Topological Photonic Crystals Research Articles

Nonlinear LiNbO3 topological Tamm interface state photonic crystal with static visible and intelligent laser protection

The rapid advancement of high-energy laser and LiDAR technologies imposes heightened demands on intelligent laser protection windows. Traditional laser protection devices often face difficulty in simultaneously achieving high absorption of low-energy laser and high reflection of high-energy laser. Herein, we investigate the efficacy of one-dimensional nonlinear LiNbO3 topological Tamm interface state photonic crystal for static visible and intelligent laser protection applications. The photonic crystal's intelligent laser protection property arises from the amplification of nonlinear effects facilitated by the intense electric field localization surrounding the LiNbO3 interface. At 1064 nm laser energy levels below 18.29 mJ/cm2, the protection window exhibits up to 87.03% absorption. When the laser energy increased to 83.84 mJ/cm2, the reflectance reaches 88.07% attributed to the unsatisfied amplitude matching condition caused by the LiNbO3 nonlinear effect, thereby achieving successful intelligent laser protection. Furthermore, the fabricated sample demonstrates a maximum transmittance of 47.51% in the visible wavelength range. This research provides novel insights into the development of multifunctional advanced optical elements.

A semi-definite optimization method for maximizing the shared band gap of topological photonic crystals

Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator for a joint optical structure formed by connecting together two photonic crystals with distinct topological invariants, and the corresponding eigenfrequencies are located in the shared band gap of two individual photonic crystals. This work is concerned with maximizing the shared band gap of two photonic crystals with different topological features in order to increase the bandwidth of the edge modes. We develop a semi-definite optimization framework for the underlying optimal design problem, which enables efficient update of dielectric functions at each time step while respecting symmetry constraints and, when necessary, the constraints on topological invariants. At each iteration, we perform sensitivity analysis of the band gap function and the topological invariant constraint function to linearize the optimization problem and solve a convex semi-definite programming (SDP) problem efficiently. Numerical examples show that the proposed algorithm is superior in generating optimized optical structures with robust edge modes.

Topological State in Heterostructured Gap Waveguides and Their Transitions to Classical Transmission Line

AbstractGap waveguides play a crucial role in millimeter‐wave information transmission and processing for next‐generation wireless communication and radar sensing systems. However, they suffer from challenges, such as reflection and scattering losses at sharp bends and defects. While topological photonic crystals offer innovative solutions for robust signal transmission, their localized interface states and unique electromagnetic modes pose compatibility challenges with practical circuits and systems. In this paper, a novel heterostructured gap waveguide support valley‐locked topological guided wave transport is introduced. This design ensures robust propagation against defects and bends while maintaining compatibility with classical transmission lines. Its topological characteristic reduce sensitivity to fabrication and assembly errors. More importantly, an efficient transition structure is developed to seamlessly convert quasi‐transverse electromagnetic (quasi‐TEM) modes in planar transmission lines to topological guided wave states, thereby effectively exciting topological waves. All theoretical predictions are quantitatively verified by the simulations and experiments at millimeter wave frequency. This heterostructured gap waveguide can find unique applications, such as power divider, as verified numerically. By leveraging topological principles, the proposed gap waveguide offers a significant performance boost for antennas and passive/active components in millimeter‐wave applications, including automotive radar, 5G communication, and synthetic‐aperture radar for imaging.

High-Q coupled topological edge state in 1D photonic crystal mirror heterostructure for ultrasensitive thermal sensing

