AAA Rational Approximation in Computational Photonics

A student research group studying, implementing, and testing the AAA algorithm for resonance phenomena in photonic systems. The AAA algorithm enables efficient approximation by rational functions and has recently attracted significant attention in numerical mathematics and various application fields. The optical response of photonic systems exhibits poles in the complex frequency plane associated with resonances, making these systems particularly well suited for rational approximation. Students will study the theoretical foundations, implement the algorithm, test it on examples from the literature, and finally apply it to resonance phenomena in photonic systems to evaluate its performance and limitations. This project is intended for students with an interest in both mathematics and physics.