Source amplitudes for active exterior cloaking

TL;DR

This paper derives explicit formulas for the amplitudes of active exterior cloaking sources that cancel incident waves over a region, providing a direct solution to the inverse problem and characterizing non-radiating sources.

Contribution

It presents a novel explicit method to determine source amplitudes for active exterior cloaking in two dimensions, advancing the design of non-radiating sources.

Findings

Source amplitudes expressed as infinite sums of Bessel coefficients

Active sources produce zero total field outside a defined region

Provides a direct inverse solution for source amplitude determination

Abstract

The active cloak comprises a discrete set of multipole sources that destructively interfere with an incident time harmonic scalar wave to produce zero total field over a finite spatial region. For a given number of sources and their positions in two dimensions it is shown that the multipole amplitudes can be expressed as infinite sums of the coefficients of the incident wave decomposed into regular Bessel functions. The field generated by the active sources vanishes in the infinite region exterior to a set of circles defined by the relative positions of the sources. The results provide a direct solution to the inverse problem of determining the source amplitudes. They also define a broad class of non-radiating discrete sources.