Photonic Topological Insulators Research Articles

Nonlinear Topological Photonic Insulator in Synthetic Space

AbstractAs an emerging field, nonlinear topological photonics attracts great attention nowadays, where pioneering works show interesting phenomena including topological edge solitons and nonlinearity‐induced coupling of light into topological edge states. In this work, the nonlinear effects in a photonic topological insulator in the synthetic space including the frequency axis of light, in a ring resonant array under dynamic modulations are studied, where the four‐wave mixing nonlinear process is included. Such nonlinear process not only induces local interactions, but also creates long‐range interactions in the frequency dimension. These results show destruction on topologically protected edge states when the nonlinear effects are increasing. Moreover, it also breaks the symmetry in the synthetic space as well as the band structure, which reflects different propagation behaviors for the different input sources with positive and negative frequency shifts and exhibits short‐time robustness in weak nonlinear cases. This work hence explores the role of nonlinear effects in affecting the edge modes in the synthetic space, which may be useful in quantum many‐body simulations and find possible applications in information processing.

Topological Resistance-Free One-Way Transport in a Square-Hexagon Lattice Gyromagnetic Photonic Crystal.

We theoretically propose and experimentally realize a new configuration of a photonic Chern topological insulator (PCTI) composed of a two-dimensional square-hexagon lattice gyromagnetic photonic crystal immersed in an external magnetic field. This PCTI possesses five distinct types of edges and all of them allowed the propagation of truly one-way edge states. We proceeded to utilize this special PCTI to design topological transmission lines of various configurations with sharp turns. Although the wave impedances of the edge states on both sides of the intersections in these transmission lines were very different, definitely no back reflection occurred and no mode-mixing problems and impedance-mismatching issues at the intersections were present, leading to topological resistance-free one-way transport in the whole transmission line network. Our results enrich the geometric and physical means and infrastructure to construct one-way transport and bring about novel platforms for developing topology-driven resistance-free photonic devices.

Inverse design of photonic and phononic topological insulators: a review

Abstract Photonic and phononic topological insulators (TIs) offer numerous opportunities for manipulating light and sound with high efficiency and resiliency. On the other hand, inverse design methodologies, such as gradient-based approaches, evolutionary approaches, and deep-learning methods, provide a cost-effective strategy for developing photonic and phononic structures with unique features in steering light and sound. Here, we discuss recent advances and achievements in the development of photonic and phononic TIs employing inverse design methodologies, including one-dimensional TIs, TIs based on the quantum spin Hall effect (QSHE) and quantum valley Hall effect (QVHE), and high-order TIs in lattices with diverse symmetries. Several inversely designed photonic and phononic TIs with superior performance are exhibited. In addition, we offer our perspectives on the future of this emerging study field.

Reconfigurable Wannier-type higher-order photonic topological insulators

Recently, reconfigurable photonic topological insulators (PTIs) have been studied in the low-order PTIs and quadrupole higher-order PTIs. Different from previous works, in this paper, we report reconfigurable Wannier-type higher-order PTIs based on the kagome-lattice BaTiO3 photonic crystal (PC). Considering both intra-cell and inter-cell coupling, the traditional topological edge and corner states as well as a new type of corner state are found at the interface between the non-trivial and trivial BaTiO3 PCs. Active switching between different topological edge and corner states at the same frequency can be realized by freely tuning the refractive index of BaTiO3.

Deterministic generation of multiple topological corner states based on an extremely expanded coupling condition

Photonic higher-order topological insulators (HOTIs) based on kagome photonic crystals (PCs) possess rich physics of corner states for the unignorable long-range interactions. Theoretically, there should be multiple corner states, i.e., type I, antisymmetric type II, and symmetric type II corner states, in the kagome PCs. However, for the generation of some corner states, especially the symmetric type II corner states, it is necessary to obtain a large ratio of intercell coupling to intracell coupling, which makes the spacing between dielectric units very small and difficult to achieve experimentally. Here, we propose a scheme for the deterministic generation of multiple topological corner states based on an extremely expanded coupling condition. We construct an equilateral triangular cavity that consists of nontrivial unit cells in triangular PCs. All three topological corner states can exist robustly in the triangular cavity with large dielectric unit spacing. By establishing a tight-binding model for the nontrivial unit cell, we reveal that the extremely expanded coupling condition is the core physical mechanism for the deterministic generation of multiple corner states. The study provides a simple and deterministic method to generate multiple topological corner states, which has great potential in topological robust cavity, optical switches and lasers in integrated photonics on a silicon-on-insulator (SOI) or III-V active semiconductor platform.

