Experimental Realization of a Reflections-Free Compact Delay Line Based on a Photonic Topological Insulator

Mode-order conversion in a Mach-Zehnder interferometer based on Chern insulators

Mode-order conversion devices can provide a flexible platform to achieve mode coupling and optimizing in mode division multiplex (MDM) that can eliminate the restrain of capacity and density in photonic integration and communication. However, mode-order converters based on traditional photonic crystal (PC) waveguides are susceptible to defects, which always render device incapacitation in mode-order conversion. Herein, a mode converter designed by the Mach-Zehnder interferometer (MZI) structure is proposed to manipulate the conversion of topological edge states (TESs) based on Chern insulators consisting of gyromagnetic PCs. The back-and-forth conversion between fundamental and high-order modes is numerically demonstrated based on phase modulation in our proposed device, in which each mode can be immune to defects. This unique approach for converting the mode order of TES exploits a new perspective in MDM to design a high-performance multimode device, leading to potential applications in photonic integrated circuits (PIC), on-chip processors, and optical fiber communication.

Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs

The statistical properties of wave chaotic systems of varying dimensionalities and realizations have been studied extensively. These systems are commonly characterized by the statistics of the eigenmode spacings and the statistics of the eigenfunctions. Here, we propose photonic crystal (PC) defect waveguide graphs as a physical setting for chaotic graph studies. Photonic crystal waveguides possess a dispersion relation for the propagating modes, which is engineerable. Graphs constructed by joining these waveguides possess junctions and bends with distinct scattering properties. We present numerically determined statistical properties of an ensemble of such PC graphs including both eigenfunction amplitude and eigenmode-spacing studies. Our proposed system is compatible with silicon nanophotonic technology and opens chaotic graph studies to a new community of researchers.

Topological Refraction in Kagome Split-Ring Photonic Insulators

A valley-Hall-like photonic insulator based on C3v Kagome split-ring is proposed. Theoretical analysis and numerical calculations illustrate that C3v symmetry can be broken not only by global rotation α but also individual rotation θ of the split rings, providing topological phase transitions. Furthermore, refraction of the edge state from the interface into the background space at Zigzag termination is explored. It is shown that positive/negative refraction of the outgoing beam depends on the type of valley (K or K′), from which the edge state is projected. These results provide a new way to manipulate terahertz wave propagation and facilitate the potential applications in directional collimation, beam splitting, negative refraction image, etc.

Broadband Topological Slow Light through Brillouin Zone Winding

Topological photonic insulators have attracted significant attention for their robust transport of light, impervious to scattering and disorder. This feature is ideally suited for slow light applications, which are typically limited by disorder-induced attenuation. However, no practical approach to broadband topologically protected slow light has been demonstrated yet. In this work, we achieve slow light in topologically unidirectional waveguides based on periodically loading an edge termination with suitably tailored resonances. The resulting edge state dispersion can wind around the Brillouin zone multiple times sustaining broadband, topologically robust slow light, opening exciting opportunities in various photonic scenarios.

Synthetic-Space Photonic Topological Insulators Utilizing Dynamically Invariant Structure

Synthetic-space topological insulators are topological systems with at least one spatial dimension replaced by a periodic arrangement of modes, in the form of a ladder of energy levels, cavity modes, or some other sequence of modes. Such systems can significantly enrich the physics of topological insulators, in facilitating higher dimensions, nonlocal coupling, and more. Thus far, all synthetic-space topological insulators relied on active modulation to facilitate transport in the synthetic dimensions. Here, we propose dynamically invariant synthetic-space photonic topological insulators: a two-dimensional evolution-invariant photonic structure exhibiting topological properties in synthetic dimensions. This nonmagnetic structure is static, lacking any kind of modulation in the evolution coordinate, yet it displays an effective magnetic field in synthetic space, characterized by a Chern number of one. We study the evolution of topological states along the edge, and on the interface between two such structures with opposite synthetic-space chirality, and demonstrate their robust unidirectional propagation in the presence of defects and disorder. Such topological structures can be realized in photonics and cold atoms and provide a fundamentally new mechanism for topological insulators.

Topology-Controlled Photonic Cavity Based on the Near-Conservation of the Valley Degree of Freedom

We demonstrate a novel path to localizing topologically nontrivial photonic edge modes along their propagation direction. Our approach is based on the near-conservation of the photonic valley degree of freedom associated with valley-polarized edge states. When the edge state is reflected from a judiciously oriented mirror, its optical energy is localized at the mirror surface because of an extended time delay required for valley index flipping. The degree of energy localization at the resulting topology-controlled photonic cavity is determined by the valley-flipping time, which is in turn controlled by the geometry of the mirror. Intuitive analytic descriptions of the "leaky" and closed topology-controlled photonic cavities are presented, and two specific designs-one for the microwave and the other for the optical spectral ranges-are proposed.

Identifying Topological Phase Transitions in Experiments Using Manifold Learning

We demonstrate the identification of topological phase transitions from experimental data using diffusion maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system undergoing a topological phase transition and demonstrate the ability of this approach to identify topological phase transitions even when the data originates from a small part of the system, and does not even include edge states.

Recent advances in 2D, 3D and higher-order topological photonics

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.

