Generalized Impedance Boundary Conditions Research Articles

Diffraction in the high frequency regime by a thin layer of dielectric material I: The equivalent impedance boundary condition

We discuss in this paper a generalized impedance boundary condition that can be used locally to replace a thin layer of material with dielectric absorbing constants. This condition takes into account the curvature of the body and the angle of incidence of the incident wave, which can be more general than a plane wave. We use this condition to obtain a system of equations outside the object equivalent to the system of Maxwell equations.

Diffraction in the High Frequency Regime by a Thin Layer of Dielectric Material II: the Trace of the Wave in the Shadow of the Obstacle

We use in this paper a generalized impedance boundary condition equivalent to a thin layer of material with dielectric absorbing constants to compute in the high frequency regime the trace of the normal derivative of the magnetic field on the boundary, in the shadow of an analytic obstacle. In particular, we prove that there exist creeping rays in the shadow of the obstacle. This is true for any incident electromagnetic wave characterized by an analytic wave front.

Diffraction of a plane electromagnetic wave obliquely incident upon the edge of a wedge with a dielectric coating

The diffraction of a plane electromagnetic wave obliquely incident upon the edge of a coated wedge is considered. The generalized impedance boundary conditions (GIBC's) on the wedge's faces are used to simulate the effect of the coatings. To insure the well-posedness of the problem, special contact conditions (CC's) on the edge are additionally imposed. By using Sommerfeld integrals, the problem is reduced to a system of coupled functional equations, which is solved by the perturbation method. It is shown that, for a certain range of the angles of oblique incidence, the solution can be represented in the form of convergent series that are Neumann series for linear equations with contracting operators. Nonuniform asymptotics of the wave field for regions outside a neighborhood of the edge of the wedge are constructed. Bibliography: 9 titles.

Higher order impedance and absorbing boundary conditions

Traditionally, generalized impedance boundary conditions (GIBCs) have been used to model dielectrics and coated surfaces, and absorbing boundary conditions (ABCs) have been used to simulate nonreflecting surfaces. The two types have the same mathematical form and, in most instances, a higher order condition involving higher order field derivatives has a better accuracy. We demonstrate that there is a close connection between the two and this enables us to use a systematic method which is available for generating GIBCs of any desired order to derive new two- and three-dimensional ABCs. The method is applicable to curvilinear/doubly-curved surfaces and examples are given. Finally, curves are presented that quantify the accuracy of two-dimensional ABCs up to the fourth order, and show how higher order ABCs can improve the efficiency of large scale partial differential equation (PDE) solutions.

Generalized boundary conditions with applications to submillimeter and optical waveguides

In this paper, generalized impedance boundary conditions (GIBC) are derived at an interface between isotropic, homogeneous dielectric media. The advantage of this technique is that rather than requiring that the tangential components of the and fields be continuous over the interface, an equivalent set of boundary conditions involving the electric field and its space derivatives is applied, reducing the problem dimension and therefore the computational needs significantly. The equivalence between the two sets of boundary conditions is validated for the case of an infinite dielectric slab. Finally, an application of the concept of GIBC to the analysis of dielectric waveguiding structures for high‐frequency applications is described.

Diffraction of a plane wave by a wedge with thin material coatings

The problem of diffraction of a normally incident plane wave by a wedge with thin material coatings is studied. The thin coatings are simulated by the generalized impedance boundary conditions of the third order. At the points of junction of the coatings, that is, on the edge of the wedge, additional constraints are formulated. These constraints, or contact conditions, ensure uniqueness of the solution in the diffraction problem. The solution is determined in an explicit form by means of the Maliuzhinets' technique. The uniform and local asymptotics of the far field are deduced.

Diffraction at a Curved Grating: TM and TE Cases, Homogenization

A hierarchy of effective boundary conditions is derived for a Helmholtz equation with Dirichlet or Neumann boundary conditions. These generalized impedance boundary conditions approximate the effect of thin dielectric layers with perfectly conducting inclusions covering an object. Well-posedness of the problems with these new boundary conditions is proved and optimal error estimates are given.

