Photonic Flatband Resonances in Multiple Light Scattering.

We introduce the concept of photonic flatband resonances and demonstrate it for an array of high-index dielectric particles. We employ the multiple Mie scattering theory and demonstrate that both short- and long-range interactions between the resonators are crucial for the emerging collective resonances and their associated photonic flatbands. By examining both near- and far-field characteristics, we uncover how the flatbands emerge due to a fine tuning of resonators' radiation fields, and predict that hybridization of a flatband resonance with an electric hot spot can lead to giant values of the Purcell factor for the electric dipolar emitters.

Res-U2Net: untrained deep learning for phase retrieval and image reconstruction.

Conventional deep learning-based image reconstruction methods require a large amount of training data, which can be hard to obtain in practice. Untrained deep learning methods overcome this limitation by training a network to invert a physical model of the image formation process. Here we present a novel, to our knowledge, untrained Res-U2Net model for phase retrieval. We use the extracted phase information to determine changes in an object's surface and generate a mesh representation of its 3D structure. We compare the performance of Res-U2Net phase retrieval against UNet and U2Net using images from the GDXRAY dataset.

Moiré Lattice in One-Dimensional Synthetic Frequency Dimension.

The moiré lattice has recently attracted broad interest in both solid-state physics and photonics where exotic phenomena in manipulating the quantum states are explored. In this work, we study the one-dimensional (1D) analogs of "moiré" lattices in a synthetic frequency dimension constructed by coupling two resonantly modulated ring resonators with different lengths. Unique features associated with the flatband manipulation as well as the flexible control of localization position inside each unit cell in the frequency dimension have been found, which can be controlled via the choice of flatband. Our work therefore provides insight into simulating moiré physics in 1D synthetic frequency space, which holds important promise for potential applications toward optical information processing.

Boosting topological zero modes using elastomer waveguide arrays.

We employ the Su-Schrieffer-Heeger model in elastic polymer waveguide arrays to design and realize traveling topologically protected modes. The observed delocalization of the optical field for superluminal defect velocities agrees well with theoretical descriptions. We apply mechanical strain to modulate the lattices' coupling coefficient. This work demonstrates a novel, to the best of our knowledge, platform for rapid prototyping of topological photonic devices and establishes strain-tuning as a viable design parameter for topological waveguide arrays.

Anomalous Single-Mode Lasing Induced by Nonlinearity and the Non-Hermitian Skin Effect.

Single-mode operation is a desirable but elusive property for lasers operating at high pump powers. Typically, single-mode lasing is attainable close to threshold, but increasing the pump power gives rise to multiple lasing peaks due to inter-modal gain competition. We propose a laser with the opposite behavior: multimode lasing occurs at low output powers, but pumping beyond a certain value produces a single lasing mode, with all other candidate modes experiencing negative effective gain. This phenomenon arises in a lattice of coupled optical resonators with non-fine-tuned asymmetric couplings, and is caused by an interaction between nonlinear gain saturation and the non-Hermitian skin effect. The single-mode lasing is observed in both frequency domain and time domain simulations. It is robust against on-site disorder, and scales up to large lattice sizes. This finding might be useful for implementing high-power laser arrays.

Dark soliton detection using persistent homology.

Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers but require extensive data and computational resources to train. We show how a topological data analysis technique, persistent homology, can be used to rapidly and reliably identify qualitative features in experimental image data. The identified features can be used as inputs to simple supervised machine learning models, such as logistic regression models, which are easier to train. As an example, we consider the identification of dark solitons using a dataset of 6257 labeled atomic Bose-Einstein condensate density images.

Probing Band Topology Using Modulational Instability.

We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations of the nonlinear Bloch waves are sensitive to topological band inversions. At longer timescales, nonlinear wave mixing induces spreading of energy through the entire band and spontaneous creation of wave polarization singularities determined by the band Chern number. Our analytical and numerical results establish modulational instability as a tool to probe bulk topological invariants and create topologically nontrivial wave fields.

Edge mode bifurcations of two-dimensional topological lasers.

Topological lasers are of growing interest as a way to achieve disorder-robust single-mode lasing using arrays of coupled resonators. We study lasing in a two-dimensional coupled resonator lattice exhibiting transitions between trivial and topological phases, which allows us to systematically characterize the lasing modes throughout a topological phase. We show that, unlike conventional topological robustness that requires a sufficiently large bulk band gap, bifurcations in topological edge mode lasing can occur even when the band gap is maximized. We show that linear mode bifurcations from single-mode to multi-mode lasing can occur deep within the topological phase, sensitive to both the pump shape and lattice geometry. We suggest ways to suppress these bifurcations and preserve single-edge mode lasing.

