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

We combine theory and experiment to demonstrate that a carefully designed gradient meta-surface supports high-efficiency anomalous reflections for near-infrared light following the generalized Snell's law, and the reflected wave becomes a bounded surface wave as the incident angle exceeds a critical value. Compared to previously fabricated gradient meta-surfaces in infrared regime, our samples work in a shorter wavelength regime with a broad bandwidth (750-900 nm), exhibit a much higher conversion efficiency (∼80%) to the anomalous reflection mode at normal incidence, and keep light polarization unchanged after the anomalous reflection. Finite-difference-time-domain (FDTD) simulations are in excellent agreement with experiments. Our findings may lead to many interesting applications, such as antireflection coating, polarization and spectral beam splitters, high-efficiency light absorbers, and surface plasmon couplers.

High-efficiency broadband anomalous reflection by gradient meta-surfaces.

Transformation optics describes the capability to design the path of light waves almost at will through the use of metamaterials that control effective materials properties on a subwavelength scale. In this review, the physics and applications of transformation optics are discussed.

Transformation optics and metamaterials

Like their optical counterparts, acoustic metamaterials are capable of manipulating sound waves in unusual ways. An acoustic hyperlens is now demonstrated that is capable of magnifying subwavelength acoustic waves, and could therefore find applications in medical imaging or underwater sonar. Acoustic metamaterials can manipulate sound waves in surprising ways, which include collimation, focusing, cloaking, sonic screening and extraordinary transmission1,2,3,4,5,6,7,8,9,10,11,12,13,14. Recent theories suggested that imaging below the diffraction limit using passive elements can be realized by acoustic superlenses or magnifying hyperlenses15,16. These could markedly enhance the capabilities in underwater sonar sensing, medical ultrasound imaging and non-destructive materials testing. However, these proposed approaches suffer narrow working frequency bands and significant resonance-induced loss, which hinders them from successful experimental realization. Here, we report the experimental demonstration of an acoustic hyperlens that magnifies subwavelength objects by gradually converting evanescent components into propagating waves. The fabricated acoustic hyperlens relies on straightforward cutoff-free propagation and achieves deep-subwavelength resolution with low loss over a broad frequency bandwidth.

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Experimental demonstration of an acoustic magnifying hyperlens.

We designed a metamaterial field rotator that can rotate electromagnetic wave fronts. Our starting point was the transformation-media concept. Effective medium theories and full simulations facilitated the actual design process. We created at a very simple structure comprising of an array of identical aluminum metal plates. We made and measured a sample and we experimentally demonstrated the field rotation effect as well as the broadband functionality at microwave frequencies.

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Design and experimental realization of a broadband transformation media field rotator at microwave frequencies.

We study the edge states in two-dimensional photonic crystals arising from a singular point in $k$ space at which two dispersion surfaces intersect. The zigzag edge states in a honeycomb lattice for TM polarization are analogous to the electronic ones in graphene nanoribbons. Electromagnetic modes at the zigzag edges of such photonic crystals consisting of ferrite rods are allowed to propagate only along one direction. The one-way propagation is insensitive to imperfections on the zigzag edge.

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One-way edge mode in a magneto-optical honeycomb photonic crystal

A kind of two-dimensional acoustic metamaterial is designed so that it exhibits strong anisotropy along two orthogonal directions. Based on the rectangular equal frequency contour of this metamaterial, magnifying lenses for acoustic waves, analogous to electromagnetic hyperlenses demonstrated recently in the optical regime, can be realized. Such metamaterial may offer applications in imaging for systems that obey scalar wave equations.

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Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials

We examine the complex band structures and effective medium descriptions of a periodic acoustic composite system. It is shown that if the system exhibits a negative velocity band, the assignment of the system as a phononic crystal or as a ``double negative'' metamaterial is unambiguous only in some cases. An example is given where the system properties can be tuned gradually and continuously from an acoustic metamaterial to a phononic crystal, and there is no sharp dividing line between these two regimes.

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Complex band structures and effective medium descriptions of periodic acoustic composite systems

We investigate two routes to obtain negative group velocity bands in two-dimensional phononic crystal structures. The negative dispersion originates from the resonances of sub-wavelength building blocks and as such, the system should be regarded as acoustic metamaterials. The first kind of acoustic metamaterial exhibits effectively negative bulk modulus and negative mass density simultaneously. Monopolar and dipolar Mie resonances are combined to achieve an effective medium with negative refractive index. In particular, we present a double negative metamaterial for airborne sonic waves. We then show that we can obtain negative group velocity from quadrupole resonances, and the result is explained using the quasi-static approximation. The negative dispersion in quadrupole bands cannot be described by standard effective medium theories even though the frequency can be very low.

Xianyu Ao

Papers

Design and experimental realization of a broadband transformation media field rotator at microwave frequencies.

One-way edge mode in a magneto-optical honeycomb photonic crystal

Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials

Complex band structures and effective medium descriptions of periodic acoustic composite systems

Negative group velocity from resonances in two-dimensional phononic crystals