ÖPG-CMD Joint Meeting 2026

AAA rational approximation for nanophotonic resonance problems

Sep 22, 2026, 5:30 PM

15m

HS 15.05 (University of Graz)

3) Contributed talk M17 - Emerging trends in dielectric nanophotonics Mini-Colloquium

Speaker

Felix Binkowski (Zuse Institute Berlin)

Description

We investigate numerical approaches based on AAA rational approximation [1, 2] for applications in nanophotonics. The AAA algorithm provides a powerful framework for constructing low-dimensional models of photonic systems by identifying and approximating dominant resonances [3], which are critical for understanding the electromagnetic response functions of the systems [4,5].

Resonances are characterized by the poles of the response functions, and often only a few are required to model the system’s behavior within a given frequency range [4]. We demonstrate the effectiveness of rational approximation across three photonic systems: (i) We study a chiral metasurface, where resonance modes are computed and modal expansions are performed. This example emphasizes that using rational approximation can be computationally efficient with respect to the required number of sampling points [6]. (ii) A photonic crystal fiber is investigated, where the method yields relevant resonance modes while filtering out cladding and higher-order modes [7]. (iii) We study systems with scattering thresholds, where hidden resonances can be revealed through rational approximation [8].

We acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - The Berlin Mathematics Research Center MATH+ (EXC-2046/1, EXC-2046/2, project ID: 390685689) and by the German Federal Ministry of Research, Technology and Space (BMFTR, Forschungscampus MODAL, project 05M20ZBM).

[1] Y. Nakatsukasa, O. Sete, L. N. Trefethen, SIAM J. Sci. Comput. 40, A1494 (2018).
[2] Y. Nakatsukasa, L. N. Trefethen, arXiv:2510.16237 (2025).
[3] M. Zworski, Notices Amer. Math. Soc. 46, 319 (1999).
[4] P. Lalanne, W. Yan, K. Vynck, C. Sauvan, J. P. Hugonin, Laser Photonics Rev. 12, 1700113 (2018).
[5] F. Binkowski, F. Betz, R. Colom, P. Genevet, S. Burger, Phys. Rev. B. 109, 045414 (2024).
[6] F. Betz, M. Hammerschmidt, L. Zschiedrich, S. Burger, F. Binkowski, Laser Photonics Rev. 18, 2400584 (2024).
[7] F. Binkowski, F. Betz, M. Hammerschmidt, L. Zschiedrich, S. Burger, Nanophotonics 14, 1665 (2025).
[8] F. Betz, F. Binkowski, J. D. Fischbach, N. Feldman, L. Zschiedrich, C. Rockstuhl, A. F. Koenderink, S. Burger, Laser Photonics Rev. 19, e00811 (2025).