Topological photonics: robustness and beyond

Topological photonics has expanded our understanding of electromagnetic wave propagation and unraveled new methods of electromagnetic wave shaping. Among the various topological photonic systems, valley photonic crystal (VPC) is a highly versatile platform for constructing interfaces that supports unidirectional edge state to enable the robust topological transport of light. Although silicon VPC waveguides has demonstrated the lossless propagation of terahertz (THz) waves through multiple sharp bends, existing designs are mostly based on the standard zigzag-interface. Here, we explore interfacial topological photonics by designing a composite interface junction for an air-slot-like VPC waveguide with a 60° bend and an unchanging bearded-interface to allow the topologically protected propagation of THz waves over a 20% relative bandwidth. We employ particle swarm optimization to design the geometry of a bearded-interface silicon VPC waveguide to achieve a 42% relative bandgap and a topological edge state spanning a usable 25% relative bandwidth. Our work illustrates the prospects and challenges of interfacial topological photonics in the design of broadband silicon topological waveguides for potential applications across the electromagnetic spectrum, including the on-chip THz sixth-generation (6G) communication.

The field of topological photonics has seen tremendous and wide‐ranging developments in recent years. Evolving from the broader field of topological insulators, topological photonics systems today harness a variety topological phases. These include the Su–Schreifer–Heeger, quantum Hall, quantum valley Hall and quantum spin Hall topologies. Importantly, the latter two generate edge states with opposite group velocities and opposite spin, respectively, allowing unidirectional light propagation and advanced photonic routing to occur. Amongst these exciting developments is a subset of advancements made in topological silicon photonics, which could potentially lend its appeal to complementary metal–oxide–semiconductor (CMOS) photonics applications, including telecommunications, data communications, quantum photonics, future exascale supercomputers, photonic neuromorphic computing, and infrared sensing. The fundamental underpinnings of these topological phases lead to interesting features, including chirality, scatter‐free light propagation around sharp bends, and importantly topological protection against defects, disorder, and scattering. This topological protection may be harnessed toward tunable light propagation, photon‐pair generation, quantum spatial entanglement, robust photonic routing, and beyond. Herein, the recent advancements made in the burgeoning field of topological silicon photonics are discussed.

Topological photonics attract significant interests due to their intriguing fundamental physics and potential applications. Researchers are actively exploring various artificial platforms to realize novel topological phenomena, which provides promising pathways for the development of robust photonic devices. Among these platforms, femtosecond laser direct-written photonic waveguides show unique ability to visualize intricate light dynamics in 2 + 1 dimensions, which rendering them ideal tools for investigating topological photonics. By integrating topological concepts into these waveguides, researchers not only deepen their understanding of topological physics but also provide potential methodology for developing advanced topological photonic integrated devices. In this review, we discuss recent experimental implementations of different topological phases within femtosecond laser direct-written photonic waveguides, as well as the fascinating physical phenomena induced by the interplay of topology with non-Hermiticity, nonlinearity and quantum physics are also introduced. The exploration of topological waveguide arrays shows great promise in advancing the field of topological photonics, providing a solid foundation for further research and innovation in this rapidly developing domain.

The topological photonics plays an important role in the fields of fundamental physics and photonic devices. The traditional method of designing topological system is based on the momentum space, which is not a direct and convenient way to grasp the topological properties, especially for the perturbative structures or coupled systems. Here, we propose an interdisciplinary approach to study the topological systems in real space through combining the information entropy and topological photonics. As a proof of concept, the Kagome model has been analyzed with information entropy. We reveal that the bandgap closing does not correspond to the topological edge state disappearing. This method can be used to identify the topological phase conveniently and directly, even the systems with perturbations or couplings. As a promotional validation, Su–Schrieffer–Heeger model and the valley-Hall photonic crystal have also been studied based on the information entropy method. This work provides a method to study topological photonic phase based on information theory, and brings inspiration to analyze the physical properties by taking advantage of interdisciplinarity.Graphical

