Photonic Topological States Research Articles

Broadband Multiple Topological Rainbows

AbstractTopological photonics offers enhanced control over electromagnetic fields by providing a platform for robust trapping and guiding topological states of light. The topological rainbow can separate and distribute different wavelengths of topological photonic states into different positions, but related topological devices have not yet been fully explored. In this work, topological rainbows are realized by inserting a sandwiched gradient structure in the topological waveguide to realize the topological edge states. A robust one‐way slow‐light coupling state is realized to broaden the frequency range of the formed topological rainbow with the robust transmission. Thus, multiple topological rainbows are realized by combining the topological property with immunity to backscattering and coupling states of the slow light. Accordingly, light can spread, separate, and thus be trapped at different positions in different directions. This work provides a new way to reconfigure the topological rainbow and brings opportunities to study nanophotonic topological devices.

Small mode volume topological photonic states in one-dimensional lattices with dipole-quadrupole interactions

We study the topological photonic states in one-dimensional lattices analog to the Su-Schrieffer-Heeger model beyond the dipole approximation. The electromagnetic resonances of the lattices supported by near-field interactions between the plasmonic nanoparticles are studied analytically with coupled dipole-quadrupole method. The topological phase transition in the bipartite lattices is determined by the change of Zak phase. Our results reveal the contribution of quadrupole moments to the near-field interactions and the band topology. It is found that the topological edge states in nontrivial lattices have both dipolar and quadrupolar nature. The quadrupolar edge states are not only orthogonal to the dipolar edge states, but also spatially localized at different sublattices. Furthermore, the quadrupolar topological edge states, which coexist at the same energy with the quadrupolar flat band have shorter localization length and hence smaller mode volume than the conventional dipolar edge states. The findings deepen our understanding in topological systems that involve higher-order multipoles, or in analogy to the wave functions in quantum systems with higher-orbital angular momentum, and may be useful in designing topological systems for confining light robustly and enhancing light-matter interactions.

On-chip nanophotonic topological rainbow

The era of Big Data requires nanophotonic chips to have large information processing capacity. Multiple frequency on-chip nanophotonic devices are highly desirable for density integration, but such devices are more susceptible to structural imperfection because of their nano-scale. Topological photonics provides a robust platform for next-generation nanophotonic chips. Here we give an experimental report of an on-chip nanophotonic topological rainbow realized by employing a translational deformation freedom as a synthetic dimension. The topological rainbow can separate, slow, and trap topological photonic states of different frequencies into different positions. A homemade scattering scanning near-field optical microscope with high resolution is introduced to directly measure the topological rainbow effect of the silicon-based photonic chip. The topological rainbow based on synthetic dimension have no restrictions for optical lattice types, symmetries, materials, wavelength band, and is easy for on-chip integration. This work builds a bridge between silicon chip technologies and topological photonics.

Asymptotically exact photonic approximations of chiral symmetric topological tight-binding models

Topological photonic edge states, protected by chiral symmetry, are attractive for guiding wave energy as they can allow for more robust guiding and greater control of light than alternatives; however, for photonics, chiral symmetry is often broken by long-range interactions. We look to overcome this difficulty by exploiting the topology of networks, consisting of voids and narrow connecting channels, formed by the spaces between closely spaced perfect conductors. In the limit of low frequencies and narrow channels, these void–channel systems have a direct mapping to analogous discrete mass–spring systems in an asymptotically rigorous manner and therefore only have short-range interactions. We demonstrate that topological tight-binding models that are protected by chiral symmetries, such as the SSH model and square-root semimetals, are reproduced for these void–channel networks with appropriate boundary conditions. We anticipate, moving forward, that this paper provides a basis from which to explore continuum photonic topological systems, in an asymptotically exact manner, through the lens of a simplified tight-binding model.

