Speaker: Jinghao Cao (Caltech)
Title: Computational and analytical methods for subwavelength metamaterials
Abstract: Subwavelength metamaterials exhibit rich resonance phenomena driven by geometry and material contrast at scales far below the wavelength. In this presentation, we develop analytical and computational frameworks combining asymptotic analysis, boundary integral formulations, and Fourier–Galerkin discretizations. In particular, I introduce a Fourier–Galerkin approach for two-dimensional scattering problems, reducing the boundary integral operator to a finite-dimensional effective matrix whose singularity characterizes resonances. In the subwavelength regime, I derive asymptotic expansions of this matrix, revealing the leading-order operators and enabling a low-dimensional nonlinear eigenvalue formulation. This framework yields efficient, FFT-accelerated algorithms that avoid large-scale discretizations and provide robust tools for computing resonances in general geometries.