Anisotropic Impedance Boundary Conditions Research Articles

Electromagnetic Analysis of Anisotropic Impedance Spherical Metasurfaces

We investigate the interaction of electromagnetic (EM) waves with a spherical conformal metasurface, described by a anisotropic surface impedance. To this end, a full-wave method is developed, based on the expansion of the fields in terms of spherical vector wave functions. Appropriate treatment of the anisotropic impedance boundary condition leads to sets of linear equations that allow for the determination of the involved EM fields. The developed method can be used for design and anal- ysis purposes, as well as for the study of metasurface-based EM scattering control. We examine a related application of a cloaking setup and show that anisotropy breaks the spherical symmetry and leads to interesting new effects, such as a polarization-dependent switch function. The presented results suggest that metasurfaces with appropriately engineered impedance tensors may lead to desired scattering responses that otherwise cannot be obtained with their isotropic counterparts.

Sensitivity analysis of rectangular waveguides with different anisotropic surface impedance boundaries using modal extended theory

This article presents a sensitivity analysis of rectangular waveguides loaded with anisotropic surface impedance boundaries on their vertical walls, by using modal extended theory (MET). Using this method, several dispersion diagrams are computed for various anisotropic impedance boundary conditions of the surface walls of the waveguides in order to assess how the slight changes on the surface impedance can affect on the bandwidth and the fundamental cutoff frequency of the waveguide. The results obtained with MET were validated by comparison with the commercial software ANSYS HFSS. The results show that small anisotropic variations of the surface wall impedances lead to variation on the fundamental cutoff frequency and the bandwidth of the waveguide. Most significantly, and compared to an isotropic metasurface case, the variation of the transverse impedance of the metasurface is the one that have more significant effect over the waveguide parameters. This is an useful information for the metasurface design in order to take into account the fabrication tolerance of these structures and how they can have an influence over the final constructed device.

Surface Integral Equation Method for Generalized Soft-and-Hard Boundary Condition

A surface integral equation (SIE) method is developed for analyzing electromagnetic scattering by objects with generalized soft-and-hard (GSH) boundary conditions. GSH boundary condition is an anisotropic impedance boundary condition, which limits the tangential electric and magnetic fields in specified directions. In the developed SIE formulation, the GSH boundary condition is expressed in a vector form with two sets of orthogonal vectors, which can be combined with the field integral equations. The resulting equation can be discretized with the standard method of moments (MoM) using triangular elements and the Rao-Wilton-Glisson (RWG) functions. By varying the GSH condition, the direction of the tangential electric and magnetic fields on the surface can be flexibly changed.

Metasurface Antennas: New Models, Applications and Realizations

This paper presents new designs, implementation and experiments of metasurface (MTS) antennas constituted by subwavelength elements printed on a grounded dielectric slab. These antennas exploit the interaction between a cylindrical surface wave (SW) wavefront and an anisotropic impedance boundary condition (BC) to produce an almost arbitrary aperture field. They are extremely thin and excited by a simple in-plane monopole. By tailoring the BC through the shaping of the printed elements, these antennas can be largely customized in terms of beam shape, bandwidth and polarization. In this paper, we describe new designs and their implementation and measurements. It is experimentally shown for the first time that these antennas can have aperture efficiency up to 70%, a bandwidth up to 30%, they can produce two different direction beams of high-gain and similar beams at two different frequencies, showing performances never reached before.

The Method of Calculation of Open and Closed Waveguides, Which Is Based on the Modified Method of Discrete Sources

The problem of calculation of eigenmode characteristics is considered for 3D open dielectric waveguides and waveguides with the anisotropic impedance boundary condition. An efficient algorithm is proposed for finding eigenmodes of waveguides having different cross-sections. It is based on the solution of the auxiliary problem of diffraction of the field of a filamentous source located inside the waveguide. The method is tested using weakly directing dielectric waveguides having circular and elliptical sections and a waveguide with the two-sheeted section. The results of calculation of dielectric waveguides obtained with the help of the proposed method, the method of finite elements, and the method of the integral equation over the waveguide section are compared. The circular and elliptical waveguides and the waveguide having a two-sheeted section with an anisotropic impedance are also investigated. The calculation results are compared with the results obtained with the use of the method of separation of variables and the Galerkin method.

