Synthesis of resonant modes in electromagnetics

TL;DR

This paper presents an analytical method to design dielectric objects with tailored resonant modes by controlling the dielectric susceptibility tensor, enabling precise electromagnetic device responses.

Contribution

It introduces a novel analytical approach for synthesizing dielectric susceptibility tensors to achieve desired resonant modes in electromagnetic systems.

Findings

Analytical form for dielectric susceptibility tensor for prescribed resonances

Controlled tunability of resonant modes demonstrated

Applicable to any linear, local constitutive electromagnetic system

Abstract

Resonant modes determine the response of electromagnetic devices, including dielectric and plasmonic resonators. Relying on the degrees of freedom that metamaterials provide, this contribution shows how to design, at will, the resonant modes of a dielectric object placed in an unbounded space. Specifically, the proposed method returns in analytical form the spatial distribution of the dielectric susceptibility tensor for which the object exhibits resonances at prescribed frequencies and spatial distribution of the polarization. Together with the synthesis of the material, two key concepts are introduced: the controlled tunability of the resonant modes and the number of essential modes, i.e. the number of modes that uniquely characterize the spatial distribution of the dielectric susceptibility. Moreover, this approach can be applied to design the resonant modes of any system where the constitutive relationship is linear and local.