arXiv subjects

Liqin Tang

Publications and source records attributed to Liqin Tang.

At least 19 recordsLinked to original sources

arXiv2026

Fractal hierarchy enables exponential scaling of topological boundary states

Exponential growth describes an extremely rapid process ubiquitous across mathematics and diverse physical, biological, and technological systems. Here, we introduce a class of fractal-inspired lattices that combine long-range periodic order with self-similar hierarchy, establishing a structural motif that enables exponential scaling of topological boundary states. We demonstrate this phenomenon in (i) a quasi-one-dimensional lattice chain constructed from Koch-curve unit cells and (ii) a two-dimensional periodic tiling lattice composed of Sierpinski-gasket unit cells. We show that, for suitable coupling parameters, both the number of topological boundary states $N_{\ell}$ and the number of topological minigaps $M_{\ell}$ grow exponentially with the fractal generation index $\ell$. We find that $N_{\ell}$ is an integer multiple of $M_{\ell}$, with the integer determined by the underlying symmetry. This hierarchical scaling law is captured by multi-topological-phase theory and confirmed experimentally in laser-written photonic lattices. Our results identify fractal hierarchy as a materials architecture principle for controlling boundary-state multiplicity, revealing an interplay between topology, self-similar geometry, and periodic order. More broadly, this work suggests a route to synthetic materials and integrated photonic platforms in which large numbers of robust boundary modes can be engineered within compact architectures.

physics.optics↗

arXiv2026

A Non-Abelian Route to Z2 Non-Hermitian Skin Effects

The non-Hermitian skin effect (NHSE), characterized by extensive boundary accumulation of eigenstates under open boundary conditions, has emerged as a central phenomenon in non-Hermitian physics. Conventionally, the NHSE arises from either non-reciprocal couplings or onsite gain and loss combined with synthetic gauge fields. Existing studies, however, have been largely confined to frameworks with Abelian-coupling, leaving the role of non-Abelian couplings essentially unexplored. Here, we demonstrate that non-Abelian-couplings can generate the NHSE, giving rise to a time-reversal-symmetry-protected Z2 skin effect with pseudospin-dependent boundary localization and dynamical pseudospin separation. Experimentally, we implement a representative four-level model using a programmable topolectrical circuit and directly observe both the predicted NHSE and the boundary-induced pseudospin-inversion reflection. Our work establishes a fundamental link between non-Abelian coupling and non-Hermitian topology, opening new avenues for realizing non-reciprocity-free topological materials and devices.

physics.optics↗

arXiv2026

Topological photonics in one-dimensional settings

Over the past decade, topological photonics has emerged as a vibrant field, attracting significant attention and witnessing remarkable advancements. This growth can be attributed to its fundamental appeal and the unique opportunities it offers for unconventional control of light, promising innovations in next-generation photonic devices. At the heart of topological photonics lies the one-dimensional (1D) SSH model. Originally conceived to elucidate the physics of a molecular chain of polyacetylene, this model has found widespread applications in exploring a wide range of topological phenomena in photonics and beyond. In this chapter, we aim to provide an overview of topological photonics in one-dimensional (1D) settings. After briefly introducing paradigmatic 1D models, including the SSH, Rice-Mele, and AAH models, we review recent advances in experimental studies and applications of topological photonics based on 1D platforms. Our discussion highlights demonstrated examples, such as the nonlinear tuning of topological states in both Hermitian and non-Hermitian photonic SSH lattices, as well as nonlinear harmonic generation and topological lasing in SSH-type photonic microstructures. We further discuss characteristic topological phenomena in other representative 1D settings, including Floquet systems, topological pumping, quasicrystals, and synthetic non-Hermitian systems. Finally, we examine selected examples of two-dimensional (2D) photonic topological crystalline insulators that are closely linked to the SSH model. Towards the end, we summarize the chapter and provide a list of key contributions, together with an outlook on possible future directions in 1D topological photonics. While this review focuses specifically on 1D topological photonics, it is not intended to be comprehensive or exhaustive.

physics.optics↗

arXiv2026

Optical Self-Trapping and Nonlinear Light-Matter Interactions in Biological Soft Matter

