Electromagnetic field expansion in a Wilson basis

A Wilson basis is an ingenious modification of a Gabor frame, with basis functions that have a notionally compact support in phase space. We shall give a short description of an algorithm for the construction of a Wilson basis. Through spatial scaling of the Wilson basis relative to a higher-order LP-mode, the basis may appear to vary from effectively local to effectively global. For mode-matching purposes local is advantageous. However, the field expansion requires fewer coefficients in the more global basis

Electromagnetic modelling of large complex 3-D structures with LEGO and the eigencurrent expansion method

Linear embedding via Green's operators (LEGO) is a computational method in which the multiple scattering between adjacent objects - forming a large composite structure - is determined through the interaction of simple-shaped building domains, whose electromagnetic (EM) behavior is accounted for by means of scattering operators. This method has been successfully demonstrated for 2-D electromagnetic band-gaps (EBG) and other structures, and for very simple 3-D configurations. In this communication we briefly report on the full extension of LEGO to large complex 3-D structures, which may be EBG-based but may also include finite antenna arrays as well as frequency selective surfaces, to name but a few applications. In particular, we shall outline two modifications that were crucial for scaling up the LEGO method, namely, the introduction of a total inverse scattering operator S_1 and the eigencurrent expansion method (EEM)

Sensitivity analysis of 3-D composite structures through linear embedding via green's operators

We propose a methodology --- based on linear embedding via Green's operators (LEGO) and the eigencurrent expansion method (EEM) --- for solving electromagnetic problems involving large 3-D structures comprised of ND = 1 bodies. In particular, we address the circumstance when the electromagnetic properties or the shape of one body differ from those of the others. In real-life structures such a situation may be either the result of a thoughtful design process or the unwanted outcome of fabrication tolerances. In order to assess the sensitivity of physical observables to localized deviations from the "ideal" structure, we follow a deterministic approach, i.e., we allow for a finite number of different realizations of one of the bodies. Then, for each realization we formulate the problem with LEGO and we employ the EEM to determine the contribution of the ND - 1 "fixed" bodies. Since the latter has to be computed only once, the overall procedure is indeed efficient. As an example of application, we investigate the sensitivity of a 2-layer array of split-ring resonators with respect to the shape and the offset of one element in the array

An eigencurrent approach to the analysis of electrically large 3-D structures using linear embedding via Green's operators

We present an extension of the Linear Embedding via Greens Operators (LEGO) procedure for efficiently dealing with 3-D electromagnetic composite structures. In LEGOs notion, we enclose the objects forming a structure within arbitrarily shaped domains (bricks), which (by invoking the Equivalence Principle) we characterize through scattering operators. In the 2-D instance, we then combined the bricks numerically, in a cascade of successive embedding steps, to build increasingly larger domains and obtain the scattering operator of the whole aggregate of objects. In the 3-D case, however, this process becomes quite soon impracticable, in that the resulting scattering matrices are too big to be stored and handled on most computers. To circumvent this hurdle, we propose a novel formulation of the electromagnetic problem based on an integral equation involving the total inverse scattering operator of the structure, which can be written analytically in terms of scattering operators of the bricks and transfer operators among them. We then solve this equation by the Method of Moments combined with the Eigencurrent Expansion Method, which allows for a considerable reduction in size of the system matrix and thereby enables us to study very large structures

Intrinsic attenuation in multi-mode fiber interconnects

A Wilson basis is an ingenious modification of a Gabor frame, with basis functions that have a notionally compact support in phase space. We shall give a short description of an algorithm for the construction of a Wilson basis. Through spatial scaling of the Wilson basis relative to a higher-order LP-mode, the basis may appear to vary from effectively local to effectively global. For mode-matching purposes local is advantageous. However, the field expansion requires fewer coefficients in the more global basis

Enhancing the computational speed of the modal Green function for the electric-field integral equation for a body of revolution

We propose an interpolation technique to reduce the computation time of the integrals involved in the electric field integral equation modal Green function for a perfectly conducting body of revolution in free space. The proposed technique is based on applying an appropriate interpolation to the singular part of the modal Green function, which is computationally expensive. By analyzing the electromagnetic scattering of various objects, it is shown that the proposed interpolation scheme can reduce the corresponding computational time by more than a factor of 100

A priori error estimate and control in the eigencurrent expansion method applied to linear embedding via Green's operators (LEGO)

Linear embedding via Green's operators (LEGO) [1,2] is a domain decomposition method in which the electromagnetic scattering by an aggregate of Np bodies (immersed in a homogeneous background medium) is tackled by enclosing each object within an arbitrarily-shaped bounded domain T>k (brick), k = 1,... ,Nd (e.g., see Fig. 1). The bricks are characterized electromagnetically by means of scattering operators Skk, which are subsequently combined to form the total inverse scattering operator S_1 of the structure [1]. Finally, we use the eigencurrent expansion method