Effective Hamiltonian for Photonic Topological Insulator with Non-Hermitian Domain Walls

The gain and loss in photonic lattices provide possibilities for many functional phenomena. In this Letter, we consider photonic topological insulators with different types of gain-loss domain walls, which will break the translational symmetry of the lattices. A method is proposed to construct effective Hamiltonians, which accurately describe states and the corresponding energies at the domain walls for different types of photonic topological insulators and domain walls with arbitrary shapes. We also consider domain-induced higher-order topological states in two-dimensional non-Hermitian Aubry-André-Harper lattices and use our method to explain such phenomena successfully. Our results reveal the physics in photonic topological insulators with gain-loss domain walls, which provides advanced pathways for manipulation of non-Hermitian topological states in photonic systems.

Strain induced photonic topological insulator

Strain can be used to tune the electromagnetic properties of photonic crystals by altering their structural and mechanical properties. Nonetheless, photonic topological states associated with electromagnetic one-way edged modes induced by strain have never been observed in photonic crystals, and the connection between photonic topological states and strain remains unclear. Using COMSOL Multiphysics calculations, we demonstrated that strain can trigger photonic topological states with appropriate strain engineering. We also identified that these photonic topological states are insensitive to crystal defects (impurities, vacancies). Our results may promote future studies of novel applications in quantum computing and quantum simulations.

Pair-partitioned bulk localized states induced by topological band inversion

Photonic topological insulators have recently received widespread attention mainly due to their ability to provide directions in the development of photonic integration platforms. The proposal for a topological bulk cavity with a single-mode expands upon previous research works on topological cavities; thus, interest in topological edge states and corner states is beginning to shift into analysis on bulk properties and their applications. However, there remains a gap in research on a multi-mode cavity of the topological photonic crystals (PCs). In this Letter, a cavity of the topological PCs is proposed involving pair-partitioned bulk localized states (BLSs) from a two-dimensional inner and outer nested square lattice (2D IONSL), which can enable a multi-mode cavity for the topological PCs. First, the topological characteristics are described in terms of a Zak phase, and band inversions are achieved by changing the size of scatterers in the inner and outer circles that reside within the unit cell. Afterwards, analogous to the tight-binding model for electronic systems, the Hamiltonian and topological phase transition conditions of 2D IONSL PCs are derived. Furthermore, it is proposed that the demonstrated optical field reflection and confinement mechanism induced by topological band inversions due to the opposite parities of wavefunctions may lead to the phenomenon of pair-partitioned BLSs. This research increases the research works of bulk topological effects, creating a route for photonic integration platforms for near-infrared.

Dispersion-tunable photonic topological waveguides

Dispersion-tunable photonic topological waveguides have recently attracted much attention, due to their promising applications on topological devices with tunable operational frequencies. Since dispersions of topological waveguides traverse the whole bandgaps of bulk structures, tuning the dispersions (especially the bandwidths) requires changing the whole bulk of corresponding photonic topological insulators. A previously reported material-modification approach provided a parallel tuning on such numerous lattices; however, the increased material loss deteriorated transmissions of the topological waveguide. Here, a parallel tuning approach on structures is theoretically proposed and demonstrated, which spawns dispersion-tunable photonic topological waveguides without increasing material loss. Based on the bilayer honeycomb model, a topological valley waveguide by utilizing bilayer designer plasmonic structures is constructed, accomplished with dispersion tunings by altering interlayer distance. Experimental results validate the theoretical model and display a 61%-relative-tuning range of frequency, with a tunable relative bandwidth up to 16%. This approach may promise applications in tunable topological lasers, robust delay lines, and intelligent photonic devices.

Three-dimensional photonic topological insulator without spin–orbit coupling

Spin–orbit coupling, a fundamental mechanism underlying topological insulators, has been introduced to construct the latter’s photonic analogs, or photonic topological insulators (PTIs). However, the intrinsic lack of electronic spin in photonic systems leads to various imperfections in emulating the behaviors of topological insulators. For example, in the recently demonstrated three-dimensional (3D) PTI, the topological surface states emerge, not on the surface of a single crystal as in a 3D topological insulator, but along an internal domain wall between two PTIs. Here, by fully abolishing spin–orbit coupling, we design and demonstrate a 3D PTI whose topological surface states are self-guided on its surface, without extra confinement by another PTI or any other cladding. The topological phase follows the original Fu’s model for the topological crystalline insulator without spin–orbit coupling. Unlike conventional linear Dirac cones, a unique quadratic dispersion of topological surface states is directly observed with microwave measurement. Our work opens routes to the topological manipulation of photons at the outer surface of photonic bandgap materials.

