Silence is bliss in a Platonic relationship

TL;DR

This paper presents an efficient active cloaking method for scalar wave fields in three dimensions using multipole sources at Platonic solid vertices, creating a silent zone with minimal external disturbance.

Contribution

It introduces a novel active cloaking strategy employing multipole sources at Platonic vertices, enabling efficient and scalable wave field cloaking in 3D.

Findings

Creates a silent zone interior to Platonic solids

Source amplitudes can be computed via simple post-processing

Applicable to various scalar wave fields like acoustics and electromagnetism

Abstract

We describe an effective active cloaking strategy for the scalar Helmholtz equation in three dimensions where multipole active sources are located at the vertices of the Platonic solids. A "silent zone" is created interior to the imaginary Platonic solid and only the incident field remains in a defined region exterior to the silent zone and active source configuration. This distribution of the sources ensures that the implementation of the cloaking strategy is extremely efficient. In particular, once the multipole source amplitudes required at a single source location are determined, the other source amplitudes can be calculated by simple post-processing involving multiplication of the multipole source vector by a rotation matrix. The general nature of the problem means that the technique is relevant to any scalar wave field, including both acoustics and electromagnetism.