Dissipation Factors of Spherical Current Modes on Multiple Spherical Layers

Radiation efficiencies of modal current densities distributed on a spherical shell are evaluated in terms of dissipation factor. The presented approach is rigorous, yet simple and straightforward, leading to closed-form expressions. The same approach is utilized for a two-layered shell and the results are compared with other models existing in the literature. Discrepancies in this comparison are reported and reasons are analyzed. Finally, it is demonstrated that radiation efficiency potentially benefits from the use of internal volume which contrasts with the case of the radiation Q-factor.Comment: 5 pages, 5 figure

Inversion-Free Evaluation of Nearest Neighbors in Method of Moments

A recently introduced technique of topology sensitivity in method of moments is extended by the possibility of adding degrees-of-freedom (reconstruct) into underlying structure. The algebraic formulation is inversion-free, suitable for parallelization and scales favorably with the number of unknowns. The reconstruction completes the nearest neighbors procedure for an evaluation of the smallest shape perturbation. The performance of the method is studied with a greedy search over a Hamming graph representing the structure in which initial positions are chosen from a random set. The method is shown to be effective data mining tool for machine learning-related applications.Comment: 5 pages, 8 figures (one of them is animated), 1 table, accepted to AWP

Conditional Euclidean distance optimization via relative tangency

We introduce a theory of relative tangency for projective algebraic varieties. The dual variety $X_Z^\vee$ of a variety $X$ relative to a subvariety $Z$ is the set of hyperplanes tangent to $X$ at a point of $Z$. We also introduce the concept of polar classes of $X$ relative to $Z$. We explore the duality of varieties of low rank matrices relative to special linear sections. In this framework, we study the critical points of the Euclidean Distance function from a data point to $X$, lying on $Z$. The locus where the number of such conditional critical points is positive is called the ED data locus of $X$ given $Z$. The generic number of such critical points defines the conditional ED degree of $X$ given $Z$. We show the irreducibility of ED data loci, and we compute their dimensions and degrees in terms of relative characteristic classes.Comment: 40 pages, 4 figure

Optimal Planar Electric Dipole Antenna

Considerable time is often spent optimizing antennas to meet specific design metrics. Rarely, however, are the resulting antenna designs compared to rigorous physical bounds on those metrics. Here we study the performance of optimized planar meander line antennas with respect to such bounds. Results show that these simple structures meet the lower bound on radiation Q-factor (maximizing single resonance fractional bandwidth), but are far from reaching the associated physical bounds on efficiency. The relative performance of other canonical antenna designs is compared in similar ways, and the quantitative results are connected to intuitions from small antenna design, physical bounds, and matching network design.Comment: 10 pages, 15 figures, 2 tables, 4 boxe

Method of Moments and T-matrix Hybrid

Hybrid computational schemes combining the advantages of a method of moments formulation of a field integral equation and T-matrix method are developed in this paper. The hybrid methods are particularly efficient when describing the interaction of electrically small complex objects and electrically large objects of canonical shapes such as spherical multi-layered bodies where the T-matrix method is reduced to the Mie series making the method an interesting alternative in the design of implantable antennas or exposure evaluations. Method performance is tested on a spherical multi-layer model of the human head. Along with the hybrid method, an evaluation of the transition matrix of an arbitrarily shaped object is presented and the characteristic mode decomposition is performed, exhibiting fourfold numerical precision as compared to conventional approaches.Comment: 15 pages, 19 figures, 3 table

Iterative Calculation of Characteristic Modes Using Arbitrary Full-wave Solvers

An iterative algorithm is adopted to construct approximate representations of matrices describing the scattering properties of arbitrary objects. The method is based on the implicit evaluation of scattering responses from iteratively generated excitations. The method does not require explicit knowledge of any system matrices (e.g., stiffness or impedance matrices) and is well-suited for use with matrix-free and iterative full-wave solvers, such as FDTD, FEM, and MLFMA. The proposed method allows for significant speed-up compared to the direct construction of a full transition matrix or scattering dyadic. The method is applied to the characteristic mode decomposition of arbitrarily shaped obstacles of arbitrary material distribution. Examples demonstrating the speed-up and complexity of the algorithm are studied with several commercial software packages.Comment: 5 pages, 2 figures, 2 algorithm

The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices

We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over a linear space of symmetric matrices. We obtain new formulae for the ML degree, one via Schubert calculus, and another using Segre classes from intersection theory. We settle the case of codimension one models, and characterize the degenerate case when the ML degree is zero.Comment: 21 pages and 1 figur

Trade-offs in absorption and scattering by nanophotonic structures

Trade-offs between feasible absorption and scattering cross sections of obstacles confined to an arbitrarily shaped volume are formulated as a multi-objective optimization problem solvable by Lagrangian-dual methods. Solutions to this optimization problem yield a Pareto-optimal set, the shape of which reveals the feasibility of achieving simultaneously extremal absorption and scattering. Two forms of the trade-off problems are considered involving both loss and reactive material parameters. Numerical comparisons between the derived multi-objective bounds and several classes of realized structures are made. Additionally, low-frequency (electrically small, long wavelength) limits are examined for certain special cases.Comment: 16 pages, 9 figure

Characteristic Modes of Frequency-Selective Surfaces and Metasurfaces from S-parameter Data

Characteristic modes of arbitrary two-dimensional periodic systems are analyzed using scattering parameter data. This approach bypasses the need for periodic integral equations and allows for characteristic modes to be computed from generic simulation or measurement data. Example calculations demonstrate the efficacy of the method through comparison against a periodic method of moments formulation for a simple, single-layer conducting unit cell. The effect of vertical structure and electrical size on the number of modes is studied and its discrete nature is verified with example calculations. % Additional examples verify the binary impact of vertical structure on the number of radiating characteristic modes. A multiband polarization-selective surface and a beamsteering metasurface are presented as additional examples.Comment: 11 pages, 11 figure