About the course

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. Miloslav Capek
prof. Mats Gustafsson

Course schedule

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
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 Lukas Jelinek, Miloslav Capek
9:50 Coffee break
10:10 P03: Pareto fronts (Q, rad. eff., D) Jakub Liska, Miloslav Capek
11:00 L09: MIMO, capacity, degrees-of-freedom Mats Gustafsson
12:00 Lunch*
13:00 L10: Arrays, matching Miloslav Capek
14:00 P04: Arrays (optimal beam steering, optimal matching) Miloslav Capek
14:50 Coffee break
15:10 P05: Degeneracies, uniqueness of the solution, symmetries Miloslav Capek
16:00 L11: Symmetries, von Neumann-Wigner theorem, crossing avoidance Kurt Schab (online)
Wednesday 12th June
8:00 L12: Overview of automatic antenna design techniques Mats Gustafsson
9:00 L13: Parameter-based optimization, inverse design Mats Gustafsson
9:50 Coffee break
10:10 L14: Topology sensitivity based on exact reanalysis Miloslav Capek
11:00 P06: Exact reanalysis: minimum Q Miloslav Capek
12:00 Lunch*
13:00 L15: Memetic scheme Miloslav Capek
14:00 P07: Co-simulation of topology optimization and bounds, Part 1 Miloslav Capek
14:50 Coffee break
15:10 P08: Co-simulation of topology optimization and bounds, Part 2 Miloslav Capek
16:00 L16: Modes, model-order-reduction (CMs, radiation modes, port quantities) Kurt Schab (online)
18:30 Social dinner
Thursday 13th June
8:00 L17: The Role of AI and Machine Learning in Antenna Design Lasse Hjuler Christiansen
9:00 L18: Enhancing Antenna Design with Surrogate Modeling Techniques Lasse Hjuler Christiansen
9:50 Coffee break
10:10 L19: Fundamentals of Topology Optimization Niels Aage, Rasmus Ellebæk Christiansen
11:00 P09: Design of MetaLenses Rasmus Ellebæk Christiansen, Niels Aage
12:00 Lunch*
13:00 L20: Antenna/Waveguide design (GHz) Niels Aage, Rasmus Ellebæk Christiansen
14:00 P10: Extension to waveguides and antennas Rasmus Ellebæk Christiansen, Niels Aage
14:50 Coffee break
15:10 L21: Optimal design and theoretical bounds in photonics Owen Miller (online)
16:00 L22: Near-field antenna design at optical frequencies Owen Miller (online)
Friday 14th June
8:00 L23: Optimization applied in commercial solvers I Tonny Rubæk
9:00 L24: Optimization applied in commercial solvers II Tonny Rubæk
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 EM department (optional)

*Lunch is included in the registration. Should you have any dietary constraints, please let us know via email.


Mats Gustafsson
Lund University, Sweden

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
CTU in Prague, Czech Republic

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
Santa Clara University, USA

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
Yale University, USA

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
DTU, Denmark

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
DTU, Denmark

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 Hjuler Christiansen
TICRA, Denmark

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.


Tonny Rubæk
TICRA, Denmark

Tonny Rubæk received the M.Sc. and PhD degree in Electrical Engineering in 2004 and 2008, respectively, all from the Technical University of Denmark (DTU). He was a Post Doc at DTU and Chalmers University of Technology, Sweden, between 2008 to 2013. Between 2013-2017, he was an antenna system engineer at OHB System in Bremen, Germany, where he was responsible for subcontract management, system-level performance analyses, EMC engineering, and antenna design on communication, navigation, and radar satellites. Since 2017, Tonny holds the position of a Senior Research Engineer at TICRA as a member of the applied electromagnetics team. At TICRA, he actively participates in the test and development cycle of all TICRA software products and assists TICRA’s customers under their technical support contract. In addition, he is the Product Lead for TICRA’s reflector antenna software and is responsible for the development of the GRASP and POS software packages.


There will be at least 5 scholarships for full time university students:

  • 1 grant funded by RF spin,
  • 2 grant funded by Rohde & Schwarz,
  • 1 grant funded by Humusoft.
The grant recipients will be announced within five days of the submission deadline.

