Frank Olyslager

An efficient series expansion for the 2D Green's function of a microstrip substrate using perfectly matched layers

A new efficient technique is proposed to derive a series representation for the two-dimensional (2-D) Greens function of a planar substrate. A perfectly matched layer (PML) is used to turn the original open configuration into a closed one. The resulting structure is regarded as a waveguide and the resulting-analytically known-discrete set of eigenmodes is then used to expand the Greens function. The method turns out to be elegant and efficient for distances larger than 0.1/spl lambda/ away from the source.

New fast and accurate line parameter calculation of general multiconductor transmission lines in multilayered media

An enhanced method to calculate the C, L, and R of a multiconductor bus in a multilayered medium is presented. Different board technologies, conductors of complicated shape, and conductors embedded in different layers can be handled without loss of accuracy or substantial increase in CPU time compared with existing simulation techniques. Correct determination of skin effect losses is shown to depend critically on surface charge modeling. Surface charge discontinuities are explicitly taken into account which results in reduced computation time. A further reduction of computation time is obtained by a particular treatment of the calculation of the Greens function. >

New reciprocal circuit model for lossy waveguide structures based on the orthogonality of the eigenmodes

In this contribution, we present a new consistent equivalent transmission line model to describe the propagation along lossy hybrid waveguide structures. All existing consistent transmission line models are based on the assumption that the power propagated by the modes considered in the waveguide is the same as the power propagated in the model. In a lossy reciprocal waveguide, this leads to a nonreciprocal transmission line model because the modes are not power orthogonal. We start from the Lorentz orthogonality condition to construct a reciprocal transmission line model, even for lossy waveguides. For multiconductor waveguides, we discuss what we call RI-and RV-models, in analogy with the existing PI- and PV-models. We also present a generalisation of these RI- and RV-models to general waveguide structures. The theory is illustrated with a comparison of an RI- and PI-model for a lossy thick microstrip structure. >

The diaphanous wedge

Complete solutions for the scattering by a diaphanous wedge, meaning a wedge with identical wavenumbers inside and outside the wedge, are presented. The results are obtained from an integral equation for the fields on the wedge, which is solved by the Mellin and Kantorovich-Lebedev transforms in the static and dynamic cases, respectively. Pertinent formulations of Gegenbauers addition theorems play an important part in the derivation of the results, which are presented in closed form.

Electromagnetics and exotic media: a quest for the holy grail

During the past eight years, the authors have extensively studied the properties of linear homogeneous bianisotropic media. They have studied the Greens dyadics, the factorization of the Helmholtz determinant operator, the field and source decomposition, and plane-wave propagation in various classes of these media. We give an overview of our findings, and we place these findings in historical order. The results we found provide insight into the nature of Maxwells equations, in general, and into the field propagation mechanisms in the different media, in particular. Finally, we mention that closed-form solutions are valuable as benchmarking results for numerical solutions.

Study of eigenmodes in periodic waveguides using the Lorentz reciprocity theorem

Photonic crystals, frequency-selective surfaces, gratings, and many so-called metamaterials are composed of periodic arrangements of objects. Such an arrangement of objects quickly forms a periodic waveguide. In this paper, we investigate a number of properties of the eigenmodes in general periodic waveguides using the Lorentz reciprocity theorem. Such an analysis seems to be missing in the literature. We present an original proof for the intimate relation between bidirectionality of a periodic waveguide and reciprocity. We also derive compact expressions for the excitation coefficients of the eigenmodes when the waveguide is excited by a source density or an incident field. The analysis is generalized to include periodic waveguides composed of anisotropic and bianisotropic materials.

Fast analysis of 2-D electromagnetic crystal devices using a periodic Green function approach

A novel integral equation-based method for simulating wave propagation in two-dimensional (2-D) electromagnetic crystal (EC) devices is presented. A small number of irregular defects aside, the targeted devices are obtained by removing cylinders from infinite, doubly periodic, and defectless electromagnetic crystals. Integral equations in terms of equivalent currents that reside on the surfaces of the voids left by the removed cylinders are constructed by using Green functions innate to the defectless electromagnetic crystal. The sparse system of equations that results upon discretizing these integral equations is solved efficiently by a multifrontal method. The scheme is ideally suited to extract electromagnetic crystal device S parameters as it permits imposing modal excitations and exact absorbing boundary conditions. The scheme is applied to the analysis of two multiplexer-demultiplexer devices, a filter, and a bended EC waveguide, thereby demonstrating its versatility and computational efficiency.

Comparative study of three methods for the simulation of two-dimensional photonic crystals

Three methods for the efficient simulation of two-dimensional photonic crystal structures are compared, namely, a semianalytical multiple-scattering technique; a vectorial eigenmode expansion technique; and a FDTD-ROM technique. The basic principles of each method are presented. For the semianalytical technique and for the vectorial eigenmode expansion technique, we show how reflections coming from abruptly terminated waveguides can be avoided. The main advantages and disadvantages of each method are discussed. Results from use of the three methods are compared for several photonic crystal structures.

Automatic generation of subdomain models in 2D FDTD using reduced order modeling

A new method combining a finite difference method and a reduced order model (ROM) algorithm is presented for two-dimensional (2-D) electromagnetic problems. The problem space is subdivided into subdomains of a generic type. By discretizing the spatial derivatives in a way similar to the finite-difference in time-domain technique (FDTD), the state equations are written down in each subdomain. From that, an FDTD-subdomain model is derived. Finally, the different subdomains are reconnected and the original problem is solved by a leapfrog time-stepping algorithm. Some numerical results are presented to illustrate the new approach.

An integral equation approach to the prediction of indoor wave propagation

A two-dimensional method of moments solution technique for the simulation of electrically large structures is presented. This technique is based on a boundary integral equation description, and was designed to keep CPU time and memory requirements within acceptable limits even for problems of several thousands of unknowns. This is achieved through an optimized calculation of the interaction integrals leading to the moment method interaction matrix and through a so-called impedance matrix transformation of this matrix to a sparse form. The resulting sparse system of linear equations is efficiently solved using a conjugate gradient algorithm. The entire solution technique is applied to the simulation of indoor wave propagation problems and is illustrated by two examples.