Non-Abelian physics in light and sound.

Non-Abelian phenomena arise when the sequence of operations on physical systems influences their behaviors. By possessing internal degrees of freedom such as polarization, light and sound can be subjected to various manipulations, including constituent materials, structured environments, and tailored source conditions. These manipulations enable the creation of a great variety of Hamiltonians, through which rich non-Abelian phenomena can be explored and observed. Recent developments have constituted a versatile testbed for exploring non-Abelian physics at the intersection of atomic, molecular, and optical physics; condensed matter physics; and mathematical physics. These fundamental endeavors could enable photonic and acoustic devices with multiplexing functionalities. Our review aims to provide a timely and comprehensive account of this emerging topic. Starting from the foundation of matrix-valued geometric phases, we address non-Abelian topological charges, non-Abelian gauge fields, non-Abelian braiding, non-Hermitian non-Abelian phenomena, and their realizations with photonics and acoustics and conclude with future prospects.

Acoustic Amplifying Diode Using Nonreciprocal Willis Coupling.

We propose a concept called acoustic amplifying diode combining signal isolation and amplification in a single device. The signal is exponentially amplified in one incident direction with no reflection and is perfectly absorbed in another. The reflection is eliminated from the device in both directions with impedance matching, preventing backscattering to the signal source. Here, we demonstrate the amplifying diode using an active metamaterial with nonreciprocal Willis coupling. We also discuss the situation with the presence of both reciprocal and nonreciprocal Willis couplings for more flexibility in implementation. The coexistence of both amplifier and perfect absorber in opposite incident directions extends the regime of sound isolation and further enables applications in sensing and communication, in which nonreciprocity can play an important role.

Transient non-Hermitian skin effect.

The discovery of non-Hermitian skin effect (NHSE) has opened an exciting direction for unveiling unusual physics and phenomena in non-Hermitian system. Despite notable theoretical breakthroughs, actual observation of NHSE's whole evolvement, however, relies mainly on gain medium to provide amplified mode. It typically impedes the development of simple, robust system. Here, we show that a passive system is fully capable of supporting the observation of the complete evolution picture of NHSE, without the need of any gain medium. With a simple lattice model and acoustic ring resonators, we use complex-frequency excitation to create virtual gain effect, and experimentally demonstrate that exact NHSE can persist in a totally passive system during a quasi-stationary stage. This results in the transient NHSE: passive construction of NHSE in a short time window. Despite the general energy decay, the localization character of skin modes can still be clearly witnessed and successfully exploited. Our findings unveil the importance of excitation in realizing NHSE and paves the way towards studying the peculiar features of non-Hermitian physics with diverse passive platforms.

Polarization coincidence images from metasurfaces with HOM-type interference.

Metasurfaces provide a promising route for structuring light and generating holograms with designed amplitude, phase, and polarization profiles, leading to a versatile platform for integrating and constructing optical components beyond the conventional ones. At the same time, incorporating coincidence in imaging allows a high signal-to-noise ratio for imaging in very low light levels. As beneficial from the recent development in both metasurfaces and single-photon avalanche diode (SPAD) cameras, we combine the polarization-sensitive capability of metasurfaces with Hong-Ou-Mandel (HOM)-type interference in generating images with tailor-made two-photon interference and polarization coincidence signatures. By using orthogonal linear-polarized photons as incidence, correlated, anticorrelated, and uncorrelated polarization coincidence features can be observed within the same image from the pairwise second-order coherence statistics across different pixels of the image. Our work adds polarization to the demonstrated amplitude and phase sensitivity in the domain of "HOM microscopy" and can be useful for biological and security applications.

Spin-orbit interactions of transverse sound.

