Questions regarding the efficacy of electromagnetic devices and their optimal design are central to antenna and microwave technology, optics, and plasmonics. This edition of the European School of Antennas equips participants with both theoretical and practical tools to address these questions and ultimately create optimal devices. The term “optimality” is addressed first, determined from physical bounds formulated as optimization problems over electromagnetic quantities (surface current density, terminal voltages). These problems are solved using convex optimization techniques and contribute to understanding the trade-offs between studied metrics, electrical size, material parameters, or matching. The bounds are compared with classical and optimized designs and put into the context of historical attempts to demarcate various performance metrics.
The course covers inverse design techniques, including topology optimization, surrogate modeling, machine learning, and heuristics. We also emphasize a recently developed technique based on topology optimization in a method-of-moments setting. This technique is computationally efficient and can often automatically design antennas with performance close to the physical bounds. Many figures of merit are to be defined and optimized - Q-factor, radiation efficiency, antenna gain, realized gain, directivity, capacity, focusing efficiency, and extinct power, to name a few. The participants will receive the presented codes and worksheets summarizing the theory. The course concludes with a discussion of open problems related to optimality in antenna design.
The course is offered in a hybrid form. If you want to participate online, please contact the course coordinators.
Coordinated by: prof. Mats Gustafsson prof. Miloslav Capek
Course duration: 35 hours (5 days)
Prerequisites: Basics of electromagnetic theory and mathematics. Some skills in programming is advantageous.
Availability: 25 students
Credits: 3 ECTS
| Monday 10th June |
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|---|---|---|
| 8:00 | L01: Course introduction Overview of bounds and inverse design |
Mats Gustafsson |
| 9:00 | L02: Basic mathematical formalism MoM operators |
Miloslav Capek |
| 9:50 | Coffee break |
|
| 10:10 | L03: Impedance matrix and DOF, Rayleigh quotients, eigenvalues |
Miloslav Capek |
| 11:00 | L04: Convex optimization, duality, QCQP, Lagrange solution | Mats Gustafsson |
| 12:00 | Lunch* | |
| 13:00 | L05: Fundamental bounds in EM and antenna design | Mats Gustafsson |
| 14:00 | L06: Minimum Q, substructures |
Mats Gustafsson |
| 14:50 | Coffee break |
|
| 15:10 | P01: Software introduction | Miloslav Capek |
| 16:00 | P02: Minimum Q | Miloslav Capek |
| 17:00 | Short introduction of the course participants | |
| 18:30 | Getting together dinner (self-paid) |
|
| Tuesday 11th June |
||
|---|---|---|
| 8:00 | L07: Bounds on antenna gain, efficiency, ... | Mats Gustafsson |
| 9:00 | L08: Trade-offs in antenna design, Pareto fronts | Miloslav Capek |
| 9:50 | Coffee break |
|
| 10:10 | P03: Pareto fronts (Q, rad. eff., D) | Miloslav Capek |
| 11:00 | L09: MIMO, capacity, degrees-of-freedom | Mats Gustafsson |
| 12:00 | Lunch* | |
| 13:00 | L10: Fundamental limits in photonics and EM: Material response and global symmetries | Owen Miller |
| 14:00 | L11: Fundamental limits in photonics and EM: Local constraints and near-field antennas | Owen Miller |
| 14:50 | Coffee break |
|
| 15:10 | P04: Degeneracies, uniqueness of the solution, symmetries | Miloslav Capek |
| 16:00 | L12: Symmetries, von Neumann-Wigner theorem, crossing avoidance | Kurt Schab (online) |
| Wednesday 12th June |
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|---|---|---|
| 8:00 | L13: Overview of automatic antenna design techniques | Mats Gustafsson |
| 9:00 | L14: Parameter-based optimization, inverse design | Mats Gustafsson |
| 9:50 | Coffee break |
|
| 10:10 | L15: Fundamentals of Topology Optimization | Niels Aage, Rasmus Ellebæk Christiansen |
| 11:00 | P05: Design of MetaLenses | Rasmus Ellebæk Christiansen, Niels Aage |
| 12:00 | Lunch* | |
| 13:00 | L16: Antenna/Waveguide design (GHz) | Niels Aage, Rasmus Ellebæk Christiansen |
| 14:00 | P06: Extension to waveguides and antennas | Rasmus Ellebæk Christiansen, Niels Aage |
| 14:50 | Coffee break |
|
| 15:10 | L17: Arrays, matching | Miloslav Capek |
| 16:00 | P07: Arrays (optimal beam steering, optimal matching) | Miloslav Capek |
| 18:30 | Social dinner | |
| Thursday 13th June |
||
|---|---|---|
| 8:00 | L18: The Role of AI and Machine Learning in Antenna Design | Lasse Hjuler Christiansen |
| 9:00 | L19: Enhancing Antenna Design with Surrogate Modeling Techniques | Lasse Hjuler Christiansen |
| 9:50 | Coffee break |
|
| 10:10 | L20: Topology sensitivity based on exact reanalysis | Miloslav Capek |