Parallelized multilevel fast multipole algorithm for scattering by objects with anisotropic impedance surfaces

SUMMARYA parallelized multilevel fast multipole algorithm (MLFMA) is presented for simulating electromagnetic scattering from complex targets with anisotropic impedance surfaces. By employing both surface electric and magnetic currents as unknowns and weakly enforcing the anisotropic impedance boundary condition, a combined integral equation is formulated to generate a set of well‐conditioned linear systems to be solved by MLFMA. To further improve the iterative convergence of the linear systems, a parallel sparse approximate inverse preconditioner is constructed from the near‐field interaction of the system matrix. The MLFMA is parallelized to enable computation on a large number of processors for large‐scale problems. Several numerical examples are presented to validate the algorithm and demonstrate its accuracy, scalability, and capability in handling large complex objects with anisotropic impedance surfaces. Copyright © 2014 John Wiley & Sons, Ltd.

Pattern equation method for the solution of electromagnetic scattering by axially-symmetric particles with complex anisotropic surface impedance

The pattern equation method (PEM) has been extended to solve the scattering problems of electromagnetic waves by particles with mixed anisotropic surface impedance. Thus, the anisotropic impedance boundary conditions are imposed on lateral surface of the particle, and isotropic impedance boundary conditions are imposed on end faces of the particle. The method is formulated for axially-symmetric bodies. The scattering characteristics of the bodies with artificially soft and hard lateral surfaces are presented. The comparison of the results with those obtained by other methods is carried out. The analysis of convergence’s rate of numerical algorithm of the PEMand accuracy of numerical calculations are presented. Comparison of our data with numerical results obtained earlier by the PEM in absence of an anisotropic impedance is carried out.

Oblique Incidence Diffraction by Edges in Anisotropic Impedance Surfaces: A Collection of Exact Solutions for Specific Non-Axial Tensor Boundary Conditions

The electromagnetic scattering of an arbitrarily polarized plane wave obliquely impinging on the edge of anisotropic impedance half-planes and planar junctions featuring inclined anisotropy axes is analyzed. Exact spectral representations for the total field are derived when the wedge faces are characterized by a set of specific homogeneous anisotropic impedance boundary conditions exhibiting an impedance matrix with no vanishing diagonal terms, as implied by the arbitrary orientation of the principal anisotropy axes with respect to the edge. The proposed solutions, which extend previous formulations valid for direction of the anisotropy axes either parallel or perpendicular to the edge, are derived by resorting to the Sommerfeld–Maliuzhinets method and exploiting the properties of the special function χΦ, originally introduced in the study of the scattering from wedges in gyroelectric media. Explicit uniform asymptotic expressions for the fields are provided along with samples of numerical results proving their validity.

An effect of excitation of a transverse magnetic creeping wave when a transverse electric wave crosses the line of the coincidence of propagation constants

Transverse electromagnetic electric (TE) and transverse magnetic (TM) creeping waves on a surface with an anisotropic impedance boundary condition are considered. An asymptotic theory is developed for creeping waves. The theory is valid near the line where the attenuation parameters of two different types of waves coincide and, therefore, standard asymptotics are inapplicable. Asymptotic formulas describing physical effects that occur when a creeping wave propagates across the degeneracy line are derived. It is found that, behind the degeneracy line, a propagating TE wave excites a TM wave with a small amplitude (of order O(k−1/6)) and a propagating TM wave excites a TE wave.

Degeneration of Electromagnetic Creeping Waves in a Vicinity of Critical Values of Anisotropic Impedance

Electromagnetic creeping waves on a 3-dimensional surface with an anisotropic impedance boundary condition are considered. The influence of the impedance is examined. The standard asymptotic formula for the creeping waves contains the factor 1/(tau-q2) where tau is the attenuation parameter and q is the Fock parameter which depends on the impedance matrix. Analysis of the equation for the attenuation parameter which describes its dependence on q shows that there exist such critical values of q when the factor 1/(tau-q2) diverges and the usual asymptotic formula gives infinite result. The equation for the critical values of the parameter q is derived and the 4 first critical values are found numerically. The new local asymptotics valid in domain of the size k-2/9 (where k is the wave number) is derived in the supposition that the divergence takes place on a curve crossed by creeping waves. This new asymptotic decomposition is carried out by powers of the small parameter k-1/9. The effect of creeping wave passing through the line where the usual asymptotics diverges is examined.

