Prof. Mats Gustafsson
Department of Electrical and Information Technology
Lund University
Box 118, SE-221 00 Lund, Sweden
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http://www.eit.lth.se/staff/mats.gustafsson

Mats Gustafsson received the M.Sc. degree in Engineering Physics in 1994, the Ph.D. degree in Electromagnetic Theory in 2000, was appointed Docent in 2005, and Professor of Electromagnetic Theory 2011, all from Lund University, Sweden.

He co-founded the company Phase holographic imaging AB in 2004.  His research interests are in scattering and antenna theory and inverse scattering and imaging with applications in microwave tomography and digital holography. He has written over 60 peer reviewed journal papers and over 75 conference papers. 

Prof. Gustafsson received the best antenna poster prize at EuCAP 2007 and the IEEE Schelkunoff Transactions Prize Paper Award 2010.

Convex Optimization for Analysis of Small Antennas

Design of small antennas is challenging as the Q-factor, efficiency, and radiation resistance must be controlled simultaneously. In this presentation, it is shown that convex optimization together with closed form expressions of the stored electromagnetic energies provide a general method for analyzing many fundamental antenna problems. The solution to the convex optimization problem determines optimal currents, offers insight for antenna design, and presents performance bounds for antennas.

We present optimization formulations for the maximal gain Q-factor quotient, minimal Q for superdirectivity, and minimal Q for given far field. The effects of antennas embedded in metallic structures and effects of losses are also discussed. Results are shown for various antenna geometries and compared to state of the art designs. It is also shown that many antennas perform almost optimally. A tutorial description of a method of moment implementation together with a Matlab package for convex optimization to determine optimal current distributions on arbitrarily shaped antennas is also presented.

Sum Rules and Physical Bounds in Electromagnetics

Sum rules can be used to construct physical bounds on many types of physical systems.  The physical bounds answer questions like; what is the minimal temporal dispersion of passive metamaterials, how does the thickness influence the performance of absorbers and high-impedance surfaces, how does the inter-element coupling affect frequency selective surfaces, how does the bandwidth and directivity depend on the size of antennas, and what is the available bandwidth in extra-ordinary transmission of electromagnetic waves through sub-wavelength apertures. These types of identities and bounds are of great interest in many areas of physics and engineering. They also provide insight into the relationship between design parameters. The mathematical analysis is based on integral identities for Herglotz (or positive real) functions. These integral identities are referred to as sum rules and generalize the classical Kramers-Kronig dispersion relations to physical systems satisfying the underlying principles of linearity and passivity.

In the talk, we present the mathematical background based on time domain passive systems, Herglotz (or positive real) functions, and integral identities (sum rules) for passive systems. We analyze and present physical bounds for; broadband matching, radar absorbers, high-impedance surfaces, temporal dispersion of metamaterials, sub-wavelength scatterers, extraordinary transmission, and small antennas. We also compare the theoretical results with state of the art designs.

Near-field Diagnostics of Antennas and Radomes

Visualization of electromagnetic field and currents facilitates our understanding of the interaction between fields and devices. This is easily done in numerical simulations where the electromagnetic fields can be computed directly. It is much harder in most measurement situations where the fields cannot be measured directly and must instead be reconstructed from measurements of the fields outside the object or volume of interest. This reconstruction requires the solution of an inverse source problem. Reconstructions of field and current distributions are useful in applications such as non-destructive diagnostic of antennas and radomes and assessment of specific absorption ration (SAR) in the human body due to base station radiation.

In this presentation, we show how the field and current distribution can be reconstructed and visualized from near- and far-field measurement data. We illustrate how they can be used in antenna and radome diagnostics to, for example, identify faulty components. We discuss recent developments in inverse source problems to accurately reconstruct electromagnetic fields on a surface or volume from near- and far-field measurements. We review the theory for inverse source problems, non-uniqueness, and regularization. We present formulations based on equivalent currents using integral equations and integral representations for planar, spherical, body of revolution, and general geometries.