arXiv subjects

C. T. Chan

Publications and source records attributed to C. T. Chan.

At least 19 recordsLinked to original sources

arXiv2026

Exceptional Points in Photonics: From Non-Hermitian Physics to Applications

Open photonic systems provide a versatile platform for non-Hermitian physics, enabling control over complex spectra, transport, and light-matter interactions. Exceptional points (EPs), at which eigenvalues and eigenvectors coalesce and the governing operator becomes defective, play a central role because they combine branch-point spectral topology, nonanalytic perturbative response, and controllable eigenstate conversion. This Review provides a unified framework for EP photonics by systematically distinguishing exceptional degeneracies according to the underlying operator, spectral variable, boundary conditions, and experimentally accessible observables. We discuss Hamiltonian EPs, absorbing EPs associated with scattering zeros, real-frequency scattering-matrix and Jones-matrix EPs, Bloch and Floquet EPs, and Liouvillian EPs in open quantum systems. We review their spectral topology, static and dynamical encircling, higher-order exceptional structures, and coexistence with bound states in the continuum, together with applications in sensing, lasing, coherent absorption, directional scattering, polarization and wavefront control, nonlinear optics, optical storage, nonreciprocal photonics, and quantum photonics. We also critically assess the current limitations, practical challenges, and future perspectives of EP-based photonic technologies, with particular attention to robustness, noise, scalability, and experimentally measurable performance.

physics.optics↗

arXiv2026

Non-Hermitian Skin Effect from Radiative Coupling in a Reciprocal Chiral Medium

We find that long-range radiative coupling through a passive reciprocal chiral medium produces an unusual non-Hermitian skin effect in a chain of electric dipoles. Although the system is reciprocal, the chirality generates polarization-dependent phase accumulation and attenuation, leading to degenerate pairs of skin modes localized at opposite boundaries. We find that the skin mode profile consists of an exponential contribution from an isolated complex-$\beta$ pole and a longer-range tail proportional to $1/[n(\ln n)^2]$, where $n$ is the distance from the occupied boundary measured in lattice sites. Finite-chain calculations show that part of the OBC spectrum contracts toward the Bloch spectrum, whereas the number of boundary-localized modes remains extensive.

cond-mat.other↗

arXiv2026

Integer-Graded Reciprocal Skin Effect from Internal Rotation

A prominent class of reciprocal non-Hermitian skin effects has a $\Z_{2}$ partner structure, in which a binary label records which of two partners occupies which edge. We show that conserved internal rotation extends this binary structure to an unbounded integer-graded hierarchy. Every angular momentum channel is an exactly solvable asymmetric chain with its own integer point-gap winding, while conjugate channels accumulate at opposite edges so that reciprocity is preserved globally. For conserved channels, the classification contains one integer per conjugate pair, with the number of independent integers determined by the internal multiplet. Half-integer spin realizes the symplectic class AII$^{\dagger}$, whose $\Z_{2}$ index is recovered as the parity of the grading. Conjugate-channel mixing destroys the grading and leaves a critical, scale-free skin effect. A cyclic three-site lattice and a passive array of lossy resonators provide minimal realizations.

cond-mat.other↗

arXiv2026

Scalar-Wave Dispersion in Vectorial Photonic Crystals via Site-Adapted p Orbitals

Electromagnetic waves are intrinsically vectorial and require description via polarization, unlike scalar fields such as acoustic pressure or electronic wavefunctions. In three dimensions, the transversality constraint further prevents any globally smooth transverse-polarization frame at the $\Gamma$ point, which would apparently rule out a simple scalar band structure for three-dimensional (3D) photonic crystals. We show here that site-adapted $p$-orbitals can realize scalar-wave dispersion: the induced band representation is isomorphic to the scalar elementary band representation up to a one-dimensional character twist, so the symmetry-enforced degeneracies and compatibility relations are the same. We demonstrate this mechanism experimentally in 3D photonic meta-crystals, where the local $p$-orbital axes adapt from site to site according to symmetry. In contrast to a fixed-polarization reduction (e.g., in 2D), our construction preserves site-polarization textures while simultaneously supporting a scalar network with one amplitude per site. Thus, it offers a pathway from vectorial photonic degrees of freedom to scalar band engineering, keeping polarization as an active design knob.

physics.optics↗

arXiv2026

Exact flat bands in a 3D photonic crystal

Photonic flat bands are hard to engineer because Maxwell's equations are vectorial: transversality obstructs the localized scalar-like bases that generate destructive-interference flat bands in tight-binding models. We show that a three-dimensional metallic network of dipolar cavities joined by waveguide channels--a fully vectorial photonic crystal belonging to space group No. 224--hosts an exact scalar sector, carrying exact flat bands. The twelve-band vector problem contains one self-adaptive radial dipole axis per site whose projection is exactly the scalar four-band Hamiltonian of the same network. A microwave-scale coupled-dipole calculation confirms this scalar-vectorial duality. The result is a symmetry-based design rule for scalar-like flat bands in reciprocal vector media.