Topological photonic crystal fibers and ring resonators.

With an exact recursive approach, we study photonic crystal fibers and resonators with topological features induced by Aubry-Andre-Harper cladding modulation. We find nontrivial gaps and edge states at the interface between regions with different topological invariants. These structures show topological protection against symmetry-preserving local perturbations that do not close the gap and sustain strong field localization and energy concentration at a given radial distance. As topological light guiding and trapping devices, they may bring about many opportunities for both fundamentals and applications unachievable with conventional devices.

Direct Observation of Flatband Loop States Arising from Nontrivial Real-Space Topology.

Topological properties of lattices are typically revealed in momentum space using concepts such as the Chern number. Here, we study unconventional loop states, namely, the noncontractible loop states (NLSs) and robust boundary modes, mediated by nontrivial topology in real space. While such states play a key role in understanding fundamental physics of flatband systems, their experimental observation has been hampered because of the challenge in realizing desired boundary conditions. Using a laser-writing technique, we optically establish photonic kagome lattices with both an open boundary by properly truncating the lattice, and a periodic boundary by shaping the lattice into a Corbino geometry. We thereby demonstrate the robust boundary modes winding around the entire edge of the open lattice and, more directly, the NLSs winding in a closed loop akin to that in a torus. We prove that the NLSs due to real-space topology persist in ideal Corbino-shaped kagome lattices of arbitrary size. Our results could be of great importance for our understanding of the singular flatbands and the intriguing physics phenomenon applicable for strongly interacting systems.

Parity anomaly laser.

We propose a novel supersymmetry-inspired scheme for achieving robust single-mode lasing in arrays of coupled microcavities, based on factorizing a given array Hamiltonian into its "supercharge" partner array. Pumping a single sublattice of the partner array preferentially induces lasing of an unpaired zero mode. A chiral symmetry protects the zero mode similar to 1D topological arrays, but it need not be localized to domain walls or edges. We demonstrate single-mode lasing over a wider parameter regime by designing the zero mode to have a uniform intensity profile.

Disorder-Robust Entanglement Transport.

We study the disorder-perturbed transport of two noninteracting entangled particles in the absence of backscattering. This situation is, for instance, realized along edges of topological insulators. We find profoundly different responses to disorder-induced dephasing for the center-of-mass and relative coordinates: While a mirror symmetry protects even highly delocalized relative states when resonant with the symmetry condition, delocalizations in the center of mass [e.g., two-particle (N=2) N00N states] remain fully sensitive to disorder. We demonstrate the relevance of these differences to the example of interferometric entanglement detection. Our platform-independent analysis is based on the treatment of disorder-averaged quantum systems with quantum master equations.

Third-Harmonic Generation in Photonic Topological Metasurfaces.

We study nonlinear effects in two-dimensional photonic metasurfaces supporting topologically protected helical edge states at the nanoscale. We observe strong third-harmonic generation mediated by optical nonlinearities boosted by multipolar Mie resonances of silicon nanoparticles. Variation of the pump-beam wavelength enables independent high-contrast imaging of either bulk modes or spin-momentum-locked edge states. We demonstrate topology-driven tunable localization of the generated harmonic fields and map the pseudospin-dependent unidirectional waveguiding of the edge states bypassing sharp corners. Our observations establish dielectric metasurfaces as a promising platform for the robust generation and transport of photons in topological photonic nanostructures.

Photonic Anomalous Quantum Hall Effect.

We experimentally realize a photonic analogue of the anomalous quantum Hall insulator using a two-dimensional (2D) array of coupled ring resonators. Similar to the Haldane model, our 2D array is translation invariant, has a zero net gauge flux threading the lattice, and exploits next-nearest neighbor couplings to achieve a topologically nontrivial band gap. Using direct imaging and on-chip transmission measurements, we show that the band gap hosts topologically robust edge states. We demonstrate a topological phase transition to a conventional insulator by frequency detuning the ring resonators and thereby breaking the inversion symmetry of the lattice. Furthermore, the clockwise or the counterclockwise circulation of photons in the ring resonators constitutes a pseudospin degree of freedom. The two pseudospins acquire opposite hopping phases, and their respective edge states propagate in opposite directions. These results are promising for the development of robust reconfigurable integrated nanophotonic devices for applications in classical and quantum information processing.

Valley Vortex States and Degeneracy Lifting via Photonic Higher-Band Excitation.

