This work presents a framework for the efficient and accurate computation of fundamental resonance modes in photonic waveguides, based on the AAA rational approximation. The method computes modes selectively, prioritizing those most relevant by applying specially chosen light sources, thereby avoiding the need to calculate many unwanted modes (e.g., cladding or higher-order modes). The approach was demonstrated by computing the fundamental mode of a hollow-core photonic crystal fiber, with numerical solutions obtained using the finite element solver JCMsuite.
F. Binkowski, et al. Resonance modes in microstructured photonic waveguides: efficient and accurate computation based on AAA rational approximation. Nanophotonics 14, 1665 (2025).