Applicants must send a motivation letter and CV to the course organizers (miloslav.capek@fel.cvut.cz) before 28th 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 2nd, 2024
The deadline for payment is: June 2nd, 2024
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.


Czech Technical University in Prague
Faculty of Electrical Engineering
Department of Electromagnetic Field
Technická 2
166 27 Praha 6 - Dejvice

About Prague

Nestled along the Vltava River, Prague beckons with its timeless charm and rich history. Wander cobblestone streets to marvel at the Gothic Prague Castle, the iconic Charles Bridge, and the Old Town Square's astronomical clock. Immerse yourself in a vibrant cultural scene, from classical concerts to cutting-edge art. Indulge in diverse culinary delights, explore quaint neighborhoods, and revel in the city's lively nightlife.

So, welcome to Prague, the enchanting heart of Europe where history meets modernity!

How to get from Prague airport

Upon arriving at Prague Airport, opt for the convenient Airport Express bus, which will directly connect the airport to Dejvice in approximately 25 minutes. Alternatively, taxis and rideshare services are readily available outside the arrival’s hall. For a budget-friendly option, utilize the efficient public transportation – take trolley 59 to Nadrazi Veleslavin and transfer to Metro Line A, reaching Dejvicka station. The faculty building is located approx. 200 meters from Dejvicka station.

Notice that public transport in Prague is cheap, popular, and safe and repeatedly ranks in the top 5 public transport systems in Europe.

You can acquire a ticket for public transport directly at the airport (yellow ticket machines) with several options: 30 min ticket (30 CZK), 24 hrs ticket (120 CZK), or 72 hrs ticket (330 CZK). Do not forget to stamp a paper ticket to make it valid!

You can also buy ticket through an app "PID LÍTAČKA" (download).


The course takes place at the Faculty of Electrical Engineering located in the middle of the Dejvice district. You might also consider Letna, Holesovice, or any other part of Prague with a good connection to Dejvice.

A good option is Masaryk Dormitory Hotel, situated within walking distance from the faculty and operated by the university.




RF Spin

RFspin is leading manufacturer of top-notch broadband antennas, relied upon by customers worldwide for over 20 years. The antennas find application in a wide range of areas including wireless and satellite communications, and radar systems. Among its customers are global companies such as Airbus Defence and Space, Apple, SpaceX, Mercedes-Benz, NASA, and significant foreign universities. RFspin develops, designs, and manufactures its antennas using innovative technologies and the latest machining equipment in its own production facility in Nová Paka.


Rohde & Schwarz

Rohde & Schwarz develops, produces and markets a wide range of electronic capital goods for industry, infrastructure operators and government customers. The independent group is among the technology and market leaders in all of its business fields, including wireless communications and RF test and measurement, broadcast and media, air traffic control and military radiocommunications, cybersecurity and network technology.



The Faculty of Electrical Engineering of the Czech Technical University in Prague (FEE CTU) stands as one of the eight faculties within the esteemed Czech Technical University (CTU), the oldest and most prestigious technical institution in the Czech Republic, with a lineage tracing back to 1707. Presently, FEE CTU comprises 17 departments housed across two distinguished edifices: situated within the main campus of CTU in Dejvice and our historic edifice at Karlovo náměstí. Since 1950, FEE CTU has conferred upwards of 30,000 diplomas, each in high esteem as a testament to premier education.



MathWorks is a leading software company that specializes in mathematical computing software. It is best known for its flagship product MATLAB, a high-level programming language and environment used for numerical computation, data analysis, and visualization. MATLAB is widely used across various industries, including engineering, science, finance, and academia. MathWorks also offers Simulink, a graphical programming environment for modeling, simulating, and analyzing dynamic systems, which is particularly popular in the control systems and automotive industries. Established in 1984, MathWorks continues to innovate and provide tools that empower engineers and scientists to solve complex technical challenges.

The products of MathWorks are distributed in Czech Republic by company Humusoft s.r.o.


Contact Us

Miloslav Capek
CTU in Prague

Mats Gustafsson
Lund University

Local organizers: CEM group
J. Tucek, V. Neuman, J. Liska, S. Bosak, L. Jelinek