Low-scattering, deep-penetration light transport in biological media remains a pivotal challenge for biophotonic technologies, including biomedical imaging, optical diagnostics, and photodynamic therapy. This review builds upon and extends our earlier studies of nonlinear optical self-trapping and optically induced waveguiding in biological suspensions, such as human erythrocytes and cyanobacteria, where light-matter coupling is governed by optical-force-mediated particle redistribution. Recent progress has revealed increasingly rich and complex regimes, including the propagation and nonlinear self-action of structured (vortex) beams in biological environments, as well as nonlinear responses dominated by thermally driven mechanisms in absorptive biomolecular solutions (e.g., heme and chlorophyll). We place particular emphasis on distinctive nonlinear phenomena observed in these systems, including spatial self-phase modulation, optical-force-induced sculpturing of effective energy landscapes, and quasi-waveguide formation in soft, heterogeneous biological media. We conclude by highlighting emerging opportunities to harness these nonlinear behaviors for deep-tissue imaging, label-free biosensing, and the realization of biocompatible photonic structures and devices assembled directly from living or hybrid biological matter.

physics.optics↗

arXiv2026

Controllable Lateral Optical Forces on Janus Particles in Fluid Media

Optical forces - studied since the earliest days of laser physics - continue to reveal rich dynamics and enable powerful tools for manipulation of objects on micro- and nanoscales, and even individual atoms. Lateral optical forces, which act perpendicular to the direction of beam propagation, are particularly intriguing but have largely been restricted to interface geometries such as air - water boundaries. Here, we realize tunable lateral optical force entirely within a fluid environment by using Janus particles: dielectric microspheres half-coated with gold. We show that the lateral optical force arises from scattering asymmetry induced by the asymmetric structure of the particles; it can be tuned by adjusting the polarization angle of a linearly polarized beam, but also particle parameters including their size and orientation. Experimentally, we directly observe fully reversible lateral propulsion of Janus particles in water merely by rotating the polarization direction, in excellent agreement with theoretical predictions. These results establish a new mechanism for programmable, polarization-controlled optical manipulation, with promising implications for biophotonics, microfluidics, and active soft-matter systems.

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arXiv2026

Phase Transitions and Topological Protection in Anyonic-PT-Symmetric Lattices

Parity-time (PT) symmetry and anti-PT symmetry have attracted extensive interest for their non-Hermitian spectral properties, particularly the emergence of purely real and imaginary eigenvalues in their symmetry-unbroken regime, respectively. Recently, these two scenarios have been unified under a more general framework known as anyonic-PT symmetry, yet its physical implications in waveguide platforms and corresponding topological features in extended lattice systems remain largely unexplored. Here, the phase transitions and topological protection in anyonic-PT-symmetric systems are systematically investigated in waveguide lattices. In the symmetry-unbroken regime, the arguments of all bulk eigenvalues are constrained to two discrete values separated by {\pi}, leading to distinctive oscillatory propagation dynamics accompanied by controlled amplification or dissipation. In the case of one-dimensional lattice, the energy bands exhibit a gap closing and reopening during phase transition. Moreover, in the symmetry-unbroken regime, the topological edge states emerge within the bulk gap and are protected by a generalized pseudo-anyonic-Hermiticity (PAH) symmetry. Our results establish anyonic-PT symmetry as a new tunable degree of freedom for non-Hermitian waveguide systems, where the eigenvalue argument provides a natural quantity for information encoding. This work broadens the conceptual foundation of topological protection under generalized non-Hermitian symmetries.

physics.optics↗

arXiv2026

Subsymmetry-protected compact edge states

Sub-symmetry (SubSy) protected topological states represent a concept that goes beyond the conventional framework of symmetry-protected topological (SPT) phases, demonstrating that topological boundary states can remain robust even when the pertinent symmetry holds only in a subset of Hilbert space. Typical SPT and SubSy boundary states decay exponentially into the bulk, which means they are not confined in just few lattice sites close to the boundary. Here, we introduce topologically compact edge states protected by SubSy, featuring extreme two-site localization at boundaries of a lattice, without any decay into the bulk. The compactness arises from local destructive interference at the boundary, while topological protection is ensured by SubSy, characterized by quantized winding numbers. Experimentally, we observe compact edge states in laser-written photonic lattices with engineered rhombic-like unit cells, confirming their robustness against perturbations under both chiral symmetry and SubSy conditions. Our results highlight the potential of SubSy protection for achieving topological confinement of light, paving the way for applications in compact waveguides, lasers, and high-sensitivity photonic sensors.

