Advances in topological photonics and non-Hermitian optics have drastically changed our perception on how interdisciplinary concepts may empower unprecedented applications. Bridging the two areas could uncover reciprocity between topology non-Hermiticity complex systems. So far, such endeavors focused mainly linear-optics regime. Here, we establish a nonlinear platform for control of parity-time (PT) symmetry edge states. Experimentally, demonstrate that optical nonlinearity effectively...

Abstract Higher-order topological insulators (HOTIs) are recently discovered phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these and the seemingly unrelated phenomenon of bound in continuum (BICs) was unveiled. When nonlinearity is added to HOTI system, a number fundamentally important questions arise. For example, how does couple higher-order BICs rest including states? In fact, thus far nonlinear HOTIs have remained...

Abstract The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena solid-state materials as well exotic quantum states matter including superfluidity and topological semimetals. Despite tremendous efforts engineering synthetic cold-atom, electronic photonic lattices to explore physics, thus far high orbitals an important class materials, namely, higher-order insulators (HOTIs), have not been realized. Here, we demonstrate $$p$$ <mml:math...

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 photonic Lieb lattice (LL), such conventional flatband states are found be inherently incomplete, the missing modes manifested as extended line that form noncontractible loops winding around entire lattice. Experimentally, we develop continuous-wave laser writing technique establish finite-sized...

The flourishing of topological photonics in the last decade was achieved mainly due to developments linear photonic structures. However, when nonlinearity is introduced, many intriguing questions arise. For example, are there universal fingerprints underlying topology modes coupled by nonlinearity, and what can happen invariants during nonlinear propagation? To explore these questions, we experimentally demonstrate nonlinearity-induced coupling light into topologically protected edge states...

Abstract Flat-band systems have attracted considerable interest in different branches of physics the past decades, providing a flexible platform for studying fundamental phenomena associated with completely dispersionless bands within whole Brillouin zone. Engineered flat-band structures now been realized variety systems, particular, field photonics. localization, as an important phenomenon solid-state physics, is fundamentally interesting exploration exotic ground-state properties many-body...

Topological properties of lattices are typically revealed in momentum space using concepts such as the Chern number. Here, we study unconventional loop states, namely, noncontractible states (NLSs) and robust boundary modes, mediated by nontrivial topology real space. While play a key role understanding fundamental physics flatband systems, their experimental observation has been hampered because challenge realizing desired conditions. Using laser-writing technique, optically establish...

Type-II Dirac/Weyl points, although impermissible in particle physics due to Lorentz covariance, were uncovered condensed matter physics, driven by fundamental interest and intriguing applications of topological materials. Recently, there has been a surge exploration such generic points using various engineered platforms including photonic crystals, waveguide arrays, metasurfaces, magnetized plasma polariton micropillars, aiming towards relativistic quantum emulation understanding exotic...

We study both theoretically and experimentally the effect of nonlinearity on topologically protected linear interface modes in a photonic Su-Schrieffer-Heeger (SSH) lattice. It is shown that under either focusing or defocusing nonlinearity, this topological mode SSH lattice turns into family gap solitons. These solitons are stable. However, they exhibit only low amplitude power thus weakly nonlinear, even when bandgap wide. As consequence, if initial beam has modest high power, it will...

Cutting a honeycomb lattice (HCL) ends up with three types of edges (zigzag, bearded, and armchair), as is well known in the study graphene edge states. Here, we propose demonstrate distinctive twig-shaped edge, thereby observing new states using photonic platform. Our main findings are (i) twig generic type HCL complementary to armchair formed by choosing right primitive cell rather than simple cutting or Klein modification; (ii) form complete flat band across Brillouin zone zero-energy...

Topological entities based on bulk-boundary correspondence are ubiquitous, from conventional to higher-order topological insulators, where the protected states typically localized at outer boundaries (edges or corners). A less explored scenario involves that inner boundaries, sharing same energy as bulk states. Here, we propose and demonstrate what refer "bulk-hole correspondence''-a relation between robust boundary modes (RBMs) existence of multiple "holes" in singular flatband lattices,...

Abstract Edge states in 2D materials are vital for advancements spintronics, quantum computing, and logic transistors. For uniform graphene, it is well known that the zigzag edges can host edge states, but realization of armchair has been challenging without engineered strain or breaking time‐reversal symmetry. Here, by using a photonic analog recently synthesized graphene‐like biphenylene network (BPN), topological in‐gap demonstrated, particularly at edges. Interestingly, several bulk...