physics.optics↗

arXiv2026

Emerging Multidimensional Real-Space Topological Structures at Chiral Bound States in the Continuum

As widely studied topological singularities, bound states in the continuum (BICs) have revealed rich physical properties through their momentum-space topology. Here, we reveal and experimentally demonstrate that magnetically induced chiral BICs possess multidimensional topological structures extending into real space. We design and realize a gyromagnetic photonic crystal slab where magnetic field breaks the time-reversal symmetry and lifts the degeneracy of BICs, creating a pair of chiral BICs with opposite circular polarizations. Near-field scanning measurements reveal phase vortices with quantized topological charges, spatially distributed near-field chirality, and skyrmionic Stokes textures arising from magnetic control. Our work unveils a previously unexplored dimension of BIC topology and establishes gyromagnetic photonic crystals as versatile platforms for manipulating complex topological states.

physics.optics↗

arXiv2025

Scalable Generalized Meta-Spanners Enabling Parallel Multitasking Optical Manipulation

Optical manipulation techniques offer exceptional contactless control but are fundamentally limited in their ability to perform parallel multitasking. To achieve high-density, versatile manipulation with subwavelength photonic devices, it is essential to sculpt light fields in multiple dimensions. Here, we overcome this challenge by introducing generalized optical meta-spanners (GOMSs) based on metasurfaces. Relying on complex-amplitude modulation, this platform generates lens-free, customizable optical fields that suppress diffractive losses. As a result, several advanced functionalities are simultaneously achieved, including longitudinally varying manipulation and in-plane spanner arrays, which outperforms the same operations realized by conventional donut-shaped orbital flows. Furthermore, the particle dynamics is reconfigurable simply by switching the input and output polarizations, facilitating robust multi-channel control. We experimentally validate the proposed approach by demonstrating single-particle dynamics and the parallel manipulation of particle ensembles, revealing exceptional stability for multitasking operations. These results demonstrate an ultracompact platform scalable to a much larger number of optical spanners, advancing metadevices from wavefront sculptors to particle manipulators. We envision that the GOMS will catalyze innovations in cross-disciplinary fields such as targeted drug delivery and cell-level biomechanics.

physics.optics↗

arXiv2025

Analogs of spontaneous emission and lasing in photonic time crystals

We report the first direct mapping of the frequency-resolved local density of states (LDOS) in a photonic time crystal (PTC) implemented as an array of time-periodically modulated LC resonators at microwave frequencies. Broadband white noise probes the system and yields an LDOS lineshape near the momentum gap that can be decomposed into absorptive and dispersive Lorentzian components. The finite LDOS peak at the gap frequency, which grows with modulation strength, implies that the spontaneous emission rate of an emitter coupled to the PTC would be maximized at that frequency. The measured spectra are in good agreement with classical non-Hermitian Floquet theory. As the modulation-induced gain exceeds intrinsic losses, the system undergoes a transition to a narrow-band self-oscillation (lasing) regime. These results open a route to nonequilibrium photonics and bring time-periodic LDOS engineering closer to practical realization.

physics.optics↗

arXiv2025

Unsupervised learning of non-Abelian multi-gap topological phases

Recent experiments have successfully realized multi-band non-Abelian topological insulators with parity-time symmetry. Their topological classification transcends the conventional ten-fold classification, necessitating the use of non-Abelian groups, manifesting novel properties that cannot be described using integer topological invariants. The unique non-commutative multiplication of non-Abelian groups, along with the distinct topological classifications in the context of homotopy with or without a fixed base point, makes the identification of different non-Abelian topological phases more nuanced and challenging than in the Abelian case. In this work, we present an unsupervised learning method based on diffusion maps to classify non-Abelian multi-gap topological phases. The automatic adiabatic pathfinding process in our method can correctly sort the samples in the same phase even though they are not connected by adiabatic paths in the sample set. Most importantly, our method can deduce the multiplication table of the non-Abelian topological charges in a data-driven manner without requiring \textit{a priori} knowledge. Additionally, our algorithm can provide the correct classifications for the samples within both the homotopy with and without a fixed base point. Our results provide insights for future studies on non-Abelian phase studies using machine learning approaches.

cond-mat.mes-hall↗

arXiv2025

Unconventional topological edge states in one-dimensional gapless systems stemming from nonisolated hypersurface singularities

