Search

In this contribution, we demonstrate that recent improvements in "fast methods" allow for fully error-controlled full-wave simulations of two-dimensional objects with sizes over a million wavelengths using relatively simple computing environments. We review how a fully scalable parallel version of the Multilevel Fast Multipole Algorithm (MLFMA) is obtained to accelerate a two-dimensional boundary integral equation for the scattering by multiple large dielectric and/or perfectly conducting objects. Several complex and large-scale examples demonstrate the capabilities of the algorithm. This implementation is available as open source under GPL license (http://www.openfmm.net).

Micromagnetic hysteresis models for large, bulk like samples are useful for the identification of relations between microscopic material properties and macroscopic magnetic behavior. To bridge the gap between the nanometer space scale of the micromagnetic theory and the large sample dimensions, time and memory efficient numerical schemes are needed. In micromagnetic computations, fast Fourier transforms (FFTs) have been widely adopted to speed up magnetostatic field computations. In this paper, two FFT schemes are compared. The first scheme evaluates the magnetostatic field directly starting from the magnetization and has a large accuracy, while in the second scheme the magnetostatic field is derived from the scalar magnetic potential resulting in a reduced accuracy but also in a CPU time reduction for a magnetostatic field evaluation to 65% and a reduction of memory requirements to 55%. The influence of the low accuracy evaluations on the simulated macroscopic hysteresis behavior is studied. Therefore, comparison is made with the influence of thermal effects in hysteresis simulations. It is found that the resulting changes in macroscopic hysteresis behavior are of the same order of magnitude as the ones obtained when thermal fluctuations are taken into account in the high accuracy computations.

The present paper numerically investigates the micromagnetic behavior of permalloy nanostrips, starting from the space-time integration of the Landau-Lifshitz-Gilbert equation. The analysis is performed on objects with variable longitudinal size of the order of some hundreds of nanometers. The attention is focused on the role of geometrical properties (e.g., scaling factor and end shape) and of thermal agitation on magnetization reversal processes. The thermal effects are included in the model following the Langevin approach.

Magnetic field integral equation (MFIE) and Calderon preconditioned electric field integral equation (EFIE) operators applied to toroidal surfaces have nontrivial nullspaces in the static limit. The nature of these nullspaces is elucidated and a technique for generating a basis for them presented. In addition, the effects of these nullspaces on the numerical solution of both frequency and time-domain MFIE and CalderOacuten preconditioned EFIEs are investigated. The theoretical analysis is accompanied by corroborating numerical examples that show how these operators' nullspaces affect real-world problems.

A Calderon multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Calderon-preconditioned CFIEs, a localization procedure is employed to ensure that the equation is resonance-free. The iterative solution of the linear system of equations obtained via the CMP-based discretization of the CFIE converges rapidly regardless of the discretization density and the frequency of excitation.

Time domain electric field integral equations often are used to analyze transient scattering from perfect electrically conducting objects. When discretized using marching-on-in-time recipes they give rise to linear systems of equations that can be solved for the induced currents for all time steps. Unfortunately, when the scatterer is approximated by increasingly dense meshes, the condition number of these systems grows rapidly, slowing down the convergence of iterative solvers. Here, time domain Calderon identities are derived and subsequently used to construct a Calderon-preconditioned time domain electric field integral equation that can be discretized even with dense meshes using Buffa-Christiansen basis functions. Numerical results that demonstrate the effectiveness and accuracy of the proposed method are presented.

A novel method, called the nondirective stable plane wave multilevel fast multipole algorithm (NSPWMLFMA), is presented to evaluate the low-frequency (LF) interactions that cannot be handled by the multilevel fast multipole algorithm (MLFMA). It is well known that the MLFMA cannot be used for LF interactions, since it suffers from numerical instability. Contrary to current techniques, the proposed technique is not based on the spectral representation of the Green function. Instead the addition theorem of the MLFMA is manipulated into a form that allows numerically stable translations along the z axis. The translation operator for these translations is derived in closed form. A QR-based method is devised to allow stable translations in all the other directions. Interpolations and anterpolations are also provided, allowing a full multilevel algorithm. Since the NSPWMLFMA is based on the same mathematical foundations as the MLFMA, it requires limited adaptations to existing MLFMA codes. The fact that a QR is needed limits this algorithm to LF interactions. However, a coupling with the MLFMA is straightforward, allowing the easy construction of a broadband algorithm. The DC limit of the algorithm is also presented and it is shown that the algorithm remains valid for static problems. Finally, it is shown that the error introduced in the different steps of the algorithm is controllable, and a single-level vectorial version of the algorithm is applied to a generic scattering application to demonstrate its validity.

