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Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to the HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures. However, when nonlinearity is introduced, many intriguing questions arise. For example, are there universal fingerprints of the underlying topology when modes are coupled by nonlinearity, and what can happen to topological invariants during nonlinear propagation? To explore these questions, we experimentally demonstrate nonlinearity-induced coupling of light into topologically protected edge states using a photonic platform and develop a general theoretical framework for interpreting the mode-coupling dynamics in nonlinear topological systems. Performed on laser-written photonic Su-Schrieffer-Heeger lattices, our experiments show the nonlinear coupling of light into a nontrivial edge or interface defect channel that is otherwise not permissible due to topological protection. Our theory explains all the observations well. Furthermore, we introduce the concepts of inherited and emergent nonlinear topological phenomena as well as a protocol capable of revealing the interplay of nonlinearity and topology. These concepts are applicable to other nonlinear topological systems, both in higher dimensions and beyond our photonic platform.Topological photonics: nonlinear couplingAn engineered photonic system has provided insights into the interplay between nonlinearity and topology. Shiqi Xia and coworkers used laser-writing technique to fabricate refractive-index patterns that form a Su-Schrieffer-Heeger lattice in a nonlinear optical crystal of strontium-barium-niobate (SBN:61), a well-known photorefractive material. Due to the presence of the nonlinearity, two optical beams of sufficient power propagating in different directions can, when they collide, couple into a non-trivial interface state in the system, which is otherwise not accessible due to topological protection. Theoretical analysis correctly explains the observed behavior and the nonlinear coupling phenomenon. The researchers say that their findings are of a general nature and can be applied to other nonlinear topological systems.

Robust high-order optical vortices are much in demand for applications in optical manipulation, optical communications, quantum entanglement and quantum computing. However, in numerous experimental settings, a controlled generation of optical vortices with arbitrary orbital angular momentum remains a challenge. Here, we present a concept of “optical vortex ladder” for the stepwise generation of optical vortices through Sisyphus pumping of pseudospin modes in photonic graphene. The ladder is applicable in various lattices with Dirac-like structures. Instead of conical diffraction and incomplete pseudospin conversion under conventional Gaussian beam excitations, the vortices produced in the ladder arise from non-trivial topology and feature diffraction-free Bessel profiles, thanks to the refined excitation of the ring spectrum around the Dirac cones. By employing a periodic “kick” to the photonic graphene, effectively inducing the Sisyphus pumping, the ladder enables tunable generation of optical vortices of any order even when the initial excitation does not involve any orbital angular momentum. The optical vortex ladder stands out as an intriguing non-Hermitian dynamical system, and, among other possibilities, opens a pathway for applications of topological singularities in beam shaping and wavefront engineering. Controlled generation of OAM modes holds promise for applications in classical and quantum communication networks. Here the authors develop an optical vortex ladder in which an input beam transforms into vortices mediated by the Berry phase winding around topological singularities at the Dirac points.

The interactions between coupled photonic resonators influence the properties of the whole network. Dissipative coupling extends the ability to engineer photonic networks and brings fully controllable, ‘utopian’ networks within reach.

Topological properties of materials are typically presented in momentum space. Here, we demonstrate a universal mapping of topological singularities from momentum to real space. By exciting Dirac-like cones in photonic honeycomb (pseudospin-1/2) and Lieb (pseudospin-1) lattices with vortex beams of topological charge  l , optimally aligned with a given pseudospin state s , we directly observe topological charge conversion that follows the rule l  →  l + 2 s . Although the mapping is observed in photonic lattices where pseudospin-orbit interaction takes place, we generalize the theory to show it is the nontrivial Berry phase winding that accounts for the conversion which persists even in systems where angular momentum is not conserved, unveiling its topological origin. Our results have direct impact on other branches of physics and material sciences beyond the 2D photonic platform: equivalent mapping occurs for 3D topological singularities such as Dirac-Weyl synthetic monopoles, achievable in mechanical, acoustic, or ultracold atomic systems, and even with electron beams. Topological properties of materials are typically presented in momentum space. Here, the authors show a universal mapping of topological singularities from momentum to real space, potentially applicable to a wide range of systems.

Graphene plasmons have been found to be an exciting plasmonic platform, thanks to their high field confinement and low phase velocity, motivating contemporary research to revisit established concepts in light–matter interaction. In a conceptual breakthrough over 80 years old, Čerenkov showed how charged particles emit shockwaves of light when moving faster than the phase velocity of light in a medium. To modern eyes, the Čerenkov effect offers a direct and ultrafast energy conversion scheme from charge particles to photons. The requirement for relativistic particles, however, makes Čerenkov emission inaccessible to most nanoscale electronic and photonic devices. Here we show that graphene plasmons provide the means to overcome this limitation through their low phase velocity and high field confinement. The interaction between the charge carriers flowing inside graphene and the plasmons enables a highly efficient two-dimensional Čerenkov emission, giving a versatile, tunable and ultrafast conversion mechanism from electrical signal to plasmonic excitation. Graphene plasmons have gained significant interest thanks to their high field confinement and low phase velocity. Here the authors show theoretically that charge carriers propagating in graphene can excite plasmons through a quantum Čerenkov emission process in two dimensions, in the form of plasmonic shock waves.

Platforms enabling control over strong light–matter interactions in optical cavities provide a challenging but promising way to manipulate emergent light–matter hybrids. Spin selectivity of transitions has now been demonstrated in a two-dimensional hole gas microcavity system, paving the way towards the study of new spin physics phenomena in hybrid excitations.

The discovery of topological phases of matter and topological boundary states had a tremendous impact on condensed matter physics, photonics, and material sciences, where topological phases are defined via energy bands, described by the topological band theory. However, there are topological materials that cannot be described by this theory, which support non-trivial boundary states but are little-known and largely unexplored. Here, we uncover a new class of topological phases—termed \"multi-topological phase\" (MTPs)—arising from constrained inter-cell coupling in lattice systems, and experimentally demonstrate them in a photonic platform. The MTP features multiple sets of boundary states, where each set is associated with one distinct topological invariant. Unlike conventional topological phases, the MTP cannot be identified via the original band structure, being a \"hidden\" topological phase, where the phase transition can occur without band-gap closing. We present typical examples of MTPs in both one- and two-dimensional structures, as well as in indirectly gapped Chern insulators, beyond the regime where the conventional bulk-boundary correspondence predicts the existence of boundary states. Furthermore, we directly observe the MTPs in the first two examples using laser-written photonic lattices. Our work offers a new design strategy for topological materials, paving the way for future exploration and applications in photonics.

We propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. We compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.