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The paradigmatic example of a topological phase of matter, the two-dimensional Chern insulator1-5, is characterized by a topological invariant consisting of a single integer, the scalar Chern number. Extending the Chern insulator phase from two to three dimensions requires generalization of the Chern number to a three-vector6,7, similar to the three-dimensional (3D) quantum Hall effect8-13. Such Chern vectors for 3D Chern insulators have never been explored experimentally. Here we use magnetically tunable 3D photonic crystals to achieve the experimental demonstration of Chern vectors and their topological surface states. We demonstrate Chern vector magnitudes of up to six, higher than all scalar Chern numbers previously realized in topological materials. The isofrequency contours formed by the topological surface states in the surface Brillouin zone form torus knots or links, whose characteristic integers are determined by the Chern vectors. We demonstrate a sample with surface states forming a (2, 2) torus link or Hopf link in the surface Brillouin zone, which is topologically distinct from the surface states of other 3D topological phases. These results establish the Chern vector as an intrinsic bulk topological invariant in 3D topological materials, with surface states possessing unique topological characteristics. Ministry of Education (MOE) National Research Foundation (NRF) Submitted/Accepted version We acknowledge funding from the Singapore National Research Foundation Competitive Research Program (grant no. NRF-CRP23-2019-0007) and Singapore Ministry of Education Academic Research Fund Tier 3 (grant no. MOE2016-T3-1-006). P.Z., Z.G. and Y.Y. acknowledge funding from the National Natural Science Foundation of China (grant nos. 52022018, 52021001, 12104211, 6101020101 and 62175215) and Chinese Academy of Engineering (grant no. 2022-XY-127).

Confining photons in a finite volume is highly desirable in modern photonic devices, such as waveguides, lasers and cavities. Decades ago, this motivated the study and application of photonic crystals, which have a photonic bandgap that forbids light propagation in all directions1–3. Recently, inspired by the discoveries of topological insulators4,5, the confinement of photons with topological protection has been demonstrated in two-dimensional (2D) photonic structures known as photonic topological insulators6–8, with promising applications in topological lasers9,10 and robust optical delay lines11. However, a fully three-dimensional (3D) topological photonic bandgap has not been achieved. Here we experimentally demonstrate a 3D photonic topological insulator with an extremely wide (more than 25 per cent bandwidth) 3D topological bandgap. The composite material (metallic patterns on printed circuit boards) consists of split-ring resonators (classical electromagnetic artificial atoms) with strong magneto-electric coupling and behaves like a ‘weak’ topological insulator (that is, with an even number of surface Dirac cones), or a stack of 2D quantum spin Hall insulators. Using direct field measurements, we map out both the gapped bulk band structure and the Dirac-like dispersion of the photonic surface states, and demonstrate robust photonic propagation along a non-planar surface. Our work extends the family of 3D topological insulators from fermions to bosons and paves the way for applications in topological photonic cavities, circuits and lasers in 3D geometries. A three-dimensional photonic topological insulator is presented, made of split-ring resonators with strong magneto-electric coupling, which has an extremely wide topological bandgap, forbidding light propagation.

We construct an electrical circuit to realize a modified Haldane lattice exhibiting the phenomenon of antichiral edge states. The circuit consists of a network of inductors and capacitors with interconnections reproducing the effects of a magnetic vector potential. The next nearest neighbor hoppings are configured differently from the standard Haldane model, and as predicted by earlier theoretical studies, this gives rise to antichiral edge states that propagate in the same direction on opposite edges and coexist with bulk states at the same frequency. Using pickup coils to measure voltage distributions in the circuit, we experimentally verify the key features of the antichiral edge states, including their group velocities and ability to propagate consistently in a Möbius strip configuration. Ministry of Education (MOE) This work was supported by the National Natural Science Foundation of China (Grant Nos. 11874274, and 12004425), the Natural Science Foundation of Jiangsu Province (Grant Nos. BK20170058, and BK20200630), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). YiDong Chong was supported by the Singapore MOE Academic Research Fund Tier 3 (Grant No. MOE2016-T3-1-006).