We present a full-wave homogenization method to determine the effective material parameters of metamaterials by considering a spherical piece of metamaterial. We use a T-matrix approach that is accelerated by a multilevel fast multipole method that is stable at low frequencies. To determine the T-matrix of one inclusion in the metamaterial a Method of Moments surface integral equation is used that is also accelerated using another multilevel fast multipole method that is stable at low frequencies. We also derive a new closed-form expression to extract the effective material parameters from the T-matrix of the spherical piece of material. Examples verify the accuracy and limitations of the method. We show results for metamaterials comprising more than 40,000 particles.

In this paper the reader is introduced to an algorithm that revolutionized the complexity of problems that could be handled in electromagnetics in the past decennium. The algorithm, called fast multipole method, has allowed the solution of problems with many millions of degrees of freedom with reasonable computer resources. The method is explained on different levels of abstraction. It is illustrated by means of a wire scattering problem that is applied for the exact simulation of a piece of metamaterial with a negative index of refraction. It is the first time that an exact numerical verification of the lens effect in a negative index metamaterial is performed.

In this paper, a multilevel fast-multipole algorithm (MLFMA) for simulating electromagnetic-wave propagation in photonic-crystal (PhC)-slab devices is presented. The scheme accelerates the 3-D multiple-scattering technique (MST) for characterizing open PhC-slab devices comprising air holes in multilayered stacks proposed in a recent work by Boscolo and Midrio. This 3D MST truncates open PhC-slab devices by conductor-backed perfectly matched layers, expands total fields in the resulting closed structures in terms of discrete radial modes of the associated closed slab waveguides, and uses scattering tensors to evaluate air-hole interactions. Here, this last step is accelerated using a hybrid MLFMA that leverages low- and high-frequency fast-multipole constructs in conjunction with a mode-trimming feature. The computational complexity of the resulting hybrid MLFMA-MST scales almost linearly in the number of air holes, thereby enabling the analysis of electromagnetically large PhC- slab devices on readily available computer hardware. The scheme is applied to the analysis of a variety of practical PhC-slab devices, including a straight PhC-slab waveguide, a couple of bended PhC-slab waveguides, and a large PhC-slab coupler.

An important branch in electromagnetic research is the construction of circuit models for devices starting from electromagnetic field simulations. Among the first of such descriptions was the transmission line representation of TEM fields along a coaxial cable, the so-called telegrapher’s equations. Although the transmission line representation directly follows from Maxwell’s equations only in the pure TEM and, at low frequencies, also in the quasi-TEM situations, many authors have published representations that are valid for the propagation at arbitratry frequencies in general waveguides. These representations usually are based on the assumption that equal complex power is propagated in both the waveguide and the transmission line. However, this leads to problems regarding the reciprocity of such transmission line representations. About 10 years ago Prof. de Hoop suggested the present authors a solution to these problems. In honor of the celebration of Prof. de Hoop’s 75th anniversary, we present in this paper these “reciprocity based transmission line representations” in a new and concise manner and apply them to a new problem dealing with higher order eigenmodes in single conductor waveguides. It is shown that again reciprocity leads to simple and hence esthetically pleasing results.

In this paper we present an optimization technique for microstrip antennas based on combining a genetic algorithm (GA) and a Mixed Potential based Method of Moments technique. The GA optimizes the shape of the metallisation pattern in order to obtain a specific frequency response. Recalculation of the MoM interaction matrix for each individual in the GA is avoided. The technique is applied to design a broad-band antenna which can be used as a Ground Penetrating Radar. In order to detect the 'Vampire Signature' of the buried objects and in order to minimize the effect of ground reflections at the ground air interface, an antenna which detects cross-polarization is used. It is shown by measurements on the designed antenna that the optimization procedure is able to significantly reduce the return loss in a wide frequency band. The broadband characteristics of the antenna proved to be sufficient to detect buried objects and their vampire signature.