High‐frequency asymptotic solutions benchmarking skew incidence diffraction by anisotropic impedance half and full planes

The diffraction of plane waves obliquely incident on the edge of anisotropic impedance half and full planes is investigated. Homogeneous anisotropic impedance boundary conditions are defined on both faces of the canonical structures under study, the principal anisotropy axes being parallel and perpendicular to the edge. Rigorous integral representations for the longitudinal field components are derived by applying the Sommerfeld‐Maliuzhinets method for a set of specific electrical configurations. Explicit uniform asymptotic expressions for the fields are given in the format of the Uniform Geometrical Theory of Diffraction (UTD). Although obtained for a specific class of geometrical and electrical configurations, these high‐frequency solutions provide a contribution for investigating the effects of material anisotropy on edge diffraction, as they represent a new set of reference cases for either developing perturbative solutions or testing numerical and approximate analytical methods of more general validity. Furthermore, these solutions extend the applicability of the Sommerfeld‐Maliuzhinets technique and represent a step forward to the solution of more general wedge canonical problems.

Fractional Operators Approach in Electromagnetic Wave Reflection Problems

Applications of fractional operators approach to electromagnetic waves reflection problems are considered. Reflection properties of fractional or intermediate solutions are analyzed. It is shown that this approach is a useful technique for the description of solutions to the reflection problems for some known media in terms of the fractional order and also obtaining boundaries with new features. In this paper intermediate boundaries are modeled with BI slab with a PEC backing and also using anisotropic impedance boundary conditions. The twist-polarizer effect (crosspolarizing reflector) is described in terms of the specific value of the fractional order.

Diffraction of a Plane Skew Electromagnetic Wave by a Wedge With General Anisotropic Impedance Boundary Conditions

The three dimensional problem of diffraction of a skew incident plane wave by a wedge with anisotropic impedance boundary conditions is explicitly solved by the probabilistic random walk method. The problem is formulated in terms of two certain components of the electric and magnetic fields which satisfy independent Helmholtz equations but are coupled through the first-order boundary conditions. The solution is represented as a superposition of the geometric waves that are completely determined by elementary methods and of the waves diffracted by the apex of the wedge. The diffracted field is explicitly represented as the mathematical expectation computed over the trajectories of a two-state random motion which runs in a complex space and switches states under the control of stochastic equations determined by the problem's geometry and by the boundary conditions

A probabilistic approach to wave propagation and scattering

The probabilistic approach to wave propagation starts in a way that is similar to ray theory, from the representation of the wave field as a product of the amplitude and of the exponent of the eikonal, which is computed by a canonical technique of analytical mechanics. However, an important difference is that the amplitude is not approximated but is represented by exact probabilistic formulas that admit efficient numerical evaluation, and that is a direct improvement of many asymptotic solutions. This approach is shown to be an effective tool for the analysis of numerous wave propagation problems, including those of wave diffraction by a screen occupying a plane angular sector and of electromagnetic diffraction by a wedge with anisotropic impedance boundary conditions.