Topological chiral edge states in photonic Chern insulators, which exhibit the one-way propagation property with reflection-free behavior and excellent robustness against perturbations, have become an important frontier in topological photonics. Currently, there have been many studies on its robust propagation behavior, but few studies have focused on its radiation properties. In developing functional photonic devices (e.g., topological antennas) for real-world applications, studying traveling-wave radiation characteristics based on chiral edge states deserves more attention. In this Letter, we propose a topological traveling-wave radiation system based on chiral edge states in photonic Chern insulators that show a steerable beam and reflection-free property. By introducing the perturbation controlled by magnetic fields, we demonstrate that exploiting a certain strength of perturbation can flexibly manipulate the radiation beam. In particular, the proposed dual-channel topological traveling-wave radiation system can not only improve the gain but also overcome the issue of impedance matching. The proposed configurations provide a novel way to manipulate topological-wave radiation and have potential applications for designing topological traveling-wave antennas with a reflection-free property.

The recent realization of all-dielectric valley photonic crystals (VPCs) in nanoscale not only provides a standard platform to explore many topological phases of light with protected edge modes, but also shows promising applications for designing high-performance nanophotonic devices. However, the widely reported all-dielectric VPCs are limited to one single polarization, and it is challenging to manipulate the polarization degree of freedom of light and design polarizing devices using VPCs. Here, we design a dual-polarization all-dielectric VPC and propose a topological polarization beam splitter. The phase vortex distributions of bulk modes at different valleys characterize the nonzero valley Chern numbers for both TE and TM polarizations, indicating the implementation of topologically nontrivial dual-polarization band gaps. This leads to dual-polarization valley-dependent edge modes located at interfaces with different shapes. The topological valley transport around sharp-bends is also demonstrated for both TE and TM polarizations. Finally, a harpoon-shaped polarization beam splitter is proposed, and the simulated results confirm the good functionality of polarization separation. Our work shows the flexible control of light in topological photonic systems with the polarization degree of freedom, and has promising applications in polarization multiplexing photonic devices owing to the enlarged the optical information-processing capacity.

Inspired by topological insulators, topological photonics has attracted the attention of researchers since its discovery. Many phenomena like topological state bring numerous new opportunities to the entire photonics. Previous studies have proved that topological systems can protect photonic orbital angular momentum (OAM). In this work, two Su–Schrieffer–Heeger (SSH) waveguide chains are combined, and the interface waveguide is designed to generate next‐nearest‐neighbor coupling (NNC) between itself and the waveguides in the SSH chains. It is discovered that with NNC, more modes are topologically protected. Laguerre‐Gaussian (LG) modes are typical OAM light beams, which are composed of several Hermite‐Gaussian (HG) modes. With NNC and special design of the waveguide, which is located at the interface, it is proven that SSH chains can protect more OAM modes. This model is named the NNC‐SSH model. Thus, this study expands the field of topological photonics and presents a new idea of topological protection, which has a very high potential in many fields such as OAM multiplexing.

Ultrahigh-[formula omitted] Fano resonance in a cavity-waveguide coupled system based on second-order topological photonic crystals with elliptical holes

Over the past decade, topology has emerged as a major branch in broad areas of physics, from atomic lattices to condensed matter. In particular, topology has received significant attention in photonics because light waves can serve as a platform to investigate nontrivial bulk and edge physics with the aid of carefully engineered photonic crystals and metamaterials. Simultaneously, photonics provides enriched physics that arises from spin-1 vectorial electromagnetic fields. Here, we review recent progress in the growing field of topological photonics in three parts. The first part is dedicated to the basics of topological band theory and introduces various two-dimensional topological phases. The second part reviews three-dimensional topological phases and numerous approaches to achieve them in photonics. Last, we present recently emerging fields in topological photonics that have not yet been reviewed. This part includes topological degeneracies in nonzero dimensions, unidirectional Maxwellian spin waves, higher-order photonic topological phases, and stacking of photonic crystals to attain layer pseudospin. In addition to the various approaches for realizing photonic topological phases, we also discuss the interaction between light and topological matter and the efforts towards practical applications of topological photonics.

We present efficient algorithms for calculating the surface state density spectra in topological photonic crystals, which facilitates the investigation of topological surface effects and enables direct comparison with near-field scanning experimental observables.

