Resolvent Analysis of Subwavelength Resonators

In this proposal, we focus on the wave propagation in the presence of subwavelength resonators. Examples of such resonators are bubbles in acoustics, dielectric and plasmonic nanoparticles in electromagnetism and cavities in elasticity. The key feature here is that under certain critical ratios between their size and contrast, these particles can resonate at certain proper frequencies. Precisely, local spots are created around the particles when they are excited with incident waves having a spectral bandwidth containing those proper frequencies. The overall objective of this proposal is to provide qualitative and quantitative properties of the fields propagating inside such resonant composites. A specific feature of classical scattering systems consists in the fact that the total field identifies with a generalized eigenfunction of an auxiliary Schrödinger operator which may depend on the frequency, unlike the quantum mechanics counterpart. Therefore, we adopt the approach of describing the scattering in terms of the asymptotic resolvent analysis of frequency-dependent Schrödinger type operators. The advantages of this approach, as compared to the known literature, are twofold. First, we provide the dominating fields at all the frequencies including the resonating ones. Second, these characterized fields are estimated everywhere, i.e. inside, near and far away from the composite. With such double advantage, we expect to produce innovative results that will compete with traditional imaging methods using remote measurements but also go beyond what the traditional homogenization can provide in material sciences. The project will be conducted by the PI: Mourad Sini, from the Austrian Academy of Sciences, assisted by one PhD student and one post-doctor.