Diffraction by a plane sector

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Budaev Bair V. and Bogy David B. 2004Diffraction by a plane sectorProc. R. Soc. Lond. A.4603529–3546http://doi.org/10.1098/rspa.2004.1322SectionRestricted accessDiffraction by a plane sector Bair V. Budaev Bair V. Budaev Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA (; ) Google Scholar Find this author on PubMed Search for more papers by this author and David B. Bogy David B. Bogy Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA (; ) Google Scholar Find this author on PubMed Search for more papers by this author Bair V. Budaev Bair V. Budaev Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA (; ) Google Scholar Find this author on PubMed Search for more papers by this author and David B. Bogy David B. Bogy Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA (; ) Google Scholar Find this author on PubMed Search for more papers by this author Published:08 December 2004https://doi.org/10.1098/rspa.2004.1322AbstractThe problem of diffraction by a perfectly reflecting screen occupying an infinite sector of the equatorial plane is addressed by the random–walk method. The solution is represented as a superposition of the wave field completely determined by an elementary ray analysis and of the field formed by the waves diffracted by the tip of the screen. The diffracted field is explicitly represented as the mathematical expectation of a specified functional on trajectories of the random motion, the radial component of which runs in a complex space while the two–dimensional angular component remains real valued. The numerical results confirm the efficiency of the random–walk approach to the analysis of diffraction by wedge–shaped screens of arbitrary angles. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Castro L and Kapanadze D (2008) Exterior Wedge Diffraction Problems with Dirichlet, Neumann and Impedance Boundary Conditions, Acta Applicandae Mathematicae, 10.1007/s10440-008-9408-y, 110:1, (289-311), Online publication date: 1-Apr-2010. Castro L and Kapanadze D (2008) Wave diffraction by a 45 degree wedge sector with Dirichlet and Neumann boundary conditions, Mathematical and Computer Modelling, 10.1016/j.mcm.2007.09.004, 48:1-2, (114-121), Online publication date: 1-Jul-2008. Budaev B and Bogy D (2008) Diffraction by a Nonconvex Polygon, SIAM Journal on Applied Mathematics, 10.1137/070699548, 69:2, (398-418), Online publication date: 1-Jan-2008. Budaev B and Bogy D (2007) Diffraction by a wedge with a face of variable impedance, Radio Science, 10.1029/2006RS003597, 42:6, Online publication date: 1-Dec-2007. Budaev B and Bogy D (2007) Novel solutions of the Helmholtz equation and their application to diffraction, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463:2080, (1005-1027), Online publication date: 8-Apr-2007. Budaev B and Bogy D (2006) Diffraction by a convex polygon with side-wise constant impedance, Wave Motion, 10.1016/j.wavemoti.2006.05.007, 43:8, (631-645), Online publication date: 1-Oct-2006. Budaev B and Bogy D (2006) Diffraction of a Plane Skew Electromagnetic Wave by a Wedge With General Anisotropic Impedance Boundary Conditions, IEEE Transactions on Antennas and Propagation, 10.1109/TAP.2006.874317, 54:5, (1559-1567), Online publication date: 1-May-2006. Budaev B and Bogy D (2005) A probabilistic approach to wave propagation and scattering, Radio Science, 10.1029/2004RS003176, 40:6, (n/a-n/a), Online publication date: 1-Dec-2005. Budaev B and Bogy D Two-dimensional diffraction by a wedge with impedance boundary conditions, IEEE Transactions on Antennas and Propagation, 10.1109/TAP.2005.848512, 53:6, (2073-2080) Budaev B and Bogy D Diffraction of a plane wave by a sector with Dirichlet or Neumann boundary conditions, IEEE Transactions on Antennas and Propagation, 10.1109/TAP.2004.841303, 53:2, (711-718) Budaev B and Bogy D Probabilistic representation of waves scattered by inhomogeneities of the medium 2005 IEEE Antennas and Propagation Society International Symposium, 10.1109/APS.2005.1551671, 0-7803-8883-6, (751-753) Budaev B and Bogy D (2004) Wave scattering by surface-breaking cracks and cavities, Wave Motion, 10.1016/j.wavemoti.2004.02.003, 40:2, (163-172), Online publication date: 1-Aug-2004. This Issue08 December 2004Volume 460Issue 2052 Article InformationDOI:https://doi.org/10.1098/rspa.2004.1322Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/12/2004Published in print08/12/2004 License: Citations and impact Keywordsdiffractionwave propagationray methodBrownian motion

Time Domain Version of the Uapo Solution for the Field Diffracted by an Anisotropic Impedance Half-Plane

This work deals with the time domain version of the Uniform Asymptotic Physical Optics solution for the field diffracted by the edge of a nonpenetrable half-plane characterized by an anisotropic impedance boundary condition. A transient plane wave is assumed obliquely incident on the scatterer in the more general case of principal axes of anisotropy not coincident with the edge. The time domain solution is obtained from the knowledge of the corresponding frequency domain expression in the hypothesis that the impedance tensor components along the principal axes of anisotropy do not depend on the frequency. An inverse Laplace's transform is used to this end. The response to an incident unit step function plane wave is explicitly considered.

