Topological Corner States Research Articles

Polarization-independent Topological Corner States Based on All-dielectric Valley Photonic Crystals

Polarization-independent Topological Corner States Based on All-dielectric Valley Photonic Crystals

Higher-order topological corner states and origin in monolayer LaBrO

Abstract Intrinsic higher-order topological insulators driven solely by orbital coupling are rare in electronic materials. Here, we propose that monolayer LaBrO is an intrinsic two-dimensional second-order topological insulator. The generalized second-order topological phase arises from the coupling between the 5d orbital of the La atom and the 2p orbital of the O atom. The underlying physics can be thoroughly described by a four-band generalized higher-order topological model. Notably, the edge states and corner states of monolayer LaBrO exhibit different characteristics in terms of morphology, number, and location distribution under different boundary and nanocluster configurations. Furthermore, the higher-order topological corner states of monolayer LaBrO are robust against variations in spin-orbit coupling and different values of Hubbard U. This provides a material platform for studying intrinsic 2D second-order topological insulators.

Two types of corner states in two dimensional photonic crystals with finite sizes

Abstract Using two-dimensional (2D) square lattice photonic crystals (PCs) with different topological properties, we design different combined structures to construct two types of topological corner states (CSs), named as Type I and Type II CSs. Then by tuning sizes of inner PCs in the combined structures, we systematically investigate size effects on the two types of CSs. Numerical results demonstrate as the structures decrease to their critical sizes, due to the interactions of opposite interfaces and the couplings of corners, size changes of inner PCs in the combined structures have significant effects on the frequencies, degeneracies and mode field distributions of the two types of CSs. Moreover, Type I CSs peform better topological stability than Type II CSs during the size changes of structures. We also monitor mode field localizations of the two types of CSs and reveal that their localizations are only related to the types of the CSs, and have no relations to sizes and overall symmetries of the combined structures. Our research enriches the study of higher order topological CSs and paves the way for design and manufacture of optical micro-nano devices with photonic topological CSs.

Space- and frequency-division multiplexing in photonic second-order topological insulators

Higher-order topological insulators, originally proposed in quantum condensed matters, have provided a new avenue for localizing and transmitting light in photonic devices. Nontrivial band topology in crystals with certain symmetries can host robust topological edge states and lower dimensional topological corner states (TCS), making them a promising platform for photonics applications. Here, we have designed several types of TCS with only two specific C6v-symmetric photonic crystals with various seamless splicing boundaries, where all the supposed TCS with diverse electromagnetic characteristics are visualized via numerical simulations and experimental measurements. More interestingly, we have observed that those TCS overlapping in spectral and spatial space tend to interweaved, inducing spectrum division. Meanwhile, the equivalent corners appear to have TCS with a phase difference, which is critical for directional activation of pseudospin dependence. Our findings demonstrate that coupled TCS with phase difference at different nanocavities can be selectively excited by a chiral source, which indicates that the TCS at this time have pseudospin-dependent properties. We further design a specific splicing structure to prevent coupling between adjacent TCS. This work provides a flexible approach for space- and frequency-division multiplexing in photonic devices.

Data-driven inverse design of a multiband second-order phononic topological insulator

Second-order phononic topological insulators (SPTIs) have sparked vast interest in manipulating elastic waves, owing to their unique topological corner states with robustness against geometric perturbations. However, it remains a challenge to develop multiband SPTIs that yield multi-frequency corner states using prevailing forward design approaches via trial and error, and most inverse design approaches substantially rely on time-consuming numerical solvers to evaluate band structures of phononic crystals (PnCs), showing low efficiency particularly when applied to different optimization tasks. In this study, we develop and validate a new inverse design framework, to enable the multiband SPTI by integrating data-driven machine learning (ML) with genetic algorithm (GA). The relationship between shapes of scatterers and frequency bounds of multi-order bandgaps of PnCs is mapped via developing artificial neural networks (ANNs), and a multiband SPTI with multi-frequency topological corner states is cost-effectively designed using the proposed inverse optimization framework. Our results indicate that the data-driven approach can provide a high-efficiency solution for on-demand inverse designs of multiband second-order topological mechanical devices, enabling diverse application prospects including multi-frequency robust amplification and confinement of elastic waves.

