Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

Bound states in the continuum (BICs) are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their very existence defies conventional wisdom. Although BICs were first proposed in quantum mechanics, they are a general wave phenomenon and have since been identified in electromagnetic waves, acoustic waves in air, water waves and elastic waves in solids. These states have been studied in a wide range of material systems, such as piezoelectric materials, dielectric photonic crystals, optical waveguides and fibres, quantum dots, graphene and topological insulators. In this Review, we describe recent developments in this field with an emphasis on the physical mechanisms that lead to BICs across seemingly very different materials and types of waves. We also discuss experimental realizations, existing applications and directions for future work. The fascinating wave phenomenon of ‘bound states in the continuum’ spans different material and wave systems, including electron, electromagnetic and mechanical waves. In this Review, we focus on the common physical mechanisms underlying these bound states, whilst also discussing recent experimental realizations, current applications and future opportunities for research.

Bound states in the continuum

Dynamics of quantum many-body systems is one of the most complex problems in physics since it involves the time evolution of a large number of particles that interact with each other under the influence of external forces. With ultracold atoms in optical atomic lattices it can be done in a controlled environment by applying a periodic force. This Colloquium covers the experimental and theoretical developments in this exciting field of physics.

Colloquium: Atomic quantum gases in periodically driven optical lattices

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Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures. Topological photonic structures offer unique features such as reflection-free and non-reciprocal devices. This Review highlights the experimental progress in the relatively new field of photonic topology.

Two-dimensional topological photonics

We demonstrate the first experimental realization of a dispersionless state, in a photonic Lieb lattice formed by an array of optical waveguides. This engineered lattice supports three energy bands, including a perfectly flat middle band with an infinite effective mass. We analyze, both experimentally and theoretically, the evolution of well-prepared flat-band states, and show their remarkable robustness, even in the presence of disorder. The realization of flat-band states in photonic lattices opens an exciting door towards quantum simulation of flat-band models in a highly controllable environment.

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Observation of a Localized Flat-Band State in a Photonic Lieb Lattice

Topological quantum matter can be realized by subjecting engineered systems to time-periodic modulations. In analogy with static systems, periodically driven quantum matter can be topologically classified by topological invariants, whose non-zero value guarantees the presence of robust edge modes. In the high-frequency limit of the drive, topology is described by standard topological invariants, such as Chern numbers. Away from this limit, these topological numbers become irrelevant, and novel topological invariants must be introduced to capture topological edge transport. The corresponding edge modes were coined anomalous topological edge modes, to highlight their intriguing origin. Here we demonstrate the experimental observation of these topological edge modes in a 2D photonic lattice, where these propagating edge states are shown to coexist with a quasi-localized bulk. Our work opens an exciting route for the exploration of topological physics in time-modulated systems operating away from the high-frequency regime.

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Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice.

We present the first experimental demonstration of a new type of localized state in the continuum, namely, compacton-like linear states in flat-band lattices. To this end, we employ photonic Lieb lattices, which exhibit three tight-binding bands, with one being perfectly flat. Discrete predictions are confirmed by realistic continuous numerical simulations as well as by direct experiments. Our results could be of great importance for fundamental physics as well as for various applications where light needs to be conducted in a diffractionless and localized manner over long distances.

A Viewpoint on: Observation of Localized States in Lieb Photonic Lattices

We observe Wannier-Stark (W-S) localization in curved photonic lattices, realized using arrays of evanescently coupled optical waveguides. By correctly tuning the strength of inter-site coupling in the lattice, we observe that W-S states become increasingly localized, and eventually fully localized to one site, as the curvature of the lattice is increased. We then demonstrate that tunneling can be successfully restored in the lattice by applying a resonant sinusoidal modulation to the lattice position, an effect that is a direct analogue of photon-assisted tunneling. This precise tuning of the tunneling matrix elements, through resonant modulation-assisted tunneling, opens a novel route for the creation of gauge fields in laser-fabricated photonic lattices.

https://iopscience.iop.org/article/10.1088/1367-2630/17/11/115002/pdf

Modulation-assisted tunneling in laser-fabricated photonic Wannier-Stark ladders

We report on the experimental realization of a photonic system that simulates the one-dimensional two-particle Hubbard model. This analogy is realized by means of two-dimensional arrays of coupled optical waveguides, fabricated using femtosecond laser inscription. By tuning the analogous ``interaction strength,'' we reach the strongly interacting regime of the Hubbard Hamiltonian, and demonstrate the suppression of standard tunneling for individual ``particles.'' In this regime the formation of bound states is identified through the direct observation of pair tunneling. We then demonstrate the coherent destruction of tunneling (CDT) for the paired particles in the presence of an engineered oscillating force of high frequency. The precise control over the analogous ``interaction strength'' and driving force offered by our experimental system opens an exciting route towards quantum simulation of few-body physics in photonics.

Alexander Spracklen

Papers

Observation of a Localized Flat-Band State in a Photonic Lieb Lattice

Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice.

A Viewpoint on: Observation of Localized States in Lieb Photonic Lattices

Modulation-assisted tunneling in laser-fabricated photonic Wannier-Stark ladders

Observation of pair tunneling and coherent destruction of tunneling in arrays of optical waveguides