# Computational Electromagnetics (CEM)

CEM group concentrates on theoretical research in classical electromagnetic theory. Among the currently developed topics belong radiation properties of electrically small radiators and scatterers and their optimizations. Members of the group have for many years been also involved in classical antenna theory and field propagation in artificial composite materials.

Current research activities are strongly entangled with a “source concept” paradigm, in which all involved field quantities as well as engineering metrics are described solely in terms of electromagnetic sources. The idea of the source concept is sketched in the following figure.

CEM team collaborates with other department’s teams.

### Past Members

Vit Losenicky
Michal Masek
Jakub Liska
Jonas Tucek
Vojtech Neuman

Martin Strambach
Lamyae Akrou

## Projects

• Virtual Prototyping and Validation of Electromagnetic Systems (2018-2021, TH04010373)
• Fundamental Bounds on Electromagnetic Radiation and Scattering Phenomena and Associated Realizable Subforms (2019-2021, GA19-06049S)
• Tools for Synthesis of Antennas and Sensors (2014-2017, TA04010457)
• Source Concept of Electrically Small Antenna Synthesis  (2015-2017, GA15-10280Y)

## Active External Collaborations

• University of Lund, Sweden (Mats Gustafson, Doruk Tayli, Casimir Ehrenborg)
• University of Santa Clara, USA (Kurt Schab)
• KTH Royal Institute of Technology, Sweden (Lars Johnsson)
• Catholic University of Leuven, Belgium (Guy Vandenbosch)
• Université Nice Sophia Antipolis (Fabien Ferrero)

