# Closed-form Harmonic Contrast Control with Surface Impedance Coatings for Conductive Objects

## TL;DR

This paper presents a closed-form solution for surface impedance coatings that suppress scattering from conductive objects across all frequency regimes, enabling improved harmonic filtering and cloaking.

## Contribution

It introduces a unique, exact closed-form surface impedance design method for harmonic contrast reduction applicable at any frequency.

## Key findings

- Closed-form impedance solution valid across frequency regimes.
- Enhanced scattering suppression and harmonic filtering.
- Special case of mantle cloaking in the quasi-static limit.

## Abstract

The problem of suppressing the scattering from conductive objects is addressed in terms of harmonic contrast reduction. A unique compact closed-form solution for a surface impedance $Z_s(m,kr)$ is found in a straightforward manner and without any approximation as a function of the harmonic index $m$ (scattering mode to suppress) and of the frequency regime $kr$ (product of wavenumber $k$ and radius $r$ of the cloaked system) at any frequency regime. In the quasi-static limit, mantle cloaking is obtained as a particular case for $kr \ll 1$ and $m=0$. In addition, beyond quasi-static regime, impedance coatings for a selected dominant harmonic wave can be designed with proper dispersive behaviour, resulting in improved reduction levels and harmonic filtering capability.