lens eliminates the potential of an air gap between the antenna and lens. Additionally, the accuracy of alignment between the antenna and the center of the lens is controlled at the lithographic step. As a result, there is increased responsivity is observed in the antenna-coupled microbolometer when illuminated from the substrate-side compared to air-side illumination.

Angular radiation pattern of electric dipoles embedded in a thin film in the vicinity of a dielectric half space

We report measurements on the angular radiation pattern from an array of dye molecules embedded in a polymethylmethacrylate film deposited on a dielectric hemispherical lens. The radiation pattern is both highly structured and directed, with most of the power being radiated into the media having the higher refractive index. We also present a simulation of the far-field radiation pattern of a dipole embedded in a thin dielectric layer, which apparently has not been investigated before. The simulation matches the experimental results rather well.

Iterative reconstruction of dielectric rough surface profiles at fixed frequency

A new, simple and fast method is presented for determining the location and the shape of a one-dimensional rough interface between two lossy dielectric half-spaces. The reconstruction is obtained from a set of reflected field measurements for a single illumination by a plane wave at a fixed frequency. Through a special representation of the scattered field in the half-spaces above and below the interface in terms of a Fourier transform and a Taylor expansion the problem is first reduced to the solution of a system of two nonlinear operator equations. Then this system is solved iteratively by alternating between a linear equation for a spectral coefficient of the scattered wave and a linearization of a nonlinear equation for the surface profile. The numerical simulations show that the method yields satisfactory reconstructions for slightly rough surface profiles.

Quantum electrodynamics near a dielectric half-space

Radiative corrections in systems near imperfectly reflecting boundaries are investigated. As an example, the self-energy of an unbound electron close to a single surface is calculated at one-loop level. The surface is modeled by a nondispersive dielectric half-space of a constant refractive index $n$. In contrast to previous, perfectly reflecting models, the evanescent modes in the optically thinner medium are taken into account and are found to play a physically very important role. The Feynman propagator of the photon field is determined and given in two alternative representations, which include the evanescent modes either as a separate contribution or through analytic continuation and deformation of the integration path for the normal component of the complex wave vector $\mathbf{k}$. The evaluation of the self-energy diagram encounters a number of problems that are specific to the boundary dependence and to the imperfect reflection at the boundary. These problems and methods for their resolution are discussed in depth.

A quasi-planar incident wave excitation for time-domain scattering analysis of periodic structures

We present a quasi-planar incident wave excitation for time-domain scattering analysis of periodic structures. It uses a particular superposition of plane waves that yields an incident wave with the same periodicity as the periodic structure itself. The duration of the incident wave is controlled by means of its frequency spectrum or equivalently the angular spread in its constituting plane waves. Accuracy and convergence properties of the method are demonstrated by scattering computations for a planar dielectric half-space. Equipped with the proposed source a time-domain solver based on linear elements yields an error of roughly 1 percent for a resolution of 20 points per wavelength and second order convergence is achieved for smooth scatterers. Computations of the scattering characteristics for a sinusoidal surface and a random rough surface show similar performance.

Born expansion of the Casimir–Polder interaction of a ground-state atom with dielectric bodies

Within leading-order perturbation theory, the Casimir–Polder potential of a ground-state atom placed within an arbitrary arrangement of dispersing and absorbing linear bodies can be expressed in terms of the polarizability of the atom and the scattering Green tensor of the body-assisted electromagnetic field. Based on a Born series of the Green tensor, a systematic expansion of the Casimir–Polder potential in powers of the electric susceptibilities of the bodies is presented. The Born expansion is used to show how and under which conditions the Casimir–Polder force can be related to microscopic many-atom van der Waals forces, for which general expressions are presented. As an application, the Casimir–Polder potentials of an atom near a dielectric ring and an inhomogeneous dielectric half space are studied and explicit expressions are presented that are valid up to second order in the susceptibility.

A Novel Method for Determination of Dielectric Properties of Materials Using a Combined Embedded Modulated Scattering and Near-Field Microwave Techniques—Part II: Dielectric Property Recalculation

The use of combined embedded modulated scattering technique and near-field microwave nondestructive testing techniques is investigated as a novel method for evaluating the dielectric properties of a material. The forward formulation for determining the reflection coefficient at the aperture of a waveguide radiating into a dielectric half-space in which a PIN diode-loaded dipole (i.e., modulated scattering technique probe) is embedded was presented in Part I of this paper. Here, in Part II, the recalculation of the dielectric properties, using the results of the forward model, is presented along with some associated experimental results.

