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 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 lattices in real space with a predesigned spectrum of mode eigenvalues,and thus to validly design the dynamics in synthetic mode dimensions.By employing judiciously chosen perturbations(wiggling of waveguides at desired frequencies),we show resonant mode coupling and tailored dynamics in SDs.Two distinct examples are illustrated:one features uniform synthetic mode coupling,and the other showcases the edge defects that allow for tailored light transport and confinement.Furthermore,we demonstrate morphing of light into a topologically protected edge mode with modified Su-Schrieffer-Heeger photonic lattices.Such an ANN-assisted construction of SDs may advance toward“utopian networks,”opening new avenues for fundamental research beyond geometric limitations as well as for applications in mode lasing,optical switching,and communication technologies.

Realization of photonic p-orbital higher-order topological insulators

The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter including orbital superfluidity and topological semimetals.Despite tremendous efforts in engineering synthetic cold-atom,as well as electronic and photonic lattices to explore orbital physics,thus far high orbitals in an important class of materials,namely,higher-order topological insulators(HOTIs),have not been realized.Here,we demonstrate p-orbital corner states in a photonic HOTI,unveiling their underlying topological invariant,symmetry protection,and nonlinearity-induced dynamical rotation.In a Kagome-type HOTI,we find that the topological protection of p-orbital corner states demands an orbital-hopping symmetry in addition to generalized chiral symmetry.Due to orbital hybridization,nontrivial topology of the p-orbital HOTI is“hidden”if bulk polarization is used as the topological invariant,but well manifested by the generalized winding number.Our work opens a pathway for the exploration of intriguing orbital phenomena mediated by higher-band topology applicable to a broad spectrum of systems.

Symmetry-protected third-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 a challenge due to the strict requirement of the system symmetries. Here we demonstrate that higher-order EPs can be judiciously fabricated in parity–time(PT)-symmetric staggered rhombic lattices by introducing not only on-site gain/loss but also non-Hermitian couplings. Zero-energy flatbands persist and symmetry-protected third-order EPs(EP3s) 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 toward 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.

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.

Nontrivial coupling of light into a defect:the interplay of nonlinearity and topology

The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures.However,when nonlinearity is introduced,many intriguing questions arise.For example,are there universal fingerprints of the underlying topology when modes are coupled by nonlinearity,and what can happen to topological invariants during nonlinear propagation?To explore these questions,we experimentally demonstrate nonlinearity-induced coupling of light into topologically protected edge states using a photonic platform and develop a general theoretical framework for interpreting the mode-coupling dynamics in nonlinear topological systems.Performed on laser-written photonic Su-Schrieffer-Heeger lattices,our experiments show the nonlinear coupling of light into a nontrivial edge or interface defect channel that is otherwise not permissible due to topological protection.Our theory explains all the observations well.Furthermore,we introduce the concepts of inherited and emergent nonlinear topological phenomena as well as a protocol capable of revealing the interplay of nonlinearity and topology.These concepts are applicable to other nonlinear topological systems,both in higher dimensions and beyond our photonic platform.

Free-space realization of tunable pin-like optical vortex beams

We demonstrate,both analytically and experimentally,free-space pin-like optical vortex beams (POVBs). Such angular-momentum-carrying beams feature tunable peak intensity and undergo robust antidiffracting propagation,realized by judiciously modulating both the amplitude and the phase profile of a standard laser beam.Specifically,they are generated by superimposing a radially symmetric power-law phase on a helical phase structure,which allows the inclusion of an orbital angular momentum term to the POVBs. During propagation in free space,these POVBs initially exhibit autofocusing dynamics,and subsequently their amplitude patterns morph into a high-order Bessel-like profile characterized by a hollow core and an annular main lobe with a constant or tunable width during propagation. In contrast with numerous previous endeavors on Bessel beams,our work represents the first demonstration of long-distance free-space generation of optical vortex "pins" with their peak intensity evolution controlled by the impressed amplitude structure. Both the Poynting vectors and the optical radiation forces associated with these beams are also numerically analyzed,revealing novel properties that may be useful for a wide range of applications.

Nonlinear topological valley Hall edge states arising from type-Ⅱ Dirac cones

A Dirac point is a linear band crossing point originally used to describe unusual transport properties of materials like graphene.In recent years,there has been a surge of exploration of type-II Dirac/Weyl points using various engineered platforms including photonic crystals,waveguide arrays,metasurfaces,magnetized plasma and polariton micropillars,aiming toward relativistic quantum emulation and understanding of exotic topological phenomena.Such endeavors,however,have focused mainly on linear topological states in real or synthetic Dirac/Weyl materials.We propose and demonstrate nonlinear valley Hall edge(VHE)states in laserwritten anisotropic photonic lattices hosting innately the type-Ⅱ Dirac points.These self-trapped VHE states,manifested as topological gap quasi-solitons that can move along a domain wall unidirectionally without changing their profiles,are independent of external magnetic fields or complex longitudinal modulations,and thus are superior in comparison with previously reported topological edge solitons.Our finding may provide a route for understanding nonlinear phenomena in systems with type-Ⅱ Dirac points that violate the Lorentz invariance and may bring about possibilities for subsequent technological development in light field manipulation and photonic devices.

Specially shaped Bessel-like self-accelerating beams along predesigned trajectories

Over the past several years, spatially shaped self-accelerating beams along different trajectories have been studied extensively. Due to their useful properties such as resistance to diffraction, self-healing, and selfbending even in free space, these beams have attracted great attention with many proposed applications. Interestingly, some of these beams could be designed with controllable spatial profiles and thus propagate along various desired trajectories such as parabolic, snake-like, hyperbolic, hyperbolic secant, three-dimensional spiraling, and even self-propelling trajectories. Experimentally, suchbeams are realized typically by using a spatial light modulator so as to imprint a desired phase distribution on a Gaussian-like input wave front propagating under paraxial or nonparaxial conditions. In this paper, we provide a brief overview of our recent work on specially shaped self-accelerating beams, including Bessel-like, breathing Bessellike, and vortex Bessel-like beams. In addition, we propose and demonstrate a new type of dynamical Bessel-like beams that can exhibit not only self-accelerating but also self-propelling during propagation. Both theoretical and experimental results are presented along with a brief discussion of potential applications.

Topologically tuned terahertz confinement in a nonlinear photonic chip

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 and detection,has remained a challenge especially for chip-scale devices due to low-coupling efficiency and unavoidable absorption losses.Here,based on the topological protection of electromagnetic waves,we demonstrate nonlinear generation and topologically tuned confinement of THz waves in an engineered lithium niobate chip forming a wedge-shaped Su-Schrieffer-Heeger lattice.Experimentally measured band structures provide direct visualization of the THz localization in the momentum space,while robustness of the confined mode against chiral perturbations is also analyzed and compared for both topologically trivial and nontrivial regimes.Such topological control of THz waves may bring about new possibilities in the realization of THz integrated circuits,promising for advanced photonic applications.

Synthetic optical vortex beams from the analogous trajectory change of an artificial satellite

We propose a method to generate specially shaped high-order singular beams of pre-designed intensity distributions. Such a method does not a priori assume a phase formula, but rather relies on the 'cake-cutting and assembly' approach to achieve the azimuthal phase gradient for beam shaping, inspired by the orbital motion trajectory change of an artificial satellite. Based on our method, several typical vortex beams with desired intensity patterns are experimentally generated. As an example, we realize optical trapping and transportation of microorganisms with a triangle-shaped vortex beam, demonstrating the applicability of such unconventional vortex beams in optical trapping and manipulation.