Homogenization of metamaterials using full-wave simulations

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.     

High-frequency reciprocity-based circuit model for the incidence ofelectromagnetic waves on general waveguide structures

In the present contribution we construct a high-frequency circuit model for the excitation of eigenmodes in general waveguides due to externally impinging electromagnetic waves. The circuit model, consisting of distributed sources in a transmission line model, is based on Lorentz's reciprocity theorem. The classical quasi-TEM solution of this problem is found as a special case from the full-wave model. The theory is illustrated with numerical examples of electric dipoles radiating above thick coupled lossy microstrip lines     

Rigorous analysis of the propagation characteristics of generallossless and lossy multiconductor transmission lines in multilayeredmedia

The frequency-dependent propagation characteristics of lossless and lossy open coupled polygonal conductor transmission lines in a multilayered medium are determined based on a rigorous full-wave analysis. A boundary integral equation technique is used in conjunction with the method of moments. Losses in conductors and layers are included in an exact way without making use of a perturbation approach. Dispersion curves for the complex propagation constants and impedances are presented for a number of relevant examples and, where possible, compared with published data     

Full-wave analysis of coupled perfectly conducting wires in amultilayered medium

A full-wave analysis of coupled perfectly conducting cylindrical wires in a multilayered dielectric medium is presented. The analysis is based on a Fourier series expansion of the unknown surface currents on each wire and on an integral equation for the longitudinal field on the wires. The calculations are not restricted to the propagation constants of the different modes, but explicit results are presented for the impedances associated with each wire and each eigenmode as a function of frequency. Propagation constants, longitudinal currents on the wires, and impedances lead to a complete equivalent circuit for the structures being considered     

Efficient calculation of far-field patterns of waveguidediscontinuities using perfectly matched layers

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     

Generation of FDTD subcell equations by means of reduced order modeling

Adapted finite-difference time-domain (FDTD) update equations exist for a number of objects that are smaller than the grid step, such as wires and thin slots. We provide a technique that automatically generates new FDTD update equations for small objects. Our presentation focusses on 2D-FDTD. We start from the FDTD equations in a fine grid where the time derivative is not discretised. This yields a large state-space model that is drastically reduced with a reduced order modeling technique. The reduced state-space model is then translated into new FDTD update equations that can be used in an FDTD simulation in the same way as the existing update equations for wires and thin slots. This technique is applied to a number of numerical problems showing the accuracy and versatility of the proposed method.     

Series representation of Green dyadics for layered media using PMLs

The Green dyadics for closed layered media, i.e., layered media bounded by a perfectly conducting plate at the bottom and top of the structure, can be expanded in a discrete surface wave series. For open layered media with semi-infinite layers at the top and/or bottom of the structure, the discrete series needs to be complemented by a branch-cut integral of space waves. In this paper, we present a technique to circumvent this branch-cut integral by truncating the semi-infinite layers with a perfectly matched layer (PML) that is backed by a perfect electric conductor (PEC). It is demonstrated that in this way it is possible to obtain an accurate series or closed-form representation for the Green dyadic of the open layered medium. The series allows a very efficient calculation and storage of the Green dyadic if it is needed for multiple observation and or excitation points. Very close to the source the series loses efficiency. It is shown that the determination of the surface waves in the PML truncated layered medium has the same complexity as the determination of the surface waves in a PEC truncated layered medium without a PML.     

High-frequency reciprocity based circuit model for the incidence ofelectromagnetic waves on general circuits in layered media

Traditionally a circuit on a high-speed multichip module (MM) or a microwave monolithic integrated circuit (MMIC) is represented in an equivalent circuit by S-parameters for the different components, such as filters or bends, and by transmission lines for the interconnections between the components. Nowadays the S-parameters of the components are easily determined by a numerical electromagnetic analysis. Different components close to each other will interact, often this interaction is unwanted. In the present contribution we develop a circuit model for these interactions without having to perform a global electromagnetic analysis of the interacting components. These interactions are then represented by discrete and distributed sources in the equivalent circuit. Our technique is based on reciprocity and is focused on the surface wave interaction which is often the most important one. Each component is characterized by a surface wave radiation pattern     

A fast multipole method for layered media based on the application of perfectly matched layers - the 2-D case

An efficient fast multipole method (FMM) formalism to model scattering from two-dimensional (2-D) microstrip structures is presented. The technique relies on a mixed potential integral equation (MPIE) formulation and a series expression for the Green functions, based on the use of perfectly matched layers (PML). In this way, a new FMM algorithm is developed to evaluate matrix-vector multiplications arising in the iterative solution of the scattering problem. Novel iteration schemes have been implemented and a computational complexity of order O(N) is achieved. The theory is validated by means of several illustrative, numerical examples. This paper aims at elucidating the PML-FMM-MPIE concept and can be seen as a first step toward a PML based multilevel fast multipole algorithm (MLFMA) for 3-D microstrip structures embedded in layered media.     

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 Green's 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 Maxwell's 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