Spin separation and filtering assisted by topological corner states in the Kekulé lattice

Spin separation and filtering assisted by topological corner states in the Kekulé lattice

Observation of nonlinear fractal higher order topological insulator

Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states, whose dimensionality is at least by 2 lower than that of the bulk. Topological states in such insulators may be strongly confined in their corners which leads to considerable enhancement of nonlinear processes involving such states. However, all nonlinear HOTIs demonstrated so far were built on periodic bulk lattice materials. Here, we demonstrate the first nonlinear photonic HOTI with the fractal origin. Despite their fractional effective dimensionality, the HOTIs constructed here on two different types of the Sierpiński gasket waveguide arrays, may support topological corner states for unexpectedly wide range of coupling strengths, even in parameter regions where conventional HOTIs become trivial. We demonstrate thresholdless spatial solitons bifurcating from corner states in nonlinear fractal HOTIs and show that their localization can be efficiently controlled by the input beam power. We observe sharp differences in nonlinear light localization on outer and multiple inner corners and edges representative for these fractal materials. Our findings not only represent a new paradigm for nonlinear topological insulators, but also open new avenues for potential applications of fractal materials to control the light flow.

Ferrimagnetic second-order topological insulator with valley polarization in two-dimensional magnet

Two-dimensional (2D) ferromagnetic and antiferromagnetic second-order topological insulators (SOTIs) coexisting with valley polarization have received increasing attention recently, while 2D valley-polarized ferrimagnetic (ferri-valley) SOTI has not been reported yet. In this work, we propose an effective six-band tight-binding model based on structural symmetry to confirm the possibility of coexistence of ferrimagnetism, second-order topological corner states, and valley polarization in 2D systems, and predict Mo2CSCl monolayer as the robust 2D ferri-valley SOTI with good structural stability, considerable Curie temperature estimated to be 100 K, and distinct valley polarization up to 109 meV under out-of-plane exchange field based on our model and first-principles calculations. Also, we find that the spin polarization direction of corner states combined with valley polarization can be controlled by switching the direction of the magnetization direction using an external magnetic field. These findings of the combination of intrinsic ferrimagnetism, second-order topological properties, and valley polarization in single 2D materials provide an ideal platform for practical applications in multifield-control spintronic devices.

Near-field coupling between topological corner states.

In this Letter, we investigate the near-field coupling between topological corner states. As a proof of concept, we build a higher-order topological photonic structure with a square lattice, based on the 2D Su-Schrieffer-Heeger (SSH) model. It is demonstrated that the topological corner state can be hosted at a corner via engineering its two boundaries, whereupon the near-field coupling between two corner states is investigated by bringing them close together. Numerical and theoretical results show that the near-field coupling between two corner states results in hybridized local resonances and significant enhancement of density of states, which are similar to the plasmonic resonances and Mie resonances. Moreover, the extraordinary advantage of the coupled corner states is verified via enhancing third-harmonic generation. Our results may provide insight into studying topological photonics with multimodes as well as an effective approach for manipulation of light.

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

We present a novel configuration of second-order topological photonic crystal (SOTPC) comprising interconnected dielectric material with elliptical air holes. Based on this SOTPC design, we construct a topological corner state (TCS) cavity and a topological edge state (TES) waveguide. Through the coupling of the TCS cavity with the TES waveguide, we establish a topological cavity-waveguide coupled system (TCWCS) that exhibits an ultrasharp asymmetric topological Fano resonance. Numerical simulations demonstrate that the proposed TCWCS achieves an exceptionally high quality factor exceeding 108, surpassing previously reported results by several orders of magnitude. Moreover, the refractive index sensing application implemented with TCWCS shows a sensitivity of 278 nm/RIU and a figure of merit surpassing 107 1/RIU. Notably, our simulations reveal that the lineshape and quality factor of the Fano resonance, as well as the index sensing performance in the TCWCS, are highly robust against structural defects. The demonstrated capabilities of the TCWCS open up avenues for further exploration and development in the field of topological photonics based on our proposed SOTPC.

Multi-Fano resonances by TCS and resonance-enhanced TES in hybrid photonic crystals for ultracompact sensing

This work introduces a novel hybrid photonic crystal (PC) architecture exploiting topologically multi-Fano resonances employing an inverted π-shape structure filled with a nontrivial PC flanked by M−shaped trivial PCs for ultracompact and high-sensitivity sensing, harnessing their immense potential for miniaturized sensing applications. Topological corner state (TCS) is formed in the structure. Moreover, a waveguide-branch resonator or a resonant ring for the topological edge state (TES) mode is formed to increase the Fano resonance. We demonstrate the existence of engineered quasi-bound multi-Fano resonances within this structure, exhibiting tunable quality factors exceeding 108 (ultrahigh Q) and a remarkable figure of merit (FOM), reaching 2.6×107RIU-1. By precisely controlling the nontrivial PC dimensions, we achieve exquisite control over the resonance’s Q factor and spectral line shape, revealing characteristics of quasi-bound states in the continuum (BICs). This hybrid architecture exhibits exceptional sensitivity to refractive index changes, with tunability ranging from 320 to 392 nm/RIU. Our work paves the way for a new paradigm in sensing, enabling the development of ultracompact on-chip nanophotonic devices with unprecedented sensitivity and control.