Topologically protected edge states have been extensively studied in systems characterized by the topological invariants in band gaps (also called line gaps). In this study, we unveil a whole new form of edge states that transcends the established paradigms of band-gap topology. In contrast to the traditional stable edge states in topological insulators with specific band gaps, the one-dimensional systems we investigate are inherently gapless with the Brillouin zones being mapped to the loops encircling hypersurface singularities in a higher-dimensional space with parity-time symmetry. These hypersurface singularities are nonisolated degeneracies embedded entirely on exceptional surfaces, rendering the energy gaps in our systems inevitably closed at the intersections of the Brillouin zone loop and the exceptional surfaces. Unexpectedly, such gapless systems still afford topologically protected edge states at system boundaries, challenging the conventional understanding based on band gaps. To elucidate the existence of these edge states in the absence of a band-gap-based invariant, we propose a theoretical framework based on eigen-frame rotation and deformation that incorporates non-Bloch band theory. Finally, we experimentally demonstrate this new form of topological edge states with nonreciprocal circuits for the first time. Our work constitutes a major advance that extends topological edge states from gapped phases to gapless phases, offering new insights into topological phenomena.

cond-mat.mes-hall↗

arXiv2024

Observation of non-Hermitian boundary induced hybrid skin-topological effect excited by synthetic complex frequencies

The hybrid skin-topological effect (HSTE) has recently been proposed as a mechanism where topological edge states collapse into corner states under the influence of the non-Hermitian skin effect (NHSE). However, directly observing this effect is challenging due to the complex frequencies of eigenmodes. In this study, we experimentally observe HSTE corner states using synthetic complex frequency excitations in a transmission line network. We demonstrate that HSTE induces asymmetric transmission along a specific direction within the topological band gap. Besides HSTE, we identify corner states originating from non-chiral edge states, which are caused by the unbalanced effective onsite energy shifts at the boundaries of the network. Furthermore, our results suggest that whether the bulk interior is Hermitian or non-Hermitian is not a key factor for HSTE. Instead, the HSTE states can be realized and relocated simply by adjusting the non-Hermitian distribution at the boundaries. Our research has deepened the understanding of a range of issues regarding HSTE, paving the way for advancements in the design of non-Hermitian topological devices.

physics.optics↗

arXiv2024

Topological Singularities in Metasurface Scattering Matrices: From Nodal Lines to Exceptional Lines

Topological properties of photonic structures described by Hamiltonian matrices have been extensively studied in recent years. Photonic systems are often open systems, and their coupling with the environment is characterized by scattering matrices, which can exhibit topological features as well. In this work, we uncover that topological singularities can be manifested in the scattering matrices of two-dimensional periodic photonic systems with open boundaries in the third dimension, introducing a new topological approach to describe scattering. We elaborate the importance of symmetry and demonstrate that mirror symmetry gives rise to the formation of diabolic points and nodal lines in the three-dimensional frequency-momentum space, which transform into exceptional points and lines in the presence of material loss. These topological features in the eigenvalue structure of the scattering matrix manifest as vortex lines in the cross-polarization scattering phase, providing a direct link between the eigen-problem and observable scattering phenomena in the frequency-momentum space. We demonstrate these phenomena numerically and experimentally using a reflective non-local metasurface. These findings extend the concept of topological singularities to scattering matrices and pave the way for novel photonic devices and wavefront engineering techniques.

physics.optics↗

arXiv2024

Nonreciprocal Local-Resonance Induced Complex Band Hybridization

We study the complex band hybridization induced by nonreciprocal local resonances in photonic crystals. Composed of trimer unit cells, a two-dimensional (2D) magnetophotonic crystal with an analytically obtainable solution is considered. We find that nonreciprocal spectral gap may appear without nonreciprocal transmission and that the imaginary parts of the complex wavevectors $\text{Im}(\mathbf{k})$ may blow up at resonance to give extreme nonreciprocal transmission. We further show that, for a subwavelegnth lattice, the isolation ratio for the nonreciprocal transmission is determined solely by $\text{Im}(\mathbf{k})$ instead of the extensively studied real part $\text{Re}(\mathbf{k})$. Our finding contradicts the common belief that "spectral nonreciprocity [$\omega(\mathbf{k})\neq\omega(-\mathbf{k})$] always implies nonreciprocal transmission".

physics.optics↗

arXiv2024

Realization of time-reversal invariant photonic topological Anderson insulators

Disorder, which is ubiquitous in nature, has been extensively explored in photonics for understanding the fundamental principles of light diffusion and localization, as well as for applications in functional resonators and random lasers. Recently, the investigation of disorder in topological photonics has led to the realization of topological Anderson insulators characterized by an unexpected disorder-induced phase transition. However, the observed photonic topological Anderson insulators so far are limited to the time-reversal symmetry breaking systems. Here, we propose and realize a photonic quantum spin Hall topological Anderson insulator without breaking time-reversal symmetry. The disorder-induced topological phase transition is comprehensively confirmed through the theoretical effective Dirac Hamiltonian, numerical analysis of bulk transmission, and experimental examination of bulk and edge transmissions. We present the convincing evidence for the unidirectional propagation and robust transport of helical edge modes, which are the key features of nontrivial time-reversal invariant topological Anderson insulators. Furthermore, we demonstrate disorder-induced beam steering, highlighting the potential of disorder as a new degree of freedom to manipulate light propagation in magnetic-free systems. Our work not only paves the way for observing unique topological photonic phases but also suggests potential device applications through the utilization of disorder.