| 11:00 | P08: Exact reanalysis: minimum Q | Miloslav Capek |
| 12:00 | Lunch* | |
| 13:00 | L21: Memetic scheme | Miloslav Capek |
| 14:00 | P09: Co-simulation of topology optimization and bounds, Part 1 | Miloslav Capek |
| 14:50 | Coffee break |
|
| 15:10 | P10: Co-simulation of topology optimization and bounds, Part 2 | Miloslav Capek |
| 16:00 | L22: Modes, model-order-reduction (CMs, radiation modes, port quantities) | Kurt Schab (online) |
| Friday 14th June |
||
|---|---|---|
| 8:00 | L23: TBA | Andreas Ericsson Ahlgren |
| 9:00 | L24: TBA | Andreas Ericsson Ahlgren |
| 9:50 | Coffee break |
|
| 10:10 | L25: Future topics, pointwise, time-domain, analog computers | Mats Gustafsson, Miloslav Capek |
| 11:00 | L26: Closing remarks, important takeaways, feedback, discussion | Mats Gustafsson, Miloslav Capek |
| 12:00 | Lunch* | |
| 13:00 | Final test, certificate awarding | |
| 14:00 | Visit at Department of Electrical and Information Technology (optional) | |
*Lunch is included in the registration. Should you have any dietary constraints, please let us know via email.
Mats Gustafsson received the M.Sc. degree in Engineering Physics 1994, the Ph.D. degree in Electromagnetic Theory 2000, was appointed Docent 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. He has written over 100 peer-reviewed journal papers and over 100 conference papers. Prof. Gustafsson received the IEEE Schelkunoff Transactions Prize Paper Award 2010, IEEE Uslenghi Letters Prize Paper Award 2019, and Best Paper Awards at EuCAP 2007 and 2013. He served as an IEEE AP-S Distinguished Lecturer 2013-15
Miloslav Capek is a Full Professor at the Czech Technical University in Prague, Czech Republic. Miloslav is a senior member of the IEEE. He serves as an associate editor of IET Microwaves, Antennas & Propagation. He was a member of the Delegate Assembly of EurAAP between 2015 and 2020 (Group 8). He leads the development of the AToM (Antenna Toolbox for MATLAB) package and serves as a vice-chair of EurAAP “Software and Modeling” working group. He is the author or co-author of over 160 journal and conference papers. His current research interests include the area of electromagnetic theory, electrically small antennas, numerical techniques, and optimization. He received the 2023 IEEE Antennas and Propagation Edward E. Altshuler Prize Paper Award and the ESoA Best Teachers 2023.
Kurt Schab is an Assistant Professor of Electrical Engineering at Santa Clara University, Santa Clara, CA USA. He received the B.S. degree in electrical engineering and physics from Portland State University in 2011 and the M.S. and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana-Champaign in 2013 and 2016, respectively. From 2016 to 2018 he was a Postdoctoral Research Scholar at North Carolina State University in Raleigh, North Carolina. His research focuses on the intersection of numerical methods, electromagnetic theory, and antenna design.
Owen Miller is an Assistant Professor of Applied Physics and the Energy Sciences Institute at Yale. His research group uses techniques from applied mathematics to explore the extreme limits of nanophotonics and broader wave physics. This research, in collaboration with experimental and industrial teams, has led to record-performance demonstrations in applications ranging from photovoltaics to smoke grenades. He is the recipient of AFOSR and DARPA young investigator awards, as well as the Yale Graduate Mentor award.
Rasmus Ellebæk Christiansen holds a bachelor’s degree in physics and a master’s degree in computational mathematics. He received his PhD from the Technical University of Denmark (DTU) in 2016 for his work on topology optimization for frequency domain applications. During his PhD he visited Prof. Jan Hesthaven at École Polytechnique Fédérale de Lausanne where he performed research on efficient numerical solvers for wave propagation problems. During a subsequent Post Doc, he visited Prof. Steven G. Johnson at Massachusetts Institute of Technology, where he performed research on developing tools and exploring inverse design applied to plasmonically enhanced Raman scattering and optical metasurfaces. He has become an expert in the field of inverse design through his continued focus, and today he works as an Associate Professor out of the Topology Optimization group at DTU. His primary research interest is inverse design applied to wave-propagation problems within electromagnetics and mechanics. A key focus of his work is ensuring highly accurate experimental realization of inversely designed device blueprints. This, through integration of fabrication constraints in the design process. Done right, this enables direct fabrication of highly optimized devices, accurately replicating numerically predicted performance without the need for calibration or post processing of the optimized blueprints.