The class of decomposable bi-anisotropic media was recently defined to consist of media in which any electromagnetic field can be decomposed in two individual electromagnetic fields satisfying certain conditions for the electromagnetic fields. Also it was shown that, for a medium in this class, the fourth-order Helmholtz determinant operator governing the basic electromagnetic fields can be factorized, i.e., expressed as a product of two second-order operators. In the present paper, plane-wave propagation in the general decomposable medium is studied. Analytical solutions are derived for the dispersion equation and the polarizations of the eigenwaves are also determined in analytic form. As a check the expressions are applied to a medium with previously known solutions. In an appendix, conditions for the medium dyadics of the decomposable bi-anisotropic medium are derived for the case when the medium is lossless.

The line parameters (such as propagation constants, C and L) of a multiconductor transmission line in a multilayered medium show statistical variations, due to variations on the design parameters of the line. This statistical behaviour is analysed in the quasi-TEM approximation using a sensitivity based technique, requiring the computation of the derivatives of the line parameters with respect to the design parameters. Since we also need this information for most efficient optimisation techniques, we can perform optimisation and statistical analysis in one run. We compute the derivatives using adjoint style sensitivity evaluation. From the original quasi-TEM integral equation we derive a new integral equation with same kernel but with different right-hand side and with new unknowns equal to the derivatives of the original ones. All derivatives can be obtained with only one inversion of the integral equation.

Based on a spectral domain technique, asymptotic expressions for Green's functions in infinitely extended bianisotropic media are determined. This is achieved by considering the spectral representation of the Green's dyadic, which can be represented as a rational function in the spectral variables. Extraction of pole singularities and the spectral behavior at infinity leads to the far field-and the source point asymptotics in the spatial domain, respectively. The extraction procedure and its peculiarities are discussed and explicit formulas and sample results for diagonally bianisotropic media show the applicability of the approach.

In this contribution we determine the eigenmodes propagated along structures consisting of a waveguide embedded in a general multilayered bianisotropic medium. This includes for example microstrips or strip dielectric waveguides on bianisotropic substrates. The analysis presented here is a generalization to bianisotropic layered media of the boundary integral equation technique described in previous publications for isotropic layered media. The set of integral equations is solved by a spectral domain technique. In this spectral technique the layered medium is taken into account by determining the scattering of plane waves in the layered medium. Hence the major part of this publication deals with the scattering of plane waves in a multilayered bianisotropic medium. The described analysis is illustrated with the dispersion curves for thick microstrip lines on various bianisotropic substrates.

Calderon preconditioners have recently been demonstrated to be very successful in stabilizing the electric field integral equation (EFIE) for perfect electric conductors at lower frequencies. Previous authors have shown that, by using a dense matrix preconditioner based on the Calderon identities, the low frequency instability is removed while still maintaining the inherent accuracy of the EFIE. It was also demonstrated that the spectral properties of the Calderon preconditioner are conserved during discretization if the EFIE operator is discretized with Rao-Wilton-Glisson expansion functions and the preconditioner with Buffa-Christiansen expansion functions. In this article we will show how the Calderon multiplicative preconditioner (CMP) can be combined with fast multipole methods to accelerate the numerical solution, leading to an overall complexity of O(N long N) for the entire iterative solution. At low frequencies, where the CMP is most useful, the traditional multilevel fast multipole algorithm (MLFMA) is unstable and we apply the nondirectional stable plane wave MLFMA (NSPWMLFMA) that resolves the low frequency breakdown of the MLFMA. The combined algorithm will be called the CMP-NSPWMLFMA. Applying the CMP-NSPWMLFMA at open surfaces or very low frequencies leads to certain problems, which will be discussed in this article.

A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well-posed even when applied to densely discretized volumes, a classically formulated S-EFIE operator is ill-posed when applied to densely discretized surfaces. This renders the discretized coupled S-EFIE and V-EFIE system ill-conditioned, and its iterative solution inefficient or even impossible. The proposed scheme regularizes the coupled set of S-EFIE and V-EFIE using a Calderon multiplicative preconditioner (CMP)-based technique. The resulting scheme enables the efficient analysis of electromagnetic interactions with composite structures containing fine/subwave-length geometric features. Numerical examples demonstrate the efficiency of the proposed scheme.

The Multilevel Fast Multipole Algorithm (MLFMA) is widely used for the acceleration of matrix-vector products in the iterative solution of scattering problems. The MLFMA, however, suffers from a low-frequency (LF) breakdown. This breakdown is usually avoided by hybridizing the MLFMA with a method that does not fail at LF. For example, the Green function can be decomposed using the spectral representation or multipoles. Recently, a novel decomposition was presented, which uses so-called pseudospherical harmonics in the translation operator. In this contribution, the coupling of this method and the MLFMA will be investigated in detail.

