arXiv subjects

Mats Gustafsson

Publications and source records attributed to Mats Gustafsson.

At least 19 recordsLinked to original sources

arXiv2026

Near-Field Sampling for Line Sources

Near-field sampling seeks to represent electromagnetic fields between transmitting and receiving regions using a minimal number of measurement points while preserving the dominant spatial modes. This paper develops a geometry-aware sampling framework based on spatial degrees of freedom (DoF). A view-length formulation is used to derive closed-form expressions for the propagating-mode DoF density for simple line-source geometries, providing both the total DoF and its local distribution. One-DoF sampling points are obtained from equal increments of the cumulative DoF density, yielding an adaptive nonuniform sampling strategy up to the knee of the singular-value spectrum. To improve the representation of the remaining modes beyond the knee, a reactive-mode density is introduced to guide the placement of additional edge samples. An operator-based sampling error functional is formulated and shown to be lower-bounded by the neglected singular values of the continuous channel operator. Numerical results demonstrate that the proposed sampling strategy closely approaches the optimal performance obtained from singular-value decomposition and significantly outperforms sampling based solely on the propagating-mode DoF density.

eess.SP↗

arXiv2026

Degrees of Freedom and Beamforming for Large Intelligent Surfaces

Spatial degrees of freedom (DoF), sampling, and beamforming are fundamental to multi-user large intelligent surfaces (LISs), where electromagnetic fields must be shaped, resolved, and focused at multiple near-field locations. This work estimates the number of DoF using closed-form expressions derived from the mutual shadow area for representative LIS configurations. The resulting DoF predictions are validated through numerical singular-value spectra, whose spectral knee points closely match the theoretical estimates. For line-source configurations, an analytic sampling scheme is developed by partitioning the source or observation line into unit-DoF intervals, enabling the selection of spatial samples. Beamforming results using maximum-ratio transmission and zero-forcing demonstrate that approximately the number of DoF independent beams can be formed. Attempting to exceed this limit results in increased interference and degraded performance. For surface-based LIS configurations, sampling points are instead determined numerically using the discrete empirical interpolation method. The corresponding beamforming results further confirm that the target region can support approximately as many independent beams as predicted by the DoF analysis. Finally, a polarization-aware study reveals that the electric-field components contribute unequally to the DoF and that the total-field DoF is twice that of a single polarization component.

eess.SP↗

arXiv2026

Spatial Degrees of Freedom and Channel Strength for Antenna Systems

The number of spatial degrees of freedom (NDoF) and channel strength in antenna systems are examined within a geometric framework. Starting from a correlation-operator representation of the channel between transmitter and receiver regions, we analyze the associated eigenspectrum and relate the NDoF to its spectral transition (corner). We compare the spectrum-based effective NDoF and effective rank metrics, clarifying their behavior for both idealized and realistic eigenvalue distributions. In parallel, we develop geometry-based asymptotic estimates in terms of mutual shadow (view) measures and coupling strength. Specifically, we show that while the projected length or area predicts the number of usable modes in two- and three-dimensional settings, the coupling strength determines the average eigenvalue level. Canonical configurations of parallel lines and regions are used to derive closed-form asymptotic expressions for the effective NDoF, revealing significant deviations from the spectral corner in closely spaced configurations. The results illustrate that these are physically grounded. The proposed theory and techniques are computationally efficient and form a toolbox for estimating the modal richness in near-field channels, with implications for array design, inverse problems, and high-capacity communication systems.

eess.SP↗

arXiv2026

Properties of Near Field Focusing for Three-Dimensional Large Intelligent Surface

This work investigates near-field focusing using a three-dimensional (3D) large intelligent surface (LIS) across frequencies and polarizations. Specifically, the LIS elements are distributed in 3D space within a long corridor, rather than being confined to a single planar aperture, and the focal point is located at a prescribed position in the radiating near field. By formulating optimization problems under both local and global power constraints, we obtain the corresponding optima. For continuous apertures, the optimal current magnitude distribution matches time-reversal (TR) solution under the global constraint and conjugate-phase (CP) solution when the local constraint dominates. When both constraints are active, the solution assigns larger excitation magnitudes to elements closer to the illumination field. This behavior remains invariant with respect to frequency and polarization for a fixed-size LIS. These findings are consistent to the more practical case of using discretized apertures in the form of Hertzian dipole arrays, studied using both analytical results and full-wave simulation. In addition, with the CP method, specific polarizations lead to identical transverse and longitudinal resolution, in contrast, under the TR method, these quantities can differ across polarizations.