Topological states in Penrose-square photonic crystals

Topological edge states (TESs) and topological corner states (TCSs) in photonic crystals (PCs) provide an effective way to control the propagation and localization of light. The topological performance of integrated photonic devices can be improved by introducing the basic structural unit of photonic quasicrystals (PQCs) into PCs. However, the previous works arranged the basic structural unit of Stampfli-type and 12-fold Penrose-type photonic quasicrystals into triangular lattices, which have a complex structure and allow light to only propagate around 60° or 120° corners, limiting their applications. In this paper, a Penrose-square PC is proposed, which realizes both TESs and TCSs, and light successfully propagates around 90° corners. This work may reduce the difficulties encountered in the preparation of topological photonic crystals (TPCs) structured by arranging the basic structural units of PQCs periodically. It also provides a new, to the best of our knowledge, platform for studying TPCs and new ideas for improving the performance of integrated photonic devices.

Observation of Topological Corner State Arrays in Photonic Quasicrystals (Laser Photonics Rev. 18(7)/2024)

Observation of Topological Corner State Arrays in Photonic Quasicrystals (Laser Photonics Rev. 18(7)/2024)

Design of photonic topological corner states for electrically pumped terahertz quantum cascade laser

Photonic topological corner states (PTCS) represent discrete zero modes whose frequencies stay in the topological bandgap and wavefunctions exhibit strong spatial localization, which is highly desirable for efficient surface-emitting lasers. While being extensively investigated in optically pumped lasers, the electrically pumped PTCS lasers are merely reported due to the lack of suitable configurations. In this paper, we propose a photonic cavity design based on the PTCSs that can be applied for electrically pumped terahertz quantum cascade lasers (QCLs). The cavity is constructed by following the canonical trivial-nontrivial domain, where the nontrivial domain with expanded and merged four QCL rods is surrounded by the trivial domain with shrunk and merged four QCL rods. Both domains follow the 2D Su–Schrieffer–Heeger (SSH) model. To further construct a fabrication-favorable 3D device, the designed QCL rod array is connected by 2D veins, which functionalize simultaneously as the intermedium for enhanced inter-/intra-cell coupling and the conductive connection to the device. The 3D numerical calculation is finally investigated.

Selective topological valley transport of elastic waves in a Bragg-type phononic crystal plate

Based on the quantum valley Hall effect analogy, this work proposes a phononic crystal plate with ligament-type beams to obtain the topological valley transmission of elastic waves. A pure Bragg degenerate state appears in the high-frequency region with a resonator introduced. By rotating the central scatterer and the beams, the mirror symmetry is broken to form a topological bandgap. Subsequently, this work finds that two selective edge states also appear beside the commonly non-trivial crossing edge states in the topological bandgap by calculating the projected band and eigenvalue spectrum of the supercell with different valley Hall phases phononic crystals. Their appearance is due to band separation of the topological edge states caused by an increase in the rotation angle. Both selective edge states can transmit topologically in specific paths. They will help further to broaden the width of the frequency band of topological transmission. Besides, an elastic wave splitter is designed and demonstrated numerically, which can form two channels and three channels in different frequency bands. With the topological selective edge state disappearing, a topological corner state exists in the edge bandgap. This work provides a theoretical reference for practical applications of broadband elastic wave topological transmission and elastic energy trapping.

Rainbow Trapping with Engineered Topological Corner States and Cavities in Photonic Crystals

AbstractThis work presents a pioneering photonic crystal (PC) heterostructure design exploiting tailored topological corner states and cavities to unleash a fascinating topological rainbow effect. This effect arises from the strategic integration of a nontrivial topological PC with sharp corners within a trivial PC matrix, resulting in a heterostructure rich in corner states and cavities. The critical innovation lies in manipulating the sector angle of circular columns, granting dynamic control over the rainbow effect and light localization. This manipulation induces distinct group velocities for different light frequencies, leading to their separation and localization at specific corner states. This remarkable “rainbow trapping” phenomenon manifests as highly confined light exhibiting exceptional resilience against disorder. These findings illuminate a pathway toward crafting next‐generation photonic devices boasting unparalleled functionalities. The reconfigurable rainbow trapping holds immense potential for applications in wavelength division multiplexing, optical sensing, and even venturing into quantum information processing.