Application of GIBCs to the computation of resonant frequencies for uniaxial cylindrical resonators

Numerical analysis for computing resonant frequencies of uniaxially anisotropic cylindrical resonators is presented. The resonator is placed on a grounded isotropic substrate and is covered with a metallic tuning plate. The generalized impedance boundary conditions are employed along the axis of the resonator to simplify the boundary-value problem. Ample numerical results are presented, explicitly showing the dependent of the resonant frequency on the variation in the elements of the permittivity tensor. © 1996 John Wiley & Sons, Inc.

Asymptotic theory of the reflection of electromagnetic radiation by moderately and highly conductive bodies

In this paper a method of deriving generalized impedance boundary conditions continuing tangential derivatives of high order is proposed. The case of reflection of an arbitrary electromagnetic wave by a curvilinear surface on which a generalized impedance condition holds is considered. The phenomenon of diffusion polarization dependent on the material and geometric properties of the reflecting surface is investigated. Bibliography: 5 titles.

Generalized impedance boundary conditions and model of a point conductor

The presence of derivatives of high order in generalized impedance boundary conditions (GIBCs) makes possible the simulation of point defects or point conductors placed on a surface. In case of the second‐order GIBC, the model of a point conductor is formulated via appropriate contact condition. For a plane boundary the problem of diffraction by a point defect is accurately solvable. A scattering diagram for an arbitrary point conductor is computed. The resulting formula depends on relative Wiener capacity, which is an integral characteristic of a two‐dimensional scatterer. The problem of diffraction by a periodic set of point conductors on a plane surface is solved in a closed form.

Sommerfeld Half‐plane Problems with Higher Order Boundary Conditions

AbstractSommerfeld‐type diffraction problems for a half‐plane with arbitrary n‐th order generalized impedance boundary conditions arc examined in a Sobolev space setting. The corresponding boundary‐transmission problems for the two dimensional Helmholtz equation are shown to be well‐posed in a family of Sobolev spaces with finite energy norms, through a reduction to equivalent systems of boundary integral equations of Wiener‐Hopf type in [L2+ (IR)]2. Formulas for the solutions as well as the so‐called edge conditions arc obtained for any n, by explicit canonical generalized factorization of the presymbols of the associated Wiener‐Hopf operators.

High-frequency scattering of a whispering gallery mode by a cylindrically curved surface with second-order generalized impedance boundary conditions

A high-frequency solution is derived for the diffraction of electromagnetic waves by a cylindrically curved metallic sheet whose concave and convex faces are coated by dielectric layers of the same physical properties and thicknesses. After simulating the effects of the grounded dielectric layer by second-order generalized impedance boundary conditions, a canonical problem is formulated in an infinitely extended angular space from which explicit asymptotic expressions for the diffraction coefficients are obtained through the asymptotic solution of a Hilbert problem.

EM plane‐wave diffraction by a material‐coated perfectly conducting half‐plane‐ oblique incidence

AbstractA high‐frequency solution is developed for the electromagnetic diffraction of an obliquely incident plane wave by a material‐coated perfectly conducting half‐plane. It is assumed that the coating is electrically thin so that it can be modeled by a generalized impedance boundary condition of O(t), where t is the coating's thickness. © 1994 John Wiley & Sons, Inc.

A Half-Space Boundary Element Method for Acoustic Problems With a Reflecting Plane of Arbitrary Impedance

In this paper, the boundary element method (BEM) is used to model acoustic radiation and scattering from bodies of arbitrary shape in close proximity of an infinite plane that has a general impedance boundary condition. A new half-space Green's function for positive reactance boundary conditions is derived and incorporated in the boundary element formulation so that there is no need to model the infinite plane. Attempt is also made to derive the Green's function for negative reactance boundary conditions. However, the derived Green's function for negative reactance boundary conditions contains a term that is not known a priori. Only an approximate Green's function for negative reactance boundary conditions is used in the BEM. Several numerical examples are given to verify this new formulation.