Hyperbolic shear polaritons in low-symmetry crystals

The lattice symmetry of a crystal is one of the most important factors in determining its physical properties. Particularly, low-symmetry crystals offer powerful opportunities to control light propagation, polarization and phase1–4. Materials featuring extreme optical anisotropy can support a hyperbolic response, enabling coupled light–matter interactions, also known as polaritons, with highly directional propagation and compression of light to deeply sub-wavelength scales5. Here we show that monoclinic crystals can support hyperbolic shear polaritons, a new polariton class arising in the mid-infrared to far-infrared due to shear phenomena in the dielectric response. This feature emerges in materials in which the dielectric tensor cannot be diagonalized, that is, in low-symmetry monoclinic and triclinic crystals in which several oscillators with non-orthogonal relative orientations contribute to the optical response6,7. Hyperbolic shear polaritons complement previous observations of hyperbolic phonon polaritons in orthorhombic1,3,4 and hexagonal8,9 crystal systems, unveiling new features, such as the continuous evolution of their propagation direction with frequency, tilted wavefronts and asymmetric responses. The interplay between diagonal loss and off-diagonal shear phenomena in the dielectric response of these materials has implications for new forms of non-Hermitian and topological photonic states. We anticipate that our results will motivate new directions for polariton physics in low-symmetry materials, which include geological minerals10, many common oxides11 and organic crystals12, greatly expanding the material base and extending design opportunities for compact photonic devices.

Cavity confinement in defect-based honeycomb photonic crystals and the design of waveguide–cavity Fano-coupler for dielectric loss sensing

Honeycomb photonic crystal (PhCs) also known as photonic graphene exhibits salient features such as common complete photonic bandgap, topological states, and degrees of freedom to manipulate local density of states for efficient light–matter interactions. In this work, we report the cavity confinement offered by the six different point defect geometries of honeycomb PhCs. It is found that the reported point defect geometries are capable of supporting high confinement with low effective mode area of the order of 10−4 m2. To make use of this cavity confinement, a Fano-coupler is designed based on waveguide–cavity (WG-C) interactions in honeycomb PhC. The transmission/reflection profiles of a WG-C geometry shows typical Fano resonances with the quality factor of the order of 104. Comparing square and triangular PhCs, honeycomb WG-C shows a relatively stable Fano-lineshape resonance for a variation in imaginary part of the dielectric permittivity (ɛr′′) of an unknown dielectric material loaded at the center of the cavity from 0 to 0.01. The proposed WG-C Fano-coupler is suitable for dielectric loss sensing over a conventional cavity perturbation method, in which Fano resonance is sustained with Q factor variation of 25,805 to 2431 for ɛr′′ variation from 0 to 0.01, respectively. Due to the nature of PhC cavity decay dynamics, two different linear sensitive regimes with the dielectric loss sensitivity of 96.901/ɛr′′ (for ɛr′′=0 to 0.005) and 26.911/ɛr′′ (for ɛr′′=0.005 to 0.01) are observed. We anticipate that the cavity confinement and Fano-interactions reported in honeycomb PhCs might be useful not only to explore sensing elements but also for unraveling light–matter interactions in cavity quantum electrodynamics, quantum optics and lasing systems.

Experimental observation of multiple edge and corner states in photonic slabs heterostructures

The photonic topological insulator has become an important research topic with a wide range of applications. Especially the higher-order topological insulator, which possesses gapped edge states and corner or hinge states in the gap, provides a new scheme for the control of light in a hierarchy of dimensions. In this paper, we propose a heterostructure composed of ordinary-topological-ordinary (OTO) photonic crystal slabs. Two coupled edge states (CESs) are generated due to the coupling between the topological edge states of the ordinary-topological interfaces, which opens up an effective way for high-capacity photonic transport. In addition, we obtain a new band gap between the CESs, and the two kinds of coupled corner states (CCSs) appear in the OTO bend structure. In addition, the topological corner state is also found, which arises from the filling anomaly of a lattice. Compared with the previous topological photonic crystal based on C-4 lattice, CESs, CCSs, and the topological corner state are all directly observed in experiment by using the near-field scanning technique, which makes the manipulation of the electromagnetic wave more flexible. We also verify that the three corner states are all robust to defects. Our work opens up a new way for guiding and trapping the light flow and provides a useful case for the coupling of topological photonic states.