physics.optics↗

arXiv2024

Bulk-hole correspondence and inner robust boundary modes in singular flatband lattices

Topological entities based on bulk-boundary correspondence are ubiquitous, from conventional to higher-order topological insulators, where the protected states are typically localized at the outer boundaries (edges or corners). A less explored scenario involves protected states that are localized at the inner boundaries, sharing the same energy as the bulk states. Here, we propose and demonstrate what we refer to as the bulk-hole correspondence - a relation between the inner robust boundary modes (RBMs) and the existence of multiple "holes" in singular flatband lattices, mediated by the immovable discontinuity of the bulk Bloch wavefunctions. We find that the number of independent flatband states always equals the sum of the number of independent compact localized states and the number of nontrivial inner RBMs, as captured by the Betti number that also counts the hole number from topological data analysis. This correspondence is universal for singular flatband lattices, regardless of the lattice shape and the hole shape. Using laser-written Kagome lattices as a platform, we experimentally observe such inner RBMs, demonstrating their real-space topological nature and robustness. Our results may extend to other singular flatband systems beyond photonics, including non-Euclidean lattices, providing a new approach for understanding nontrivial flatband states and topology in hole-bearing lattice systems.

physics.optics↗

arXiv2023

Multiple flat bands and localized states in photonic super-Kagome lattices

We demonstrate multiple flat bands and compact localized states (CLSs) in a photonic super-Kagome lattice (SKL) that exhibits coexistence of singular and nonsingular flat bands within its unique band structure. Specifically, we find that the upper two flat bands of an SKL are singular - characterized by singularities due to band touching with their neighboring dispersive bands at the Brillouin zone center. Conversely, the lower three degenerate flat bands are nonsingular, and remain spectrally isolated from other dispersive bands. The existence of such two distinct types of flat bands is experimentally demonstrated by observing stable evolution of the CLSs with various geometrical shapes in a laser-written SKL. We also discuss the classification of the flat bands in momentum space, using band-touching singularities of the Bloch wave functions. Furthermore, we validate this classification in real space based on unit cell occupancy of the CLSs in a single SKL plaquette. These results may provide insights for the study of flatband transport, dynamics, and nontrivial topological phenomena in other relevant systems.

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arXiv2023

Observation of topologically distinct corner states in "bearded" photonic Kagome lattices

Kagome lattices represent an archetype of intriguing physics, attracting a great deal of interest in different branches of natural sciences, recently in the context of topological crystalline insulators. Here, we demonstrate two distinct classes of corner states in breathing Kagome lattices (BKLs) with "bearded" edge truncation, unveiling their topological origin. The in-phase corner states are found to exist only in the topologically nontrivial regime, characterized by a nonzero bulk polarization. In contrast, the out-of-phase corner states appear in both topologically trivial and nontrivial regimes, either as bound states in the continuum or as in-gap states depending on the lattice dimerization conditions. Furthermore, the out-of-phase corner states are highly localized, akin to flat-band compact localized states, and they manifest both real- and momentum-space topology. Experimentally, we observe both types of corner states in laser-written photonic bearded-edge BKLs, corroborated by numerical simulations. Our results not only deepen the current understanding of topological corner modes in BKLs, but also provide new insight into their physical origins, which may be applied to other topological BKL platforms beyond optics.

physics.optics↗

arXiv2023

Deep learning empowered synthetic dimension dynamics: morphing of light into topological modes

Synthetic dimensions (SDs) opened the door for exploring previously inaccessible phenomena in high-dimensional synthetic space. However, construction of synthetic lattices with desired coupling properties is a challenging and unintuitive task, largely limiting the exploration and current application of SD dynamics. Here, we overcome this challenge by using deep learning artificial neural networks (ANNs) to validly design the dynamics in SDs. We use ANNs to construct a lattice in real space that has a predesigned spectrum of mode eigenvalues. By employing judiciously chosen perturbations (wiggling of waveguides), we show experimentally and theoretically resonant mode coupling and tailored dynamics in SDs, which leads to effective transport or confinement of a complex beam profile. As an enlightening example, we demonstrate morphing of light into a topologically protected edge mode in ANN-designed Su-Schrieffer-Heeger photonic lattices. Such ANN-assisted construction of SDs advances towards utopian networks, opening new avenues in fundamental research beyond geometric limitations. Our findings may offer a flexible and efficient solution for mode lasing, optical switching, and communication technologies.

