Valley Photonic Crystals Research Articles

Bound valley edge states in the continuum

Topological valley photonics provides a unique way to manipulate the flow of light. In general, valley edge states that exhibit unidirectional propagation and are immune to defects and disorders could be realized at the interface between two valley photonic crystals with opposite valley Chern numbers. Herein, by merging the physics of valley edge states and bound states in the continuum, we propose and numerically demonstrate a novel, to the best of our knowledge, concept of edge states termed bound valley edge states in the continuum, which enjoys the topological features of valley edge states, such as, unidirectional propagation and immunity to disorders, but are formed at the interface between air and a single valley photonic crystal. Our results not only provide an effective way to reduce the size of valley photonic structures but also facilitate new applications where the proposed concept of bound valley edge states in the continuum could be exploited for optical sensing and unidirectional waveguiding.

Boundary configured chiral edge states in valley topological photonic crystal.

Chiral edge states (CESs) have been demonstrated at the external boundary of a valley photonic crystal (VPC), with flexibly tunable group velocity and frequency range by adjusting the boundary structure. In this work, we show parallel and antiparallel CESs located at two opposite VPC-air boundaries, which contain wave components belonging to opposite valleys or the same valley. In addition, we design a meta-structure with four types of air-contacted boundary that support CESs in different frequency ranges. The structure also has an internal interface channel supporting the valley edge state that bridges the top and bottom boundaries. We show that the CESs, while excited at a given port, can be exclusively guided to the other three ports, depending on the operating frequency. Our work provides an alternative way to design compact topological devices for optical waveguides and wave splitters.

On/Off Switching of Valley Topological Edge States in the Terahertz Region

Topological photonic devices provide a powerful platform to control the flow of light because their topologically protected edge states can be immune to backscattering and be robust to impurities, disorders, and defects. As one of the topological photonic systems, valley photonic crystals have attracted great attention because they can achieve a large bandgap and be easily combined with modern micro-nano fabrication technology. Terahertz photonic devices are of enormous interest in next-generation communications. Here, we design a valley photonic crystal consisting of a triangular lattice with three metal rod scatterers. By rotating the three metal rods in opposite directions to break the inversion symmetry, we achieve a bandgap width of up to 70% and observe the transport of the edge states in the terahertz region. By replacing part of the structure with phase change material VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , on/off switching of the terahertz photonic topological edge states is realized, and the attenuation can be also modeled by adjusting the size of the VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> region. The proposed regime has potential applications in sensing and 6G communications.

Role of unit-cell defects in terahertz topological ring resonators

We demonstrate a terahertz topological ring resonator based on all-dielectric valley photonic crystals. A triangular ring-shaped topological edge is coupled to a straight topological waveguide by suitably merging two valley photonic crystals. The resonant characteristics are investigated for different asymmetry parameters as well as for different domain interfaces (zigzag and bridge type) constituting the ring resonator. In the topological ring resonator, ultra-narrowband high quality (Q)-factor resonances are excited. Then, multiple defect states are intentionally introduced into the domain interfaces, and the influences of defects on the terahertz propagation and the Q-factors are examined for both types of domain interfaces. Numerical simulation studies on terahertz transmission reveal a resonance redshift of ∼ 10 G H z due to the introduction of multiple defect states. Such resonance redshift is attributed to the alteration in the effective refractive indices of the structure. Very high Q-factors within the range of 1240–840 are achieved even in the presence of several unit-cell defects owing to strong field confinements in the domain interface. This research can open up new routes for the development of nonlinear technologies and other advanced on-chip topological devices at THz frequencies.

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.

Engineering rainbow trapping and releasing in valley photonic crystal with electro-optical material

Topological photonic insulators provide a robust platform for controlling the flow of light. Here, we propose a method to realize slow light rainbow trapping and releasing based on valley photonic crystals, which is created by gradually increasing the structure parameter. The edge waves of different frequencies are spatially separated and trapped at different positions to form topological rainbow trapping. Furthermore, the system is constructed by electric-optical material whose refractive index is tuned by applied voltages. Therefore, the switchable between slow light trapping states and releasing states can be realized by tuning the external voltage. The position where the wave stops propagating is given by theoretical analysis and numerical simulation. These results offer a novel, to the best of our knowledge, scheme for realizing multi-frequency routing. Such a structure could find application prospects in optical buffers, optical storage, and other optical communication devices.