Electromagnetic scattering by dielectric bodies can be described by two integral equations: the PMCHWT equation and the Mu¨ller equation. The spectral properties of the former resemble those of the EFIE, while the spectral properties of the latter resemble those of the MFIE. Indeed, the PMCHWT equation is susceptible to the low frequency and dense grid breakdowns. Recently, a solution for the dense grid breakdown of the EFIE has been proposed: Calderon preconditioning [1]. In this contribution, the Calderon preconditioning scheme is extended to the PMCHWT equation. the well-posedness of this new formulation is proven and numerical results testifying to the scheme's validity are presented.

The scattering of time-harmonic electromagnetic waves by perfect electrical conductors (PECs) can be modelled by several boundary integral equations, the magnetic and electric field integral equations (MFIE and EFIE) being the most prominent ones[1]. These equations can be discretized by expanding current distributions in terms of Rao-Wilton-Glisson (RWG) functions defined on a triangular mesh approximating the scatterer's surface and by testing the equations using the same RWG functions [2].

The interaction matrices originating from the Method of Moments (MoM) discretization of the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation pertinent to the analysis from (piecewise) homogeneous penetrable objects become ill-conditioned when either part or the entire scattering surface requires a dense discretization. This behavior is similar to that of the Electric Field Integral Equation (EFIE) for the scattering from perfectly conducting surfaces and finds its origin in the presence of compact and hypersingular components in the integral equation kernel.

We have indicated how the hierarchical partitioning approach can be used to obtain a scalable parallel MLFMA implementation in both two and three dimensions. In three dimensions, the radiation patterns need to be repartitioned at every level, both in elevation and azimuth. The hierarchical approach was implemented in an asynchronous fashion in an open-source two-dimensional solver which can be downloaded free of charge (http://www.openfmm.net). The accurate scattering at a very large two-dimensional cylinder with a diameter of 1.2 million of wavelengths was reported.

Calderon preconditioning is very succesful in stabilising the EFIE and the use of BC functions makes the formalism valid on open surfaces. Through applying a broadband fast multipole method, the complexity can be reduced from O (N2) to O(N log N), allowing the simulation of very large structures. In the high frequency case a localised version of the preconditioner must be used to avoid excessive scattering of the eigenvalues of the combined operator.

Progress in science is usually an almost continuous process only taking small steps at a time. The invention of the PML [1] by J.-P. Berenge definitely was not continuous. The impact of this invention on computational electromagnetics and beyond cannot be overestimated. This was immediately clear for the audience that in 1994 attended the dedicated lecture at the IEEE Antennas and Propagation Symposium in Seattle. A short conversation of the first author with Berenger several years later in Paris revealed that for J.-P. Berenger this invention was a simple and obvious solution to a problem on his desk. He needed something that absorbed without reflection incident waves that arrived from almost any direction and for all frequencies.

Using the proposed preconditioning technique, fast convergence can be obtained. This is illustrated for a simulation of a straight wire. In Fig. 1 the number of iterations needed by the proposed regularized Green function preconditioned EFIE solver is compared with that needed by a Calderon preconditioned [3] and unpreconditioned solver. The number of iterations required by the proposed preconditioner is almost independent of the number of unknowns. The number of iterations needed using the unpreconditioned system, or the Calderon preconditioned system, is O(N). Similar results apply for wires of other lengths.

Large planar microwave structures, such as frequency selective surfaces and reflectarrays, are of practical use in many applications. These structures' scattering cross sections are of great interest to the design engineer. During the design cycles, reliable full-wave simulations of these large planar structures can provide useful information. Often, however, the computational requirements (both in term of memory consumption and CPU solving time), needed to accurately compute such scattering cross sections, are huge.

A new approach to discretize the electric field integral equation (EFIE) that hybridizes Calderon and hierarchical techniques is presented. The benefits of these two techniques are combined and inherited by the proposed method. The result is an EFIE solver which is immune from low-frequency breakdown, well-conditioned in the presence of densely discretized structures and exhibits only minimal computational overhead. The hybridization is achieved by observing that hierarchical techniques link the conditioning of the global EFIE problem to that of a reduced size problem that can be successfully regularized by a properly tailored Calderon approach. Numerical results will show the performance of the proposed method and its advantages over to the state of the art.