Spin-orbit interactions (SOIs) endow light with intriguing properties and applications such as photonic spin-Hall effects and spin-dependent vortex generations. However, it is counterintuitive that SOIs can exist for sound, which is a longitudinal wave that carries no intrinsic spin. Here, we theoretically and experimentally demonstrate that airborne sound can possess artificial transversality in an acoustic micropolar metamaterial and thus carry both spin and orbital angular momentum. This enables the realization of acoustic SOIs with rich phenomena beyond those in conventional acoustic systems. We demonstrate that acoustic activity of the metamaterial can induce coupling between the spin and linear crystal momentum k, which leads to negative refraction of the transverse sound. In addition, we show that the scattering of the transverse sound by a dipole particle can generate spin-dependent acoustic vortices via the geometric phase effect. The acoustic SOIs can provide new perspectives and functionalities for sound manipulations beyond the conventional scalar degree of freedom and may open an avenue to the development of spin-orbit acoustics.

Topological Corner Modes Induced by Dirac Vortices in Arbitrary Geometry.

Recently, higher-order topologies have been experimentally realized, featuring topological corner modes (TCMs) between adjacent topologically distinct domains. However, they have to comply with specific spatial symmetries of underlying lattices, hence their TCMs only emerge in very limited geometries, which significantly impedes generic applications. Here, we report a general scheme of inducing TCMs in arbitrary geometry based on Dirac vortices from aperiodic Kekulé modulations. The TCMs can now be constructed and experimentally observed in square and pentagonal domains incompatible with underlying triangular lattices. Such bound modes at arbitrary corners do not require their boundaries to run along particular lattice directions. Our scheme allows an arbitrary specification of numbers and positions of TCMs, which will be important for future on-chip topological circuits. Moreover, the general scheme developed here can be extended to other classical wave systems. Our findings reveal rich physics of aperiodic modulations, and advance applications of TCMs in realistic scenarios.

Designing plasmonic exceptional points by transformation optics.

Exceptional points (EPs) have been shown to be useful in bringing about sensitive optical properties based on non-Hermitian physics. For example, they have been applied in plasmonics to realize nano-sensing with extreme sensitivity. While the exceptional points are conventionally constructed by considering parity-time symmetric or anti-parity-time symmetric media, we theoretically demonstrate the possibility of generating a series of non-Hermitian systems by transforming a seed system with conventional parity-time symmetry within the transformation optics framework. The transformed systems do not possess PT-symmetry with a conventional parity operator after a spatial operation, i.e. hidden from conventional sense, but are equipped with exceptional points and phase transitions, hinting an alternative method to design non-Hermitian plasmonic systems with sensitive spectra or eigenmodes.

Non-Hermitian effective medium theory and complex Dirac-like cones.

In this work, we propose a non-Hermitian effective medium theory to interpret the spawning rings of exceptional points out of the Dirac cones in the band structures of photonic crystals with loss/gain. Based on this theory, we predict and demonstrate two unique types of band dispersions of fully passive photonic crystals. In one type, the exceptional ring shrinks into a complex Dirac point associated with a complex Dirac-like cone. In the other type, a point of quadratic degeneracy is realized in the imaginary frequency spectrum. Our theory provides a unified picture for the exceptional points in effective media and gives rise to novel concepts like complex Dirac-like cones in non-Hermitian photonics.

Ultra-broadband reflectionless Brewster absorber protected by reciprocity.

The Brewster's law predicts zero reflection of p-polarization on a dielectric surface at a particular angle. However, when loss is introduced into the permittivity of the dielectric, the Brewster condition breaks down and reflection unavoidably appears. In this work, we found an exception to this long-standing dilemma by creating a class of nonmagnetic anisotropic metamaterials, where anomalous Brewster effects with independently tunable absorption and refraction emerge. This loss-independent Brewster effect is bestowed by the extra degrees of freedoms introduced by anisotropy and strictly protected by the reciprocity principle. The bandwidth can cover an extremely wide spectrum from dc to optical frequencies. Two examples of reflectionless Brewster absorbers with different Brewster angles are both demonstrated to achieve large absorbance in a wide spectrum via microwave experiments. Our work extends the scope of Brewster effect to the horizon of nonmagnetic absorptive materials, which promises an unprecedented wide bandwidth for reflectionless absorption with high efficiency.

Tailor-made unitary operations using dielectric metasurfaces.

