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

The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.

Edge States and Topological Invariants of Non-Hermitian Systems.

INTRODUCTION Physical systems that exhibit topological invariants are naturally endowed with robustness against perturbations, as was recently demonstrated in many settings in condensed matter, photonics, cold atoms, acoustics, and more. The most prominent manifestations of topological systems are topological insulators, which exhibit scatter-free edge-state transport, immune to perturbations and disorder. Recent years have witnessed intense efforts toward exploiting these physical phenomena in the optical domain, with new ideas ranging from topology-driven unidirectional devices to topological protection of path entanglement. But perhaps more technologically relevant than all topological photonic settings studied thus far is, as proposed by the accompanying theoretical paper by Harari et al ., an all-dielectric magnet-free topological insulator laser, with desirable properties stemming from the topological transport of light in the laser cavity. RATIONALE We demonstrate nonmagnetic topological insulator lasers. The topological properties of the laser system give rise to single-mode lasing, robustness against fabrication defects, and notably higher slope efficiencies compared to those of the topologically trivial counterparts. We further exploit the properties of the active topological platform by assembling topological insulator lasers from S -chiral microresonators that enforce predetermined unidirectional lasing even in the absence of magnetic fields. RESULTS Our topological insulator laser system is an aperiodic array of 10 unit cell–by–10 unit cell coupled ring resonators on an InGaAsP quantum wells platform. The active lattice uses the topological architecture suggested in the accompanying theoretical paper. This two-dimensional setting is composed of a square lattice of ring resonators coupled to each other by means of link rings. The intermediary links are judiciously spatially shifted to introduce a set of hopping phases, establishing a synthetic magnetic field and two topological band gaps. The gain in this laser system is provided by optical pumping. To promote lasing of the topologically protected edge modes, we pump the outer perimeter of the array while leaving the interior lossy. We find that this topological insulator laser operates in single mode even considerably above threshold, whereas the corresponding topologically trivial realizations lase in multiple modes. Moreover, the topological laser displays a slope efficiency that is considerably higher than that in the corresponding trivial realizations. We further demonstrate the topological features of this laser by observing that in the topological array, all sites emit coherently at the same wavelength, whereas in the trivial array, lasing occurs in localized regions, each at a different frequency. Also, by pumping only part of the topological array, we demonstrate that the topological edge mode always travels along the perimeter and emits light through the output coupler. By contrast, when we pump the trivial array far from the output coupler, no light is extracted from the coupler because the lasing occurs at stationary modes. We also observe that, even in the presence of defects, the topological protection always leads to more efficient lasing compared to that of the trivial counterpart. Finally, to show the potential of this active system, we assemble a topological system based on S -chiral resonators, which can provide new avenues to control the topological features. CONCLUSION We have experimentally demonstrated an all-dielectric topological insulator laser and found that the topological features enhance the lasing performance of a two-dimensional array of microresonators, making them lase in unison in an extended topologically protected scatter-free edge mode. The observed single longitudinal-mode operation leads to a considerably higher slope efficiency as compared to that of a corresponding topologically trivial system. Our results pave the way toward a new class of active topological photonic devices, such as laser arrays, that can operate in a coherent fashion with high efficiencies.

Topological insulator laser: Experiments

Nearly one century after the birth of quantum mechanics, parity–time symmetry is revolutionizing and extending quantum theories to include a unique family of non-Hermitian Hamiltonians. While conceptually striking, experimental demonstration of parity–time symmetry remains unexplored in quantum electronic systems. The flexibility of photonics allows for creating and superposing non-Hermitian eigenstates with ease using optical gain and loss, which makes it an ideal platform to explore various non-Hermitian quantum symmetry paradigms for novel device functionalities. Such explorations that employ classical photonic platforms not only deepen our understanding of fundamental quantum physics but also facilitate technological breakthroughs for photonic applications. Research into non-Hermitian photonics therefore advances and benefits both fields simultaneously. General concepts and recent developments of parity–time symmetry in classical photonics are reviewed.

