Acoustic waveguides have been used to implement the long-theorized phenomenon of non-Abelian braiding, in which abstract geometric constructions are used to generate transformations between different ...modes.
Higher-order topological insulators
are a family of recently predicted topological phases of matter that obey an extended topological bulk-boundary correspondence principle. For example, a ...two-dimensional (2D) second-order topological insulator does not exhibit gapless one-dimensional (1D) topological edge states, like a standard 2D topological insulator, but instead has topologically protected zero-dimensional (0D) corner states. The first prediction of a second-order topological insulator
, based on quantized quadrupole polarization, was demonstrated in classical mechanical
and electromagnetic
metamaterials. Here we experimentally realize a second-order topological insulator in an acoustic metamaterial, based on a 'breathing' kagome lattice
that has zero quadrupole polarization but a non-trivial bulk topology characterized by quantized Wannier centres
. Unlike previous higher-order topological insulator realizations, the corner states depend not only on the bulk topology but also on the corner shape; we show experimentally that they exist at acute-angled corners of the kagome lattice, but not at obtuse-angled corners. This shape dependence allows corner states to act as topologically protected but reconfigurable local resonances.
The recent discoveries of higher-order topological insulators (HOTIs) have shifted the paradigm of topological materials, previously limited to topological states at boundaries of materials, to ...include topological states at boundaries of boundaries, such as corners. So far, all HOTI realisations have been based on static systems described by time-invariant Hamiltonians, without considering the time-variant situation. There is growing interest in Floquet systems, in which time-periodic driving can induce unconventional phenomena such as Floquet topological phases and time crystals. Recent theories have attempted to combine Floquet engineering and HOTIs, but there has been no experimental realisation so far. Here we report on the experimental demonstration of a two-dimensional (2D) Floquet HOTI in a three-dimensional (3D) acoustic lattice, with modulation along a spatial axis serving as an effective time-dependent drive. Acoustic measurements reveal Floquet corner states with double the period of the underlying drive; these oscillations are robust, like time crystal modes, except that the robustness arises from topological protection. This shows that space-time dynamics can induce anomalous higher-order topological phases unique to Floquet systems.
The recent discovery of higher-order topological insulators (TIs) has opened new possibilities in the search for novel topological materials and metamaterials. Second-order TIs have been implemented ...in two-dimensional (2D) systems exhibiting topological "corner states," as well as three-dimensional (3D) systems having one-dimensional (1D) topological "hinge states." Third-order TIs, which have topological states three dimensions lower than the bulk (which must thus be 3D or higher), have not yet been reported. Here, we describe the realization of a third-order TI in an anisotropic diamond-lattice acoustic metamaterial. The bulk acoustic band structure has nontrivial topology characterized by quantized Wannier centers. By direct acoustic measurement, we observe corner states at two corners of a rhombohedronlike structure, as predicted by the quantized Wannier centers. This work extends topological corner states from 2D to 3D, and may find applications in novel acoustic devices.
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.
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 directions
. Recently, inspired by the discoveries of topological insulators
, the confinement of photons with topological protection has been demonstrated in two-dimensional (2D) photonic structures known as photonic topological insulators
, with promising applications in topological lasers
and robust optical delay lines
. 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.
Recently discovered1,2 valley photonic crystals (VPCs) mimic many of the unusual properties of two-dimensional (2D) gapped valleytronic materials3,4,5,6,7,8,9. Of the utmost interest to optical ...communications is their ability to support topologically protected chiral edge (kink) states3,4,5,6,7,8,9 at the internal domain wall between two VPCs with opposite valley-Chern indices. Here we experimentally demonstrate valley-polarized kink states with polarization multiplexing in VPCs, designed from a spin-compatible four-band model. When the valley pseudospin is conserved, we show that the kink states exhibit nearly perfect out-coupling efficiency into directional beams, through the intersection between the internal domain wall and the external edge separating the VPCs from ambient space. The out-coupling behaviour remains topologically protected even when we break the spin-like polarization degree of freedom (DOF), by introducing an effective spin–orbit coupling in one of the VPC domains. This also constitutes the first realization of spin–valley locking for topological valley transport.
Multimode fibers (MMFs) have the potential to carry complex images for endoscopy and related applications, but decoding the complex speckle patterns produced by mode-mixing and modal dispersion in ...MMFs is a serious challenge. Several groups have recently shown that convolutional neural networks (CNNs) can be trained to perform high-fidelity MMF image reconstruction. We find that a considerably simpler neural network architecture, the single hidden layer dense neural network, performs at least as well as previously-used CNNs in terms of image reconstruction fidelity, and is superior in terms of training time and computing resources required. The trained networks can accurately reconstruct MMF images collected over a week after the cessation of the training set, with the dense network performing as well as the CNN over the entire period.
At photonic Dirac points, electromagnetic waves are governed by the same equations as two-component massless relativistic fermions. However, photonic Dirac points are known to occur in pairs in ..."photonic graphene" and other similar photonic crystals, which necessitates special precautions to excite only one valley state. Systems hosting unpaired photonic Dirac points are significantly harder to realize, as they require broken time-reversal symmetry. Here, we report on the observation of an unpaired Dirac point in a planar two-dimensional photonic crystal. The structure incorporates gyromagnetic materials, which break time-reversal symmetry; the unpaired Dirac point occurs when a parity-breaking parameter is fine-tuned to a topological transition between a photonic Chern insulator and a conventional photonic insulator phase. Evidence for the unpaired Dirac point is provided by transmission and field-mapping experiments, including a demonstration of strongly non-reciprocal reflection. This unpaired Dirac point may have applications in valley filters and angular selective photonic devices.
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