Robust topological one-way edge states in radius-fluctuated photonic Chern topological insulators.

Recent developments in topological photonics have shown that the introduction of disorders can yield the innovative and striking transport phenomena. Here, we theoretically investigate topological one-way edge states in radius-fluctuated photonic Chern topological insulators (PCTIs), which are composed of two-dimensional gyromagnetic photonic crystals with cylinder site fixed but with cylinder radius fluctuated. We use a fluctuation index to characterize the degree of radius fluctuation, employ two empirical parameters to inspect the evolution of topological one-way edge states, and verify the stability of topological one-way edge states by calculating massive samples with various random numbers. We find that as the radius-fluctuation strength increases, there arises a competition between topological one-way edge state, Anderson localization state and trivial bulk state. We reveal that the Anderson localization state appears far more easily in the radius-fluctuation PCTI with even a weak strength compared with the position-perturbed PCTI with a strong randomness. We also demonstrate that the topological one-way edge states are protected against a strong fluctuation much larger than the fabrication errors in practical experiments. Our results show that the PCTIs consisting of gyromagnetic photonic crystals have a high-tolerance for the material and sample fabrication errors, and this would provide a deeper understanding of fundamental topology physics.

Disorder‐Driven Collapse of Topological Phases in Photonic Topological Insulator

By embedding the position disorder of rods in 2D gyromagnetic photonic crystal, the influences of increasing random disorder on the photonic topological phases (PTPs) in a photonic topological insulator are numerically investigated. When the disorder is small, the PTPs almost have no change. With the increase in disorder, the PTPs at the edge of the original topological bandgap are first affected, and those at center of the bandgap have the best robustness. As disorder increases to a critical value, the PTPs collapse ultimately. During the collapse of the PTPs, disorders can induce the Anderson localization of electromagnetic (EM) wave, and produce localized hot spots in the system. When the disorder is not too large, the hot spots are excited at the edge area near the excitation source, and have little influence on the one‐way propagation of the topological edge state (TES). As disorder increases continuously, the hot spots would penetrate the system deeply and affect the propagation of EM waves significantly, which leads to the collapse of the PTPs and destruction of one‐way propagation of TES. Even so, there are still remaining long‐range and short‐range orders in the system. This research provides a theoretical model and an experiment platform for further studying the relationship between topological phases and disorders.

Ideal nodal rings of one-dimensional photonic crystals in the visible region

Three-dimensional (3D) artificial metacrystals host rich topological phases, such as Weyl points, nodal rings, and 3D photonic topological insulators. These topological states enable a wide range of applications, including 3D robust waveguides, one-way fiber, and negative refraction of the surface wave. However, these carefully designed metacrystals are usually very complex, hindering their extension to nanoscale photonic systems. Here, we theoretically proposed and experimentally realized an ideal nodal ring in the visible region using a simple 1D photonic crystal. The π-Berry phase around the ring is manifested by a 2π reflection phase’s winding and the resultant drumhead surface states. By breaking the inversion symmetry, the nodal ring can be gapped and the π-Berry phase would diffuse into a toroidal-shaped Berry flux, resulting in photonic ridge states (the 3D extension of quantum valley Hall states). Our results provide a simple and feasible platform for exploring 3D topological physics and its potential applications in nanophotonics.

Fractal photonic topological insulators.

Topological insulators constitute a newly characterized state of matter that contains scatter-free edge states surrounding an insulating bulk. Conventional wisdom regards the insulating bulk as essential, because the invariants that describe the topological properties of the system are defined therein. Here, we study fractal topological insulators based on exact fractals composed exclusively of edge sites. We present experimental proof that, despite the lack of bulk bands, photonic lattices of helical waveguides support topologically protected chiral edge states. We show that light transport in our topological fractal system features increased velocities compared with the corresponding honeycomb lattice. By going beyond the confines of the bulk-boundary correspondence, our findings pave the way toward an expanded perception of topological insulators and open a new chapter of topological fractals.

Inversely Designed Second-Order Photonic Topological Insulator With Multiband Corner States

Second-order photonic topological insulators (SPTIs) with topologically protected corner states possess extraordinary abilities of robust light steering in lower dimensions. However, previous SPTIs are difficult for multiband on-chip applications. To overcome this challenge, we design, via the inverse design method, a SPTI supporting four highly localized corner states within four sizeable band gaps that are robust to bulk impurities. Importantly, the designed SPTI is made of fully connected dielectric materials, which can be readily fabricated in nanoscale via electron-beam lithography and integrated into on-chip circuits. Our work offers potential applications in designing multiband on-chip photonic integrated devices with high efficiency, high capacity, and high robustness for both linear and nonlinear optical processing.

