We introduce a framework for programmable acoustic wave manipulation using active meta-atoms embedded with feedback circuits. These meta-atoms support both gain and non-reciprocal responses, offering unprecedented control over non-Hermitian acoustic dynamics. For instance, embedding them in a 1-D array enables unidirectional wave amplification. Here, we demonstrate dynamic switching between system normal modes, enabled by temporal control of cross-site nonlinear gain–loss coupling for these meta-atoms in resonator arrays such as Helmholtz resonators. In this scheme, the gain or loss in each cavity is determined by the amplitude in neighboring sites, resulting in energy-conserving dynamics that converge toward designated eigenstates of an effective linear Hamiltonian—a process we refer to as selective mode amplification. This approach provides a unique framework for shaping the temporal evolution of acoustic waves through an eigenmode perspective. Spatially distributed gain–loss profiles can be tailored to shape specific eigenmodes for wave guiding; Parity-time symmetry considerations dictate whether the wave dynamics exhibit oscillatory behavior or collapse into desired eigenmodes; and temporal perturbations can be designed to accelerate or control transitions between target modes. Together, these elements define a spatiotemporal platform in which eigenmodes act as engineered fixed points guiding controlled wave evolution.
Jensen Li (Wed,) studied this question.