Surface lattice modes, generated by the evanescent coupling between localized modes of optical resonators arranged in a two-dimensional (2D) array, generally exhibit remarkable optical response beyond the single photonic particle. Here, by employing the lattice mode concept, we demonstrate that lattice topological edge and corner modes can be achieved in properly designed photonic crystal (PhC) slabs. Such slabs consist of an array of finite-sized second-order topological insulators mimicking the 2D Su-Schrieffer-Heeger model. The proposed lattice edge and corner modes emerge within the topological band gap of the PhC slab, which dictates their topological nature. In particular, the band diagram of the lattice corner modes shows that they possess non-degenerate eigenfrequencies and dispersive bands. In addition, we show that the eigenfrequency of the lattice topological modes can be shifted by tuning the intercell and/or intracell optical coupling. Finally, by finely tuning the geometric parameters of the slab, we realize a lattice corner mode possessing flatband dispersion characteristics. Our study can find applications to topological lasing, nonlinearity enhancement, and slow-light effects in topological photonic systems.

Finite-size effect plays a significant role in topology photonics not to mention in reality all experimental setups are in finite-size. A photonic bandgap is opened in the topological edge state dispersion if a topological photonic crystal with finite width is considered, and the bandgap size relies on the finite-size effect. Pseudospin-preserving and pseudospin-flipping processes can be realized when a selectively switch of the pseudospin of edge states are customized by our designs. Our microwave experiments also successfully demonstrate pseudospin switch-on and -off behaviors in a finite-width photonic crystal. By combining photonic crystals with finite widths, a multi-tunneling proposal of topological photonic crystals can also be achieved. Our study of the finite-size effect will provide new approaches and thoughts to improve the development of topological photonic devices in the future.

Floquet topological physics, an area exploring periodically driven systems and leveraging degrees of freedom in the temporal dimension, has opened new avenues in photonics by enabling the creation of novel topological phases, new control mechanisms, and intriguing phenomena that are inaccessible or challenging to realize in static systems. These include anomalous Floquet topological insulators, anomalous Floquet Anderson insulators, and topological phases with broken time-reversal symmetry without the need for magnetic fields. Unlike conventional topological photonics, which relies on fixed structural or material properties to induce topological states, Floquet topological photonics leverages time-periodic modulation to access a broader range of topological effects, introducing flexibility in tuning topological transitions and wave dynamics. This review aims to provide a comprehensive overview of Floquet topological phases in photonic systems, explaining the theoretical basics, highlighting experimental platforms, the interplay with disorder, as well as the latest advancements beyond linear, Hermitian, Euclidean-geometry photonic systems, and recent progress in applications.

Topological materials have been at the forefront of research across various fields of physics in hopes of harnessing properties such as scatter-free transport due to protection from defects and disorder. Photonic systems are ideal test beds for topological models and seek to profit from the idea of topological robustness for applications. Recent progress in 3D-printing of microscopic structures has allowed for a range of implementations of topological systems. We review recent work on topological models realized particularly in photonic crystals and waveguide arrays fabricated by 3D micro-printing. The opportunities that this technique provides are a result of its facility to tune the refractive index, compatibility with infiltration methods, and its ability to fabricate a wide range of flexible geometries.

Nonreciprocal interlayer coupling is difficult to practically implement in bilayer non-Hermitian topological photonic systems. In this work, we identify a similarity transformation between the Hamiltonians of systems with nonreciprocal interlayer coupling and on-site gain/loss. The similarity transformation is widely applicable, and we show its application in one- and two-dimensional bilayer topological systems as examples. The bilayer non-Hermitian system with nonreciprocal interlayer coupling, whose topological number can be defined using the gauge-smoothed Wilson loop, is topologically equivalent to the bilayer system with on-site gain/loss. We also show that the topological number of bilayer non-Hermitian C6v-typed domain-induced topological interface states can be defined in the same way as in the case of the bilayer non-Hermitian Su–Schrieffer–Heeger model. Our results show the relations between two microscopic provenances of the non-Hermiticity and provide a universal and convenient scheme for constructing and studying nonreciprocal interlayer coupling in bilayer non-Hermitian topological systems. This scheme is useful for observation of non-Hermitian skin effect in three-dimensional systems.Graphical