This work explores a novel 1D topological photonic crystal (PC) mirror heterostructure for high-performance thermal sensing. The design leverages a unique coupled topological edge state mode (CTES) exhibiting exceptional light confinement at the interface, characterized by a record-high quality (Q) factor. The study investigates the effects of nematic liquid crystal (NLC) integration and temperature variations to enhance functionality. Two NLC defect configurations are explored: complete replacement of silica layers and localized replacement within one topological PC. In both scenarios, the CTES mode exhibits tunability in frequency and Q factor due to the thermo-optic properties of the NLC. This dynamic control offers advantages for various applications beyond thermal sensing, including filtering and switching. The first NLC configuration achieves an outstanding Q factor of 107, surpassing the intrinsic value. Additionally, it demonstrates exceptional thermal sensitivity (−0.12317 nm/°C) and a remarkable figure of merit (1002.48 °C−1). These superior sensing characteristics are attributed to the strong light localization at the interface and the intensified light-matter interaction facilitated by the NLC. The second configuration offers a trade-off between sensitivity and tunability, exhibiting a Q factor in the 106 range, a sensitivity of −0.05853 nm/°C, and a figure of merit of 86.53 °C−1. This study presents a groundbreaking design for 1D topological PC mirror heterostructures with integrated NLC. This platform holds immense promise for developing high-performance, tunable narrowband filters and ultrasensitive thermal sensors, paving the way for advancements in diverse photonic applications.

Selective IR wavelengths multichannel filter based on the one-dimensional topological photonic crystals comprising hyperbolic metamaterial

In this research article, we have theoretically introduced a one-dimensional topological photonic crystal (1D TPC) design to provide a better stability due to imperfections and fluctuations in geometry compared to the traditional PC structures. The considered structure is designed by the combination of two different PCs, i.e., PC1 and PC2. PC1 consists of two layers of silicon (Si) and magnesium fluoride (MgF2), while PC2 contains a multilayer stack of MgF2 and hyperbolic metamaterial (HMM). Interestingly, the HMM layer is introduced as a composite of a dielectric material of indium arsenide (InAs), and nanocomposite of Ag nanoparticles inside a hosting medium of Y2O3. The foundations of our theoretical framework are based on Effective Medium Theory (EMT), the Transfer Matrix Method (TMM), and the Maxwell-Garnett model. Our research primarily focuses on utilizing our design as a pass/stop band filter for near-infrared (NIR) applications. Notably, this proposed design exhibits significant stability in the face of imperfections and variations. Our numerical findings highlight the influence of several geometric parameters including the refractive index of hosting medium for Ag nanoparticles, thicknesses, and filling fraction on the characteristics of the resulting filter. Remarkably, the results also reveal the emergence of multiple resonance peaks that maintain high stability against geometric tolerances. We believe our work presents a finite photonic crystal (PC) whose wave localization properties are resilient to random geometric imperfections, making it suitable for NIR filtering applications.

Design of a beam splitter based on an adjustable beam-splitting ratio of a hexagonal star-like topological photonic crystal

We propose a new, to the best of our knowledge, mechanism to realize topological phase transition, that is, in a hexagonal star-like honeycomb lattice photonic crystal (PC), the optical quantum spin Hall effect (QSHE) can be realized by changing the materials of the outer or inner ring dielectric rods in the cells. We calculated the energy band and analyzed the topological phase transition law of a hexagonal star-like honeycomb PC. By changing the permittivity of the PC, the disturbance is introduced to the edge state. It is found that with the decrease of the permittivity of the PC, the gap decreases, the lower boundary state gradually redshifts, and the maximum transmittance in the straight waveguide can reach 98.8%. On this basis, a topological beam splitter was designed and analyzed. Results show that the beam splitting ratio obtained by the system is in the wide range of 0.2–3.5. Our research enriches the implementation of topological photonics, provides potential applications for topological boundary states in terahertz technology, and offers a new avenue for the design of current optical integrated devices.

Highly Tunable Light Absorber Based on Topological Interface Mode Excitation of Optical Tamm State.

