Optimal Inverse Design of Antennas

2022 IEEE APS/URSI Short Course, Denver, Colorado, USA, July 10th, 8:20 – 12:00


Questions about how good an antenna can be and how to design such antennas are at the core of antenna technology. In this short course, we provide the participants with tools to answer these questions and ultimately design optimal antennas. Optimality is determined from physical bounds which are formulated as optimization problems over the current density. These problems are solved using convex optimization techniques and contribute to a fundamental understanding of the tradeoffs between electrical size, Q-factor, radiation efficiency, gain, and directivity for antennas of arbitrary size and shape. The bounds are compared with classical and optimized antenna designs. Here, we put forward a recently developed technique based on topology optimization in a method of moments setting. This technique is shown to be computationally efficient and able to automatically design antennas with performance close to the physical bounds. Two practical case studies will be completely solved during the course, starting from the definition of relevant metrics, to the determination of fundamental bounds, and to the optimization of the radiator’s shape. The participants will be provided with the presented codes and worksheets summarizing the theory.


Mats Gustafsson (Lund University, Sweden, EU)
Miloslav Capek (Czech Technical University, Czech Republic, EU)


  • (08:20 – 09:00) Introduction
  • (09:00 – 09:10) Coffee break, discussion
  • (09:10 – 09:50) Fundamental bounds – lecture
  • (09:50 – 10:20) Fundamental bounds – practical part
  • (10:20 – 10:30) Coffee break, discussion
  • (10:30 – 11:10) Inverse design – lecture
  • (11:10 – 11:30) Inverse design – practical part
  • (11:40 – 12:00) Summary, conclusion


The lectures can be downloaded from THIS link with the password received via e-mail or on-site.

Bonus materials for the practical part:

Practical part – Instructions

  • The participants are welcome to bring their laptops to actively participate in the practical part.
  • The examples are prepared in MATLAB (version 2019a and newer are recommended) and can be downloaded HERE. To unzip, use the password received via e-mail or on-site.
  • To run the examples, download the software package consisting of AToM (Antenna Toolbox for MATLAB), FOPS (Fast Optimization Routines), and two AToM add-ons (FunBo – evaluation of fundamental bounds, TSGA – shape synthesis package). All required packages are available in one archive HERE. To unzip, use the password received via e-mail or on-site.
  • Add all four packages to MATLAB paths (including sub-folders).
  • Run the m-file Ex0_HelloBounds.m to verify that all packages are available and the hardware is compatible.
  • Should you have any persisting problem with the test example Ex0_HelloBounds.m, contact us and attach the automatically generated file Ex0_LogFile.out to the e-mail.