Qubit operation belonging to unitary transformation is the fundamental operation to realize quantum computing and information processing. Here, we show that the complex and flexible light-matter interaction between dielectric metasurfaces and incident light can be used to perform arbitrary U(2) operations. By incorporating both coherent spatial-mode operation together with two polarizations on a single metasurface, we further extend the discussion to single-photon two-qubit U(4) operations. We believe the efficient usage of metasurfaces as a potential compact platform can simplify optical qubit operation from bulky systems into conceptually subwavelength elements.

Exceptional point-based plasmonic metasurfaces for vortex beam generation.

An exceptional point occurring in a tailor-made lossy optical system has been recently found to alter optical properties in counter-intuitive ways. In the context of tunable plasmonic devices, exceptional points can be useful as a driving mechanism to enhance tunability. Here, we experimentally demonstrate how a plasmonic exceptional point can be incorporated in metasurface Q-plates to have the generated vortex beam tuned through a change of structural parameter. We have observed an orbital rotation in the far-field by 45 degrees in crossing the exceptional point. We expect a new generation of tunable plasmonic devices in polarization control, beam structuring and holograms, which can take advantage of the huge sensitivity from exceptional points.

Circular Phase-Dichroism of Chiral Metasurface Using Birefringent Interference.

Circular phase-dichroism (CPD) has been suggested for the characterization of chiral metasurfaces in supplementing the conventional circular dichroism (CD). Conventional CD probes the bulk properties while the CPD, reported recently in 2D chiral metasurfaces using an air-gap Fabry-Perot setup, is based on the surface properties. Here we propose and demonstrate a robust birefringent interference approach to obtain the CPD by replacing the air-gap with a uniaxial birefringent material in which interference is realized by the difference in the refractive indexes for the ordinary and extraordinary components of the material. We measure the transmission phases of metasurfaces fabricated on birefringent sapphire substrates and obtain clear CPDs for chiral metasurfaces but vanishing for achiral metasurfaces. Importantly, our approach can be applied to metasurfaces fabricated on nonbirefringent substrates by add-on birefringent materials. We confirm our results by a Jones matrix method using data obtained from full-wave simulations, and good agreements with experiments are obtained.

Digitally virtualized atoms for acoustic metamaterials.

By designing tailor-made resonance modes with structured atoms, metamaterials allow us to obtain constitutive parameters outside their limited range from natural materials. Nonetheless, tuning the constitutive parameters depends on our ability to modify the physical structure or external circuits attached to the metamaterials, posing a fundamental challenge to the range of tunability in many real-time applications. Here, we propose the concept of virtualized metamaterials on their signal response function to escape the boundary inherent in the physical structure of metamaterials. By replacing the resonating physical structure with a designer mathematical convolution kernel with a fast digital signal processing circuit, we demonstrate a decoupled control of the effective bulk modulus and mass density of acoustic metamaterials on-demand through a software-defined frequency dispersion. Providing freely software-reconfigurable amplitude, center frequency, bandwidth of frequency dispersion, our approach adds an additional dimension to constructing non-reciprocal, non-Hermitian, and topological systems with time-varying capability as potential applications.

Anti-Parity-Time Symmetric Optical Four-Wave Mixing in Cold Atoms.

Non-Hermitian optical systems with parity-time (PT) symmetry have recently revealed many intriguing prospects that outperform conservative structures. The previous works are mostly rooted in complex arrangements with controlled gain-loss interplay. Here, we demonstrate anti-PT symmetry inherent in the nonlinear optical interaction based upon forward optical four-wave mixing in a laser-cooled atomic ensemble with negligible linear gain and loss. We observe that the pair of frequency modes undergo a nontrivial anti-PT phase transition between coherent power oscillation and optical parametric amplification in presence of a large phase mismatch.

Non-Abelian gauge field optics.

The concept of gauge field is a cornerstone of modern physics and the synthetic gauge field has emerged as a new way to manipulate particles in many disciplines. In optics, several schemes of Abelian synthetic gauge fields have been proposed. Here, we introduce a new platform for realizing synthetic SU(2) non-Abelian gauge fields acting on two-dimensional optical waves in a wide class of anisotropic materials and discover novel phenomena. We show that a virtual non-Abelian Lorentz force arising from material anisotropy can induce light beams to travel along Zitterbewegung trajectories even in homogeneous media. We further design an optical non-Abelian Aharonov-Bohm system which results in the exotic spin density interference effect. We can extract the Wilson loop of an arbitrary closed optical path from a series of gauge fixed points in the interference fringes. Our scheme offers a new route to study SU(2) gauge field related physics using optics.