GIBC formulation for the resonant frequencies and field distribution of a substrate-mounted dielectric resonator

Dielectric resonators (DR's) are widely used in telecommunication systems. A method is proposed here to find the resonant frequency and field distribution in a substrate-mounted DR structure. The field of a dielectric rod has been decomposed into a combination of guided modes with unknown coefficients and an unknown continuous spectrum of radiation field. The unknowns are then obtained by applying two generalized impedance boundary conditions (GIBC's) representing the substrate and air layers at the top and bottom of the DR. This leads to the calculation of the total (guided+radiation) field as well as the resonant frequency of the structure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Higher order impedance boundary conditions revisited: application to chiral coatings

In this paper, a novel spectral domain method for obtaining higher order impedance boundary conditions for the problem of electromagnetic scattering from complex coatings is described. The method is then applied to the specific case of chiral coatings on conductors. The present method for obtaining the boundary conditions is quite general, and is applicable to coatings with arbitrary constitutive relations, including anisotropic coatings, such as dielectric layers with tensor permittivity, and non-reciprocal coatings, such as magnetically biased ferrites. Multiple layers may also be handled in a systematic manner. Although the examples presented focus on boundary conditions containing tangential derivatives no higher than second order, an extension to higher order conditions is also straight forward. The standard impedance boundary condition (SIBC), tensor impedance boundary condition (TIBC), and the generalized impedance boundary conditions (GIBC), are contained as special cases of the general method des...

Implementation of generalized impedance boundary condition in the split‐step Fourier parabolic equation

The parabolic wave equation (PE) is a powerful numerical method for computing the full‐wave complex acoustic pressure field in range‐dependent environments. The split‐step Fourier PE algorithm (SSFPE) of Hardin and Tappert provides a very efficient computational implementation of PE when the surface boundary condition is of the Dirichlet or Neumann form, and when the solution decays sufficiently with depth. This allows use of fast Fourier transform (FFT) methods to implement the SSFPE algorithm. Typically the infinite domain radiation condition is approximated on a finite calculation grid by employing an artificial absorber or sponge. In some cases involving strong bottom interaction, however, the required absorber region may be quite large. This results in an increased computational load. A new method for truncating the absorber region will be described that is based upon splitting the PE field into two components that are in turn propagated on different vertical wave‐number grids. Illustrative examples that use this new method will be shown. [Work supported by NRaD IR program.]

Boundary-contact problems of the electromagnetic theory of diffraction

A new class of problems of electromagnetic diffraction associated with the generalized impedance boundary condition (GIBC) is investigated. Methods for obtaining the GIBC and the conditions of its applicability for an arbitrary cylindrical surface are described. The simulation of defects in electromagnetic coatings is studied. A class of problems that can be solved exactly by factorization is isolated. Models of point defects in coatings are constructed and the limits of their applicability are established.

Analysis of diffraction by material discontinuities in thin material‐coated planar surfaces based on Maliuzhinets method

The electromagnetic diffraction of a plane wave (transverse electric case) by a two‐part material coated perfectly conducting ground plane and a material‐coated perfectly conducting half plane is studied using the Maliuzhinets method. Each of the coatings is assumed to be electrically thin so that it can be replaced in the analysis by a generalized impedance boundary condition of 0(t), where t is the corresponding coating thickness. To solve each of the boundary value problems completely, one needs to impose an additional constraint which is determined here by matching an approximate quasi‐static solution with the corresponding Maliuzhinets solution in the common region of overlap. This requires the asymptotic evaluation of the Maliuzhinets functions in various regions of the spectral domain. Furthermore, several constants that appear in the analysis are exactly related to the field and its derivatives evaluated at the edge or junction of the body under study. The backscattered and bistatic echo widths of a partially coated perfectly conducting half plane are computed with the solutions developed here (including multiple interaction) and compared with an independent moment method solution. The agreement between the two solutions is excellent.

EM plane wave diffraction by a a planar junction of two thin material half-planes-oblique incidence

A uniform geometrical theory of diffraction (UTD) solution is developed for analyzing the high-frequency diffraction of an obliquely incident plane wave by a two-part, thin, planar, transparent material slab. The solution is obtained by appropriately combining two solutions for the two related configurations involving perfectly conducting electric and magnetic ground plane bisections of the original slab. The analysis is based on the Wiener-Hopf technique, and each of the grounded material half-planes is assumed to be electrically thin so that it can be modeled by a generalized impedance boundary condition of 0(t), where t is the corresponding slab thickness. To solve the boundary value problem completely, an additional condition related to the field behavior at the junction of the two material half-planes is imposed. This junction condition is determined by matching an approximate quasi-static solution, which is developed in the proximity of the discontinuity, with the corresponding external Wiener-Hopf solution in the common region of overlap. The solution thus obtained automatically satisfies reciprocity. >