Mathematical Analysis of Resonances for an Array of Subwavelength Annular Holes and Its Application in Superresolution Imaging

.This work presents a mathematical analysis of resonances for an array of subwavelength coaxial annular holes and a new superresolution imaging approach using the resonant structure. By employing a multiscale analytical framework based on a combination of the integral equation in the exterior domain and the waveguide mode expansion inside the small three-dimensional holes, we derive asymptotic expansions of complex-valued scattering resonances for the underlying subwavelength structure and analyze the electromagnetic field amplification at the resonant frequencies. In particular, it is shown that the resonant modes oscillate on a subwavelength scale in the near field if the annular holes are placed close to each other. By leveraging this observation, we develop a novel superresolution imaging approach that utilizes resonant modes through the subwavelength resonant structure as they illuminate patterns and present a numerical reconstruction algorithm to solve the underlying inverse problem. Numerical examples show that a tenfold improvement can be achieved in image resolution with the new imaging method.