My research lies at the interface of partial differential equations, spectral theory and mathematical physics. I investigate how geometry, material dispersion and dissipation shape wave propagation in metamaterials and other resonant structures, particularly at subwavelength scales. Using asymptotic analysis and mathematical modelling, I study the mechanisms underlying resonance, wave localisation and field enhancement. I also develop methods for electromagnetic inverse problems, connecting the analysis of wave phenomena to the recovery of material and structural information from scattering measurements.
List of publications
Preprints
K. Alexopoulos. Subwavelength exceptional points in dispersive resonator arrays. arXiv:2609.15200, 2026. Submitted. (link)
K. Alexopoulos. Frequency sorting in graded dispersive resonator arrays via volume-interaction matrices. hal-05743831, 2026. Submitted. (link)
K. Alexopoulos and J. Garnier. Asymptotics-guided learning and symbolic regression for dispersive resonances. arXiv:2608.16152, 2026. Submitted. (link)
K. Alexopoulos and J. Garnier. Reduced-order modeling for electromagnetic inverse problems: a layered medium benchmark. arXiv:2608.03996, 2026. Submitted. (link)
K. Alexopoulos, B. Davies and P. Millien. Non-singular hotspots between closely spaced high-index nanoparticles. arXiv:2607.24204, 2026. Submitted. (link)
Published
K. Alexopoulos, B. Davies, and E. O. Hiltunen. Topological interface modes in systems with damping. SIAM Journal on Applied Mathematics, 85(4):1500–1518, 2025. (link)
K. Alexopoulos and B. Davies. Topologically protected modes in dispersive materials: the case of undamped systems. Multiscale Modeling & Simulation, 23(1), 611-639. (link)
K. Alexopoulos and B. Davies. The effect of singularities and damping on the spectra of photonic crystals. Journal of Mathematical Physics, 65(8):081510, 2024. (Editor's Pick). (link)
K. Alexopoulos and B. Davies. A mathematical design strategy for highly dispersive resonator systems. Mathematical Methods in the Applied Sciences, pages 1-26, 2023. (Top Viewed Article). (link)
K. Alexopoulos and B. Davies. Asymptotic analysis of subwavelength halide perovskite resonators. Partial Differential Equations and Applications, 3(4):1–28, 2022. (link)
Links: Google Scholar, Research Gate, arXiv, GitHub.