### Journal Papers (Last Three Years)

#### Current and Antenna Optimization

 M. Gustafsson and M. Capek: "Maximum Gain, Effective Area, and Directivity", 2018, eprint arXiv: xxxx.xxxx. [Online]. Available: https://arxiv.org/abs/xxxx.xxxx Abstract Fundamental bounds on antenna gain are found via convex optimization of the current density in a prescribed region. Various constraints are considered, including self-resonance and only partial control of the current distribution. Derived formulas are valid for arbitrarily shaped radiators of a given conductivity. All the optimization tasks are reduced to eigenvalue problems, which are solved efficiently. The second part of the paper deals with superdirectivity and its associated minimal costs in efficiency and Q-factor. The paper is accompanied with a series of examples practically demonstrating the relevance of the theoretical framework and entirely spanning wide range of material parameters and electrical sizes used in antenna technology. Presented results are analyzed from a perspective of effectively radiating modes. In contrast to a common approach utilizing spherical modes, the radiating modes of a given body are directly evaluated and analyzed here. All crucial mathematical steps are reviewed in the appendices, including a series of important subroutines to be considered making it possible to reduce the computational burden associated with the evaluation of electrically large structures and structures of high conductivity. M. Capek, L. Jelinek, K. Schab, M. Gustafsson, B.L.G. Jonsson, F. Ferrero, and C. Ehrenborg: "Optimal Planar Electric Dipole Antenna", 2018, eprint arXiv: 1808.10755. [Online]. Available: https://arxiv.org/abs/1808.10755 Abstract 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. M. Capek, L. Jelinek, and M. Gustafsson: "Shape Synthesis Based on Topology Sensitivity", 2018, eprint arXiv: 1808.02479. [Online]. Available: https://arxiv.org/abs/1808.02479 Abstract A method evaluating the sensitivity of a given parameter to topological changes is proposed within the method of moments paradigm. The basis functions are used as degrees of freedom which, when compared to the classical pixeling technique, provide important advantages, one of them being impedance matrix inversion free evaluation of the sensitivity. The devised procedure utilizes port modes and their superposition which, together with only a single evaluation of all matrix operators, leads to a computationally effective procedure. The proposed method is approximately one hundred times faster than contemporary approaches, which allows the investigation of the sensitivity and the modification of shapes in real-time. The method is compared with known approaches and its validity and effectiveness is verified using a series of examples. The procedure can be implemented in up-to-date EM simulators in a straightforward manner. It is shown that the iterative repetition of the topology sensitivity evaluation can be used for gradient-based topology synthesis. This technique can also be employed as a local step in global optimizers. M. Gustafsson, M. Capek, and K. Schab, "Trade-off Between Antenna Efficiency and Q-Factor", 2017, eprint arXiv: 1802.01476. [Online]. Available: https://arxiv.org/abs/1802.01476 Abstract The trade-off between radiation efficiency and antenna bandwidth, expressed in terms of Q-factor, for small antennas is formulated as a multi-objective optimization problem in current distributions of predefined support. Variants on the problem are constructed to demonstrate the consequences of requiring a self-resonant current as opposed to one tuned by an external reactance. The resulting Pareto-optimal sets reveal the relative cost of valuing low Q-factor over high efficiency, the cost in efficiency to require a self-resonant current, and other insights. L Jelinek, K. Schab, and M. Capek, "The Radiation Efficiency Cost of Resonance Tuning", IEEE Trans. Antennas Propag, vol. 66, pp. 6716 - 6723, 2018. Abstract Existing optimization methods are used to calculate the upper-bounds on radiation efficiency with and without the constraint of self-resonance. These bounds are used for the design and assessment of small electric-dipole-type antennas. We demonstrate that the assumption of lossless, lumped, external tuning skews the true nature of radiation efficiency bounds when practical material characteristics are used in the tuning network. A major result is that, when realistic (e.g., finite conductivity) materials are used, small antenna systems exhibit dissipation factors which scale as (ka)^(−4), rather than (ka)^(−2) as previously predicted under the assumption of lossless external tuning. M. Capek, M. Gustafsson, and K. Schab, "Minimization of antenna quality factor", IEEE Trans. Antennas Propag., vol. 65, pp. 4115 - 4123, 2017. Abstract The optimal currents on arbitrarily shaped radiators with respect to the minimum quality factor Q are found using a simple and efficient procedure. The solution starts with a reformulation of the problem of minimizing quality factor Q as an alternative, so-called dual, problem. Taking advantage of modal decomposition and group theory, it is shown that the dual problem can easily be solved and always results in minimal quality factor Q. Moreover, the optimization procedure is generalized to minimize quality factor Q for embedded antennas, with respect to the arbitrarily weighted radiation patterns, or with prescribed magnitude of the electric and magnetic near-fields. The obtained numerical results are compatible with previous results based on composition of modal currents, convex optimization, and quasi-static approximations; however, using the methodology in this paper, the class of solvable problems is significantly extended. L. Jelinek and M. Capek, "Optimal currents on arbitrarily shaped surfaces," IEEE Trans. Antennas Propag., vol. 65, pp. 329 - 341, 2017. Abstract An optimization problem has been formulated to find a resonant current extremizing various antenna parameters. The method is presented on, but not limited to, particular cases of gain G, quality factor Q, gain to quality factor ratio G/Q, and radiation efficiency $\eta$ of canonical shapes with conduction losses explicitly included. The Rao-Wilton-Glisson basis representation is used to simplify the underlying algebra while still allowing surface current regions of arbitrary shape to be treated. By switching to another basis generated by a specific eigenvalue problem, it is finally shown that the optimal current can, in principle, be found as a combination of a few eigenmodes. The presented method constitutes a general framework in which the antenna parameters, expressed as bilinear forms, can automatically be extremized. M. Capek and L. Jelinek, "Optimal composition of modal currents for minimal quality factor Q", IEEE Trans. Antennas Propag., vol. 64, pp. 5230 - 5242, 2016. Abstract This work describes a powerful, yet simple, procedure how to acquire a current approaching the lower bound of quality factor Q. This optimal current can be determined for an arbitrarily shaped electrically small radiator made of a perfect conductor. Quality factor Q is evaluated by Vandenboschs relations yielding stored electromagnetic energy as a function of the source current density. All calculations are based on a matrix representation of the integro-differential operators. This approach simplifies the entire development and results in a straightforward numerical evaluation. The optimal current is represented in a basis of modal currents suitable for solving the optimization problem so that the minimum is approached by either one mode tuned to the resonance, or, by two properly combined modes. An overview of which modes should be selected and how they should be combined is provided and results concerning rectangular plate, spherical shell, capped dipole antenna and fractal shapes of varying geometrical complexity are presented. The reduction of quality factor Q and the G/Q ratio are studied and, thanks to the modal decomposition, the physical interpretation of the results is discussed in conjunction with the limitations of the proposed procedure.