Optical absorbers based on Tamm plasmon states are known for their simple structure and high operational efficiency. However, these absorbers often have limited absorption channels, and it is challenging to continuously adjust their light absorption rates. Here, we propose a Tamm plasmon state optical absorber composed of a layered stack structure consisting of one-dimensional topological photonic crystals and graphene nano-composite materials. Using the four-by-four transfer matrix method, we investigate the structural relationship of the absorber. Our results reveal that topological interface states (TISs) effectively excite the optical Tamm state (OTS), leading to multiple absorption peaks. This expands the number of absorption channels, with the coupling number of the TIS determining the transmission quality of these channels-a value further adjustable by the period number of the photonic crystals. Tuning the filling factor, refractive index, and thickness of the graphene nano-composite material allows for a wide range of control over the device's absorption rate, from 0 to 1. Additionally, adjusting the defect layer thickness, incident angle, and Fermi energy enables us to control the absorber's operational bandwidth and the switching of its absorption effect. This work presents a new approach to expanding the tunability of optoelectronic devices.

Optical properties of cylindrical topological photonic crystal heterostructures

This paper uses a modified transfer matrix method to investigate the optical properties of a cylindrical topological photonic crystal heterostructure composed of two cylindrical photonic crystals. Topological photonic crystals are novel structures with topological edge states capable of field confinement and robust propagation. Numerical results showed that when the sum of the phases of the reflection coefficients of the two cylindrical photonic crystals is zero, a topological edge state occurs inside their overlapping band gaps. In the linear regime, the peak frequency of the topological edge states undergoes a redshift as the incidence angle increases. An increase in the incidence angle leads to a decrease (increase) in the Full width at half maximum of the E-polarized (H-polarized) topological edge states. As the incidence angle increases, the frequency separation between the E-polarized and H-polarized topological edge states increases, causing the cylindrical heterostructure to work as a polarizer. The performance of the cylindrical topological photonic crystal heterostructure as a polarizer is evaluated in the linear and nonlinear regimes. We showed that the peak frequency of the topological edge states undergoes a redshift irrespective of their polarization state as the intensity of the input light increases. We found that the structure has a good performance in the nonlinear regime due to the higher displacement in E-polarized topological edge states compared to H-polarized topological edge states. The findings of this paper might be beneficial in the construction of polarization-maintaining optical fiber, which has specific applications in telecommunications, fiber optic sensing, interferometry, and quantum key distribution.

Improved performance of temperature sensors based on the one-dimensional topological photonic crystals comprising hyperbolic metamaterials

This paper seeks to progress the field of topological photonic crystals (TPC) as a promising tool in face of construction flaws. In particular, the structure can be used as a novel temperature sensor. In this regard, the considered TPC structure comprising two different PC designs named PC1 and PC2. PC1 is designed from a stack of multilayers containing Silicon (Si) and Silicon dioxide (SiO2), while layers of SiO2 and composite layer named hyperbolic metamaterial (HMM) are considered in designing PC2. The HMM layer is engineered using subwavelength layers of Si and Bismuth Germinate, or BGO (Bi4Ge3O12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{Bi}}_{4}{\ ext{Ge}}_{3}{\ ext{O}}_{12}$$\\end{document}). The mainstay of our suggested temperature sensor is mainly based on the emergence of some resonant modes inside the transmittance spectrum that provide the stability in the presence of the geometrical changes. Meanwhile, our theoretical framework has been introduced in the vicinity of transfer matrix method (TMM), effective medium theory (EMT) and the thermo-optic characteristics of the considered materials. The numerical findings have extensively introduced the role of some topological parameters such as layers’ thicknesses, filling ratio through HMM layers and the periodicity of HMM on the stability or the topological features of the introduced sensor. Meanwhile, the numerical results reveal that the considered design provides some topological edge states (TESs) of a promising robustness and stability against certain disturbances or geometrical changes in the constituent materials. In addition, our sensing tool offers a relatively high sensitivity of 0.27 nm/°C.

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.

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.

Inverse design of topological photonic time crystals via deep learning

Photonic time crystals are a new kind of photonic system in modern optical physics, leading to devices with new properties in time. However, so far, it is still a challenge to design photonic time crystals with specific topological states due to the complex relations between time crystal structures and topological properties. Here, we propose a deep-learning-based approach to address this challenge. In a photonic time crystal with time inversion symmetry, each band separated by momentum gaps can have a non-zero quantized Berry phase. We show that the neural network can learn the relationship between time crystal structures and Berry phases, and then determine the crystal structures of photonic time crystals based on given Berry phase properties. Our work shows a new way of applying machine learning to the inverse design of time-varying optical systems and has potential extensions to other fields, such as time-varying phononic devices.