Coupling of photonic topological states and their dynamical control based on liquid crystal

Optical field manipulation inspired by topology theory has recently drawn great research attention in nanophotonic. For flexible and programmable light management, the capacity to dynamically regulate the photonic topological states in fixed optical artificial microstructures is essential. Here, we propose a dynamic light manipulation of a two-dimensional (2D) photonic lattice aided by liquid crystals, which is composed of all-dielectric photonic crystals with distinct topological phases. In brief, by submerging the well-designed photonic lattice into a liquid crystal (LC), the topological edge and corner states can be actively modulated by applying external bias voltage, which offers an electrically switchable tuning capability, enabling the coupling between higher-order topological states in a structurally deterministic photonic structure. As a proof-of-principle, we use the 1D topological edge states and 0D topological corner states in one sample, respectively, to mimic line-waveguides and corner-cavities, and demonstrate their selective couplings with Fano-like profile driven by electric bias. Our work offers an effective and flexible way for light control in the potential active topological photonic devices.

Higher‐Order Topological Corner States in a Specially Distorted Photonic Kagome Lattice

AbstractKagome lattices have garnered significant interest over the decades due to their rich physics and implications for exotic superconductors and topological materials. In particular, the so‐called “breathing Kagome lattice” (BKL) is often used as a prototypical model to understand higher‐order topological insulators. Here it is demonstrated that higher‐order corner states exist in a specially distorted Kagome lattice, resembling the “Inverse Hexagram” lattice distortion originally introduced in the study of charge density waves in Kagome metals. Importantly, it is found that such an Inverse Hexagram‐like Kagome lattice with C6 rotational symmetry hosts two types of in‐gap corner states, in contrast to a flat‐cutting BKL of C3 symmetry that supports only one type of corner state under the tight‐binding condition. It is shown that the nontrivial corner states exhibit a fractional corner anomaly, revealing the feature of higher‐order topology. Using laser‐written waveguide lattices as a photonic platform, these two types of corner states are experimentally observed, along with a direct comparison with the corner excitation at their trivial counterparts. Experimental observations are further corroborated by numerical simulations and stability analysis under random perturbation. These results may prove relevant and applicable to similar phenomena in other Kagome platforms beyond photonics.

Shape unrestricted topological corner state based on Kekulé modulation and enhanced nonlinear harmonic generation

Abstract Topological corner states have been extensively utilized as a nanocavity to increase nonlinear harmonic generation due to their high Q-factor and robustness. However, the previous topological corner states based nanocavities and nonlinear harmonic generation have to comply with particular spatial symmetries of underlying lattices, hindering their practical application. In this work, we design a photonic nanocavity based on shape unrestricted topological corner state by applying Kekulé modulation to a honeycomb photonic crystal. The boundaries of such shape unrestricted topological corner state are liberated from running along specific lattice directions, thus topological corner states with arbitrary shapes and high Q-factor are excited. We demonstrate enhancement of second (SHG) and third harmonic generation (THG) from the topological corner states, which are also not influenced by the geometry shape of corner. The liberation from the shape restriction of corner state and nonlinear harmonic generation are robust to lattice defects. We believe that the shape unrestricted topological corner state may also find a way to improve other nonlinear optical progress, providing great flexibility for the development of photonic integrated devices.

Delocalization and higher-order topology in a nonlinear elastic lattice

Topological elastic waves provide novel and robust ways for manipulating mechanical energy transfer and information transmission, with potential applications in vibration control, analog computation, and more. Recently discovered higher-order topological insulators (HOTIs) with multidimensional and hierarchical edge states can further expand the capabilities of topological elastic waves. However, the effects of nonlinearity on elastic HOTIs remain elusive. In this paper, we propose a nonlinear elastic higher-order topological Kagome lattice. After briefly reviewing its linear properties, we explore the effects of nonlinearity on the higher-order band topology and topological states. To do this, we have developed a method to calculate approximate nonlinear modes in order to identify the bulk polarization and probe the higher-order topological phase in the nonlinear lattice. We find that nonlinearity induces unusual delocalization of topological corner states, band crossing, and higher-order topological phase transition. The delocalization reveals that intracell hardening nonlinearity leads to direct delocalization of topological corner states while intracell softening nonlinearity first enhances and then reduces localization. The nonlinear higher-order topological phase is amplitude dependent, and we demonstrate a transition from a trivial to a non-trivial phase, enabling amplitude induced topological corner and edge states. Additionally, this phase transition corresponds to the closing and reopening of the bandgap, accompanied by an unusual band crossing. By examining the band topology before and after the band crossing, we find that the bulk polarization becomes quantized with respect to amplitude and can predict higher-order topological phases in nonlinear lattices. The obtained results are expected to be beneficial for the development of tunable and robust elastic wave devices.