  1. Gustafsson, M., Tayli, D., Cismasu,M.: Physical Bounds of Antennas, in Handbook of Antenna Technologies, 2015, DOI 10.1007/978-981-4560-75-7_18-1.
  2. Gustafsson, M., Tayli, D., Ehrenborg, C., Cismasu, M., Norbedo, S.: Antenna Current Optimization using MATLAB and CVX, FERMAT , Vol. 15, No. 5, p. 1-29, 2016.
  3. Jelinek, L., Capek, M.: Optimal Currents on Arbitrarily Shaped Surfaces, IEEE Trans. Antennas Propag., Vol. 65, No. 1, p. 329-341, 2017.
  4. Molesky, S., Lin, Z., Piggott, A.Y. et al.: Inverse Design in Nanophotonics. Nature Photonics, Vol. 12, pp. 659 – 670, 2018.
  5. Chao, P., Strekha, B., Defo, R. K., Molesky, S., Rodriguez, A. W.: Physical Limits in Electromagnetism, Nature Reviews Physics, July 2022.
  6. Christiansen, R. E., Sigmund, O.: Compact 200 Line MATLAB Code for Inverse Design in Photonics by Topology Optimization: Tutorial, Journal of the Optical Society of America B, Vol. 38, No. 2 pp. 510-520, 2021.
  7. Harrington, R. F.: Field Computation by Moment Methods, Wiley – IEEE Press, 1993.
  8. Harrington, R. F.: Antenna Excitation For Maximum Gain, IEEE Trans. Antennas Propag., Vol. 13, No. 6, pp. 896-903, 1965.
  9. Gustafsson, M., Sohl, C., Kristensson, G.: Physical Limitations on Antennas of Arbitrary Shape, Proc. R. Soc. A , Vol. 463, pp. 2589-2607, 2007.
  10. Gustafsson, M., Nordebo, S.: Optimal Antenna Currents for Q, Superdirectivity, and Radiation Patterns Using Convex Optimization, IEEE Trans. Antennas Propag., Vol. 61, No. 3, pp. 1109-1118, 2013.
  11. Capek, M., Jelinek, L.: Optimal Composition of Modal Currents For Minimal Quality Factor Q, IEEE Trans. Antennas Propag., Vol. 64, No. 12, pp. 5230-5242, 2016.
  12. Capek, M., Jelinek, L., Hazdra, P.: On the Functional Relation between Quality Factor and Fractional Bandwidth, IEEE Trans. Antennas Propag., Vol. 63, No. 6, pp. 2787-2790, 2015.
  13. Capek, M., Gustafsson, M., Schab, K.: Minimization of Antenna Quality Factor, IEEE Trans. Antennas Propag., Vol. 65, No. 8, pp. 4115-4123, 2017.
  14. Gustafsson, M., Capek, M.: Maximum Gain, Effective Area, and Directivity, IEEE Trans. Antennas Propag., Vol. 67, No. 8, pp. 5282 – 5293, 2019.
  15. Gustafsson, M., Fridén, J., Colombi, D.: Antenna Current Optimization for Lossy Media With Near-Field Constraints, IEEE Antennas Wireless Propag. Lett., Vol. 14, pp. 1538-1541, 2015.
  16. Gustafsson, M., Capek, M., Schab, K.: Tradeoff Between Antenna Efficiency and Q-Factor, IEEE Trans. Antennas Propag., Vol. 67, No. 4, pp. 2482-2493, 2019.
  17. Gustafsson, M., Schab, K., Jelinek, L., Capek, M.: Upper bounds on absorption and scattering, New Journal of Physics, Vol. 22, No. 7, p. 073013, 2020.
  18. Ehrenborg, C., Gustafsson, M., Capek, M.: Capacity Bounds and Degrees of Freedom for MIMO Antennas Constrained by Q-Factor, IEEE Trans. Antennas Propag., Vol. 69, No. 9, pp. 5388-5400, 2021.
  19. Capek, M., Jelinek, L., Gustafsson, M.: Shape Synthesis Based on Topology Sensitivity, IEEE Trans. Antennas Propag., Vol. 67, No. 6, pp. 3889 – 3901, 2019.
  20. Capek, M., Jelinek, L., Schab, K., Gustafsson, M., Jonsson, B. L. G., Ferrero, F., Ehrenborg, C.: Optimal Planar Electric Dipole Antennas: Searching for Antennas Reaching the Fundamental Bounds on Selected Metrics, IEEE Antennas and Propagation Magazine, Vol. 61, No. 4, pp. 19-29, 2019.
  21. Capek, M., Gustafsson, M., Jelinek, L., Kadlec, P.: Memetic Scheme for Topology Optimization Using Exact Reanalysis of Method-of-Moments Models – Part 1: Theory and Implementation, arxiv: https://arxiv.org/abs/2110.13460, 2021.
  22. Capek, M., Gustafsson, M., Jelinek, L., Kadlec, P.: Memetic Scheme for Topology Optimization Using Exact Reanalysis of Method-of-Moments Models – Part 2: Examples and Properties, arxiv: https://arxiv.org/abs/2110.08044, 2021.
  23. Schab, K., Rothschild, A., Nguyen, K., Capek, M., Jelinek, L., Gustafsson, M.: Trade-Offs in Absorption and Scattering by Nanophotonic Structures, Optics Express, Vol. 28, No. 24, pp. 36584-36599, 2020.

Contacts: mats.gustafsson[at]eit.lth.se (theoretical part) and miloslav.capek[at]fel.cvut.cz (practical part). Please, add always the second lecturer into a copy as well.

Last edit: 2022-06-14 | 10:23:32 AM