Generating customized field concentration via virtual surface transmission resonance

TL;DR

This paper introduces a mathematical framework for creating highly localized electromagnetic fields around inhomogeneous media using surface transmission resonance, enabling targeted field enhancement for various applications.

Contribution

It develops a novel method to design incident fields for localized concentration and proves the existence of surface resonant eigenfunctions with specific localization properties.

Findings

Existence of transmission eigenfunctions with surface localization

Design of incident fields for targeted field concentration

Identification of spectral patterns of transmission eigenfunctions

Abstract

In this paper, we develop a mathematical framework for generating strong customized field concentration locally around the inhomogeneous medium inclusion via surface transmission resonance. The purpose of this paper is twofold. Firstly, we show that for a given inclusion embedded in an otherwise uniformly homogeneous background space, we can design an incident field to generate strong localized field concentration at any specified places around the inclusion. The aforementioned customized field concentration is crucially reliant on the peculiar spectral and geometric patterns of certain transmission eigenfunctions. Secondly, we prove the existence of a sequence of transmission eigenfunctions for a specific wavenumber and they exhibit distinct surface resonant behaviors, accompanying strong surface-localization and surface-oscillation properties. These eigenfunctions as the surface transmission resonant modes fulfill the requirement for generating the field concentration.