physics.optics↗

arXiv2024

Bulk-spatiotemporal vortex correspondence in gyromagnetic double-zero-index media

Photonic double-zero-index media, distinguished by concurrently zero-valued permittivity and permeability, exhibit extraordinary properties not found in nature. Remarkably, the notion of zero-index can be substantially expanded by generalizing the constitutive parameters from null scalars to nonreciprocal tensors with nonzero matrix elements but zero determinants. Here, we experimentally realize such a new class of gyromagnetic double-zero-index metamaterials possessing both double-zero-index features and nonreciprocal hallmarks. As an intrinsic property, this metamaterial always emerges at a spin-1/2 Dirac point of a topological phase transition. We discover and rigorously prove that a spatiotemporal reflection vortex singularity is always anchored to the metamaterial's Dirac point, with the vortex charge being determined by the topological invariant leap across the phase transition. This establishes a unique bulk-spatiotemporal vortex correspondence that extends the protected boundary effects into the time domain and exclusively characterizes topological phase transition points, setting it apart from any pre-existing bulk-boundary correspondence. Based on this correspondence, we propose and experimentally demonstrate a mechanism to deterministically generate optical spatiotemporal vortex pulses with firmly fixed central frequency and momentum, hence showing unparalleled robustness. Our findings uncover deep connections between zero-refractive-index photonics, topological photonics, and singular optics, opening the avenue for the manipulation of space-time topological light fields via the inherent topology of extreme-parameter metamaterials.

physics.optics↗

arXiv2024

Applications of Bound States in the Continuum in Photonics

Bound states in the continuum (BICs) have attracted attention in photonics owing to their interesting properties. For example, BICs can effectively confine light in a counter-intuitive way and the far-field radiation of photonic structures that exhibit BICs manifests fascinating topological characteristics. Early research into photonic BICs was primarily focused on designing artificial structures to produce BICs. However, since the mid-2010s, exploring the potential applications of BICs has been a growing trend in research. In this Review, we detail the unique properties of BICs, including the ability to achieve enhanced light confinement, sharp Fano resonances, and topological characteristics. We also explore phenomena derived from BICs including the generation of circularly polarized states and unidirectional guided resonances and the impact of BICs on various applications such as lasing, nonlinear frequency conversion, waveguiding, sensing and wavefront control. We also discuss the insights provided by BICs in several emerging research frontiers, such as parity-time symmetric systems, higher-order topology, exciton-photon coupling, and moiré superlattices.

physics.optics↗

arXiv2024

Spin-Orbit-Locking Chiral Bound States in the Continuum

Bound states in the continuum (BICs), which are confined optical modes exhibiting infinite quality factors and carrying topological polarization configurations in momentum space, have recently sparked significant interest across both fundamental and applied physics.} Here we show that breaking time-reversal symmetry by external magnetic field enables a new form of chiral BICs with spin-orbit locking. Applying a magnetic field to a magneto-optical photonic crystal slab lifts doubly degenerate BICs into a pair of chiral BICs carrying opposite pseudo-spins and orbital angular momenta. Multipole analysis verifies the non-zero angular momenta and reveals the spin-orbital-locking behaviors. In momentum space, we observe ultrahigh quality factors and near-circular polarization surrounding chiral BICs, enabling potential applications in spin-selective nanophotonics. Compared to conventional BICs, the magnetically-induced chiral BICs revealed here exhibit distinct properties and origins, significantly advancing the topological photonics of BICs by incorporating broken time-reversal symmetry.

physics.optics↗

arXiv2024

Three-dimensional non-reciprocal transport in photonic topological heterostructure of arbitrary shape

Electromagnetic wave propagation in three-dimensional space typically suffers omnidirectional scattering when encountering obstacles. In this study, we employed Chern vectors to construct a topological heterostructure, where large-volume non-reciprocal topological transport in three-dimension is achieved. The shape of the cross-section in the heterostructure can be arbitrary designed, and we experimentally observed the distinctive cross-shaped field pattern transport, non-reciprocal energy harvesting, and most importantly, the remarkable ability of electromagnetic wave to traverse obstacles and abrupt structure changes without encountering reflections in 3D space.

physics.optics↗