Effective boundary conditions for planar quantum dot structures

The effective-boundary condition method is extended to nanoscale mesoscopic systems. The ~EBC's ! appear as a result of the two-dimensional ~2D!-homogenization procedure and have the form of two-side anisotropic impedance boundary conditions stated on the structure surface. It has been shown that, unlike to macroscopic electrodynamics, the surface impedance tensor exhibits sharp oscillations at frequencies of optical transitions. The EBC method supplemented with well-developed mathematical techniques of classical electrodynamics creates unified basis for solution of boundary-value problems in electrodynamics of nanostructures. We have shown that the radiative lifetime of 2D array of spherical quantum dots ~QD's ! drastically changes its depen- dence on QD radius in comparison with the case of a single QD in the range of radii smaller than Bohr radius. Fascinating electronic and optical properties of spatially confined nanostructures irreducible to properties of bulk me- dia, and great potentiality of such structures in engineering applications has motivated permanent extension of their study. Among a variety of new results in this field, the recent progress in the synthesis of sheets of nanoscale three- dimensional ~3D! confined narrow-gap insertions in a host semiconductor, quantum dots ~QD's !, is of a special interest. Indeed, QD-based structures provide practical realization of the idea proposed by Dingle and Henry 1 to use structures with size quantization of charge carriers in one or more di- rections as active media of double heterostructure laser. Such a laser will show radically changed characteristics as com- pared to conventional quantum-well ~QW! lasers. 2,3 For InxGa12xAs QD's on GaAs substrates, an exceptionally bright luminescence at 1.36 mm was realized at room temperature 4 in a spectral range far beyond those available for conventional strained InxGa12xAs-GaAs QW's. The large body of recent results on physical properties of QDs and their utilization for the QD laser design has been accumu- lated in Ref. 5. The key peculiarities of QD heterostructures are related to spatial confinement of the charge-carrier motion and intrinsic spatial inhomogeneity. Since the inhomogeneity scale is much less than the optical wavelength, inclusions ~QD's ! can be treated as electrically small objects and electromagnetic response of such heterogeneous structures, composites, can be evaluated by means of effective-medium theory. 6 Appli- cation of effective-medium approach to 3D arrays of QD's has been presented in Refs. 7 and 8. In many cases, however, a planar array of QD's with intrinsic 2D periodicity of char- acteristic period much less than the optical wavelength, can be treated as more adequate and realistic model. 5 In this paper we present a general method for evaluation of electromagnetic response of planar arrays of QD's. This method, conventionally referred to as the effective- boundary-condition ~EBC! method, has been originally de- veloped for microwaves and antenna theory, 9-11 and has found a wide application in these fields. Similar approaches have also been developed in acoustics, hydrodynamics, elas- ticity theory. Recently, the EBC method has been extended to

Approximate Diffraction Coefficients for an Anisotropic Impedance Wedge

Two approaches are proposed to determine the diffraction coefficients for a nonpenetrable wedge with the faces characterized by anisotropic impedance boundary conditions when it is illuminated at oblique incidence by an electromagnetic plane wave. In the more general case the anisotropic impedance tensors associated with the faces have their principal axes not coincident with the edge of the wedge. The first solution is obtained by using a physical optics approximation for the surface current densities on the wedge and by performing a uniform asymptotic evaluation of the radiation integral (uniform asymptotic physical optics solution). The second solution is derived by following a heuristic approach. The effectiveness of both solutions is demonstrated by comparing them with analytical solutions available for particular cases.

Electromagnetic scattering by anisotropic impedance half and full planes illuminated at oblique incidence

The three-dimensional electromagnetic (EM) scattering from half and full plane configurations, both characterized by a perfectly conducting and an anisotropic impedance face, is analyzed. The anisotropic impedance boundary condition considered for the loaded face is suitable for modeling corrugated surfaces or strip-loaded grounded dielectric slabs used to realize artificially hard or soft surfaces, with a tensor surface impedance exhibiting a vanishing impedance along the corrugations or strips and a diverging impedance in the orthogonal direction. Previous rigorous solutions, valid when the vanishing impedance direction is either parallel or perpendicular to the edge, are generalized here to the case in which the direction of vanishing impedance is arbitrarily oriented.

High-frequency EM scattering by edges in artificially hard and soft surfaces illuminated at oblique incidence

Uniform high-frequency expressions describing the field scattered by edges in anisotropic impedance surfaces illuminated at oblique incidence are provided. The specific anisotropic impedance boundary condition considered here exhibits a vanishing surface impedance along a principal anisotropy axis and an arbitrary one in the orthogonal direction. In certain circumstances, this tensor surface impedance may represent an accurate model for describing the scattering properties of artificially hard and soft surfaces. In order to simplify the analysis but without losing pertinence with real problems, in all canonical configurations we consider a face of the wedge to be perfectly conducting. The anisotropic impedance face is characterized by a tensor surface impedance with the principal anisotropy axes parallel and perpendicular to the edge.