Nonlinear Imaging of Nanoscale Topological Corner States

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.

Spectroscopic and Interferometric Sum-Frequency Imaging of Strongly Coupled Phonon Polaritons in SiC Metasurfaces

Phonon polaritons enable waveguiding and localization of infrared light with extreme confinement and low losses. The spatial propagation and spectral resonances of such polaritons are usually probed with complementary techniques such as near-field optical microscopy and far-field reflection spectroscopy. Here, infrared-visible sum-frequency spectro-microscopy is introduced as a tool for spectroscopic imaging of phonon polaritons. The technique simultaneously provides sub-wavelength spatial resolution and highly-resolved spectral resonance information. This is implemented by resonantly exciting polaritons using a tunable infrared laser and wide-field microscopic detection of the upconverted light. The technique is employed to image hybridization and strong coupling of localized and propagating surface phonon polaritons in a metasurface of SiC micropillars. Spectro-microscopy allows to measure the polariton dispersion simultaneously in momentum space by angle-dependent resonance imaging, and in real space by polariton interferometry. Notably, it is possible to directly image how strong coupling affects the spatial localization of polaritons, inaccessible with conventional spectroscopic techniques. The formation of edge states is observed at excitation frequencies where strong coupling prevents polariton propagation into the metasurface. The technique is applicable to the wide range of polaritonic materials with broken inversion symmetry and can be used as a fast and non-perturbative tool to image polariton hybridization and propagation.

Polaritonic states trapped by topological defects

The miniaturization of photonic technologies calls for a deliberate integration of diverse materials to enable novel functionalities in chip-scale devices. Topological photonic systems are a promising platform to couple structured light with solid-state matter excitations and establish robust forms of 1D polaritonic transport. Here, we demonstrate a mechanism to efficiently trap mid-IR structured phonon-polaritons in topological defects of a metasurface integrated with hexagonal boron nitride (hBN). These defects, created by stitching displaced domains of a Kekulé-patterned metasurface, sustain localized polaritonic modes that originate from coupling of electromagnetic fields with hBN lattice vibrations. These 0D higher-order topological modes, comprising phononic and photonic components with chiral polarization, are imaged in real- and Fourier-space. The results reveal a singular radiation leakage profile and selective excitation through spin-polarized edge waves at heterogeneous topological interfaces. This offers impactful opportunities to control light-matter waves in their dimensional hierarchy, paving the way for topological polariton shaping, ultrathin structured light sources, and thermal management at the nanoscale.

Local Markers for Crystalline Topology

Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches currently used to classify bulk topological crystalline phases cannot predict the existence, localization, or spectral isolation of any resulting boundary-localized modes. While interfaces between materials in different crystalline phases must have topological states at some energy, these states need not appear within the band gap, and thus may not be useful for applications. Here, we derive a class of local markers for identifying material topology due to crystalline symmetries, as well as a corresponding measure of topological protection. As our real-space-based approach is inherently local, it immediately reveals the existence and robustness of topological boundary-localized states, yielding a predictive framework for designing topological crystalline heterostructures. Beyond enabling the optimization of device geometries, we anticipate that our framework will also provide a route forward to deriving local markers for other classes of topology that are reliant upon spatial symmetries.

Higher-order hybrid topological bound states in a non-Hermitian system

Higher-order topological states, such as the corner and pseudo-hinge states, have been discovered in both Hermitian and non-Hermitian systems. These states have inherent high-quality factors that make them useful in the application of photonic devices. In this work, we design a non-Hermiticity solely induced Su-Schrieffer-Heeger (SSH) lattice and demonstrate the existence of diverse higher-order topological bound states in the continuum (BICs). In particular, we first uncover some hybrid topological states that occur in the form of BICs in the non-Hermitian system. Furthermore, these hybrid states with an amplified and localized field have been demonstrated to excite nonlinear harmonic generation with high efficiency. The appearance of these topological bound states will advance the study of the interplay of topology, BICs, and non-Hermitian optics.

Higher-order topological corner state in a reconfigurable breathing kagome lattice consisting of magnetically coupled LC resonators

Higher-order topological insulators are attracting attention from fundamental interest to fascinating applications, owing to the topological properties with higher-order topological corner states. Breathing kagome lattice is a prospective platform which can support higher-order topological corner states. Here, we experimentally demonstrate that higher-order topological corner states are supported in a breathing kagome lattice consisting of magnetically coupled resonant coils. The winding direction of each coil is determined to hold C₃ symmetry for each triangle unit cell, enabling to emerge higher-order topological corner states. In addition, topological and trivial phases can be switched by changing the distances between the coils. The emergence of corner states in the topological phase is experimentally observed through admittance measurements. As an illustration, wireless power transfer is performed between the corner states, and between the bulk and corner states. The proposed configuration is a promising platform for not only investigating topological properties of the breathing kagome lattice but also an alternative mechanism of selective wireless power transfer.

