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

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 a novel ground for photonic devices robust against scattering losses and disorder. Combining these topological photonic structures with nonlinear effects will unlock advanced functionalities such as nonreciprocity and active tunability. Here we introduce the emerging field of nonlinear topological photonics and highlight recent developments in bridging the physics of topological phases with nonlinear optics. This includes a 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, nonlinear topological circuits, active photonic structures exhibiting lasing from topologically-protected modes, and harmonic generation from edge states in topological arrays and metasurfaces. 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.

Valley topological materials, in which electrons possess valley pseudospin, have attracted a growing interest recently. The additional valley degree of freedom offers a great potential for its use in information encoding and processing. The valley pseudospin and valley edge transport have been investigated in photonic and phononic crystals for electromagnetic and acoustic waves, respectively. In this work, by using a micromanufacturing technology, valley topological materials are fabricated on silicon chips, which allows the observation of gyral valley states and valley edge transport for elastic waves. The edge states protected by the valley topology are robust against the bending and weak randomness of the channel between distinct valley Hall phases. At the channel intersection, a counterintuitive partition of the valley edge states manifests for elastic waves, in which the partition ratio can be freely adjusted. These results may enable the creation of on-chip high-performance micro-ultrasonic materials and devices.

On-chip valley topological materials for elastic wave manipulation.

Non-Hermiticity from nonreciprocal hoppings has been shown recently to demonstrate the non-Hermitian skin effect (NHSE) under open boundary conditions (OBCs). Here we study the interplay of this effect and the Anderson localization (AL) in a nonreciprocal quasiperiodic lattice, dubbed nonreciprocal Aubry-Andr\'e model, and a rescaled transition point is exactly proved. The nonreciprocity can induce not only NHSEs but also the asymmetry in localized states, characterized by two Lyapunov exponents. Meanwhile, this transition is also topological, in the sense of a winding number associated with complex eigenenergies under periodic boundary conditions (PBCs), establishing a bulk-bulk correspondence. This interplay can be realized straightforwardly by an electrical circuit with only linear passive RLC components instead of elusive nonreciprocal ones, showing the transport of a continuous wave undergoes a transition between insulating and amplifying. This paradigmatic scheme can be immediately accessed in experiments even for more nonreciprocal models and will definitely inspire the study of interplay of NHSEs and ALs as well as more other quantum/topological phenomena in various systems.

Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices

The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder Although considerable progress on topological phenomena has been achieved in the classical domain, the realization of strong light-matter coupling in the quantum domain remains unexplored We demonstrate a strong interface between single quantum emitters and topological photonic states Our approach creates robust counterpropagating edge states at the boundary of two distinct topological photonic crystals We demonstrate the chiral emission of a quantum emitter into these modes and establish their robustness against sharp bends This approach may enable the development of quantum optics devices with built-in protection, with potential applications in quantum simulation and sensing

A topological quantum optics interface

New structures with richer electromagnetic properties are in high demand for developing novel microwave and optic devices aimed at realizing fast light-based information transfer and information processing. Here we show theoretically that a topological photonic state exists in a hexagonal LC circuit with short-range textures in the inductance, which is induced by a band inversion between p- and d-like electromagnetic modes carrying orbital angular momentum, and realize this state experimentally in planar microstrip arrays. Measuring both amplitude and phase of the out-of-plane electric field accurately using microwave near-field techniques, we demonstrate directly that topological interfacial electromagnetic waves launched by a linearly polarized dipole source propagate in opposite directions according to the sign of the orbital angular momentum. The open planar structure adopted in the present approach leaves much room for including other elements useful for advanced information processing, such as electric/mechanical resonators, superconducting Josephson junctions and SQUIDs.

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Topological LC-circuits based on microstrips and observation of electromagnetic modes with orbital angular momentum

Valley-dependent propagation of light in an artificial photonic hexagonal lattice, akin to electrons in graphene, is investigated in microwave regime. Both numerical and experimental results show that the valley degeneracy in the photonic graphene is broken when the frequency is away from the Dirac point. The peculiar anisotropic wave transport property due to distinct valleys is analyzed using the equifrequency contours. More interestingly, the valley-dependent self-collimation and beam splitting phenomena are experimentally demonstrated with the armchair and zigzag interfaces, respectively. Our results confirm that there are two inequivalent Dirac points that lead to two distinct valleys in photonic graphene, which could be used to control the flow of light and might be used to carry information in valley polarized beam splitter, collimator or guiding device.

Observation of valley-dependent beams in photonic graphene

At the Dirac-like point at the Brillouin zone center, the photonic crystals (PhCs) can mimic a zero-index medium In the band structure, an additional flat band of longitudinal mode will intersect the Dirac cone This longitudinal mode can be excited in PhCs with finite sizes at the Dirac-like point By introducing positional shift in the PhCs, we study the dependence of the longitudinal mode on the disorder At the Dirac-like point, the transmission peak induced by the longitudinal mode decreases as the random degree increases However, at a frequency slightly above the Dirac-like point, in which the longitudinal mode is absent, the transmission is insensitive to the disorder because the effective index is still near zero and the effective wavelength in the PhC is very large

Transport properties of disordered photonic crystals around a Dirac-like point

We demonstrate experimentally chirality-locked valley polarization in photonic graphene. A point source without chirality excites two inequivalent (K, K') valleys equally, whereas a chiral source selectively excites only one preferred valley depending on its chirality.

Chirality-locked valley polarization in photonic graphene

Metamaterials made of periodic arrangements of electric permittivity and magnetic permeability and arrays of resonators can provide optic properties unexperienced in conventional materials, such as negative refractive index which can be used to achieve superlensing and cloaking. Developing new simpler structures with richer electromagnetic (EM) properties and wider working frequency bands is highly demanded for fast light-based information transfer and information processing. In the present work, we propose theoretically that a honeycomb-structured LC circuit with short-range textures in inductance can generate a topological photonic state accompanied by inversion between p- and d-orbital like EM modes carrying optic orbital angular momenta (OAM). We realize experimentally the topological photonic state in planar microstrips, a sandwich structure of bottom metallic substrate, middle dielectric film and top metallic strips with hexagonal patterns in strip width, in microwave frequency. Measuring accurately the amplitude and phase of EM fields, we demonstrate explicitly that topological interfacial EM waves launched from a linearly polarized dipole source propagate in opposite directions according to the sign of OAM, with the relative weight of p- and d-orbital like EM modes tunable precisely by sweeping the frequency in the topological band gap, which can hardly be achieved in other photonic systems and condensed-matter systems. Achieving the topological photonic state in a simple and easy fabricable structure, the present work uncovers a new direction for generating and manipulating EM modes with rich internal degrees of freedom, which can be exploited for various applications.

Yuan Li

Papers

Topological LC-circuits based on microstrips and observation of electromagnetic modes with orbital angular momentum

Observation of valley-dependent beams in photonic graphene

Transport properties of disordered photonic crystals around a Dirac-like point

Chirality-locked valley polarization in photonic graphene

Generating electromagnetic modes with fine tunable orbital angular momentum by planar topological circuits