physics.optics↗

arXiv2023

Photonic realization of a generic type of graphene edge states exhibiting topological flat band

Cutting a honeycomb lattice (HCL) can end up with three types of edges (zigzag, bearded and armchair), as is well known in the study of graphene edge states. Here we theoretically investigate and experimentally demonstrate a class of graphene edges, namely, the twig-shaped edges, using a photonic platform, thereby observing edge states distinctive from those observed before. Our main findings are: (i) the twig edge is a generic type of HCL edges complementary to the armchair edge, formed by choosing the right primitive cell rather than simple lattice cutting or Klein edge modification; (ii) the twig edge states form a complete flat band across the Brillouin zone with zero-energy degeneracy, characterized by nontrivial topological winding of the lattice Hamiltonian; (iii) the twig edge states can be elongated or compactly localized along the boundary, manifesting both flat band and topological features. Such new edge states are realized in a laser-written photonic graphene and well corroborated by numerical simulations. Our results may broaden the understanding of graphene edge states, bringing about new possibilities for wave localization in artificial Dirac-like materials.

physics.optics↗

arXiv2022

Mapping and manipulation of topological singularities: from photonic graphene to T-graphene

Topological singularities (TSs) in momentum space give rise to intriguing fundamental phenomena as well as unusual material properties, attracting a great deal of interest in the past decade. Recently, we have demonstrated universal momentum-to-real-space mapping of TSs and pseudospin angular momentum conversion using photonic honeycomb (graphene-like) and Lieb lattices. Such mapping arises from the Berry phase encircling the Dirac or Dirac-like cones, and is thus of topological origin. In this paper, we briefly present previous observations of topological charge conversion, and then we present our first theoretical analysis and experimental demonstration of TS mapping in a new T-graphene lattice. Unlike other lattices, there are two coexisting but distinct TSs located at different high-symmetry points in the first Brillouin zone of T-graphene, which enables controlled topological charge conversion in the same lattice. We show active manipulation of the TS mapping, turning the two TSs into vortices of different helicities, or one into a high-order vortex but the other into a quadrupole. Such TS manipulation and pseudospin-to-orbital conversion may find applications in optical communications and quantum information, and may bring insight into the study of other Dirac-like structures with multiple TSs beyond the 2D photonic platform.

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arXiv2022

Symmetry-protected higher-order exceptional points in staggered flatband rhombic lattices

Higher-order exceptional points (EPs), which appear as multifold degeneracies in the spectra of non-Hermitian systems, are garnering extensive attention in various multidisciplinary fields. However, constructing higher-order EPs still remains as a challenge due to the strict requirement of the system symmetries. Here we demonstrate that higher-order EPs can be judiciously fabricated in PT -symmetric staggered rhombic lattices by introducing not only on-site gain/loss but also nonHermitian couplings. Zero-energy flatbands persist and symmetry-protected third-order EPs (EP3) arise in these systems owing to the non-Hermitian chiral/sublattice symmetry, but distinct phase transitions and propagation dynamics occur. Specifically, the EP3 arises at the Brillouin zone (BZ) boundary in the presence of on-site gain/loss. The single-site excitations display an exponential power increase in the PT -broken phase. Meanwhile, a nearly flatband sustains when a small lattice perturbation is applied. For the lattices with non-Hermitian couplings, however, the EP3 appears at the BZ center. Quite remarkably, our analysis unveils a dynamical delocalization-localization transition for the excitation of the dispersive bands and a quartic power increase beyond the EP3. Our scheme provides a new platform towards the investigation of the higher-order EPs, and can be further extended to the study of topological phase transitions or nonlinear processes associated with higher-order EPs.

