For the study of topological phases in photonics, while quantum-Hall-type first-order chiral edge states are routinely realized in magneto-optical photonic crystals, higher-order topological states are mostly explored in all-dielectric photonic crystals. In this work, we study both first- and second-order topological photonic states in magneto-optical photonic crystals. In specific, we revisit a simple magneto-optical photonic crystal in a square lattice with one gyromagnetic cylinder in each unit cell. However, rather than investigating the conventional unit cell where the cylinder is at the center of the square unit cell as previous works have done, we consider a configuration where the cylinders are located at the four corners of the square unit cell and show that this configuration hosts rich topological phases, such as dual-band Chern, dipole, and quadrupole topological phases. Our detailed characterizations of these topological states are based on the Wannier bands and their polarizations via the Wilson loop and nested Wilson loop methods. We study in detail both the edge and corner states of the different topological phases and show that they exhibit a special feature of ``spectrum robustness.'' For example, though the edge and corner states of the dipole phases living in a band gap could be pushed into the bulk bands by tuning the boundary conditions, they can pass through the bulk bands and reappear within a different band gap. For dual-band quadrupole phases, we can find a regime where both band gaps host a set of corner states simultaneously and, intriguingly, the filling anomaly of one set of corner states can leave their signatures in the filling anomaly of the other set of corner states though they are separated by an extensive number of bulk states. The rich topological physics revealed in a simple magneto-optical photonic crystal not only provides new insights on higher-order topological phases in time-reversal symmetry-broken photonic systems, the results may also find promising applications by harnessing the potentials of both edge and corner states. 

Chern, dipole, and quadrupole topological phases of a simple magneto-optical photonic crystal with a square lattice and an unconventional unit cell

From Self-Assembly of Colloidal Crystals toward Ordered Porous Layer Interferometry

Ultrahigh-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si115.svg" display="inline" id="d1e745"><mml:mi>Q</mml:mi></mml:math> Fano resonance in a cavity-waveguide coupled system based on second-order topological photonic crystals with elliptical holes

Responsive photonic crystals (RPCs) have the advantages of visual response, controllable response speed, and reasonable response sensitivity, enabling them attractive in sensing detection, intelligent displays, anti-counterfeiting identification and other fields. At present, the rapid development of anti-counterfeiting technology ensures product quality and brand influence, as well as human health, placing an important economic value and bringing social benefits. This review introduces the research status of visual responsive photonic crystals, and the special attention is paid to the preparation principle, classification and preparation methods of RPCs, and their application progress in the anti-counterfeiting systems for the textile industry. 

Recent advances in responsive photonic crystals and their applications in anti-counterfeiting solutions for the textile industry

Abstract This 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. 

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

• We propose a kind of topological photonic crystals (PCs) based on square lattice. • The topological edge state and corner state are achieved in the combined structure. • A Fano resonance system is constructed to realize the coupling between edge state and corner state. • The frequency shift of topological corner state is demonstrated in the system with air defects. • The coupling energy and the quality factor of resonance system are enhanced by introducing air defects. Topological photonic crystals whose topological protection makes them very robust against perturbations offer a new way of manipulating photons in micro/nano-photonic devices. In this paper, we propose a type of topological photonic crystal (PC) system with a square lattice, and we demonstrate that topological edge state (TES) and topological corner state (TCS) can coexist in the PC resonator. Coupling between the TES and TCS can be achieved in a system with a topological PC waveguide and a box-shaped topological PC resonance cavity. The results indicate that air defects introduced in the box-shaped resonator will lead to the frequency shift of TCS. These air defects can be used to narrow the bandwidth and to increase the quality factor Q of the Fano resonance system. In addition, the resonance energy coupled from the TES to the TCS is greatly enhanced by the introduction of the air defects in the box-shaped resonance cavity. This work paves a new approach for the development of topological integrated optical devices with high quality factor and strong coupling. 

Manipulation of coupling between topological edge state and corner state in photonic crystals

Mechanochromic Photonic Fibers Composed of Strain Responsive Colloidal Crystals and Spandex Yarns

Valley photonic crystals (VPCs) possess remarkable properties, being capable of supporting topological edge states and corner states. Herein, we propose a sandwich-like structure consisting of two layers of silicon-based triangle air hole topological VPCs, and an interlayer of semimetal (SM) photonic crystal. The edge state in the proposed structure has demonstrated a robust behavior even in the presence of large defects in the valley edge state waveguide. The constructed triangle box-shaped structure, comprising VPCs with opposite Chern numbers, generates valley corner states with high localization properties. Moreover, we construct a waveguide-cavity coupling system involving the triangle resonance cavity and the valley edge state waveguide, which sustains edge states and corner states. We systematically research various coupling phenomena of edge states and corner states such as edge-edge state coupling, edge-corner state coupling and extended edge-corner state coupling, realizing the versatile functionalities of delay line, wavelength division multiplexer, and filter. These findings present an approach to address challenge associated with large defects in the valley edge state waveguide and provide a means of realizing corner states on the topological VPCs platform. The proposed waveguide-cavity coupling systems hold potential applications in optical communication and on-chip integrated optical devices. 

Topological waveguide-cavity coupling system based on valley photonic crystals

Coupled waveguide–cavity system based on higher-order topological states in square lattice photonic crystals

Manipulation of topological edge and corner states in photonic Kagome crystals through different combinations

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