DMS Applied and Computational Mathematics

Speaker: Erik Hiltunen, Yale University

Title: Scattering phenomena and spectral convergence of subwavelength resonators

Abstract: We study wave propagation inside metamaterials consisting of high-contrast subwavelength resonators. In the subwavelength limit, resonant states are described by the eigenstates of the generalized capacitance matrix, which describes a long-range, fully-coupled resonator model. We achieve this by re-framing the Helmholtz equation as a non-linear eigenvalue problem in terms of integral operators. In this setting, we survey a range of subwavelength resonance phenomena such as Anderson localization, topologically protected edge modes, exceptional points, and Fano resonance. Additionally, we discuss the spectral convergence of finite structures. As the size of the structure increases, we show that defect modes induced by compact perturbations converge to localized modes of the infinite structure. Using Toeplitz eigenvalue distribution results, we additionally demonstrate the distributional convergence of the density of states as the size of the structure increases. 

Short Bio: Dr. Erik O. Hiltunen is a Gibbs Assistant Professor at Yale University, USA. Dr. Hiltunen's research focuses on developing the mathematical understanding of wave propagation in materials governed by local or non-local PDEs, using tools from PDE theory, harmonic analysis and solid-state physics. Before moving to Yale, Hiltunen earned his PhD from ETH Zurich under the supervision of prof. Habib Ammari, where his thesis dissertation was awarded the ECCOMAS award for best PhD theses on Computational Methods in Applied Sciences.