Unidirectional transmission of visible region topological edge states in hexagonal boron nitride valley photonic crystals.

Here we theoretically design valley photonic crystals (VPCs) based on two-dimensional (2D) hexagonal boron nitride (hBN) materials, which are able to support topological edge states in the visible region. The edge states can achieve spin-dependent unidirectional transmission with a high forward transmittance up to 0.96 and a transmission contrast of 0.99. We further study the effect of refractive index on transmittance and bandwidth, and it is found that with the increase of refractive index, both transmittance and bandwidth increased accordingly. This study opens new possibilities in designing unidirectional transmission devices in the visible region and will find broad applications.

Topological cavity laser with valley edge states.

Topological edge states (ES) arise at the boundary between spatial domains with diverse topological properties in photonic crystals, which can transmit unidirectionally to suppress the backscattering and robustly to be immune to defects and disorders. In addition, optical devices with arbitrary geometries of cavities, such as lasers, are expected to be designed on the basis of ES. Herein, we first propose a topological cavity laser based on a honeycomb lattice of ring holes with the bearded interface in two-dimensional (2D) all-dielectric valley photonic crystals (VPhCs) at telecommunication wavelengths. Specifically, we construct a topological cavity using topological valley edge states (VES) and further study the lasing action of the optically pumped cavity with high-quality factors. Our findings could provide opportunities for practical applications of VES-based lasers as ultra-small light sources with the topological protection.

Plasmon-induced transparency in a reconfigurable composite valley photonic crystal.

We propose a new kind of reconfigurable topological valley photonic crystal (TVPC), and a novel topological waveguide can be formed by constructing a domain wall between two TVPCs with opposite valley-Chern indices. The topological waveguide mode in the composite TVPC has large group refractive index. A topologically protected coupled waveguide cavity system is then designed by introducing a hexagonal ring cavity at the center of the straight domain wall of a combined TVPC, in which a narrow plasmon induced transparency window rises at 3.8848 GHz with a Q-factor of 1387 and a maximum group refractive index as high as 186. We propose a notch filter with a resonant frequency of 3.8852 GHz and a very high Q-factor of 10224. By changing the refractive index of liquid crystals via an external voltage applied between two parallel metal plates, the filter can be switched between band-pass and band-stop based on the reconfigurable topological interface state.

Terahertz Band Communications With Topological Valley Photonic Crystal Waveguide

The sixth generation (6 G) communication standard is expected to include support for very-high data rates (over 100 Gbit/s) and device electronics will require processors with on-chip communications able to support such high bandwidths. Although the terahertz band possesses ample bandwidth, conventional THz waveguides suffer from high bending losses and are sensitive to process defects. The recent revelation of the topological valley photonic crystal (VPC), which exhibits near zero-loss bends, zero back-scattering and zero junction-area, holds much promise for future high speed inter-device communications. Low dispersion in the photonic bandgap region as the number of bends increase is demonstrated through simulation and experiment of the transmission and group delay characteristics. Through comprehensive communications experiments we demonstrate online results below the forward error correction level including an 108-Gbit/s bit rate using multi-level modulation for a 10 mm straight VPC waveguide and a 62.5-Gbit/s bit-rate for a ten sharp bended structure.

Topological Nanophotonic Wavelength Router Based on Topology Optimization.

The topological nanophotonic wavelength router, which can steer light with different wavelength signals into different topological channels, plays a key role in optical information processing. However, no effective method has been found to realize such a topological nanophotonic device. Here, an on-chip topological nanophotonic wavelength router working in an optical telecom band is designed based on a topology optimization algorithm and experimentally demonstrated. Valley photonic crystal is used to provide a topological state in the optical telecom band. The measured topological wavelength router has narrow signal peaks and is easy for integration. This work offers an efficient scheme for the realization of topological devices and lays a foundation for the future application of topological photonics.