Berry phase associated with energy bands in crystals can lead to quantised observables like quantised dipole polarizations in one-dimensional topological insulators. Recent theories have generalised the concept of quantised dipoles to multipoles, resulting in the discovery of multipole topological insulators which exhibit a hierarchy of multipole topology: a quantised octupole moment in a three-dimensional bulk induces quantised quadrupole moments on its two-dimensional surfaces, which in turn induce quantised dipole moments on one-dimensional hinges. Here, we report on the realisation of an octupole topological insulator in a three-dimensional acoustic metamaterial. We observe zero-dimensional topological corner states, one-dimensional gapped hinge states, two-dimensional gapped surface states, and three-dimensional gapped bulk states, representing the hierarchy of octupole, quadrupole and dipole moments. Conditions for forming a nontrivial octupole moment are demonstrated by comparisons with two different lattice configurations having trivial octupole moments. Our work establishes the multipole topology and its full hierarchy in three-dimensional geometries., The concept of topological corner states in two dimensional topological insulators can be generalised to higher dimensions. Here, authors present a three dimensional acoustic metamaterial that exhibits the full hierarchy of topological multipole states including corner, hinge, surface and bulk states.

Weyl fermions are hypothetical two-component massless relativistic particles in three-dimensional (3D) space, proposed by Hermann Weyl in 1929. Their band-crossing points, called ‘Weyl points’, carry a topological charge and are therefore highly robust. There has been much excitement over recent observations of Weyl points in microwave photonic crystals and the semimetal TaAs. Here, we report on the experimental observation of ‘type-II’ Weyl points of light at optical frequencies, with the photons having a strictly positive group velocity along one spatial direction. We use a 3D structure consisting of laser-written waveguides, and show the presence of type-II Weyl points by observing conical diffraction along one axis when the frequency is tuned to the Weyl point; and observing the associated Fermi arc-like surface states. The realization of Weyl points at optical frequencies allows these novel electromagnetic modes to be further explored in the context of linear, nonlinear, and quantum optics. NRF (Natl Research Foundation, S’pore) MOE (Min. of Education, S’pore) Accepted version

Absorption of electromagnetic energy by a material is a phenomenon that underlies many applied problems, including molecular sensing, photocurrent generation and photodetection. Commonly, the incident energy is delivered to the system through a single channel, for example by a plane wave incident on one side of an absorber. However, absorption can be made much more efficient by exploiting wave interference. A coherent perfect absorber is a system in which complete absorption of electromagnetic radiation is achieved by controlling the interference of multiple incident waves. Here, we review recent advances in the design and applications of such devices. We present the theoretical principles underlying the phenomenon of coherent perfect absorption and give an overview of the photonic structures in which it can be realized, including planar and guided-mode structures, graphene-based systems, parity- and time-symmetric structures, 3D structures and quantum-mechanical systems. We then discuss possible applications of coherent perfect absorption in nanophotonics and, finally, we survey the perspectives for the future of this field.

Using a hexagonal array of helical waveguides, physicists have observed robust optical waves that move in one direction, bypassing obstacles and imperfections exactly as predicted by the theory of topological insulators. See Letter p.196 One of the hottest fields of condensed-matter research is that of topological insulators. They exist in electronic states that are robust against disorder owing to the topological protection provided by the underlying electronic structure. Their potential practical importance lies in their ability to control and manipulate electron waves without scattering. An interesting question is whether it would be possible to make a topological insulator for light. The answer is yes, and here Mordechai Segev and colleagues demonstrate the first experimental realization of a photonic topological insulator, which consists of helical waveguides arranged in a honeycomb lattice. The helicity is crucial, providing a symmetry breaking effect leading to topological insulator properties. The authors demonstrate one-way edge states that are protected from scattering.