Second harmonic generation by matching the phase distributions of topological corner and edge states

Second harmonic generation (SHG) in topological photonic crystals is chiefly concerned with frequency conversion between the same topological states. However, little attention has been paid to the effect of coupling between different topological states on the SHG. In this study, we propose a method for achieving optimal SHG in a topological cavity by matching the phase distributions of the electric fields of the topological corner state (TCS) and topological edge state (TES). Our results show that the intrinsic efficiency can be improved when the phase distributions of the fundamental wave within the TCS and the second harmonic wave within the TES have the same symmetry. Otherwise, conversion efficiency will be greatly inhibited. With this method, we achieved an optimal intrinsic efficiency of 0.165%. Such a platform may enable the development of integrated nanoscale light sources and on-chip frequency converters.

A topological nonlinear parametric amplifier

Topological boundary states are well localized eigenstates at the boundary between two different bulk topologies. As long as bulk topology is preserved, the topological boundary mode will endure. Here, we report topological nonlinear parametric amplification of light in a dimerized coupled waveguide system based on the Su-Schrieffer-Heeger model with a domain wall. The good linear transmission properties of the topological waveguide arising from the strong localization of light to the topological boundary is demonstrated through successful high-speed transmission of 30 Gb/s non-return-to-zero and 56 Gb/s pulse amplitude 4-level data. The strong localization of a co-propagating pump and probe to the boundary waveguide is harnessed for efficient, low power optical parametric amplification and wavelength conversion. A nonlinear tuning mechanism is shown to induce chiral symmetry breaking in the topological waveguide, demonstrating a pathway in which Kerr nonlinearities may be applied to tune the topological boundary mode and control the transition to bulk states.

Advances and Prospects in Topological Nanoparticle Photonics

Topological nanophotonics is a new avenue for exploring nanoscale systems from visible to THz frequencies, with unprecedented control. By embracing their complexity and fully utilizing the properties that make them distinct from electronic systems, we aim to study new topological phenomena. In this Perspective, we summarize the current state of the field and highlight the use of nanoparticle systems for exploring topological phases beyond electronic analogues. We provide an overview of the tools needed to capture the radiative, retardative, and long-range properties of these systems. We discuss the application of dielectric and metallic nanoparticles in nonlinear systems and also provide an overview of the newly developed topic of topological insulator nanoparticles. We hope that a comprehensive understanding of topological nanoparticle photonic systems will allow us to exploit them to their full potential and explore new topological phenomena at very reduced dimensions.

Metasurfaces with high-Q resonances governed by topological edge state

Achieving high-quality (Q)-factor resonances in metasurfaces is essential for various applications, including nano-lasers, nonlinear optics, and quantum optics. In this work, we propose a high-Q metasurface using a topological strategy: constructing the metasurface by stacking two conjugated nanopillar arrays with different topological invariants. Our study shows that a topological edge state steadily appears at the interfaces of the nanopillars, and a sharp transmission resonance with a Q-factor of more than 1000 can be obtained. The sensing application of such high-Q topological metasurface is also demonstrated, whose figure of merit reaches approximately 145. The proposed strategy and underlying theory can open up new avenues to realize ultrasharp resonances, which can promote numerous potential applications, such as biosensing, optical modulation, and slow-light devices.

Observation of Edge Solitons in Topological Trimer Arrays

We report the experimental observation of nonlinear light localization and edge soliton formation at the edges of fs-laser written trimer waveguide arrays, where transition from nontopological to topological phases is controlled by the spacing between neighboring trimers. We found that, in the former regime, edge solitons occur only above a considerable power threshold, whereas in the latter one they bifurcate from linear states. Edge solitons are observed in a broad power range where their propagation constant falls into one of the topological gaps of the system, while partial delocalization is observed when considerable nonlinearity drives the propagation constant into an allowed band, causing coupling with bulk modes. Our results provide direct experimental evidence of the coexistence and selective excitation in the same or in different topological gaps of two types of topological edge solitons with different internal structures, which can rarely be observed even in nontopological systems. This also constitutes the first experimental evidence of formation of topological solitons in a nonlinear system with more than one topological gap.

Spin-Polarized Fractional Corner Charges and Their Photonic Realization

We demonstrate that a spin degree of freedom can introduce additional texture to higher order topological insulators (HOTIs), manifesting in novel topological invariants and phase transitions. Spin-polarized mid-gap corner states of various multiplicities are predicted for different HOTI phases, and novel bulk-boundary correspondence principles are defined based on bulk invariants such as total and spin corner charge. Those are shown to be robust to spin-flipping perturbations. Photonic realizations of spin-linked topological phases are demonstrated in engineered systems using pseudospin.

Second harmonic generation enhancement and directional emission from topological corner state based on the quantum spin Hall effect

Topological corner state has attracted much research interests since it does not obey the conventional bulk-edge correspondence and enables tightly confined light within small volumes. In this work, we demonstrate an enhanced second harmonic generation (SHG) from a topological corner state and its directional emission. To this end, we design an all-dielectric topological photonic crystal based on optical quantum spin Hall effect. In this framework, pseudospin states of photons, topological phase, and topological corner state are subsequently constructed by engineering the structures. It is shown that a high Q-factor of 3.66×10¹¹ can be obtained at the corner state, showing strong confinement of light at the corner. Consequently, SHG is significantly boosted and manifests directional out-of-plane emission. More importantly, the enhanced SHG has robustness against a broad class of defects. These demonstrated properties offer practical advantages for integrated optical circuits.

Nonlinear control of photonic higher-order topological bound states in the continuum

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to the HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.