A Novel Method for Determination of Dielectric Properties of Materials Using a Combined Embedded Modulated Scattering and Near-Field Microwave Techniques—Part I: Forward Model

The use of combined embedded modulated scattering technique and near-field microwave nondestructive testing techniques is investigated as a novel method for evaluating the dielectric properties of a material. The forward formulation for determining the reflection coefficient at the aperture of a waveguide radiating into a dielectric half-space in which a PIN diode-loaded dipole (i.e., modulated scattering technique probe) is embedded is presented. This formulation is based upon calculating the near-field coupling between the waveguide and the dipole as a mutual impedance.

On the time-domain response of cole-cole dielectrics

We investigate time-domain electromagnetic pulse propagation in a dispersive lossy dielectric half-space whose properties are described in the frequency-domain by the Cole-Cole model ϵ(ω)=ϵ/sub ∞/+(ϵ/sub s/-ϵ/sub ∞/)/(1+(iωτ)/sup α/), 0<α<1. With asymptotic techniques we calculate the small-depth impulse response and determine it is infinitely smooth at the wavefront. This result contrasts the case of the Debye medium (α=1) in which the wavefront supports discontinuities that decay exponentially with depth. Then, with asymptotic and numerical methods we investigate the large-depth impulse response. We find that while the saddle-point method accurately predicts the space-time location of the peak of the response it is of limited applicability in the approximation of such response for times past the arrival of the peak. Significantly, we find the peak of the response for 0<α<1 arrives earlier than in the case of α=1. Our asymptotic results are validated with independent results obtained numerically.

Editorial Note: Electromagnetic field stress tensor between dielectric half-spaces [Phys. Rev. D72, 033001 (2005)

Editorial Note: Electromagnetic field stress tensor between dielectric half-spaces [Phys. Rev. D<b>72</b>, 033001 (2005)

Electromagnetic field stress tensor between dielectric half-spaces

The stress tensor for the quantized electromagnetic field is calculated in the region between a pair of dispersive, dielectric half-spaces. This generalizes the stress tensor for the Casimir energy to the case where the boundaries have finite reflectivity. We also include the effects of finite temperature. This allows us to discuss the circumstances under which the weak energy condition and the null energy condition can be violated in the presence of finite reflectivity and finite temperature.

Generalized optical theorem for reflection, transmission, and extinction of power for electromagnetic fields

We present a generalization of the optical theorem for electromagnetic fields. This result is used to obtain the power extinguished from a field by a scatterer contained in a dielectric half space. Applications to microscopy and tomography are described.

Time-Domain Modeling of Electromagnetic Field Coupling to Finite-Length Wires Embedded in a Dielectric Half-Space

The transient behavior of a single straight line embedded in a dielectric half-space and illuminated by the electromagnetic pulse (EMP) is analyzed directly in the time domain using the wire antenna approach. The formulation is based on the corresponding space-time Hallen integral equation. The effects of a two-media configuration are taken into account via the Fresnel reflection and transmission coefficient, respectively. The space-time Hallen integral equation is handled by the time-domain version of the indirect Galerkin-Bubnov boundary element method. The transient response obtained using the direct time-domain approach is compared with the results obtained via an indirect frequency-domain analysis method. Some illustrative numerical results are presented in the paper. Numerical results obtained via the different approaches agree satisfactorily, i.e., the maximum deviation between the results is around 6%.

Curvature effects in surface plasmon dispersion and coupling

We have studied the resonant coupling of surface plasmons in curved thin-film tunneling geometries by obtaining the dispersion relations for the system. The surface plasmon dispersion relations are calculated for a metal-coated dielectric probe above a dielectric half space with and without metal coating. The system is modeled in the prolate spheroidal system, and the dispersion relations are studied as functions of the parameter that defines the boundaries of the tip and the corresponding coating, and as functions of the involved coating thicknesses. Using this type of probe-substrate configuration, the nonradiative surface plasmon coupling mechanism is investigated in the visible spectrum at frequencies relevant to scanning probe microscopy. The simulations of the results predict optical access to the resonant surface modes of the system.

Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution

An analytical-numerical technique, for the solution of the two-dimensional electromagnetic plane-wave scattering by a finite set of perfectly conducting circular cylinders buried in a dielectric half-space, is presented. The problem is solved for both the near- and the far-field regions, for TM and TE polarizations. The diffracted field is represented in terms of a superposition of cylindrical waves and use is made of the plane-wave spectrum to take into account the reflection and transmission of such waves by the interface. The validity of the approach is confirmed by comparisons with results available in the literature, with very good agreement. The multiple interactions between two buried cylinders have been studied by considering both the induced currents and the scattered field diagrams. Applications of the method to objects of arbitrary cross-section simulated by a suitable configuration of circular cylinders are shown.

Fast solution of mixed-potential time-domain integral equations for half-space environments

A fast Fourier transform-accelerated integral-equation based algorithm to efficiently analyze transient scattering from planar perfect electrically conducting objects residing above or inside a potentially lossy dielectric half-space is presented. The algorithm requires O(N/sub t/N/sub s/(logN/sub s/+log/sup 2/N/sub t/)) CPU and O(N/sub t/N/sub s/) memory resources when analyzing electromagnetic wave interactions with uniformly meshed planar structures. Here, N/sub t/ and N/sub s/ are the numbers of simulation time steps and spatial unknowns, respectively. The proposed scheme is therefore far more efficient than classical time-marching solvers, the CPU and memory requirements of which scale as O(N/sub t//sup 2/N/sub s//sup 2/) and O(N/sub t/N/sub s//sup 2/). In the proposed scheme, all pertinent time-domain half-space Green functions are (pre) computed from their frequency-domain counterparts via inverse discrete Fourier transformation. In this process, in-band aliasing is avoided through the application of a smooth and interpolatory window. Numerical results demonstrate the accuracy and efficiency of the proposed algorithm.

Propagation of Radar Pulses from a Horizontal Dipole in Variable Dielectric Ground: A Numerical Approach

We numerically investigate the propagation of radar type short pulses from a horizontal dipole in the presence of some simple models of inhomogeneous ground with a flat surface. We use 3-dimensional (3-D) pseudospectral time domain (PSTD) and 2-D finite difference time domain forward modeling to determine the range and azimuth dependence of electric field components and to simulate events in a moveout profile. The models are: (i) a uniform half space with either high or low conductivity; (ii) a vertical dielectric wedge; (iii) a surface thin layer with a monocline wedge overlaid on the dielectric half space. Our homogeneous results agree with the analytical solutions, and more clearly show the significant vertical electric field component, which occurs for all models. The incorporation of an anomalous dielectric quadrant does not affect the air wave and only complicates ground wave propagation near the boundary. Modeling of a monocline dielectric wedge shows predictable subsurface reflections and refractions, some of which are highly dispersive events, depending on the direction of propagation. We present two field examples that appear to demonstrate some of our findings. We conclude that air waves make suitable references for moveout profiles regardless of dielectric complications, and that our results provide some insight into the interpretation of unique events seen in moveout profiles.

Propagation of Electromagnetic Pulse Onto a Moving Lossless Dielectric Half-Space: One-Dimensional Simulation Using Characteristic-Based Method

This paper provides one-dimensional numerical simulation results of the propagation of plane electromagnetic (EM) pulse onto a dielectric half-space that is constantly moving. The governing equations are numerically solved using characteristic-based method. The medium employed in the one-dimensional model is assumed to be homogeneous, isotropic, lossless, and linear, and moving with a constant velocity of one tenth of the light speed. The velocities of EM pulses inside moving media are investigated by comparing with the analytical values predicted by the theory of relativity. The effects of the moving dielectrics on the reflected and transmitted electric fields are examined by comparing them side-by-side. Also shown are the corresponding spectra.

Improved Analysis of the Coupling of Optical Waves into Multimode Waveguides Using Overlap Integrals

The optical multimode interconnection technology has become important due to increasing data rates in modern multi-processor systems. In this context, the coupling of optical waves into multimode waveguides has to be analyzed. Ray optical methods are preferred, but are not applicable for all geometries. As full-wave analysis using the mode matching technique is very extensive, we present a simple method based on overlap integrals, to calculate the coupling efficiency of impingingoptical waves. Our approach neglects reflected waves. The corresponding error is corrected by applying a transmission factor, which is that of a plane wave irradiating a dielectric half space. We verify our approach at a planar slab waveguide and a cylindrical fiber, as their mode spectra are well known. The mode matching technique is applied as reference method and the impinging wave is a Gaussian beam with varying angles of incidence and lateral displacements.