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Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), at which two eigenstates coalesce under a system parameter variation. Many interesting EP phenomena, such as level crossings in nuclear and condensed matter physics, and unusual phenomena in optics, such as loss-induced lasing and unidirectional transmission, can be understood by considering a simple 2×2 non-Hermitian matrix. At a higher dimension, more complex EP physics not found in two-state systems arises. We consider the emergence and interaction of multiple EPs in a four-state system theoretically and realize the system experimentally using four coupled acoustic cavities with asymmetric losses. We find that multiple EPs can emerge, and as the system parameters vary, these EPs can collide and merge, leading to higher-order singularities and topological characteristics much richer than those seen in two-state systems. The new physics obtained is not limited to the acoustic systems demonstrated here. It also applies to other systems as well, such as coupled photonic cavities and waveguides.

Bound states in the continuum (BICs) have attracted attention in photonics owing to their interesting properties. For example, BICs can effectively confine light in a counterintuitive way, and the far-field radiation of photonic structures that exhibit BICs has fascinating topological characteristics. Early research into photonic BICs was primarily focused on designing artificial structures to produce BICs. However, since the mid-2010s, exploring the potential applications of BICs has been a growing trend in research. In this Review, we detail the unique properties of BICs, including the ability to achieve enhanced light confinement, sharp Fano resonances and topological characteristics. We explore phenomena derived from BICs, including the generation of circularly polarized states and unidirectional guided resonances, and the impact of BICs on various applications such as lasing, nonlinear frequency conversion, waveguiding, sensing and wavefront control. We also discuss the insights provided by BICs in several emerging research frontiers, such as parity–time symmetric systems, higher-order topology, exciton–photon coupling and moiré superlattices.Photonic systems provide a versatile platform to explore and use bound states in the continuum. This Review discusses the potential of these states for enhancing light–matter interactions in various applications and investigating the physics of emerging photonic systems.

The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Because of the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al., Nature (London) 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors; i.e., encircling an EP in different directions results in different output states. Here, we propose a coupled ferromagnetic waveguide system that carries two EPs and design an experimental setup in which the trajectory of state evolution can be controlled in situ using a tunable external field, allowing us to dynamically encircle zero, one, or even two EPs experimentally. The tunability allows us to control the trajectory of encircling in the parameter space, including the size of the encircling loop and the starting/end point. We discovered that whether or not the dynamics is chiral actually depends on the starting point of the loop. In particular, dynamically encircling an EP with a starting point in the parity-time-broken phase results in nonchiral behaviors such that the output state is the same no matter which direction the encircling takes. The proposed system is a useful platform to explore the topology of energy surfaces and the dynamics of state evolution in non-Hermitian systems and will likely find applications in mode switching controlled with external parameters.

Light can exert radiation pressure on any object it encounters and that resulting optical force can be used to manipulate particles. It is commonly assumed that light should move a particle forward and indeed an incident plane wave with a photon momentum ħ k can only push any particle, independent of its properties, in the direction of k . Here we demonstrate, using full-wave simulations, that an anomalous lateral force can be induced in a direction perpendicular to that of the incident photon momentum if a chiral particle is placed above a substrate that does not break any left–right symmetry. Analytical theory shows that the lateral force emerges from the coupling between structural chirality (the handedness of the chiral particle) and the light reflected from the substrate surface. Such coupling induces a sideway force that pushes chiral particles with opposite handedness in opposite directions. Light carries momentum and therefore can be used to push small particles forward. Here, Wang and Chan demonstrate that under the right conditions a light beam can also exert sideway forces on chiral particles.

Weyl points, as monopoles of Berry curvature in momentum space, have captured much attention recently in various branches of physics. Realizing topological materials that exhibit such nodal points is challenging and indeed, Weyl points have been found experimentally in transition metal arsenide and phosphide and gyroid photonic crystal whose structure is complex. If realizing even the simplest type of single Weyl nodes with a topological charge of 1 is difficult, then making a real crystal carrying higher topological charges may seem more challenging. Here we design, and fabricate using planar fabrication technology, a photonic crystal possessing single Weyl points (including type-II nodes) and multiple Weyl points with topological charges of 2 and 3. We characterize this photonic crystal and find nontrivial 2D bulk band gaps for a fixed k z and the associated surface modes. The robustness of these surface states against k z -preserving scattering is experimentally observed for the first time. To realize Weyl points carrying topological charges higher than one is challenging. Here, Chen et al . report a photonic crystal possessing single and multiple Weyl points with topological charges of two and three using planar fabrication technology.

