Nonreciprocal Acoustics Using Programmable Boundary Conditions: From Boundary Control and Active Metamaterials to the Acoustic Diode

Abstract

In this communication, we first introduce the concept of programmable boundary conditions, and then use it to design a nonreciprocal acoustic device: an effective, broadband, acoustic diode. Previous works showed that, using sufficiently small transducers, an active acoustic metasurface can be realized: a smart active acoustic skin with tunable acoustic properties. Using distributed control, these properties can be adapted or reconfigured in real-time. Or, it can even depend on the acoustic field itself, allowing for a programming of the (meta)surface properties: a programmable boundary condition. For instance, a partial derivative equation depending on the acoustic quantities can be imposed, in a discretized form, at the surface of such a programmable boundary. This type of non-standard boundary conditions have been shown to provide the necessary basis for nonreciprocal propagation for a plane wave interacting with a boundary with non grazing incidence, ie. for wavevectors that possess a component normal to the boundary. This restriction may appear problematic when the wavevector is then parallel to the boundary, e.g. when dealing with plane waves in a 1D waveguide, as in an acoustic diode. An acoustic diode, or acoustic isolator, is a nonreciprocal device that let acoustic power pass only in one direction, hence breaking the reciprocity of normal acoustic propagation. We propose a new model of acoustic diode, based on active components: a continuous, distributed source inside the domain. However, based on the modeling of parietal sources in ducts, in the low frequency range, we show that the boundary control approach and the distributed domain sources are equivalent. The only difference is that, in the case of the programmable boundary condition, the near-field of the boundary also contains a component normal to the boundary. Hence our acoustic diode can be realized in practice using programmable boundary conditions. Moreover, the acoustic diode is effective on a broad frequency range, since it can work both on the fundamental mode (plane waves) and on higher-order mode of the waveguide.