Becker et al. (Science Advances, 2021) demonstrated, in a two-dimensional parallel-plate waveguide, the first active acoustic cloaking and holography of broadband wavefields without a priori knowledge of the incident field: microphone arrays record the passing wavefield, which is extrapolated in real time into a chosen virtual medium by convolution with precomputed Green's functions and re-emitted by loudspeaker arrays implementing immersive boundary conditions. The authors state that the methodology extends in principle to elastodynamic and electromagnetic waves, but its demonstrations were confined to 2D below a 6.9 kHz waveguide cutoff. Five years of follow-up work has resolved the object-cloning direction in 2D (Acoustic cloning, Physical Review Applied, 2023) and established a complete three-dimensional numerical framework with data-driven Green's-function retrieval (Acoustic disguising, arXiv:2606.08524, 2026 preprint), which explicitly leaves experimental demonstrations for future work. The surviving open problem is the physical realization in three dimensions: a laboratory system that cloaks or disguises unknown, broadband, and moving acoustic sources in a genuine 3D (free-field or general 3D) setting, together with the enabling components — 3D Green's-function acquisition under realistic noisy illumination, closed-surface sensor/actuator arrays with sub-millisecond latency, mitigation of non-ideal transducer behavior, and quantitative characterization of achievable bandwidth, angular coverage, and fidelity.

Background

Two long-standing goals of wave physics are acoustic cloaking — rendering an object invisible to impinging sound — and acoustic illusion or holography — making the wavefield behave as if it scattered off an object that is not physically present. Passive approaches, largely based on transformation acoustics (tailored material-parameter distributions that steer waves around a region), do not adapt to changing incident wavefields and work efficiently only over narrow frequency bands. Active approaches instead emit a secondary wavefield from arrays of control sources so that it destructively interferes with the field to be cancelled, but most active schemes require a priori knowledge of the incident or scattered field and therefore fail when the primary source is unknown or moving. A Green's function — the response of a medium at one point to an impulsive point source at another — is the central object for an exact active strategy: by recording the wavefield on a closed surface and convolving it with suitable extrapolation Green's functions, the field can be re-emitted so as to continue into any desired 'virtual' medium, not just free space. This is the framework of immersive boundary conditions (IBCs): a boundary is instrumented with pressure sensors and with monopole (volume-injecting) and dipole (force-like) sources, and the recorded field is extrapolated in real time into the virtual medium. Van Manen, Vasmel, Greenhalgh and Robertsson (JASA 137, EL415, 2015) proved the resulting broadband cloaking and holography scheme exact; Becker et al. (Phys. Rev. X 8, 031011, 2018) implemented immersive wave experimentation physically in one dimension; Börsing et al. (Phys. Rev. Applied 12, 024011, 2019) performed cloaking and holography experiments with IBCs but with a priori known incident fields. Becker et al. (Science Advances 7, eabi9627, 2021) removed the a priori-knowledge requirement experimentally: in a parallel-plate waveguide operating below its first vertical cutoff frequency of about 6.9 kHz (so that propagation is effectively two-dimensional), two circular arrays of 114 microphones each recorded the total field, which was extrapolated by a field-programmable-gate-array control system with roughly 870 microseconds of end-to-end latency and re-emitted by 20 (cloaking) or 36 (holography) loudspeakers, realizing broadband cloaking of a rigid scatterer and holograms of virtual scatterers for unknown and even moving primary sources. The authors note that any virtual medium — including nonlinear or energy-gaining ones — can be inserted as long as it is described by extrapolation Green's functions, propose 'cloning' of real objects from their recorded scattering Green's functions, attempt (without significant benefit) corrections for the non-monopolar directivity of the loudspeakers using the method of Li et al. (JASA 146, 3141, 2019), and state that the methodology 'in principle' extends to elastodynamic and electromagnetic waves, while a practical realization outside the 2D waveguide 'is significantly more challenging' and was not attempted. Multidimensional deconvolution (MDD) — a data-processing technique that retrieves a medium's Green's functions from recordings of extended illumination by deconvolving the incident wavefield, thereby removing reverberation and source-signature effects — subsequently became the standard route to acquiring the needed Green's functions from physical measurements (Li et al., JASA 149, 1813, 2021).

Problem Statement

Physically realize, in three dimensions, the Green's-function-driven methodology for real-time broadband active acoustic cloaking and illusions — that is, extend the demonstrated two-dimensional parallel-plate experiments of Becker et al. (2021) to a genuine 3D setting (free-field or general three-dimensional reverberant environment) in which primary sources that are unknown a priori, broadband, and possibly moving are cloaked, or made to scatter as an arbitrary virtual object, using immersive boundary conditions on a closed control surface. The problem comprises jointly supporting components of one experimental capability: (i) acquiring the required three-dimensional extrapolation and scattering Green's functions for desired virtual media under realistic, non-impulsive, noisy illumination — for example by multidimensional deconvolution on a closed 3D aperture; (ii) scaling the sensor and actuator arrays to a closed surface in 3D — including effective monopole and dipole emission on sound-transparent surfaces — with end-to-end latency below the physical propagation delay between the recording and emitting surfaces; (iii) mitigating non-ideal transducer behavior (directivity, transfer functions) sufficiently to reach useful fidelity, given that such corrections were already only partially effective in the 2D experiments; and (iv) quantitatively characterizing the achieved bandwidth, angular coverage, and amplitude fidelity, for instance via the scattered-field intensity-reduction metric of the source experiment. A complete answer specifies the full control system for a genuine three-dimensional setting — closed-surface sensor and actuator geometry with an explicit end-to-end latency budget, three-dimensional extrapolation and scattering Green's-function acquisition under realistic, non-impulsive, noisy illumination, and mitigation of non-ideal transducer behavior — and, by three-dimensional numerical simulation, quantifies the predicted bandwidth, angular coverage and scattered-field intensity reduction achievable for incident wavefields not known in advance, with components (i)–(iv) required jointly; the physical laboratory demonstration is the natural continuation of this work rather than part of the completion boundary. The extension to elastodynamic (vector) wavefields — so far realized only as one-dimensional beam immersion — and to electromagnetic waves remains open beyond this three-dimensional acoustic core and is a natural continuation rather than part of its completion boundary.

References

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