Non-Hermitian photonics based on parity-time symmetry

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, leads to phenomena drastically distinct from the familiar Hermitian realm is discussed. An immediate consequence is the ubiquitous occurrence of nodal NH topological phases with concomitant open Fermi-Seifert surfaces, where conventional band-touching points are replaced by the aforementioned exceptional degeneracies. Furthermore, new notions of gapped phases including topological phases in single-band systems are detailed, and the manner in which a given physical context may affect the symmetry-based topological classification is clarified. A unique property of NH systems with relevance beyond the field of topological phases consists of the anomalous relation between bulk and boundary physics, stemming from the striking sensitivity of NH matrices to boundary conditions. Unifying several complementary insights recently reported in this context, a picture of intriguing phenomena such as the NH bulk-boundary correspondence and the NH skin effect is put together. Finally, applications of NH topology in both classical systems including optical setups with gain and loss, electric circuits, and mechanical systems and genuine quantum systems such as electronic transport settings at material junctions and dissipative cold-atom setups are reviewed.

Exceptional topology of non-Hermitian systems

Topological physics provides a robust framework for strategically controlling wave confinement and propagation dynamics. However, current implementations have been restricted to the limited design parameter space defined by passive topological structures. Active systems provide a more general framework where different fundamental symmetry paradigms, such as those arising from non-Hermiticity and nonlinear interaction, can generate a new landscape for topological physics and its applications. Here, we bridge this gap and present an experimental investigation of an active topological photonic system, demonstrating a topological hybrid silicon microlaser array respecting the charge-conjugation symmetry. The created new symmetry features favour the lasing of a protected zero mode, where robust single-mode laser action in the desired state prevails even with intentionally introduced perturbations. The demonstrated microlaser is hybrid implemented on a silicon-on-insulator substrate, and is thereby readily suitable for integrated silicon photonics with applications in optical communication and computing.

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Topological hybrid silicon microlasers.

Photonic topological insulators provide a route for disorder-immune light transport, which holds promise for practical applications. Flexible reconfiguration of topological light pathways can enable high-density photonics routing, thus sustaining the growing demand for data capacity. By strategically interfacing non-Hermitian and topological physics, we demonstrate arbitrary, robust light steering in reconfigurable non-Hermitian junctions, in which chiral topological states can propagate at an interface of the gain and loss domains. Our non-Hermitian–controlled topological state can enable the dynamic control of robust transmission links of light inside the bulk, fully using the entire footprint of a photonic topological insulator.

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Non-Hermitian topological light steering.

Zero-energy particles (such as Majorana fermions) are newly predicted quasiparticles and are expected to play an important role in fault-tolerant quantum computation. In conventional Hermitian quantum systems, however, such zero states are vulnerable and even become vanishing if couplings with surroundings are of the same topological nature. Here we demonstrate a robust photonic zero mode sustained by a spatial non-Hermitian phase transition in a parity-time (PT) symmetric lattice, despite the same topological order across the entire system. The non-Hermitian-enhanced topological protection ensures the reemergence of the zero mode at the phase transition interface when the two semi-lattices under different PT phases are decoupled effectively in their real spectra. Residing at the midgap level of the PT symmetric spectrum, the zero mode is topologically protected against topological disorder. We experimentally validated the robustness of the zero-energy mode by ultrafast heterodyne measurements of light transport dynamics in a silicon waveguide lattice.

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Photonic zero mode in a non-Hermitian photonic lattice.

Topological photonics provides a robust framework for strategically controlling light confinement and propagation dynamics. By exploiting the marriage between this notion and symmetry-constrained mode competition in an active setting, we experimentally demonstrate, for the first time, a hybrid silicon microlaser structure supporting a topologically protected zero-mode lasing. This mode is distributed over an integrated array of optical microrings, each supporting multiple modes that compete for gain. However, the mode competition is diminished in favor of a pre-defined topological state, which reflects the charge conjugation symmetry induced by the gain profile. Robust single-mode operation in the desired state prevails even with intentionally introduced perturbations. The demonstrated microlaser is hybrid-implemented on a silicon-on-insulator substrate, thereby readily suitable for integrated silicon photonics with potential applications in optical communication and computing.

Topological Hybrid Silicon Microlasers

The band degeneracy, either the exceptional point of a non-Hermitian system or the Dirac point associated with a topological system, can feature distinct symmetry and topology. Their synergy will further produce more exotic topological effects in synthetic matter.

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Han Zhao

Papers

Topological hybrid silicon microlasers.

Non-Hermitian topological light steering.

Photonic zero mode in a non-Hermitian photonic lattice.

Topological Hybrid Silicon Microlasers

Non-Hermitian photonics promises exceptional topology of light