Perspective on the topological rainbow

Topological photonics provides a robust platform for the study of nanophotonic devices. The topological rainbow can be used to separate, slow, and trap topological photonic states of different frequencies at different positions. Although numerous reports have investigated the construction of traditional rainbow devices, limited methods have been proposed to realize topological rainbow phenomena and devices. In this Perspective, we provide an overview of the basic concept and mechanisms of rainbow trapping. A topological rainbow is discussed in terms of the implementation of synthetic dimensions. Additionally, recent advances of the topological rainbow are presented for elastic and acoustic waves. We introduce current physical methods of realizing the topological rainbow and discuss potential applications in physics and engineering.

Dual-mode of topological rainbow in gradual photonic heterostructures

In this letter, a method to realize topological rainbow trapping is presented, which is composed of gradual trivial-nontrivial-trivial heterostructures based on two-dimensional photonic crystals with C-4 symmetry. In the proposed sandwiched structure, the two coupled topological edge states with different frequencies are separated and trapped in different positions, due to group velocity of near to zero. We have achieved the dual-mode of topological rainbow in one structure, and the dual-mode of topological rainbow under one mode excitation is also realized by using a simple bend design. The immunity to defects is also investigated and it is found our slowing light system has strong robustness. Finite element method simulation results verify our idea, and our work opens up a new approach for frequency routing of topological photonic states.

Gauge‐Induced Floquet Topological States in Photonic Waveguides

AbstractTremendous efforts are devoted to the research of exotic photonic topological states, in which Floquet systems suggest new engineered topological phases and provide a powerful tool to manipulate the optical fields. Here, a gauge‐induced topological state localized at the interface between two gauge‐shifted Floquet photonic lattices with the same topological order is demonstrated. The quasienergy band structures reveal that these interface modes belong to the Floquet π modes, which are further found to enable an asymmetric topological transport of this interface mode thanks to the flexible control of the Floquet gauge. The intriguing propagations of the gauge‐induced topological states are experimentally verified in a silicon waveguides platform at near‐infrared wavelengths, which show broadband working wavelengths and robustness against the structural fluctuations. This work provides a new route in manipulating optical topological modes by Floquet engineering and inspires more possibilities in photonics integrations.

Corner States in 2D Square Lattice Second‐Order Photonic Topological Insulators Composed of L‐Shaped Sublattices

Higher‐order photonic topological states have recently attracted great attention due to the realizability of photonic nanocavities with high robustness against structural disorder. Herein, it is revealed that square‐lattice photonic crystals with L‐shaped sublattices exhibit second‐order photonic topological phases. In the approximation considering only the nearest‐neighbor interactions, the photonic system with an expanded sublattice exhibits topologically nontrivial phase represented by the nonzero polarization, approaching in the extreme case, whereas it is trivial for the cases of the shrunken one. Unlike the conventional square lattices with four dielectric rods, the proposed photonic systems have a single corner state for squared topological boundaries, while they exhibit three corner states when they have triangular boundaries. Although the weakly anisotropic systems with the expanded L‐shaped sublattices exhibit different corner states, they disappear for a substantial increase of anisotropy. The results obtained in this work enrich the diversity and understanding of higher‐order photonic topological systems and pave the way for wide applications of higher‐order topological phases in photonics, including coherent nanosources based on nanolasing and nonlinear frequency conversion.

