Low-rank properties in the hybrid finite element-boundary integral method

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Efficient computation of TM- and TE-polarized leaky modes in multilayered circular waveguides

In combination with the perfectly matched layer (PML)-paradigm, eigenmode expansion techniques have become increasingly important in the analysis and design of cylindrical and planar waveguides for photonics applications. To achieve high accuracy, these techniques rely on the determination of many modes of the modal spectrum of the waveguide under consideration. In this paper, we focus on the efficient computation of TM- and TE-polarized leaky modes for multilayered cylindrical waveguides. First, quasi-static estimates are derived for the propagation constants of these modes. Second, these estimates are used as a starting point in an advanced Newton iteration scheme after they have been subjected to an adaptive linear error correction. To prove the validity of the computation technique, it is applied to technologically important cases: vertical-cavity surface-emitting lasers and a monomode fiber

A perfectly matched layer based technique for the scattering from 1-D periodic microstrip structures

An efficient technique is presented to compute the scattering from one-dimensional (1-D) periodic microstrip structures, illuminated by a plane wave under perpendicular incidence. The technique relies on a Mixed Potential Integral Equation (MPIE), discretized by the Method of Moments (MoM), solving for the unknown current density flowing within a unit cell of the periodic structure. The pertinent 1-D periodic Green's functions are obtained by invoking the Perfectly Matched Layer (PML)-paradigm. The proposed formalism is illustrated and validated by evaluating the scattering from a 1-D periodic microstrip patch array

Analysis of coupled exponential microstrip lines by means of a multi-step perturbation technique

In this contribution, an iterative and adaptive multi-step perturbation technique for nonuniform transmission lines is presented and applied to the analysis of coupled exponential lines. The Telegrapher's equations for nonuniform lines, which do not have a closed-form solution, are recast as the equations for uniform lines with equivalent distributed sources, for which a well-known numerical solution procedure exists. The line voltages and currents are computed in multiple steps by iteratively updating the distributed sources. The method turns out to be faster than classical solutions based on the discretization of the line into uniform subsections. Two validation examples are proposed that deal with coupled exponential lines, which have relevant applicability in microwave components

An effective modeling framework for the analysis of interconnects subject to line-edge roughness

This letter proposes a complete and efficient simulation framework to assess the effects of line-edge roughness appearing in on-chip lines. The modeling approach consists of three steps. First, a stochastic macromodel is created for the per-unit-length RLGC parameters of the line. Secondly, random conductor edge profiles are generated using randomized splines. These are combined with the stochastic macromodel to readily provide place-dependent RLGC parameters. Finally, the resulting nonuniform transmission line is analyzed by means of a fast and accurate perturbation technique. To validate the proposed approach, a statistical analysis of the response of a coupled inverted embedded microstrip line is carried out for different roughness parameters

A hybrid MLFMM-UTD method for the solution of very large 2-D electromagnetic problems

The multilevel fast multipole method (MLFMM) is combined with the uniform theory of diffraction (UTD) to model two-dimensional (2-D) scattering problems including very large scatterers. The discretization of the very large scatterers is avoided by using ray-based methods. Reflections are accounted for by image source theory, while for diffraction a new MLFMM translation matrix is introduced. The translation matrix elements are derived based on a technique that generalizes the use of UTD for arbitrary source configurations and that efficiently describes the field over extended regions of space. O(n) scaling of the computational time and memory requirements is achieved for relevant structures, such as large antenna arrays in the presence of a wedge. The theory is validated by means of several illustrative numerical examples and is shown to remain accurate for non-line-of-sight (NLoS) scattering problems

Accurate study of the electromagnetic and circuit behavior of finite conducting wedges and interconnects with arbitrary cross-sections

The manufacturing of interconnects often leads to conductors with a non-rectangular cross-section. Especially for sharp edges, it is therefore important to study the influence of corner effects on the interconnect circuit characteristics. Firstly, the electromagnetic behavior of a finite conducting 2-D wedge is investigated. Secondly, as an application example, a broadband transmission line model is used to study the influence of the conductors' shapes on the circuit behavior of a grounded coplanar waveguide. Both frequency and time domain results are presented

An efficient 2-D MLFMM-UTD hybrid method to model non-line-of-sight propagation

We present a hybrid method that combines the Multilevel Fast Multipole Method (MLFMM) with the Uniform Theory of Diffraction (UTD) to model two-dimensional (2-D) scattering problems. The method is especially suited to model scattering in the presence of very large scatterers that obstruct the line-of-sight propagation between different devices with a more intricate geometry, such as antennas. The discretization of the large scatterers is avoided by using ray-based methods. An O(n) scaling is achieved for the computational time and required memory, n being the number of unknowns needed to discretize the antennas. The method is validated by a numerical example

A two-step perturbation technique for nonuniform single and differential lines

A novel two-step perturbation technique to analyze nonuniform single and differential transmission lines in the frequency domain is presented. Here, nonuniformities are considered as perturbations with respect to a nominal uniform line, allowing an interconnect designer to easily see what the effect of (unwanted) perturbations might be. Based on the Telegrapher's equations, the proposed approach yields second-order ordinary distributed differential equations with source terms. Solving these equations in conjunction with the pertinent boundary conditions leads to the sought-for currents and voltages along the lines. The accuracy and efficiency of the perturbation technique is demonstrated for a linearly tapered microstrip line and for a pair of coupled lines with random nonuniformities. Moreover, the necessity of adopting a two-step perturbation in order to get a good accuracy is also illustrated