Abstract For the first time, a photonic super‐honeycomb lattice (sHCL) is established experimentally by use of continuous‐wave laser writing technique, and thereby two distinct flatband line states that manifest as noncontractible loop in an infinite are demonstrated. These localized (“straight” “zigzag” lines) observed sHCL with tailored boundaries cannot be obtained superposition conventional compact because they arise from real‐space topological property certain systems. In fact,...

Square-root higher-order topological insulators (HOTIs) are recently discovered new phases, with intriguing properties inherited from a parent lattice Hamiltonian. Different conventional HOTIs, the square-root HOTIs typically manifest two paired nonzero energy corner states. In this work, we experimentally demonstrate second-order in photonics for first time to our knowledge, thereby unveiling such distinct The specific platform is laser-written decorated honeycomb (HCL), which squared...

Compact terahertz (THz) functional devices are greatly sought after for high-speed wireless communication, biochemical sensing, and non-destructive inspection. However, controlled THz generation, along with transport detection, has remained a challenge especially chip-scale due to low-coupling efficiency unavoidable absorption losses. Here, based on the topological protection of electromagnetic waves, we demonstrate nonlinear generation topologically tuned confinement waves in an engineered...

We experimentally realize fractal-like photonic lattices by use of the cw-laser-writing technique, thereby observing distinct compact localized states (CLSs) associated with different flatbands in same lattice setting. Such triangle-shaped lattices, akin to first generation Sierpinski possess a band structure where singular non-degenerate and nonsingular degenerate coexist. By proper phase modulation an input excitation beam, we demonstrate not only simplest CLSs but also their...

Abstract Noncontractible loop states (NLSs) are a recently realized topological entity in flatband lattices, arising typically from the band touching at point where flat intersects one or more dispersive bands. There exists also across plane, overlaps another all over Brillouin zone without crossing band. Such isolated plane‐touching bands remain largely unexplored. For example, what features associated with such degeneracy? Here, nontrivial NLSs and robust boundary modes system degeneracy...

Topological photonics has attracted widespread research attention in the past decade due to its fundamental interest and unique manner controlling light propagation for advanced applications. Paradigmatic approaches have been proposed achieve topological phases including insulators a variety of photonic systems. In particular, lattices composed evanescently coupled waveguide arrays employed conveniently explore investigate physics. this article, we review our recent work on demonstration...

We propose and demonstrate a generalized class of anti-diffracting optical pin-like beams (OPBs). Such exhibit autofocusing dynamics while morphing into Bessel-like shape during long-distance propagation, where the size their main lobe can be tuned by an exponent's parameter. In particular, amplitude envelope engineered to preserve peak intensity pattern. both theory experiment, OPBs are directly compared with radially symmetric abruptly (AABs) under same conditions. Furthermore, enhanced...

In this work, we study topological edge and corner states in two-dimensional (2D) Su-Schrieffer-Heeger lattices from designer surface plasmon crystals (DSPCs), where the vertical confinement of plasmons enables signal detection without need additional covers for sample. particular, formation higher-order insulator can be determined by Zak phase, zero-dimensional subwavelength are found designed DSPCs at terahertz (THz) frequency band together with states. Moreover, state tuned modifying...

Synthetic dimensions (SDs) opened the door for exploring previously inaccessible phenomena in high-dimensional space. However, construction of synthetic lattices with desired coupling properties is a challenging and unintuitive task. Here, we use deep learning artificial neural networks (ANNs) to construct real space predesigned spectrum mode eigenvalues, thus validly design dynamics dimensions. By employing judiciously chosen perturbations (wiggling waveguides at frequencies), show resonant...

Non-Hermitian topological systems simultaneously possess two antagonistic features: ultrasensitivity due to exceptional points and robustness of zero-energy modes, it is unclear which one prevails under different perturbations. We study that question by applying the pseudospectrum theory on prototypical non-Hermitian Su-Schrieffer-Heeger lattice. Topological modes around underlying third-order point (EP3) are robust with respect chiral perturbations but sensitive diagonal In fact, exactly at...

Observing critical phases in lattice models is challenging due to the need analyze finite time or size scaling of observables. We study how computational topology technique persistent homology can be used characterize a generalized Aubry-Andr\'e-Harper model. The entropy and mean squared lifetime features obtained using behave similarly conventional measures (Shannon inverse participation ratio) distinguish localized, extended, phases. However, we find that also clearly distinguishes ordered...

We demonstrate experimentally the existence of compact localized states (CLSs) in a quasi-one-dimensional photonic rhombic lattice presence two distinct refractive-index gradients (i.e., driven ribbon) acting as external electric fields. Such is composed an array periodically arranged evanescently coupled waveguides, which hosts perfect flatband that touches both remaining dispersive bands when it not driven. The driving realized by modulating relative writing beam intensity adjacent...