Metasurfaces: Near‐Field Characterization of Higher‐Order Topological Photonic States at Optical Frequencies (Adv. Mater. 18/2021)

In article number 2004376 Andrea Alù, Alexander B. Khanikaev, and co-workers apply a near-field technique to investigate a higher-order topological photonic metasurface. They show that the near-field profiles reveal the topological nature of the optical modes (depicted as a torus). Topology manifests in the displacement of the Wannier center, giving rise to the topological dipole polarization and emergence of the topological boundary states observed in the optical near-field.

Topological Rainbow Concentrator Based on Synthetic Dimension.

Synthetic dimension provides a new platform for realizing topological photonic devices. Here, we propose a method to realize a rainbow concentrator of topological photonic states based on the synthetic dimension concept. The synthetic dimension is constructed using a translational degree of freedom of the nanostructures inside the unit cell of a two-dimensional photonic crystal. The translational deformation induces a nontrivial topology in the synthetic dimension, which gives rise to robust interface states at different frequencies. The topological rainbow can trap states with different frequencies, controlled by tuning the spatial modulation of interface state group velocities. The operation frequency as well as the bandwidth of the topological rainbow can be easily tuned by controlling the band gap of the photonic crystal. The topological principle can be applied to photonic crystals of any symmetry and arbitrary material composition, as long as a complete band gap exists. This Letter provides a new and general scheme for the realization of a topological rainbow concentrator and will be useful for the development of topological photonic devices.

Near-Field Characterization of Higher-Order Topological Photonic States at Optical Frequencies.

Higher-order topological insulators (HOTIs) represent a new type of topological system, supporting boundary states localized over boundaries, two or more dimensions lower than the dimensionality of the system itself. Interestingly, photonic HOTIs can possess a richer physics than their original condensed matter counterpart, supporting conventional HOTI states based on tight-binding coupling, and a new type of topological HOTI states enabled by long-range interactions. Here, a new mechanism to establish all-dielectric infrared HOTI metasurfaces exhibiting both types of HOTI states is proposed, supported by a topological transition accompanied by the emergence of topological Wannier-type polarization. Two kinds of near-field experimental studies are performed: i) the solid immersion spectroscopy and ii) near-field imaging using scattering scanning near-field optical microscopy to directly observe the topological transition and the emergence of HOTI states of two types. It is shown that the near-field profiles indicate the displacement of the Wannier center across the topological transition leading to the topological dipole polarization and emergence of the topological boundary states. The proposed all-dielectric HOTI metasurface offers a new approach to confine the optical field in micro- and nano-scale topological cavities and thus paves the way to achieve a novel nanophotonic technology.

Topological rainbow based on graded topological photonic crystals.

Topological photonic crystal provides a robust platform for nanophotonic devices. However, few reports have been found to realize multiple frequency routing based on topological photonic states, which have restricted further applications in the field of nanophotonic devices. Here, for the first time, to the best of our knowledge, we propose an efficient method to realize a topological rainbow based on graded dielectric topological photonic crystals, which are constructed by changing the degree of lattice contraction and expansion. The topological edge states of different frequencies are separated and trapped at different positions. The all-dielectric planar nanostructures of graded topological photonic crystals are low-loss, robust, and easy for integration. This Letter plays a key role in the use of robust nanophotonic wavelength routers, optical storage, and optical buffers.

Multiband Photonic Topological Valley‐Hall Edge Modes and Second‐Order Corner States in Square Lattices

AbstractRobust multiband photonic topological edge states are of great importance for photonic applications, including nonlinear wavelength conversion. In particular, higher‐order photonic topological states provide the realizability of photonic nanoresonators with high robustness against structural disorder of photonic crystals. This work reveals that multiband photonic topological valley‐Hall edge states and second‐order corner states can be observed in square lattice photonic crystals consisting of triangular dielectric rods. For small sizes of the triangles, multiband gapless edge modes propagate through the photonic topological waveguide. Their transmission characteristics and robustness against the structural defects have been evaluated for linear and Z‐shaped interfaces. When the size of the triangles increases, most of edge bands become gapped and one can obtain disorder‐immune multiband second‐order topological corner states, which is the core result of this report. The results obtained in this work can find important applications for nonlinear topological frequency conversion.

