Sensors play an important part in many aspects of daily life such as infrared sensors in home security systems, particle sensors for environmental monitoring and motion sensors in mobile phones. High-quality optical microcavities are prime candidates for sensing applications because of their ability to enhance light-matter interactions in a very confined volume. Examples of such devices include mechanical transducers, magnetometers, single-particle absorption spectrometers, and microcavity sensors for sizing single particles and detecting nanometre-scale objects such as single nanoparticles and atomic ions. Traditionally, a very small perturbation near an optical microcavity introduces either a change in the linewidth or a frequency shift or splitting of a resonance that is proportional to the strength of the perturbation. Here we demonstrate an alternative sensing scheme, by which the sensitivity of microcavities can be enhanced when operated at non-Hermitian spectral degeneracies known as exceptional points. In our experiments, we use two nanoscale scatterers to tune a whispering-gallery-mode micro-toroid cavity, in which light propagates along a concave surface by continuous total internal reflection, in a precise and controlled manner to exceptional points. A target nanoscale object that subsequently enters the evanescent field of the cavity perturbs the system from its exceptional point, leading to frequency splitting. Owing to the complex-square-root topology near an exceptional point, this frequency splitting scales as the square root of the perturbation strength and is therefore larger (for sufficiently small perturbations) than the splitting observed in traditional non-exceptional-point sensing schemes. Our demonstration of exceptional-point-enhanced sensitivity paves the way for sensors with unprecedented sensitivity.

Exceptional points enhance sensing in an optical microcavity

The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.

Edge States and Topological Invariants of Non-Hermitian Systems.

Acoustic metamaterials can manipulate and control sound waves in ways that are not possible in conventional materials. Metamaterials with zero, or even negative, refractive index for sound offer new possibilities for acoustic imaging and for the control of sound at subwavelength scales. The combination of transformation acoustics theory and highly anisotropic acoustic metamaterials enables precise control over the deformation of sound fields, which can be used, for example, to hide or cloak objects from incident acoustic energy. Active acoustic metamaterials use external control to create effective material properties that are not possible with passive structures and have led to the development of dynamically reconfigurable, loss-compensating and parity–time-symmetric materials for sound manipulation. Challenges remain, including the development of efficient techniques for fabricating large-scale metamaterial structures and converting laboratory experiments into useful devices. In this Review, we outline the designs and properties of materials with unusual acoustic parameters (for example, negative refractive index), discuss examples of extreme manipulation of sound and, finally, provide an overview of future directions in the field. Acoustic metamaterials can be used manipulate sound waves with a high degree of control. Their applications include acoustic imaging and cloaking. This Review outlines the designs and properties of these materials, discussing transformation acoustics theory, anisotropic materials and active acoustic metamaterials.

Controlling sound with acoustic metamaterials

Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, that is, those that interact with the environment. They correspond to points in parameter space at which the eigenvalues of the underlying system and the corresponding eigenvectors simultaneously coalesce. In optics, the abrupt nature of the phase transitions that are encountered around exceptional points has been shown to lead to many intriguing phenomena, such as loss-induced transparency, unidirectional invisibility, band merging, topological chirality and laser mode selectivity. Recently, it has been shown that the bifurcation properties of second-order non-Hermitian degeneracies can provide a means of enhancing the sensitivity (frequency shifts) of resonant optical structures to external perturbations. Of particular interest is the use of even higher-order exceptional points (greater than second order), which in principle could further amplify the effect of perturbations, leading to even greater sensitivity. Although a growing number of theoretical studies have been devoted to such higher-order degeneracies, their experimental demonstration in the optical domain has so far remained elusive. Here we report the observation of higher-order exceptional points in a coupled cavity arrangement-specifically, a ternary, parity-time-symmetric photonic laser molecule-with a carefully tailored gain-loss distribution. We study the system in the spectral domain and find that the frequency response associated with this system follows a cube-root dependence on induced perturbations in the refractive index. Our work paves the way for utilizing non-Hermitian degeneracies in fields including photonics, optomechanics, microwaves and atomic physics.

Enhanced sensitivity at higher-order exceptional points

Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

Within a time span of 15 years, acoustic metamaterials have emerged from academic curiosity to become an active field driven by scientific discoveries and diverse application potentials. This review traces the development of acoustic metamaterials from the initial findings of mass density and bulk modulus frequency dispersions in locally resonant structures to the diverse functionalities afforded by the perspective of negative constitutive parameter values, and their implications for acoustic wave behaviors. We survey the more recent developments, which include compact phase manipulation structures, superabsorption, and actively controllable metamaterials as well as the new directions on acoustic wave transport in moving fluid, elastic, and mechanical metamaterials, graphene-inspired metamaterials, and structures whose characteristics are best delineated by non-Hermitian Hamiltonians. Many of the novel acoustic metamaterial structures have transcended the original definition of metamaterials as arising from the collective manifestations of constituent resonating units, but they continue to extend wave manipulation functionalities beyond those found in nature.

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Acoustic metamaterials: From local resonances to broad horizons.

The attenuation of low-frequency sound has been a challenging task because the intrinsic dissipation of materials is inherently weak in this regime. Here we present a thin-film acoustic metamaterial, comprising an elastic membrane decorated with asymmetric rigid platelets that aims to totally absorb low-frequency airborne sound at selective resonance frequencies ranging from 100-1,000 Hz. Our samples can reach almost unity absorption at frequencies where the relevant sound wavelength in air is three orders of magnitude larger than the membrane thickness. At resonances, the flapping motion of the rigid platelets leads naturally to large elastic curvature energy density at their perimeter regions. As the flapping motions couple only minimally to the radiation modes, the overall energy density in the membrane can be two-to-three orders of magnitude larger than the incident wave energy density at low frequencies, forming in essence an open cavity.

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Dark acoustic metamaterials as super absorbers for low-frequency sound

Acoustic impedance-matched surfaces do not reflect incident waves. Traditional means of acoustic absorption have so far resulted in imperfect impedance matching and bulky structures, or require costly and sophisticated electrical design. Inspired by electromagnetic metamaterials, a subwavelength acoustically reflecting surface with hybrid resonances and impedance-matched to airborne sound at tunable frequencies is now demonstrated.

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Acoustic metasurface with hybrid resonances

The study of classical wave physics has been reinvigorated by incorporating the concept of the geometric phase, which has its roots in optics, and topological notions that were previously explored in condensed matter physics. Recently, sound waves and a variety of mechanical systems have emerged as excellent platforms that exemplify the universality and diversity of topological phases. In this Review, we introduce the essential physical concepts that underpin various classes of topological phenomena realized in acoustic and mechanical systems: Dirac points, the quantum Hall, quantum spin Hall and valley Hall effects, Floquet topological phases, 3D gapless states and Weyl crystals. This Review describes topological phenomena that can be realized in acoustic and mechanical systems. Methods of symmetry breaking are described, along with the consequences and rich phenomena that emerge.

Topological phases in acoustic and mechanical systems

The behaviour of sound waves in phononic crystals—metamaterials with spatially varying acoustic characteristics—is similar to that of electrons in solids. Now, phononic band inversion and Zak phases have been measured for a 1D phononic system.

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Guancong Ma

Papers

Acoustic metamaterials: From local resonances to broad horizons.

Dark acoustic metamaterials as super absorbers for low-frequency sound

Acoustic metasurface with hybrid resonances

Topological phases in acoustic and mechanical systems

Geometric phase and band inversion in periodic acoustic systems