Direct observation of terahertz topological valley transport.

Topological photonics offers the possibility of robust transport and efficiency enhancement of information processing. Terahertz (THz) devices, such as waveguides and beam splitters, are prone to reflection loss owing to their sensitivity to defects and lack of robustness against sharp corners. Thus, it is a challenge to reduce backscattering loss at THz frequencies. In this work, we constructed THz photonic topological insulators and experimentally demonstrated robust, topologically protected valley transport in THz photonic crystals. The THz valley photonic crystal (VPC) was composed of metallic cylinders situated in a triangular lattice. By tuning the relevant location of metallic cylinders in the unit cell, mirror symmetry was broken, and the degenerated states were lifted at the K and K' valleys in the band structure. Consequently, a bandgap of THz VPC was opened, and a nontrivial band structure was created. Based on the calculated band structure, THz field distributions, and valley Berry curvature, we verified the topological phase transition in such type of THz photonic crystals. Further, we showed the emergence of valley-polarized topological edge states between the topologically distinct VPCs. The angle-resolved transmittance measurements identified the bulk bandgap in the band structure of the VPC. The measured time-domain spectra demonstrated the topological transport of valley edge states between distinct VPCs and their robustness against bending and defects. Furthermore, experiments conducted on a topological multi-channel intersectional device revealed the valley-polarized characteristic of the topological edge states. This work provides a unique approach to reduce backscattering loss at the THz regime. It also demonstrates potential high-efficiency THz functional devices such as topologically protected beam splitters, low-loss waveguides, and robust delay lines.

Higher-order topological biphoton corner states in two-dimensional photonic lattices

Higher-order topological insulators have attracted great interest for their unconventional bulk-boundary correspondence especially gapless corner states. Here, we realize topological biphoton corner states in two-dimensional lattices. In addition to the striking state localization, the correlations in topologically nontrivial cases are more than 60 times higher than those in trivial cases and the visibility of Hong-Ou-Mandel interference for output topological corner-entangled states is higher than 90.3%. We confirm that the second-order photonic topological insulators support stable biphoton states that can maintain spatial distributions in high-dimensional Hilbert space, which have potential applications in quantum algorithms, simulation, and computation.

Topological protection of partially coherent light

Topological physics exploits concepts from geometry and topology to implement systems capable of guiding waves in an unprecedented fashion. These ideas have led to the development of photonic topological insulators, which are optical systems whose eigenspectral topology allows the creation of light states that propagate along the edge of the system without any coupling into the bulk or backscattering even in the presence of disorder. Indeed, topological protection is a fully coherent effect, and it is not clear to what extent topological effects endure when the wavefronts become partially coherent. Here, we study the interplay of topological protection and the degree of spatial coherence of classical light propagating in disordered photonic topological insulators. Our results reveal the existence of a well-defined spectral window in which partially coherent light is topologically protected. This opens up the design space to a wider selection of light sources, possibly yielding smaller, cheaper, and more robust devices based on the topological transport of light.

Three-Dimensional Printed Planar Polymer Photonic Topological Insulator Waveguides and Their Robustness to Lattice Defects

Three-Dimensional Printed Planar Polymer Photonic Topological Insulator Waveguides and Their Robustness to Lattice Defects

Non-reciprocal diplexer and power combiner/divider from topological cavities with both splitting and combining functions

Multiplexers and power combiners/dividers are crucial in many applications of electromagnetic waves including microwave and terahertz communication. Full-duplex communication requires the separation of transmitted and received signals; thus, non-reciprocal multiplexers and power combiners/dividers are very essential. In this work, we present and numerically study a design concept for such non-reciprocal circuits from topological cavities. First, a quad-port circulator is made from a topological cavity and two trivial waveguides, which effectively operates as a non-reciprocal band-pass filter. Then, by parallelly connecting multiple circulators together, topological diplexers and power combiners/dividers are formed. These circuits are non-reciprocal due to the nature of photonic topological insulators, yet unlike the previously proposed non-reciprocal multiplexers or power combiners/dividers, they can both split and combine multiple frequencies or multiple power flows. The topological nature of the proposed circuits also makes them robust to any fabrication error and suitable for practical full-duplex communication applications.