Topology classification in bi-anisotropic topological photonic crystals via the Wilson loop approach [Invited

Topological photonic crystals have attracted tremendous attention due to their promise of robust optical properties and great potential for applications in on-chip devices. Numerous successful experimental demonstrations have shown or proved their topological properties, however, many of them turn out to have a nature of fragile topological phases. Here, using theoretical methods of fragile topology, we analyze two cases of topological photonic crystals with preserved time reversal symmetry, which utilize (1), the intrinsic duality and bi-anisotropy, and (2), accidental duality and structural bi-anisotropy respectively to induce their topological order. Our results show that the former case belongs to a Wannier-obstructed type of topological phase, indicating strong topological protection in their edge states. However, the latter meta-waveguide designs with structural bi-anisotropy widely implemented in experiments are Wannierizable, implying the fragile properties of their topology and gapped edge spectra. Our results provide new insights into the topological properties of photonic crystals as well as other bosonic systems with time-reversal symmetry.

1D Topological Photonic Crystal based Nanosensor for Tuberculosis Detection.

In this study, we present a nanosized biosensor based on the photobiological properties of one-dimensional (1D) topological photonic crystals (PCs). A topological structure had been designed by combining two photonic crystal structures (PC 1 and PC 2) comprised of functional material layers, Si and SiO2. These two, PC 1 and PC 2, differ in terms of the thickness and arrangement of these dielectric materials. We carried out a comparison between two distinct topological photonic crystals: one using random photonic crystals, and the other featuring a mirror heterostructure. Tuberculosis may be diagnosed by inserting a sensor layer into 1D topological photonic crystals. The sensing process is based on the refractive indexes of the analytes in the sensor layer. When the 1D-topological heterostructure-based PC and its mirror-image structures are stacked together, the sensor becomes more efficient for analyte detection than the conventional PCs. The random-based topological photonic crystal outperformed the heterostructure-based topological photonic crystal in analyte sensing. Photonic media witness notable blue shifts due to the analytes' variations in refractive index. The numerical results of the sensor are computed using the transfer matrix approach. Effective results are achieved by optimizing the thicknesses of the sensor layer and dielectric layers; number of periods and incident angle. In normal incident light, the developed sensor shows a high sensitivity of 1500 nm/RIU with a very low limit of detection in the order of 2.24E-06 RIU and a high-quality factor of 30659.54.

Reconfigurable topological wave routing based on tunable valley kink states and valley-polarized chiral edge states.

Valley kink states and valley-polarized chiral edge states, whose topologically protected one-way propagation property provides a promising solution for manipulating light waves, have recently attracted considerable attention in topological photonics. However, it remains a great challenge to realize flexibly tunable dispersion for two different topological states and to develop a dynamically controllable topological photonic platform for switching topological wave routing. In this work, we propose a reconfigurable topological wave routing structure in the telecommunication frequency range, where phase-change material Sb2S3 cylinders with tunable refractive index are embedded into each topological channel to dynamically tune the dispersion of topological edge states. Via switching the phase states of Sb2S3 between amorphous and crystalline, we numerically demonstrate some unique applications of the proposed topological photonic crystals, such as topological optical switches, dual-channel selective transport, and controllable multi-channel intersection waveguides. More importantly, by digitally encoding each waveguide channel without the requirement of controlling each unit cell in the bulk domain, the proposed topological photonic platform provides a convenient and easy-to-implement solution for achieving dynamically reconfigurable topological wave routing propagation. Besides, the unique features of immunity against bending interface with disorders demonstrate the robustness of the topological wave propagation. Our proposed topological photonic platform has potential applications for designing intelligent photonic devices and opens up an avenue for advanced integrated photonic systems with reconfigurability.