Observation of Three-Dimensional Photonic Dirac Points and Spin-Polarized Surface Arcs.

Three-dimensional (3D) Dirac points inheriting relativistic effects from high-energy physics appear as gapless excitations in the topological band theory. Hosting fourfold linear dispersion, they play the central role among various topological phases, such as representing the degeneracy of paired Weyl nodes carrying opposite chiralities. While they have been extensively investigated in solid state systems for electrons, 3D Dirac points have not yet been observed in any classical systems. Here, we experimentally demonstrate 3D photonic Dirac points in the microwave region with an elaborately designed metamaterial, where two symmetrically placed Dirac points are stabilized by electromagnetic duality symmetry. Furthermore, spin-polarized surface arcs (counterparts of Fermi arcs in electronic systems) are demonstrated, which opens the gate toward implementing spin-multiplexed topological surface wave propagation. Closely linked to other exotic states through topological phase transitions, our system offers an effective medium platform for topological photonics.

Elastic Waves in Curved Space: Mimicking a Wormhole.

Transformation optics (TO) can be used to investigate nontrivial spacetime structures with inhomogeneous materials. However, the extreme curvature and large refractive indices make the implementation of a wormhole challenging. By considering flexural waves on a curved plate with geometric curvature, the stringent material requirement can be relaxed, and we demonstrate a two-dimensional analog of a wormhole using homogeneous materials within a curved laboratory frame. TO is used to understand wave propagation in such a curved space. This curved elastic space approach allows us to investigate not only geodesics but also wave redirection, tunneling, and virtual caustics of the wormhole, and will be useful to develop curvature-driven wave front shaping in general.

Feature issue introduction: Topological Photonics and Materials.

Photonic crystals have become a very common and powerful concept in optics since its introduction in the 1980s by Eli Yablonovitch and Sajeev John. It is in fact a concept borrowed from condensed matter physics. The discussion of photonic bands and bandgaps allows us to manipulate light on an optical chip, along a photonic crystal fiber and even in the quantum optics regime. Now, we are witnessing another round of concept translation again from condensed matter physics to optics about topology. Describing photonic bands by using their topology in the reciprocal space gives us a new tool to understand wave propagation and to design optical components. Topology is also an important aspect in light-matter interaction in the field of metamaterials and 2D materials.

Controlling Surface Plasmons Through Covariant Transformation of the Spin-Dependent Geometric Phase Between Curved Metamaterials.

General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different frames. In this Letter, we use one-dimensional curved metamaterials to mimic accelerating particles in curved space-times. The different curved shapes of structures are used to mimic different accelerating frames. The different geometric phases along the structure are used to mimic different movements in the frame. Using the covariant principle of general relativity, we can obtain equivalent nanostructures based on space-time transformations, such as the Lorentz transformation and conformal transformation. In this way, many covariant structures can be found that produce the same surface plasmon fields when excited by spin photons. A new kind of accelerating beam, the Rindler beam, is obtained based on the Rindler metric in gravity. Very large effective indices can be obtained in such systems based on geometric-phase gradient. This general covariant design method can be extended to many other optical media.

Source Illusion Devices for Flexural Lamb Waves Using Elastic Metasurfaces.

Inspired by recent demonstrations of metasurfaces in achieving reduced versions of electromagnetic cloaks, we propose and experimentally demonstrate source illusion devices to manipulate flexural waves using metasurfaces. The approach is particularly useful for elastic waves due to the lack of form invariance in usual transformation methods. We demonstrate compact and simple-to-implement metasurfaces for shifting, transforming, and splitting a point source. The effects are measured to be broadband and robust against a change of source positions, with agreement from numerical simulations and the Huygens-Fresnel theory. The proposed method is potentially useful for applications such as nondestructive testing, high-resolution ultrasonography, and advanced signal modulation.