Topological protection of continuous frequency entangled biphoton states

Abstract Topological quantum optics that manipulates the topological protection of quantum states has attracted special interests in recent years. Here we demonstrate valley photonic crystals implementing topologically protected transport of the continuous frequency entangled biphoton states. We numerically simulate the nonlinear four-wave mixing interaction of topological valley kink states propagating along the interface between two valley photonic crystals. We theoretically clarify that the signal and idler photons generated from the four-wave mixing interaction are continuous frequency entangled. The numerical simulation results imply that the entangled biphoton states are robust against the sharp bends and scattering, giving clear evidence of topological protection of entangled photon pairs. Our proposal paves a concrete way to perform topological protection of entangled quantum states operating at telecommunication wavelengths.

Effect of asymmetry on terahertz transmissions in topological photonic crystals comprising of dielectric rod structures

We numerically demonstrate robust terahertz (THz) transmissions in a topological photonic crystal comprised of dielectric rod structures. Topological edge states (i.e., the vortex states) in the structure are excited via a zig-zag domain boundary at the interface of two nontrivial valley photonic crystals (VPCs). A comprehensive study of the effect of asymmetry (defined as δd=d1−d2) on transmission loss and bandwidth is performed for three different kinds of domain boundaries: straight, Z-shape, and Ω-shape. An increase in the bandwidth of the topological THz transmission is achieved with the increasing asymmetry. The study further demonstrates blue shifting of the topological transmission bandwidth with the increase in asymmetry. An optimized value of the asymmetry parameter is obtained based on the bandwidth as well as the transmission loss. The most robust propagation in terms of the widest bandwidth and low loss transmission is achieved with asymmetry ≥0.25a. The robust THz transmission is attributed to the strong edge modes confinement at the domain boundary of the VPC due to intervalley scattering suppression at this optimal value. Our observations open the path for a strong electromagnetic wave flow in the THz regime with a high transmission, which could be useful in photonic broadband communication and other on-chip applications at THz frequencies, particularly for 6G communications.

Wave Steering by Relaying Interface States in a Valley-Hall-Derived Photonic Superlattice

Topological notions in physics have become a powerful perspective that leads to the discoveries of topological interface states (TISs). In this work, we present a scheme to achieve negative refraction by leveraging the properties of TISs in a valley photonic crystal (VPC). Due to the chiral characteristics, one type of the TISs deterministically possesses negative dispersion relation, which can cause an obliquely incident wave to undergo a negative lateral shift. By stacking multiple VPC interfaces, the TIS-induced lateral shifts can relay in the transmitted wave towards the far side of incidence. The resultant outgoing wave appears to have undergone negative refraction. This finding is verified in microwave experiments. Our scheme opens new application scenarios for topological systems in bulk wave manipulations.

Novel optical XOR/OR logic gates based on topologically protected valley photonic crystals edges

Valley photonic crystals (VPCs) have provided a novel topological photonic platform to manipulate light. In this work, we construct zigzag and armchair domain walls using two-dimensional silicon VPCs, the edges between domains of opposite valley indices link to the corresponding topological invariant. We study the light transmission of these edges with defects and sharp bent corners. We design all-optical logic gates at telecommunication wavelength with both XOR and OR functions based on the valley-contrasting edges. Topologically protected waveguides own high transmission and backscattering-immune features, and the coupling process of different edge modes results in interference for logic functions. Compared with traditional photonic crystal logic gates, our device shows outstanding properties, including robust transmission, higher contrast ratio and more compact footprint. Furthermore, our work also shows the potential of topological photonics to be applied in optical logic circuits.

Topological Cavity Based on Slow-Light Topological Edge Mode for Broadband Purcell Enhancement

Slow light in topological valley photonic crystal structures offers possibilities to enhance light-matter interaction. We report a topological cavity based on slow-light topological edge modes for broadband Purcell enhancement. The topological edge modes with large group indices over 100 can be realized with a bearded interface between two topologically distinct valley photonic crystals, featuring the greatly enhanced Purcell factor because of the increased local density of states. In the slow-light regime, the topological cavity supports much more cavity modes with a higher quality factor than that in the fast-light regime, which is both demonstrated theoretically and experimentally. We demonstrate the cavity enables the broadband Purcell enhancement together with substantial Purcell factor, benefiting from dense cavity modes with a high quality factor in a wide spectral range. It has great benefit for the realization of high-efficiency quantum-dot-based single-photon sources and entangled-photon sources with less restriction on spectral match. Such a topological cavity could serve as a significant building block toward the development of photonic integrated circuits with embedded quantum emitters.