The Multilevel Fast Multipole Algorithm (MLFMA) is a well known and very successful method for accelerating the matrix‐vector products required for the iterative solution of Helmholtz problems. The MLFMA is based on an addition theorem which suffers from the so‐called low‐frequency (LF) breakdown, due to numerical roundoff error. Here, a new addition theorem will be developed which does not suffer from an LF breakdown. Instead it suffers from a High‐Frequency (HF) breakdown. The new addition theorem is based on a novel set of distributions, the so called pseudospherical harmonics, closely related to the spherical harmonics. The so‐called translation operators can be calculated in closed form, which allows the easy implementation of an LF‐stable MLFMA.

A new technique for preconditioning electric field integral equations (EFIEs) by leveraging Calderon identities is presented. In contrast to all previous Calderon EFIE preconditioners, the proposed preconditioner is purely multiplicative in nature, applicable to open and closed structures, straightforward to implement, and easily interfaced with existing method of moments codes. Numerical results demonstrate that the method of moments (MoM) matrix equations obtained using the proposed preconditioner converge rapidly, independently of the discretization density.

In this paper, a new technique for preconditioning electric field integral equations (EFIEs) by leveraging Calderon identities is presented. In contrast to all previous Calderon preconditioners, the proposed preconditioner is purely multiplicative in nature, applicable to open and closed structures, straightforward to implement, and easily interfaced with existing method of moments (MoM) code. Numerical results demonstrate that the MoM EFIE system obtained using the proposed preconditioning converges rapidly, independently of the discretization density.

In [4] we presented a new asynchronous kernel-independent parallel multilevel fast multipole algorithm (MLFMA), applied to full-wave electromagnetic simulations in two dimensions and in the time-harmonic domain. In this contribution, we report the progress in the extension of this work to three dimensions. An asynchronous algorithm becomes indispensable when more complicated geometries are considered, with multiple dielectrics and conductors, possibly attached to or embedded into each other. Previous efforts in literature were largely focused on single, perfect electric conducting (PEC) objects. The underlying method of moments (MoM) makes use of the Rao-Wilton-Glisson (RWG) basis functions and the conventional choices for the boundary integral equations (BIE). The MLFMA algorithm is applied to a variety of three dimensional simulations, demonstrating its versatility. (5 pages)

In this contribution we extend our work on the application of boundary integral equations to accurately predict the shielding properties of complex enclosure geometries. The focus of this contribution is on the power of the splay tree algorithm to efficiently extract symmetry properties from a geometry. We will show that by using these splay trees in two as well as three dimensions significant savings in CPU time can be achieved allowing for the evaluation of ever more complex structures within a given computation time. We show different results for enclosures in two dimensions and also illustrate the time savings of splay trees in three dimensions. At the time of the conference we will also show three-dimensional shielding problems.

We present a parallel multilevel fast multipole algorithm aimed at low cost parallel computers such as GRID computer environments and clusters of workstations. The algorithm is a scheduling algorithm where work packets are handled in a certain order to ensure minimal idle time of the processors and to avoid simultaneous bursts of communication between the processors. The algorithm is implemented on a method of moment discretization of a two-dimensional TM electromagnetic scattering problem. Examples of several optical devices with a size up to 28 500 wavelengths are presented.

In this contribution we present a design environment for the optimization of layered absorbers. The manufacturer has a wide set of materials with known properties available. The thickness of these materials can vary within given limits. For a given number of layers and given absorption requirements as a function of angle of incidence, polarization and frequency we try to optimize for the thicknesses of the layers and for the best possible choice of available material types. The optimization for the layer thicknesses is done using a simulated annealing technique and for selecting materials usually the whole discrete design space is sampled. The paper is illustrated with two realizations comprising comparisons between simulations and measurements.

In this paper a simplified "1.5D" modeling approach is presented which can be used to characterize and optimize an entire active millimeter wave imaging system for concealed weapon detection. The method uses Huygens' Principle to compute one field component on selected planes of the imaging set-up. The accuracy of the method is evaluated by comparing it to a rigorous 2D method of moments approach. The model includes the effects of lenses, diffusers, mirrors, object and any other component present in the system. The approach allows fast determination of the influence of each of the system components on the image projected onto the sensor, including effects such e.g. speckle. Also, the effectivity of different speckle reduction techniques, e.g. using a Hadamard diffuser or a multifrequency approach are evaluated in this paper.