Zero GVD slow-light originating from a strong coupling of one-way modes in double-channel magneto-optical photonic crystal waveguides.

We have studied the coupling effect of topological photonic states in a double-channel magneto-optical photonic crystal waveguide by introducing a two-stranded ordinary Al2O3 photonic crystal as the coupling layer. There exist both M1 (odd) and M2 (even) one-way modes simultaneously in the bandgap. Interestingly, M1 mode is always a fast-light mode with large group velocity (vg) and large group velocity dispersion (GVD) regardless what the radius (RA) of Al2O3 rods is. However, when RA is appropriate, M2 mode becomes a very slow-light mode exhibiting near-zero vg and zero GVD simultaneously. The physical reason of such slow-light is attributed to the strong coupling effect between the one-way edge modes in both sub-waveguides. Furthermore, the simulation results show that the robustness of both the fast- and slow-light modes are extremely strong against perfect electric conductor defect and the one-way transmittance is close to 100%. Besides, the PEC defect can cause significant phase delay. These results hold promise for many fields such as signal processing, optical modulation, and the design of various topological devices.

Topological photonic states in artificial microstructures [Invited

Topological photonics provides a new opportunity for the examination of novel topological properties of matter, in which the energy band theory and ideas in topology are utilized to manipulate the propagation of photons. Since the discovery of topological insulators in condensed matter, researchers have studied similar topological effects in photonics. Topological photonics can lead to materials that support the robust unidirectional propagation of light without back reflections. This ideal transport property is unprecedented in traditional optics and may lead to radical changes in integrated optical devices. In this review, we present the exciting developments of topological photonics and focus on several prominent milestones of topological phases in photonics, such as topological insulators, topological semimetals, and higher-order topological phases. We conclude with the prospect of novel topological effects and their applications in topological photonics.

Photonic Topological States Mediated by Staggered Bianisotropy

AbstractPhotonic topological structures supporting spin‐momentum locked topological states underpin a plethora of prospects and applications for disorder‐robust routing of light. One of the cornerstone ideas to realize such states is to exploit uniform bianisotropic response in periodic structures with appropriate lattice symmetries, which together enable the topological bandgap. Here, it is demonstrated that staggered bianisotropic response gives rise to the topological states even in a simple lattice geometry whose counterpart with uniform bianisotropy is topologically trivial. The reason behind this intriguing behavior is in the difference in the effective coupling between the resonant elements with the same and with the opposite signs of bianisotropy. Based on this insight, a one‐dimensional (1D) equidistant array is designed, which consists of high‐index all‐dielectric particles with alternating signs of bianisotropic response. The array possesses chiral symmetry and hosts topologically protected edge states pinned to the frequencies of hybrid magneto‐electric modes. These results pave a way toward flexible engineering of topologically robust light localization and propagation by encoding spatially varying bianisotropy patterns in photonic structures.

Details of the topological state transition induced by gradually increased disorder in photonic Chern insulators.

Using two well-defined empirical parameters, we numerically investigate the details of the disorder-induced topological state transition (TST) in photonic Chern insulators composed of two-dimensional magnetic photonic crystals (MPCs). The TST undergoes a gradual process, accompanied with some interesting phenomena as the disorder of rod positions in MPCs increases gradually. This kind of TST is determined by the competition among the topologically protected edge state, disorder-induced wave localizations and bulk states in the system. More interestingly, the disorder-induced wave localizations almost have no influence on the one-way propagation of the original photonic topological states (PTSs), and the unidirectional nature of the PTSs at the edge area can survive even when the bulk states arise at stronger disorders. Our results provide detailed demonstrations for the deep understanding of fundamental physics underlying topology and disorder and are also of practical significance in device fabrication with PTSs.