Defect modes in two-dimensional periodic photonic structures have found use in a highly diverse set of optical devices. For example, photonic crystal cavities confine optical modes to subwavelength volumes and can be used for Purcell enhancement of nonlinearity, lasing, and cavity quantum electrodynamics. Photonic crystal fiber defect cores allow for supercontinuum generation and endlessly-single-mode fibers with large cores. However, these modes are notoriously fragile: small changes in the structure can lead to significant detuning of resonance frequency and mode volume. Here, we show that a photonic topological crystalline insulator structure can be used to topologically protect the resonance frequency to be in the middle of the band gap, and therefore minimize the mode volume of a two-dimensional photonic defect mode.We experimentally demonstrate this in a femtosecond-laser-written waveguide array, a geometry akin to a photonic crystal fiber. The topological defect modes are determined by a topological invariant that protects zero-dimensional states (defect modes) embedded in a two-dimensional environment; a novel form of topological protection that has not been previously demonstrated.

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.

We experimentally demonstrate topological edge states arising from the valley-Hall effect in twodimensional honeycomb photonic lattices with broken inversion symmetry. We break inversion symmetry by detuning the refractive indices of the two honeycomb sublattices, giving rise to a boron nitride-like band structure. The edge states therefore exist along the domain walls between regions of opposite valley Chern numbers. We probe both the armchair and zig-zag domain walls and show that the former become gapped for any detuning, whereas the latter remain ungapped until a cutoff is reached. The valley-Hall effect provides a new mechanism for the realization of time-reversal invariant photonic topological insulators.Photonic topological insulators (PTIs) are dielectric structures that possess topologically protected edge states that are robust to scattering by disorder [1][2][3][4][5][6][7][8][9][10][11][12]. There are two categories of PTIs: those that break time-reversal symmetry [3,7] and those that preserve it [8,9,11]. In PTIs that break time-reversal symmetry, there exist one-way edge states, which ensure their robustness, due to the lack of counter-propagating partners at same frequency. In those that preserve it, there exist counter-propagating edge states that are protected only against certain classes of disorder. However, the latter can be more straightforward to realize because they do not require strong time-reversal breaking. Photonic topological insulators have been of interest due to the possibility of photonic devices that are less sensitive to fabrication disorder.In the valley-Hall effect, broken inversion symmetry in a two-dimensional honeycomb lattice causes opposite Berry curvatures in the two valleys of the band structure [13,14], and has been realized in solid-state twodimensional materials [15][16][17][18][19]. The valley-Hall effect is time-reversal invariant and has common characteristics with the spin Hall effect [20], where the two valleys in the band structure are used as 'pseudo-spin' degrees of freedom. It was shown theoretically that valley-Hall topological edge states would arise in analogous photonic structures [21][22][23][24][25][26][27]. In addition, valley-Hall topological edge states have also been recently studied in the context of topological valley transport of sound in sonic crystals [28].Here, we present the experimental observation of photonic topological valley-Hall edge states at domain walls between valley-Hall PTIs of opposite valley Chern numbers. The bulk-edge correspondence ensures the presence of edge states: the change in valley Chern number across the domain wall is associated with the existence of counter-propagating edge states [19,29,30]. We realize the photonic valley-Hall topological edge states in evanescently-coupled waveguide arrays, i.e., photonic lattices, fabricated using the femtosecond direct laser writing technique [31]. We probe different types of domain walls, namely the armchair and zig-zag edges. We also enter a fully gapped regime, which is not...

Weyl fermions are hypothetical two-component massless relativistic particles in threedimensional (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 first experimental observation of Weyl points of light at optical frequencies. These are also the first observations of "type-II" Weyl points for photons at any wavelength, which have 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 (1) observing conical diffraction along one axis when the frequency is tuned to the Weyl point; and(2) observing the associated Fermi arc surface states. The realization of Weyl points at optical frequencies allow these novel electromagnetic modes to be further explored in the context of linear, nonlinear, and quantum optics.

Weyl points are isolated degeneracies in reciprocal space that are monopoles of the Berry curvature. This topological charge makes them inherently robust to Hermitian perturbations of the system. However, non-Hermitian effects, usually inaccessible in condensed matter systems, are an important feature of photonics systems, and when added to an otherwise Hermitian Weyl material have been predicted to spread the Berry charge of the Weyl point out onto a ring of exceptional points, creating a Weyl exceptional ring and fundamentally altering its properties. Here, we observe the implications of the Weyl exceptional ring using real-space measurements of an evanescentlycoupled bipartite optical waveguide array by probing its effects on the Fermi arc surface states, the bulk diffraction properties, and the output power ratio of the two constituent sublattices. This is the first realization of an object with topological Berry charge in a non-Hermitian system.