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Closed, lossless optical cavities are characterized by a Hamiltonian that obeys Hermiticity, resulting in strictly real-valued resonance frequencies. By contrast, non-Hermitian wave systems are characterized by Hamiltonians with poles and zeros at complex frequencies, whose control through precise engineering of material loss and gain can lead to exotic scattering phenomena. Notably, excitation signals that oscillate at complex-valued frequencies can mimic the emergence of gain and loss, facilitating access to these non-Hermitian responses without material modifications. These findings have been advancing the fundamental understanding of wave-matter interactions and are enabling breakthroughs in metamaterials, imaging, sensing, and computing. This Review examines theoretical advances and experimental discoveries in this emerging field, demonstrating how tailored time-domain excitations offer new opportunities for wave manipulation and control. 

Abstract Optical frequency combs, featuring evenly spaced spectral lines, have been extensively studied and applied to metrology, signal processing, and sensing. Recently, frequency comb generation has been also extended to MHz frequencies by harnessing nonlinearities in microelectromechanical membranes. However, the generation of frequency combs at radio frequencies (RF) has been less explored, together with their potential application in wireless technologies. In this work, we demonstrate an RF system able to wirelessly and passively generate frequency combs. This circuit, which we name quasi-harmonic tag (qHT), offers a battery-free solution for far-field ranging of unmanned vehicles (UVs) in GPS-denied settings, and it enables a strong immunity to multipath interference, providing better accuracy than other RF approaches to far-field ranging. Here, we discuss the principle of operation, design, implementation, and performance of qHTs used to remotely measure the azimuthal distance of a UV flying in an uncontrolled electromagnetic environment. We show that qHTs can wirelessly generate frequency combs with μWatt-levels of incident power by leveraging the nonlinear interaction between an RF parametric oscillator and a high quality factor piezoelectric microacoustic resonator. Our technique for frequency comb generation opens new avenues for a wide range of RF applications beyond ranging, including timing, computing and sensing. 

Acoustic resonances in open systems, which are usually associated with resonant modes characterized by complex eigenfrequencies, play a fundamental role in manipulating acoustic wave radiation and propagation. Notably, they are accompanied by considerable field enhancement, boosting interactions between waves and matter, and leading to various exciting applications. In the past two decades, acoustic metamaterials have enabled a high degree of control over tailoring acoustic resonances over a range of frequencies. Here, we provide an overview of recent advances in the area of acoustic resonances in non-Hermitian open systems, including Helmholtz resonators, metamaterials and metasurfaces, and discuss their applications in various acoustic devices, including sound absorbers, acoustic sources, vortex beam generation and imaging. We also discuss bound states in the continuum and their applications in boosting acoustic wave–matter interactions, active phononics and non-Hermitian acoustic resonances, including phononic topological insulators and the acoustic skin effect.