Niels Aage is one of the top researchers in the field of ultra-large scale finite element methods and structural optimization approaches. He is an expert on the use of high-performance computing for the solution of heterogeneous partial differential equations for multiphysics problems incl. electromagnetics, thermofluidics, vibroacoustics, multiscale mechanics and inverse design. In 2023, Niels Aage was elected vice-president of the International Society for Structural and Multidisciplinary Optimization, an honor bestowed on him by colleagues from all over the world. He has received several prices for his pioneering work on giga-scale computational morphogenesis (Nature 2017, Nat.Comm 2020) and has authored more than 62 papers in international journals, including three “highly cited in field”. Furthermore, Niels Aage has developed several specialized structural optimization open-source codes tailored for use on high-performance computing systems as well as interactive apps for educational purposes.
Lasse Christiansen holds an M.Sc. degree in Applied Mathematics from the Technical University of Denmark (DTU), obtained in 2015. He received his Ph.D. degree in Computational Mathematics from DTU in 2019 for his work on PDE-constrained optimization, where his research focused on developing computationally efficient and scalable algorithms for large-scale optimization problems by combining elements of high-performance computing, iterative solution strategies, reduced-order modeling, and deep neural networks. Since 2021, Lasse Christiansen has worked at TICRA, the software company behind the popular antenna design and optimization software suite TICRA Tools. This software suite includes market-leading products such as GRASP (for PO-based scattering analysis of high-frequency antenna systems), ESTEAM (for integral-equation-based scattering analysis of electrically large systems), and CHAMP 3D (for analysis of feeds and feed chains), among other products. At TICRA, Lasse Christiansen holds the position of Senior Machine Learning Engineer in the Mathematics and AI team. His responsibilities encompass research and development, technical engineering, and project management. His current research interests include the interplay between scientific computing, optimization, surrogate modeling, and machine learning, focusing on how ML-based methods, including deep neural networks and Gaussian Processes, can support and augment traditional algorithms to ensure scalability, enable real-time computation, and address otherwise computationally intractable problems in the design, analysis, and optimization of antennas.
Andreas Ericsson Ahlgren received the M.Sc. degree in engineering physics and the Ph.D. degree in electrical engineering from Lund University, Lund, Sweden, in 2013 and 2017, respectively. He joined TICRA in Denmark in 2018 where he is currently working as Senior Research Engineer in the Applied Electromagnetics Team. His responsibilities include research and development, providing consultancy services and technical support, project management, and giving software training of TICRA's products to customers. Andreas is the Product Lead for the software products QUPES (for analysis of quasi-periodic surfaces), UQ (for uncertainty quantification), SNIFT (for spherical near-field to far-field transformations) and DIATOOL (for antenna diagnostics). His research interests include quasi-periodic surfaces such as frequency selective surfaces, reflectarrays, and transmitarrays, reflector antennas, and antenna measurement techniques. Since 2019, Andreas has been giving training courses in TICRA's software products, both on basic and advanced level.
There will be at three scholarships for full-time university students:
Applicants must send a motivation letter and CV to the course organizers (mats.gustafsson@eit.lth.se) before 26th May.
The grant is configured as a reimbursement of the registration fee. The grant recipients will be announced within five days of the submission deadline.
The registration fees are: University participants: 550€ Industry participants: 1100€ The deadline for registration is June 1st (Monday), 2026 The deadline for payment is: June 2nd (Tuesday), 2026 Register here You will be redirected to EurAAP webpage. Please, create a EurAAP account by clicking on "Register," log in by clicking on "Login," select "ESoA" from the Menu, and make a registration.
Lund is one of Sweden's most charming university towns, where centuries of history blend seamlessly with a vibrant, youthful atmosphere. Its cobblestone streets, medieval cathedral, and half-timbered houses create an intimate setting that feels both timeless and alive. At the same time, the presence of Lund University and world-leading research facilities gives the city an international pulse. With cozy cafes, lush parks, and easy access to both countryside and coast, Lund offers a warm and inspiring place to visit, study, or work.
So, welcome to Lund!
Traveling from Copenhagen (CPH) to Lund is quick and convenient. The easiest option is to take a direct train from Copenhagen Airport; trains run frequently (about every 20 minutes) and reach Lund Central Station in roughly 35-40 minutes. Tickets can be purchased at the airport station or via the Skanetrafiken app for a smooth trip.
Mats Gustafsson Lund University mats.gustafsson@eit.lth.se
Miloslav Capek CTU in Prague miloslav.capek@fel.cvut.cz