Harpoon-shaped topological photonic crystal for on-chip beam splitter

Harpoon-shaped topological photonic crystal for on-chip beam splitter

Ultrabroadband valley transmission and corner states in valley photonic crystals with dendritic structure

In photonic crystal systems, topologically protected edge states and corner states can be achieved by breaking spatial inversion symmetry, which is expected to be applied to topologically protected lasers, optical communication and integrated photonics. However, designing ultrabroadband topological photonic crystals is still a challenge. In this work, we propose a valley photonic crystal composed of dendritic structures, which can realize valley transmission with a relative bandwidth up to 59.65%. Compared with the previously reported two-dimensional broadband photonic crystals with 32.02% bandwidth, the relative bandwidth of the proposed valley transmission is increased by almost 100%. Theoretical analysis, numerical simulation and experimental measurement all confirm flexible manipulation of electromagnetic wave propagation paths. Ultrabroadband topological waveguides with the zigzag and armchair interface are demonstrated, which can achieve experimentally 58.71% and 36.78% relative bandwidth, respectively. In addition, several topological channel intersections are designed. Finally, two types of corner states with valley switchability and selectivity are demonstrated.

Edge and corner states in non-Hermitian second-order topological photonic crystals

The PT symmetric phase transition existing in the gain-loss boundary of non-Hermitian second-order topological photonic crystals is investigated. The variation of the 2D bulk polarization of the photonic bands is analyzed as the gain-loss quantity increases. By tuning the gain or loss strength, topological edge states can appear at the interface between different non-Hermitian topologically nontrivial photonic crystals. Both the edge and corner states are studied in a topological cavity composed of a square closed domain wall between gain and loss domains. Calculated results show the non-Hermitian cavity has better mode localization of the electric field than the Hermitian one. Besides, the existence of the non-Hermitian induced states does not require strict balance of the gain and loss.

Strain to shine: stretching-induced three-dimensional symmetries in nanoparticle-assembled photonic crystals

Stretching elastic materials containing nanoparticle lattices is common in research and industrial settings, yet our knowledge of the deformation process remains limited. Understanding how such lattices reconfigure is critically important, as changes in microstructure lead to significant alterations in their performance. This understanding has been extremely difficult to achieve due to a lack of fundamental rules governing the rearrangements. Our study elucidates the physical processes and underlying mechanisms of three-dimensional lattice transformations in a polymeric photonic crystal from 0% to over 200% strain during uniaxial stretching. Corroborated by comprehensive experimental characterizations, we present analytical models that precisely predict both the three-dimensional lattice structures and the macroscale deformations throughout the stretching process. These models reveal how the nanoparticle lattice and matrix polymer jointly determine the resultant structures, which breaks the original structural symmetry and profoundly changes the dispersion of photonic bandgaps. Stretching induces shifting of the main pseudogap structure out from the 1st Brillouin zone and the merging of different symmetry points. Evolutions of multiple photonic bandgaps reveal potential optical singularities shifting with strain. This work sets a new benchmark for the reconfiguration of soft material structures and may lay the groundwork for the study of stretchable three-dimensional topological photonic crystals.

Topological Directional Coupler

AbstractInterferometers and beam splitters are fundamental building blocks for photonic neuromorphic and quantum computing machinery. In waveguide‐based photonic integrated circuits, beam‐splitting is achieved with directional couplers that rely on transition regions where the waveguides are adiabatically bent to suppress back‐reflection. In this study, a novel, compact approach for introducing guided mode coupling is presented. Along the multimodal domain wall between topological photonic crystals, the photonic spin is conserved to suppress back‐reflection, and the topological protection of the valley degree of freedom is relaxed to implement tunable beam splitting. Rapid advancements in chip‐scale topological photonics suggest that the proposed simultaneous utilization of multiple topological degrees of freedom could benefit the development of novel photonic computing platforms.