eess.SP↗

arXiv2026

Interpreting Moment Matrix Blocks Spectra using Mutual Shadow Area

The mutual shadow area of pairs of surface regions is used for guiding the study of the spectral components and rank of their wave interaction, as captured by the corresponding moment matrix blocks. It is demonstrated that the mutual shadow area provides an asymptotically accurate predictor of the location of the singular value curve knee. This predicted knee index is shown to partition the interacting parts of the range and domain of blocks into two subspaces that can be associated with different wave phenomena: an "aperture" subspace of dimension that scales with the subdomains area (or length in 2-D) and a remainder "diffraction" subspace of dimension that scales much slower with the electrical length, depending on the geometric configuration. For interactions between open surface domains typical for the common hierarchical partitioning in most fast solvers, the latter can be attributed to the domain edges visible by its interacting counterpart. For interactions in 3-D with a small aspect angles between the source and observers, the diffraction subspace dimension is dominant in determining the rank until fairly large electrical lengths are reached. This explains the delayed asymptotic scaling of ranks and impressive fast solver performance observed in recent literature for seemingly arbitrary scatterers with no special geometric characteristics. In the extreme cases of "endfire" reduced dimensionality interactions, where the shadow area vanishes, the diffraction governs also the asymptotic rank, which translates to superior asymptotic solver performance.

math.NA↗

arXiv2025

Shadow Area and Degrees of Freedom for Free-Space Communication

The number of degrees of freedom (NDoF) in a communication channel fundamentally limits the number of independent spatial modes available for transmitting and receiving information. Although the NDoF can be computed numerically for specific configurations using singular value decomposition (SVD) of the channel operator, this approach provides limited physical insight. In this paper, we introduce a simple analytical estimate for the NDoF between arbitrarily shaped transmitter and receiver regions in free space. In the electrically large limit, where the NDoF is high, it is well approximated by the mutual shadow area, measured in units of wavelength squared. This area corresponds to the projected overlap of the regions, integrated over all lines of sight, and captures their effective spatial coupling. The proposed estimate generalizes and unifies several previously established results, including those based on Weyl's law, shadow area, and the paraxial approximation. We analyze several example configurations to illustrate the accuracy of the estimate and validate it through comparisons with numerical SVD computations of the propagation channel. The results provide both practical tools and physical insight for the design and analysis of high-capacity communication and sensing systems.

eess.SP↗

arXiv2025

Physical Limits and Optimal Synthesis of Beyond Diagonal Anomalous Scatterers

Realizing metasurfaces for anomalous scattering is fundamental to designing reflector arrays, reconfigurable intelligent surfaces, and metasurface antennas. However, the basic cost of steering scattering into non-specular directions is not fully understood. This paper derives tight physical bounds on anomalous scattering using antenna array systems equipped with non-local matching networks. The matching networks are explicitly synthesized based on the solutions of the optimization problems that define these bounds. Furthermore, we analyze fundamental limits for metasurface antennas implemented with metallic and dielectric materials exhibiting minimal loss within a finite design region. The results reveal a typical 6dB reduction in bistatic radar cross section (RCS) in anomalous directions compared to the forward direction. Numerical examples complement the theory and illustrate the inherent cost of achieving anomalous scattering relative to forward or specular scattering for canonical configurations.

physics.optics↗

arXiv2025

Fundamental Limits of Characteristic Mode Slopes

Characteristic Mode analysis is a widely used technique in antenna design, providing insight into the fundamental electromagnetic properties of radiating structures. In this paper, we establish fundamental bounds on the slope of characteristic mode eigenvalues and angles, demonstrating that their rate of change is subject to fundamental constraints for all possible realizations within a given design region. These bounds are derived using the method of moments and reformulating the frequency derivative (slope) of the eigenvalue quantities as an optimization problem over the current distribution confined to the design region. The results reveal a direct analogy between these constraints and classical antenna Q-factors, highlighting the intrinsic limitations on modal evolution and their implications for bandwidth and miniaturization in antenna design. Moreover, by iteratively enforcing orthogonality among the modes the derived bounds can be tightened for higher-order modes, providing deeper insight into the number of simultaneous, usable modes and their associated degrees of freedom. These bounds provide a feasibility criterion for achievable modal behavior, offering insights that can guide the design process. Examples are given for various surface PEC structures.

physics.comp-ph↗

arXiv2024

Characteristic Mode Analysis of Acoustic Scatterers

The explicit connection between the transition matrix and boundary element method integral operators is formulated. This enables the calculation of characteristic modes via eigenvalue problems involving either set of operators, leading to convenient orthogonality properties facilitating scattering analysis, solution of inverse problems, and the design of excitation fields.

physics.comp-ph↗

arXiv2024

Theory and Computation of Substructure Characteristic Modes

The problem of substructure characteristic modes is developed using a scattering matrix-based formulation, generalizing subregion characteristic mode decomposition to arbitrary computational tools. It is shown that the modes of the scattering formulation are identical to the modes of the classical formulation based on the background Green's function for lossless systems under conditions where both formulations can be applied. The scattering formulation, however, opens a variety of new subregion scenarios unavailable within previous formulations, including cases with lumped or wave ports or subregions in circuits. Thanks to its scattering nature, the formulation is solver-agnostic with the possibility to utilize an arbitrary full-wave method.