Transition Radiation in Photonic Topological Crystals: Quasiresonant Excitation of Robust Edge States by a Moving Charge

We demonstrate, theoretically and experimentally, that a traveling electric charge passing from one photonic crystal into another generates edge waves-electromagnetic modes with frequencies inside the common photonic band gap localized at the interface-via a process of transition edge-wave radiation (TER). A simple and intuitive expression for the TER spectral density is derived and then applied to a specific structure: two interfacing photonic topological insulators with opposite spin-Chern indices. We show that TER breaks the time-reversal symmetry and enables valley- and spin-polarized generation of topologically protected edge waves propagating in one or both directions along the interface. Experimental measurements at the Argonne Wakefield Accelerator Facility are consistent with the excitation and localization of the edge waves. The concept of TER paves the way for novel particle accelerators and detectors.

Photonic quantum information processing: a review

Photonic quantum technologies represent a promising platform for several applications, ranging from long-distance communications to the simulation of complex phenomena. Indeed, the advantages offered by single photons do make them the candidate of choice for carrying quantum information in a broad variety of areas with a versatile approach. Furthermore, recent technological advances are now enabling first concrete applications of photonic quantum information processing. The goal of this manuscript is to provide the reader with a comprehensive review of the state of the art in this active field, with a due balance between theoretical, experimental and technological results. When more convenient, we will present significant achievements in tables or in schematic figures, in order to convey a global perspective of the several horizons that fall under the name of photonic quantum information.

Photonic topological phases in dispersive metamaterials

We analyze the photonic topological phases in dispersive metamaterials which satisfy the degenerate condition at a reference frequency. The electromagnetic duality allows for the hybrid modes to be decoupled and described by the spin-orbit Hamiltonians with pseudospin 1, which result in nonzero spin Chern numbers that characterize the topological phases. In particular, the combined Hamiltonian of the hybrid modes complies with a fermionic-like pseudo time-reversal symmetry that ensures the Kramers degeneracy, leading to the topological protection of helical edge states. The transverse spin generated by the evanescent surface waves is perpendicular to the wave vector, which exhibits the spin-momentum locking as in the surface states for three-dimensional topological insulators. The topological properties of the helical edge states are further illustrated with the robust transport of a pair of counterpropagating surface waves with opposite polarization handedness at an irregular boundary of the metamaterial.

Photonics meets topology

The topological phases in materials have been studied in recent decades for their unique boundary states and transport properties. Photonic systems with band structures embrace the topological phases closely, where they not only provide platforms to testify the topological band theory, but also shed light on designing novel optical devices. In this review, we present exciting developments, supported by brief descriptions of prominent milestones of topological phases in photonic systems in recent years. These studies may sustain further developments of optical devices and offer novel methods for light manipulations.

Midinfrared Plasmonic Valleytronics in Metagate-Tuned Graphene

A valley plasmonic crystal for graphene surface plasmons is proposed. We demonstrate that a designer metagate, placed within a few nanometers of graphene, can be used to impose a periodic Fermi energy landscape on graphene. For specific metagate geometries and bias voltages, the combined metagate-graphene structure is shown to produce complete propagation band gaps for the plasmons, and to impart them with nontrivial valley-linked topological properties. Sharply curved domain walls between differently patterned metagates are shown to guide highly localized plasmons without any reflections owing to suppressed intervalley scattering. Our approach paves the way for nonmagnetic and dynamically reconfigurable topological nanophotonic devices.

Pseudo-spin-valley coupled edge states in a photonic topological insulator

Pseudo-spin and valley degrees of freedom engineered in photonic analogues of topological insulators provide potential approaches to optical encoding and robust signal transport. Here we observe a ballistic edge state whose spin–valley indices are locked to the direction of propagation along the interface between a valley photonic crystal and a metacrystal emulating the quantum spin–Hall effect. We demonstrate the inhibition of inter-valley scattering at a Y-junction formed at the interfaces between photonic topological insulators carrying different spin–valley Chern numbers. These results open up the possibility of using the valley degree of freedom to control the flow of optical signals in 2D structures.

Valleys in the photonic band structure provide an additional degree of freedom to engineer topological photonic structures and devices. Here, Kang et al. demonstrate that inter-valley scattering is inhibited at a Y-junction between three sections with different valley topology.

Spin- and valley-polarized one-way Klein tunneling in photonic topological insulators

Recent advances in condensed matter physics have shown that the spin degree of freedom of electrons can be efficiently exploited in the emergent field of spintronics, offering unique opportunities for efficient data transfer, computing, and storage (1-3). These concepts have been inspiring analogous approaches in photonics, where the manipulation of an artificially engineered pseudospin degree of freedom can be enabled by synthetic gauge fields acting on light (4-6). The ability to control these degrees of freedom significantly expands the landscape of available optical responses, which may revolutionize optical computing and the basic means of controlling light in photonic devices across the entire electromagnetic spectrum. We demonstrate a new class of photonic systems, described by effective Hamiltonians in which competing synthetic gauge fields, engineered in pseudospin, chirality/sublattice, and valley subspaces, result in bandgap opening at one of the valleys, whereas the other valley exhibits Dirac-like conical dispersion. We show that this effective response has marked implications on photon transport, among which are as follows: (i) a robust pseudospin- and valley-polarized one-way Klein tunneling and (ii) topological edge states that coexist within the Dirac continuum for opposite valley and pseudospin polarizations. These phenomena offer new ways to control light in photonics, in particular, for on-chip optical isolation, filtering, and wave-division multiplexing by selective action on their pseudospin and valley degrees of freedom.

Edge States and Topological Phase Transitions in Chains of Dielectric Nanoparticles

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.