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

Topology describes properties that remain unaffected by smooth distortions. Its main hallmark is the emergence of edge states localized at the boundary between regions characterized by distinct topological invariants. Because their properties are inherited from the topology of the bulk, these edge states present a strong immunity to distortions of the underlying architecture. This feature offers new opportunities for robust trapping of light in nano- and micrometre-scale systems subject to fabrication imperfections and environmentally induced deformations. Here, we report lasing in such topological edge states of a one-dimensional lattice of polariton micropillars that implements an orbital version of the Su–Schrieffer–Heeger Hamiltonian. We further demonstrate that lasing in these states persists under local deformations of the lattice. These results open the way to the implementation of chiral lasers in systems with broken time-reversal symmetry and, when combined with polariton interactions, to the study of nonlinear phenomena in topological photonics. Topologically protected lasing is reported in a lattice of polariton micropillars.

Lasing in topological edge states of a one-dimensional lattice

Scattering of electromagnetic waves by subwavelength objects is accompanied by the excitation of electric and magnetic Mie resonances that may modify substantially the scattering intensity and radiation pattern. Scattered fields can be decomposed into electric and magnetic multipoles, and the magnetic multipoles define magnetic response of structured materials underpinning the new field of all-dielectric resonant meta-optics. Here we review the recent developments in meta-optics and nanophotonics and demonstrate that the Mie resonances can play a crucial role offering novel ways for the enhancement of many optical effects near magnetic and electric multipolar resonances, as well as driving a variety of interference phenomena which govern recently discovered novel effects in nanophotonics. We further discuss the frontiers of all-dielectric meta-optics for flexible and advanced control of light with full phase and amplitude engineering, including nonlinear nanophotonics, anapole nanolasers, quantum optics, ...

Functional Meta-Optics and Nanophotonics Govern by Mie Resonances

Topology describes properties that remain unaffected by smooth distortions. Its main hallmark is the emergence of edge states localized at the boundary between regions characterized by distinct topological invariants. This feature offers new opportunities for robust trapping of light in nano- and micro-meter scale systems subject to fabrication imperfections and to environmentally induced deformations. Here we show lasing in such topological edge states of a one-dimensional lattice of polariton micropillars that implements an orbital version of the Su-Schrieffer-Heeger Hamiltonian. We further demonstrate that lasing in these states persists under local deformations of the lattice. These results open the way to the implementation of chiral lasers in systems with broken time-reversal symmetry and, when combined with polariton interactions, to the study of nonlinear topological photonics.

Lasing in topological edge states of a 1D lattice

Rapidly growing demands for fast information processing have launched a race for creating compact and highly efficient optical devices that can reliably transmit signals without losses. Recently discovered topological phases of light provide novel opportunities for photonic devices robust against scattering losses and disorder. Combining these topological photonic structures with nonlinear effects will unlock advanced functionalities such as magnet-free nonreciprocity and active tunability. Here, we introduce the emerging field of nonlinear topological photonics and highlight the recent developments in bridging the physics of topological phases with nonlinear optics. This includes the design of novel photonic platforms which combine topological phases of light with appreciable nonlinear response, self-interaction effects leading to edge solitons in topological photonic lattices, frequency conversion, active photonic structures exhibiting lasing from topologically protected modes, and many-body quantum topological phases of light. We also chart future research directions discussing device applications such as mode stabilization in lasers, parametric amplifiers protected against feedback, and ultrafast optical switches employing topological waveguides.

Nonlinear topological photonics

Recently introduced field of topological photonics aims to explore the concepts of topological insulators for novel phenomena in optics. Here polymeric chains of subwavelength silicon nanodisks are studied and it is demonstrated that these chains can support two types of topological edge modes based on magnetic and electric Mie resonances, and their topological properties are fully dictated by the spatial arrangement of the nanoparticles in the chain. It is observed experimentally and described how theoretically topological phase transitions at the nanoscale define a change from trivial to nontrivial topological states when the edge mode is excited.

Edge States and Topological Phase Transitions in Chains of Dielectric Nanoparticles

This work was supported by the Australian Research Council. Numerical calculations are supported by the Russian
Science Foundation (grant no.16-19-10538). Fabrication was conducted at the Center for Nanophase Materials
Sciences, being a DOE Office of Science User Facility. This material is based upon the work supported by the Air
Force Office of Scientific Research under award number FA2386-16-1-0002.

Third-Harmonic Generation from Photonic Topological States in Zigzag Arrays of Silicon Nanodisks

We introduce a novel approach for creating tunable electromagnetic metamaterials. We demonstrate experimentally that magnetic resonance of a split-ring resonator (”meta-atom” of a composite material) with a photodiode and a varactor diode can be tuned by changing the intensity of an external light source. Moreover, for two coupled resonators we show that we can achieve light-induced switching between dark and bright modes. We study experimentally dynamic tunability and self-induced nonlinearity of the light-tunable ”meta-atoms”, and also demonstrate a light-controllable magnetic reflector array based on tunable split-ring resonators.

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Aleksei Slobozhanyuk

Papers

Edge States and Topological Phase Transitions in Chains of Dielectric Nanoparticles

Third-Harmonic Generation from Photonic Topological States in Zigzag Arrays of Silicon Nanodisks

Tuning nonlinear metamaterials with light