Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

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

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 manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia It is thus noteworthy that an entirely novel class of electromagnetic waves, known as topological edge states, has recently been demonstrated These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers

Topological Acoustics

Microwave photonics with superconducting quantum circuits

Acoustic isolation and nonreciprocal sound transmission are highly desirable in many practical scenarios. They may be realized with nonlinear or magneto-acoustic effects, but only at the price of high power levels and impractically large volumes. In contrast, nonreciprocal electromagnetic propagation is commonly achieved based on the Zeeman effect, or modal splitting in ferromagnetic atoms induced by a magnetic bias. Here, we introduce the acoustic analog of this phenomenon in a subwavelength meta-atom consisting of a resonant ring cavity biased by a circulating fluid. The resulting angular momentum bias splits the ring’s azimuthal resonant modes, producing giant acoustic nonreciprocity in a compact device. We applied this concept to build a linear, magnetic-free circulator for airborne sound waves, observing up to 40-decibel nonreciprocal isolation at audible frequencies.

Sound isolation and giant linear nonreciprocity in a compact acoustic circulator.

The primary objective of acoustic metamaterial research is to design subwavelength systems that behave as effective materials with novel acoustical properties. One such property couples the stress-strain and the momentum-velocity relations. This response is analogous to bianisotropy in electromagnetism, is absent from common materials, and is often referred to as Willis coupling after J.R., Willis, who first described it in the context of the dynamic response of heterogeneous elastic media. This work presents two principal results: first, experimental and theoretical demonstrations, illustrating that Willis properties are required to obtain physically meaningful effective material properties resulting solely from local behaviour of an asymmetric one-dimensional isolated element and, second, an experimental procedure to extract the effective material properties from a one-dimensional isolated element. The measured material properties are in very good agreement with theoretical predictions and thus provide improved understanding of the physical mechanisms leading to Willis coupling in acoustic metamaterials.

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Experimental evidence of Willis coupling in a one-dimensional effective material element.

In addition to conventional acoustic properties (mass density and compressibility), recent research has shown that inhomogeneous acoustic media may require coupling tensors between effective volume strain and momentum fields. These coupling tensors imply conversion between monopolar and dipolar motion in the effective material response. Intrinsic coupling between strain and momentum is known as Willis coupling in elastodynamics, and it is analogous to bianisotropy in electromagnetism. This paper investigates the microscale and mesoscale effects that lead to Willis coupling, studies the proper homogenization of acoustic metamaterials with non-negligible Willis coupling, and demonstrates the impact of Willis coupling on defining physically meaningful effective material parameters.

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Origins of Willis coupling and acoustic bianisotropy in acoustic metamaterials through source-driven homogenization

Materials that require coupling between the stress-strain and momentum-velocity constitutive relations were first proposed by Willis (Willis 1981 Wave Motion3, 1-11 (doi:101016/0165-2125(81)90008-1)) and are now known as elastic materials of the Willis type, or simply Willis materials As coupling between these two constitutive equations is a generalization of standard elastodynamic theory, restrictions on the physically admissible material properties for Willis materials should be similarly generalized This paper derives restrictions imposed on the material properties of Willis materials when they are assumed to be reciprocal, passive and causal Considerations of causality and low-order dispersion suggest an alternative formulation of the standard Willis equations The alternative formulation provides improved insight into the subwavelength physical behaviour leading to Willis material properties and is amenable to time-domain analyses Finally, the results initially obtained for a generally elastic material are specialized to the acoustic limit

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2016.0604

Reciprocity, passivity and causality in Willis materials

In this work, a thin functionally-graded sound absorber that achieves an absorption coefficient near unity is demonstrated. The sound absorber consists of a multilayer arrangement of an interwoven sonic crystal lattice with varying filling fractions, backed by a thin elastic coating that acts as a flexural acoustic element. The overall thickness of the sound absorber is about one tenth of the wavelength in air, and it was 3D printed with a thermoplastic polyurethane. Samples were fabricated and acoustically tested in an air-filled acoustic impedance tube, from which absorption and effective acoustic properties were obtained. A theoretical formulation for the effective acoustic properties of the sonic crystal lattice was used to guide the design process, and excellent agreement was found between measured and theoretically predicted results. A range of sonic crystal filling fractions and thicknesses were tested to verify the fabrication process and robustness of the theoretical formulation, and both were found to be in excellent agreement. Based on this testing and analysis, an optimal arrangement was found that achieved simultaneous near zero reflectance and transmittance over a given frequency band, thereby resulting in an absorption coefficient near unity. [Work supported by the Office of Naval Research.]

Caleb F. Sieck

Papers

Sound isolation and giant linear nonreciprocity in a compact acoustic circulator.

Experimental evidence of Willis coupling in a one-dimensional effective material element.

Origins of Willis coupling and acoustic bianisotropy in acoustic metamaterials through source-driven homogenization

Reciprocity, passivity and causality in Willis materials

3D printed sound absorbers using functionally-graded sonic crystals