Topological edge states in an all-dielectric terahertz photonic crystal

We present an analysis of the robustness of topological edge states in an all-dielectric photonic crystal slab in the terahertz (THz) frequency domain. We initially design a valley photonic crystal (VPC) exhibiting a nontrivial band topology. The excitation of the topological edge states in the structure is facilitated through a zigzag domain wall constructed by interfacing two types of VPCs with distinct band topologies. The robustness of the excited edge states is probed with respect to the magnitude and the sign of the asymmetry in terms of the hole diameters in the VPC, for different domain interfaces. Our study reveals that the topological edge states in the VPC structure are achieved only when the domain walls are formed by the larger air holes (i.e., asymmetry parameter has a positive value). In the case of the domain walls formed by relatively smaller air holes (i.e., asymmetry parameter has a negative value), the topological protection of the edge states is forbidden. For positive asymmetry, we demonstrate that the topological transport of THz becomes more robust with the increasing magnitude of asymmetry in the VPC structure. A robust propagation of topological edge states and strong confinement of electromagnetic fields within the domain wall are observed for asymmetry ranging from 28% to 42% in our structure. We have adopted a generic technique and therefore, the results of our study could be achieved at other frequency regimes by scaling the size parameters of the structure appropriately. At THz frequencies, such extensive analysis on the robustness of the topological edge states could be relevant for the realization of low-loss waveguides for 6G communication and other integrated photonic devices.

A Topological Photonic Ring-Resonator for On-Chip Channel Filters

A topologically protected ring-resonator formed in valley photonic crystals is proposed and fabricated on a silicon slab. The unidirectional transmission and robustness against structure defects of its resonant modes are illustrated. Coupled with topological waveguides, the topological ring is functioned as notch and channel-drop filters. The work opens up a new avenue for developing advanced chip-integrated photonic circuits with attributes of topological photonics.

Experimental demonstration of topological slow light waveguides in valley photonic crystals.

We experimentally demonstrate topological slow light waveguides in valley photonic crystals (VPhCs). We employed a bearded interface formed between two topologically-distinct VPhCs patterned in an air-bridged silicon slab. The interface supports both topological and non-topological slow light modes below the light line. By means of optical microscopy, we observed light propagation in the topological mode in the slow light regime with a group index ng over 30. Furthermore, we confirmed light transmission via the slow light mode even under the presence of sharp waveguide bends. In comparison between the topological and non-topological modes, we found that the topological mode exhibits much more efficient waveguiding than the trivial one, demonstrating topological protection in the slow light regime. This work paves the way for exploring topological slow-light devices compatible with existing photonics technologies.

Design of broadband all-dielectric valley photonic crystals at telecommunication wavelength

Topological photonic crystals (TPC) can effectively suppress the backscattering from defects and achieve unidirectional transmission with high forward transmittance, thus becoming a promising candidate in integrated photonic chip applications. Among different TPCs, the valley photonic crystals (VPCs) based on quantum valley Hall effect (QVHE) originating from valley-dependent spin-split bulk bands, can achieve spin-dependent unidirectional transmission at telecommunication wavelength with conventional dielectric material, such as silicon, which can be readily fabricated by current CMOS nanofabrication techniques. Therefore, VPCs recently attract broad attention. Generally, a large working bandwidth is preferred in optical communications and information processing, which should be as large as possible. Currently, the maximum working bandwidth of VPCs at telecommunication wavelength is limited to about 130 nm. Based on theoretical analysis and numerical simulation, a triangular lattice VPC composed of all-dielectric silicon-based triangular air holes is proposed, and the working bandwidth at 1550 nm is further extended to 229 nm. By combining two mirror-inversed VPCs, we observe the valley–spin locking behavior results in selective net spin flow inside bulk VPCs to achieve unidirectional transmission with a high forward transmittance up to 0.97. Moreover, the intensity distributions of the incident light show neglectable scattering loss at the sharp edge of the zigzag and Ω shape waveguides, confirming the achievement of scattering immune propagation. The designed VPCs not only offer a possibility to expand the working bandwidth, but also can be applied to device applications in integrated photonics and information processing using spin-dependent transportation.