A novel rank-revealing shielded-block preconditioner that accelerates the iterative integral-equation-based analysis of wave propa- gation in electromagnetic crystal (EC) devices is presented. The pro- posed shielded-block preconditioner exploits the bandgap character of the background electromagnetic crystal in order to achieve both rapid convergence of the iterative solver as well as a low matrix-vector multi- plication cost. The versatility and computational efficiency of the shield- ed-block preconditioner are demonstrated by its application to the anal- ysis of wave propagation in a defectless electromagnetic crystal along an electromagnetic crystal waveguide and out of an electromagnetic crystal horn antenna array. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 783-789, 2006; Published online in Wiley Inter- Science (www.interscience.wiley.com). DOI 10.1002/mop.21475

We present a combined fast multilevel multipole technique combined with a singular value decomposition to evaluate the shielding effectiveness of enclosures with complex fillings up to very high frequencies and limited computer resources. Special preconditioners are proposed, adapted to the problem at hand, to reduce the number of iterations necessary. The accuracy is fully controlled and special care is taken to evaluate singular or quasi-singular contributions from the Green functions in closed form. As an example enclosures filled with a large number of boards are considered.

The paper deals with a two-dimensional numerical model for the evaluation of the electromagnetic hysteretic behavior of thin magnetic sheets when applying a unidirectional magnetic field. The time variation of the magnetization vector m in each space point obeys the Landau-Lifshitz equation. The effective field is the result of several contributions: the applied field, the magnetostatic field, the anisotropy field, and the exchange field. Microstructural features, such as grain size and crystallographic texture, are introduced in the micromagnetic model by dividing the geometry in subregions, each with its own magnetic preferable directions. In the article, numerical experiments are presented aiming at low-frequency applications. The presented micromagnetic model is used to study magnetic memory material properties.

The singularities of the full-wave Green dyadics for general uniaxial bianisotropic media are derived by utilising closed form representations for the static Green dyadics. The result includes previously obtained results for isotropic and bi-isotropic media as special cases.

Recent advances in the parallel multilevel fast multipole algorithm have paved the way for large-scale full-wave electromagnetic simulations. The introduction of the hierarchical partitioning technique and the use of an asynchronous parallel implementation have resulted in a scalable algorithm that runs efficiently, even on low-cost clusters. Presented is the accurate solution of the two-dimensional (2-D) transverse magnetic scattering at both a perfect electric conducting cylinder with a diameter of one million wavelengths and a dielectric cylinder with a diameter of half a million wavelengths.

In the parallel multilevel fast multipole algorithm (MLFMA), there exist two fundamental partitioning schemes for the distribution of the workload across processors: the spatial distribution of boxes and the spectral distribution of field samples. These two schemes can be combined in various manners. It is analytically and numerically shown that, in two dimensions, the recently introduced hierarchical approach yields a scalable parallel MLFMA. For the three-dimensional case, it is proved that only the combination of the hierarchical partitioning scheme and a two-dimensional partitioning of the field samples leads to a scalable algorithm.

A field simulator optimised rectangular-ring microstrip antenna covering the HiperLAN band is described. The proposed design has the advantage of operating with a single feed while avoiding linear polarisation. Measured data from an indoor environment confirm the method of moments (MoM) predictions both with respect to efficiency and with respect to polarisation.

A single-feed rectangular-ring microstrip antenna is proposed for indoor communication under the Bluetooth protocol. The dimensions of the antenna together with the location of the feed point are optimised through field simulations in order to cover the Bluetooth bandwidth and to avoid linear polarisation. The performance and the efficiency of the antenna are illustrated in a real indoor environment.

A new efficient method is outlined for calculating the far-field pattern of waveguide discontinuities. An open configuration is turned into a closed configuration using perfectly matched layers. Using a mode-matching scheme on the resulting configuration, the total field on the discontinuity can be determined. The far-field is calculated by taking the Fourier transform of this field and multiplying it by the Huygens obliquity factor. Results are presented for a GaAs-AlGaAs laser facet and a truncated grounded dielectric slab.

A new approach for determining the reflection and transmission at waveguide discontinuities is outlined. The perfectly matched layer concept is used to transform the open problem into a closed problem. The discrete modes of the resulting planar stratified uniaxially anisotropic media are then used in a mode matching scheme.