physics.optics↗

arXiv2022

Sub-symmetry protected topological states

A hallmark of symmetry-protected topological phases (SPTs) are topologically protected boundary states, which are immune to perturbations that respect the protecting symmetry. It is commonly believed that any perturbation that destroys an SPT phase simultaneously destroys the boundary states. However, by introducing and exploring a weaker sub-symmetry (SubSy) requirement on perturbations, we find that the nature of boundary state protection is in fact more complex. We demonstrate that the boundary states are protected by only the SubSy using prototypical Su-Schrieffer-Heeger (SSH) and breathing Kagome lattice (BKL) models, even though the overall topological invariant and the SPT phase are destroyed by SubSy preserving perturbations. By employing judiciously controlled symmetry breaking in photonic lattices, we experimentally demonstrate such SubSy protection of topological states. Furthermore, we introduce a long-range hopping symmetry in BKLs, which resolves a debate on the topological nature of their corner states. Our results apply to other systems beyond photonics, heralding the possibility of exploring the intriguing properties of SPT phases in the absence of full symmetry in different physical contexts.

physics.optics↗

arXiv2022

Topological flatband loop states in fractal-like photonic lattices

Noncontractible loop states (NLSs) are recently realized topological entity in flatband lattices, arising typically from band touching at a point where a flat band intersects one or more dispersive bands. There exists also band touching across a plane, where one flat band overlaps another all over the Brillouin zone without crossing a dispersive band. Such isolated plane-touching flat bands remain largely unexplored. For example, what are the topological features associated with such flatband degeneracy? Here, we demonstrate for the first time to our knowledge nontrivial NLSs and robust boundary modes in a system with such degeneracy. Based on a tailored photonic lattice constructed from the well-known fractal Sierpinski gasket, we theoretically analyze the wavefunction singularities and the conditions for the existence of the NLSs. We show that the NLSs can exist in both singular and nonsingular flat bands, as a direct reflection of the real-space topology. Experimentally, we observe directly such flatband NLSs in a laser-written Corbino-shaped fractal-like lattice. This work not only leads to a deep understanding of the mechanism behind the nontrivial flatband states, but also opens up new avenues to explore fundamental phenomena arising from the interplay of flatband degeneracy, fractal structures and band topology.

physics.optics↗

arXiv2021

Realization of second-order photonic square-root topological insulators

Square-root higher-order topological insulators (HOTIs) are recently discovered new topological phases, with intriguing topological properties inherited from a parent lattice Hamiltonian. Different from conventional HOTIs, the square-root HOTIs typically manifest two paired non-zero energy corner states. In this work, we experimentally demonstrate the second-order square-root HOTIs in photonics for the first time to our knowledge, thereby unveiling such distinct corner states. The specific platform is a laser-written decorated honeycomb lattice (HCL), for which the squared Hamiltonian represents a direct sum of the underlying HCL and breathing Kagome lattice. The localized corner states residing in different bandgaps are observed with characteristic phase structures, in sharp contrast to discrete diffraction in a topologically trivial structure. Our work illustrates a scheme to study fundamental topological phenomena in systems with coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions, and may bring about new possibilities in topology-driven photonic devices.

physics.optics↗

arXiv2021

Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices

We propose a scheme to realize parity-time (PT) symmetric photonic Lieb lattices of ribbon shape and complex couplings, thereby demonstrating the higher-order exceptional point (EP) and Landau-Zener Bloch (LZB) oscillations in presence of a refractive index gradient. Quite different from non-Hermitian flatband lattices with on-site gain/loss, which undergo thresholdless PT symmetry breaking, the spectrum for such quasi-one-dimensional Lieb lattices has completely real values when the index gradient is applied perpendicular to the ribbon, and a triply degenerated (third-order) EP with coalesced eigenvalues and eigenvectors emerges only when the amplitude of gain/loss ratio reaches a certain threshold value. When the index gradient is applied parallel to the ribbon, the LZB oscillations exhibit intriguing characteristics including asymmetric energy transition and pseudo-Hermitian propagation as the flatband is excited. Meanwhile, a secondary emission occurs each time when the oscillatory motion passes through the EP, leading to distinct energy distribution in the flatband when a dispersive band is excited. Such novel phenomena may appear in other non-Hermitian flatband systems. Our work may also bring insight and suggest a photonic platform to study the symmetry and topological characterization of higher-order EPs that may find unique applications in for example enhancing sensitivity.

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