Active Exterior Cloaking in Three-Dimensional Acoustics

International audience; Acoustic cloaking is the minimization of the scattered sound wave from the target object due to the action of a probing wave in order to render it acoustically invisible. Active exterior cloaking requires the use of sound sources in the exterior of the cloaked region which radiate to annihilate the scattered field. The Kirchhoff integral theorem states that the wave field within a closed volume can be reproduced by a continuous distribution of acoustic sources on the bounding surfaces. The amplitudes of these sources are dependent only on the information of that wave field on these surfaces. This result will be exploited to construct an active exterior cloak in three dimensions which cancels out the incident wave within the enclosed volume and therefore nullifies the scattered wave from any object inside. For realization purpose, we apply the addition theorem for Bessel functions to replace the continuous source distribution by a discrete array of multipolar point sources located outside the cloaked region. By considering certain uniform arrangement of the point sources, we derive numerical solutions for the amplitudes of the multipoles necessary for achieving the cloaking effect. They will be dependent on the total number of sources and the geometry of the source arrangement deployed. Since the acoustic scattering is prevented indirectly by eliminating the incident wave coming into contact with the target object, the cloaking device can be constructed with only the knowledge of the incoming wave. Such cloaking approach is independent of the nature of the target object and is easily implementable with a relatively small number of sources.