Metamaterials with a Dirac-like cone dispersion at the center of the Brillouin zone behave like an isotropic and impedance-matched zero refractive index material at the Dirac-point frequency. Such metamaterials can be realized in the form of either bulk metamaterials with efficient coupling to free-space light or on-chip metamaterials that are efficiently coupled to integrated photonic circuits. These materials enable the interactions of a spatially uniform electromagnetic mode with matter over a large area in arbitrary shapes. This unique optical property paves the way for many applications, including arbitrarily shaped high-transmission waveguides, nonlinear enhancement, and phase mismatch-free nonlinear signal generation, and collective emission of many emitters. This review summarizes the Dirac-like cone-based zero-index metamaterials’ fundamental physics, design, experimental realizations, and potential applications.

Surface impedance is an important concept in classical wave systems such as photonic crystals (PCs). For example, the condition of an interface state formation in the interfacial region of two different one-dimensional PCs is simplyZSL+ZSR=0 , where ZSL(ZSR) is the surface impedance of the semi-infinite PC on the left-hand (right-hand) side of the interface. Here, we also show a rigorous relation between the surface impedance of a one-dimensional PC and its bulk properties through the geometrical (Zak) phases of the bulk bands, which can be used to determine the existence or nonexistence of interface states at the interface of the two PCs in a particular band gap. Our results hold for any PCs with inversion symmetry, independent of the frequency of the gap and the symmetry point where the gap lies in the Brillouin zone. Our results provide new insights into the relationship between surface scattering properties, the bulk band properties, and the formation of interface states, which in turn can enable the design of systems with interface states in a rational manner.

In the last few decades, topological phase 1 – 11 has emerged as a new classification of matter states beyond the Ginzburg–Landau symmetry-breaking paradigm. The underlying global invariant is usually well characterized by integers, such as Chern numbers or winding numbers—the Abelian charges 12 – 15 . Very recently, researchers proposed the notion of non-Abelian topological charges 16 – 19 , which possess non-commutative and fruitful braiding structures with multiple (more than one) bandgaps tangled together. Here we experimentally observe the non-Abelian topological charges in a time-reversal and inversion-symmetric transmission line network. The quaternion-valued non-Abelian topological charges are clearly mapped onto an eigenstate-frame sphere. Moreover, we find a non-Abelian quotient relation that provides a global perspective on the distribution of edge/domain-wall states. Our work opens the door towards characterization and manipulation of non-Abelian topological charges, which may lead to interesting observables such as trajectory-dependent Dirac/Weyl node collisions in two-dimensional systems 16 , 17 , 20 , admissible nodal line configurations in three dimensions 16 , 19 , 20 , and may provide insight into certain strongly correlated phases of twisted bilayer graphene 21 . Non-Abelian topological charges and edge states in a PT-symmetric transmission line network are experimentally observed, and a non-Abelian quotient relation for the bulk–edge correspondence is found.

Many novel properties of non-Hermitian systems are found at or near the exceptional points—branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. In particular, higher-order exceptional points can result in optical structures that are ultrasensitive to external perturbations. Here we show that an arbitrary order exceptional point can be achieved in a simple system consisting of identical resonators placed near a waveguide. Unidirectional coupling between any two chiral dipolar states of the resonators mediated by the waveguide mode leads to the exceptional point, which is protected by the transverse spin–momentum locking of the guided wave and is independent of the positions of the resonators. Various analytic response functions of the resonators at the exceptional points are experimentally manifested in the microwave regime. The enhancement of sensitivity to external perturbations near the exceptional point is also numerically and analytically demonstrated. Exceptional points in non-Hermitian systems can enhance the performance of optical sensors. Here, Wang et al. demonstrate theoretically and experimentally that higher-order exceptional points, which would allow for yet higher sensitivities, can be realized in simple photonic resonator chains.

Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here, we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes due to the synthetic Weyl points, which in turn guarantees the existence of interface states between photonic crystals and any reflecting substrates. The reflection phase vortexes have been confirmed for the first time in our experiments, which serve as an experimental signature of the generalized Weyl points. The existence of these interface states is protected by the topological properties of the Weyl points, and the trajectories of these states in the parameter space resembles those of Weyl semimetal “Fermi arc surface states” in momentum space. Tracing the origin of interface states to the topological character of the parameter space paves the way for a rational design of strongly localized states with enhanced local field.