We demonstrate valley-dependent vortex generation in photonic graphene. Without breaking inversion symmetry, the excitation of two valleys leads to the formation of an optical vortex upon Bragg reflection to the third equivalent valley, with its chirality determined by the valley degree of freedom. Vortex-antivortex pairs with valley-dependent topological charge flipping are also observed and corroborated by numerical simulations. Furthermore, we develop a three-band effective Hamiltonian model to describe the dynamics of the coupled valleys and find that the commonly used two-band model is not sufficient to explain the observed vortex degeneracy lifting. Such valley-polarized vortex states arise from high-band excitation without a synthetic-field-induced gap opening. Our results from a photonic setting may provide insight for the study of valley contrasting and Berry-phase-mediated topological phenomena in other systems.

Reconfigurable Topological Phases in Next-Nearest-Neighbor Coupled Resonator Lattices.

We present a reconfigurable topological photonic system consisting of a 2D lattice of coupled ring resonators, with two sublattices of site rings coupled by link rings, which can be accurately described by a tight-binding model. Unlike previous coupled-ring topological models, the design is translationally invariant, similar to the Haldane model, and the nontrivial topology is a result of next-nearest couplings with nonzero staggered phases. The system exhibits a topological phase transition between trivial and spin Chern insulator phases when the sublattices are frequency detuned. Such topological phase transitions can be easily induced by thermal or electro-optic modulators, or nonlinear cross phase modulation. We use this lattice to design reconfigurable topological waveguides, with potential applications in on-chip photon routing and switching.

Observation of Valley Landau-Zener-Bloch Oscillations and Pseudospin Imbalance in Photonic Graphene.

We demonstrate intervalley Bloch oscillation (BO) and Landau-Zener tunneling (LZT) in an optically induced honeycomb lattice with a refractive-index gradient. Unlike previously observed BO in a gapped square lattice, we show nonadiabatic beam dynamics that are highly sensitive to the direction of the index gradient and the choice of the Dirac cones. In particular, a symmetry-preserving potential leads to nearly perfect LZT and coherent BO between the inequivalent valleys, whereas a symmetry-breaking potential generates asymmetric scattering, imperfect LZT, and valley-sensitive generation of vortices mediated by a pseudospin imbalance. This clearly indicates that, near the Dirac points, the transverse gradient does not always act as a simple scalar force, as commonly assumed, and the LZT probability is strongly affected by the sublattice symmetry as analyzed from an effective Landau-Zener Hamiltonian. Our results illustrate the anisotropic response of an otherwise isotropic Dirac platform to real-space potentials acting as strong driving fields, which may be useful for manipulation of pseudospin and valley degrees of freedom in graphenelike systems.

Unconventional Flatband Line States in Photonic Lieb Lattices.

Flatband systems typically host "compact localized states" (CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice (LL), such conventional localized flatband states are found to be inherently incomplete, with the missing modes manifested as extended line states that form noncontractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially tailored boundaries and, thereby, directly observe the unusually extended flatband line states. Such unconventional line states cannot be expressed as a linear combination of the previously observed boundary-independent bulk CLS but rather arise from the nontrivial real-space topology. The robustness of the line states to imperfect excitation conditions is discussed, and their potential applications are illustrated.

Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems.

We analyze chiral topological edge modes in a non-Hermitian variant of the 2D Dirac equation. Such modes appear at interfaces between media with different "masses" and/or signs of the "non-Hermitian charge." The existence of these edge modes is intimately related to exceptional points of the bulk Hamiltonians, i.e., degeneracies in the bulk spectra of the media. We find that the topological edge modes can be divided into three families ("Hermitian-like," "non-Hermitian," and "mixed"); these are characterized by two winding numbers, describing two distinct kinds of half-integer charges carried by the exceptional points. We show that all the above types of topological edge modes can be realized in honeycomb lattices of ring resonators with asymmetric or gain-loss couplings.

Edge Solitons in Nonlinear-Photonic Topological Insulators.

We show theoretically that a photonic topological insulator can support edge solitons that are strongly self-localized and propagate unidirectionally along the lattice edge. The photonic topological insulator consists of a Floquet lattice of coupled helical waveguides, in a medium with local Kerr nonlinearity. The soliton behavior is strongly affected by the topological phase of the linear lattice. The topologically nontrivial phase gives a continuous family of solitons, while the topologically trivial phase gives an embedded soliton that occurs at a single power and arises from a self-induced local nonlinear shift in the intersite coupling. The solitons can be used for nonlinear switching and logical operations, functionalities that have not yet been explored in topological photonics. We demonstrate using solitons to perform selective filtering via propagation through a narrow channel, and using soliton collisions for optical switching.