cs.CE↗

arXiv2024

Degrees of Freedom for Radiating Systems

Electromagnetic degrees of freedom are instrumental in antenna design, wireless communications, imaging, and scattering. Larger number of degrees of freedom enhances control in antenna design, influencing radiation patterns and directivity, while in communication systems, it links to spatial channels for increased data rates and reliability, and resolution in imaging. The correlation between computed degrees of freedom and physical quantities is not fully understood, prompting a comparison between classical estimates, Weyl's law, modal expansions, and optimization techniques. In this paper, it is shown that the number of degrees of freedom for arbitrary shaped radiating structures approaches the shadow area measured in squared wavelengths asymptotically as the wavelength decreases.

eess.SP↗

arXiv2024

Modes, Bounds, and Synthesis of Optimal Electromagnetic Scatterers

This paper presents an optimal synthesis of material distributions in obstacles for maximal extinction, scattering, or absorption. The material synthesis is based on an explicit construction utilizing the current distribution derived from physical bounds excited from the far-field. The bounds are expressed in radiation modes for materials restricted by their resistivity and characteristic modes for materials restricted by the contrast. The results are valid for arbitrary shapes, and analytical expressions are provided for spherical shapes.

math-ph↗

arXiv2024

Radiation Efficiency and Gain Bounds for Microstrip Patch Antennas

This paper presents radiation efficiency and gain bounds for microstrip patch antennas. The presented bounds are shown to be good predictors of antenna performance. Using the bounds, patch miniaturization techniques based on high permittivity substrates and geometrical shaping are compared. Further, a semi-analytic model is developed to approximate the bounds. Measurements are used to validate the bounds. Finally, maximum bandwidth of a microstrip patch antenna is linked to its maximum radiation efficiency.

eess.SP↗

arXiv2023

Characteristic Modes of Nonreciprocal Structures

The scattering formulation of characteristic mode decomposition is utilized to extend modal analysis to lossless scatterers breaking time-reversal symmetry. This enables characteristic modes analysis on devices containing gyrotropic or moving media. The resulting nonreciprocity introduces features not observed in reciprocal scenarios, such as asymmetric phase progression in characteristic far fields. These new phenomena are carefully discussed using examples of varying complexity. Indicators of nonreciprocity based on modal data are also introduced.

physics.class-ph↗

arXiv2023

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.

physics.app-ph↗

arXiv2023

Optimal Inverse Design Based on Memetic Algorithms -- Part 2: Examples and Properties

Optimal inverse design, including topology optimization and evaluation of fundamental bounds on performance, which was introduced in Part~1, is applied to various antenna design problems. A memetic scheme for topology optimization combines local and global techniques to accelerate convergence and maintain robustness. Method-of-moments matrices are used to evaluate objective functions and allow to determine fundamental bounds on performance. By applying the Shermann-Morrison-Woodbury identity, the repetitively performed structural update is inversion-free yet full-wave. The technique can easily be combined with additional features often required in practice, \eg{}, only a part of the structure is controllable, or evaluation of an objective function is required in a subdomain only. The memetic framework supports multi-frequency and multi-port optimization and offers many other advantages, such as an actual shape being known at every moment of the optimization. The performance of the method is assessed, including its convergence and computational cost.

math.OC↗

arXiv2023

Optimal Inverse Design Based on Memetic Algorithms -- Part 1: Theory and Implementation

A memetic framework for optimal inverse design is proposed by combining a local gradient-based procedure and a robust global scheme. The procedure is based on method-of-moments matrices and does not demand full inversion of a system matrix. Fundamental bounds are evaluated for all optimized metrics in the same manner, providing natural stopping criteria and quality measures for realized devices. Compared to density-based topology optimization, the proposed routine does not require filtering or thresholding. Compared to commonly used heuristics, the technique is significantly faster, still preserving a high level of versatility and robustness. This is a two-part paper in which the first part is devoted to the theoretical background and properties, and the second part applies the method to examples of varying complexity.

math.OC↗

arXiv2023

Energy Stored by Radiating Systems

Though commonly used to calculate Q-factor and fractional bandwidth, the energy stored by radiating systems (antennas) is a subtle and challenging concept that has perplexed researchers for over half a century. Here, the obstacles in defining and calculating stored energy in general electromagnetic systems are presented from first principles as well as using demonstrative examples from electrostatics, circuits, and radiating systems. Along the way, the concept of unobservable energy is introduced to formalize such challenges. Existing methods of defining stored energy in radiating systems are then reviewed in a framework based on technical commonalities rather than chronological order. Equivalences between some methods under common assumptions are highlighted, along with the strengths, weaknesses, and unique applications of certain techniques. Numerical examples are provided to compare the relative margin between methods on several radiating structures.

physics.class-ph↗