Modal Decomposition for Antenna Design and Communications (EuCAP 2026)

20th European Conference on Antennas and Propagation, 2026, Dublin, Ireland, April 19, 13:30 – 17:00, room: TBA

Official link (EuCAP webpage, see course: SC-09)

Annotation

Electromagnetic wave phenomena, particularly the guidance and radiation of electromagnetic waves, are often represented on a suitable basis. This simplifies analytical and numerical treatments and makes it possible to analyze complex engineering problems effectively. This course will review these techniques, covering classical analytical methods and recent approaches mostly connected to numerical modeling. The instructors have spent their careers studying this topic thoroughly and applying the methods in practice. During the course, they will share their knowledge and show how to treat modal decomposition techniques in a unified manner to solve practical problems effectively.

Learning objectives:

    • Classify modal techniques., enabling the effective analysis of complex engineering problems
    • Understand relevant mathematical tools (eigenvalue problems, separation of variables, orthogonality, spectral theorem, Rayleigh quotient, numerical range).
    • Implement and apply the techniques for solving given problems.
    • Apply characteristic mode theory, including the link between impedance and scattering formulations or relation to spherical waves.
    • Use the properties of radiation modes to use them in practice.

    The course will offer a good balance between mathematics, EM theory, and code implementation. The participants will be provided with codes that determine the bounds on the antenna metrics (gain, radiation efficiency, Q-factor) and perform topology optimization. A worksheet with analytical solutions will also be distributed.

    Instructors

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

    Program (estimation :))

    • (13:30 – 13:50) Introduction
    • (13:50 – 14:15) Mathematical Background
    • (14:15 – 14:35) Normal Modes
    • (14:55 – 15:25) Characteristic Modes – Part 1
    • (15:25 – 15:40) Coffee Break
    • (15:40 – 16:10) Characteristic Modes – Part 2
    • (16:20 – 17:00) Diagonalization of Optimization Problems and Radiation Modes
    • (17:00 – 17:30) Degrees of Freedom
    • (17:00+) Conclusion

    Materials

    Lectures can be downloaded from THIS link with the password received on-site.
    A cheat sheet with integral-equation-based matrix operators is here.

    References

    1. Feynman, R. P., Leighton, R. B., and Sands, M: The Feynman Lectures on Physics, Volume II. Addison-Wesley, 1964.
    2. Morse, P. M., and Feshbach, H: Methods of Theoretical Physics, Part I & II. McGraw-Hill, 1953.
    3. Harrington, R. F: Time-Harmonic Electromagnetic Fields. Wiley-IEEE Press, 2001.
    4. Stratton, J. A.: Electromagnetic Theory. Wiley-IEEE Press, 2007.
    5. Garbacz, R. J.: Modal expansions for resonance scattering phenomena, Proc. IEEE , Vol. 53, No. 8, p. 856-864, 1965.
    6. Harrington, R. F., Mautz, J. R.: Theory of Characteristic Modes for Conducting Bodies, IEEE Trans. Antennas Propag. , Vol. 19, No. 5, p. 622-628, 1971.
    7. Gustafsson, M., Jelinek, L., Schab, K., Capek, M.: Unified Theory of Characteristic Modes: Part I – Fundamentals, IEEE Trans. Antennas Propag. , Vol. 70, No. 12, p. 11801-11813, 2022.
    8. Gustaffson, M., Jelinek, L., Schab, K., Capek, M.: Unified Theory of Characteristic Modes: Part II – Tracking, Losses, and FEM Evaluation, IEEE Trans. Antennas Propag., Vol. 70, No. 13, pp. 11814-11824, 2022.
    9. Gustafsson, M., Jelinek, L., Capek, M., Lundgren, J., Schab, K.: Theory and Computation of Substructure Characteristic Modes, IEEE Trans. Antennas Propag., Vol. 73, No. 3, pp. 1321-1333, March 2025.
    10. Lundgren, J., Schab, K., Capek, M., Gustafsson, M., Jelinek, L.: Iterative Calculation of Characteristic Modes Using Arbitrary Full-wave Solvers, IEEE Antennas and Wireless Propagation Letters, Vol. 22, No. 4, pp. 799-803, 2023.
    11. Capek, M., Lundgren, J., Gustafsson, M., Schab, K., Jelinek, L.: Characteristic Mode Decomposition Using the Scattering Dyadic in Arbitrary Full-Wave Solvers, IEEE Trans. Antennas Propag., Vol. 71, No. 1, pp. 830-839, 2023.
    12. Lau, B. K., Capek M. and Hassan A. M.: Characteristic Modes: Progress, overview, and emerging topics, in IEEE Antennas and Propagation Magazine, vol. 64, no. 2, pp. 14-22, April 2022. (and the entire review series related to this paper)
    13. Sarkar T. K., Mokole E. L. and Salazar-Palma M.: An Expose on Internal Resonance, External Resonance, and Characteristic Modes, in IEEE Trans. Antennas Propag., vol. 64, no. 11, pp. 4695-4702, Nov. 2016,
    14. Gustafsson M.: Modes, Bounds, and Synthesis of Optimal Electromagnetic Scatterers, New J. Phys. 26 103039, 2024.
    15. Schab K., Chen, F. W., Jelinek L., Capek, M., Lundgren, J., Gustafsson, M.: Characteristic Modes of Frequency-Selective Surfaces and Metasurfaces from S-parameter Data, IEEE Trans. Antennas Propag, Vol. 71, No. 12, pp. 969-9706, Dec. 2023.
    16. 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.
    17. Jelinek, L., Capek, M.: Optimal Currents on Arbitrarily Shaped Surfaces, IEEE Trans. Antennas Propag., Vol. 65, No. 1, p. 329-341, 2017.
    18. Harrington, R. F.: Field Computation by Moment Methods, Wiley – IEEE Press, 1993.
    19. 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.
    20. 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.
    21. Capek, M., Gustafsson, M., Schab, K.: Minimization of Antenna Quality Factor, IEEE Trans. Antennas Propag., Vol. 65, No. 8, pp. 4115-4123, 2017.
    22. 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.

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

    Last edit: 2026-01-21 | 09:20 AM