Wave interaction with subwavelength resonators

TL;DR

This review discusses recent mathematical advances in understanding wave interactions with subwavelength resonators, highlighting techniques that enable wave control at scales smaller than the wavelength.

Contribution

It provides a comprehensive overview of mathematical methods like layer potentials and asymptotic analysis applied to subwavelength resonators in metamaterials.

Findings

Mathematical framework for wave focusing, trapping, and guiding at subwavelength scales.

Demonstration of layer potential techniques combined with asymptotic analysis.

Insights into wave manipulation in metamaterials at subwavelength dimensions.

Abstract

The aim of this review is to cover recent developments in the mathematical analysis of subwavelength resonators. The use of sophisticated mathematics in the field of metamaterials is reported, which provides a mathematical framework for focusing, trapping, and guiding of waves at subwavelength scales. Throughout this review, the power of layer potential techniques combined with asymptotic analysis for solving challenging wave propagation problems at subwavelength scales is demonstrated.