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Topological photonics has emerged as a novel paradigm for the design of electromagnetic systems from microwaves to nanophotonics. Studies to date have largely focused on the demonstration of fundamental concepts, such as nonreciprocity and waveguiding protected against fabrication disorder. Moving forward, there is a pressing need to identify applications where topological designs can lead to useful improvements in device performance. Here, we review applications of topological photonics to ring resonator–based systems, including one- and two-dimensional resonator arrays, and dynamically modulated resonators. We evaluate potential applications such as quantum light generation, disorder-robust delay lines, and optical isolation, as well as future research directions and open problems that need to be addressed.

Weyl points, as a signature of 3D topological states, have been extensively studied in condensed matter systems. Recently, the physics of Weyl points has also been explored in electromagnetic structures such as photonic crystals and metamaterials. These structures typically have complex three-dimensional geometries, which limits the potential for exploring Weyl point physics in on-chip integrated systems. Here we show that Weyl point physics emerges in a system of two-dimensional arrays of resonators undergoing dynamic modulation of refractive index. In addition, the phase of modulation can be controlled to explore Weyl points under different symmetries. Furthermore, unlike static structures, in this system the non-trivial topology of the Weyl point manifests in terms of surface state arcs in the synthetic space that exhibit one-way frequency conversion. Our system therefore provides a versatile platform to explore and exploit Weyl point physics on chip. Weyl points, point degeneracies surrounded by linear dispersions, are the 3-dimensional analogue of the Dirac points known from 2D materials. Here, Lin et al . propose a scheme for realizing on-chip electromagnetic Weyl points by utilizing the concept of synthetic dimensions.

Temporal modulations in photonics bring many exotic optical phenomena in the time dimension while metamaterials provide powerful ways in manipulating light in the spatial domain. The authors envision the connection, Floquet Metamaterials, may deliver novel opportunities in nanophotonics.

There has been significant recent interest in synthetic dimensions, where internal degrees of freedom of a particle are coupled to form higher-dimensional lattices in lower-dimensional physical structures. For these systems, the concept of band structure along the synthetic dimension plays a central role in their theoretical description. Here we provide a direct experimental measurement of the band structure along the synthetic dimension. By dynamically modulating a resonator at frequencies commensurate with its mode spacing, we create a periodically driven lattice of coupled modes in the frequency dimension. The strength and range of couplings can be dynamically reconfigured by changing the modulation amplitude and frequency. We show theoretically and demonstrate experimentally that time-resolved transmission measurements of this system provide a direct readout of its band structure. We also realize long-range coupling, gauge potentials and nonreciprocal bands by simply incorporating additional frequency drives, enabling great flexibility in band structure engineering. Internal degrees of freedom allow to expand the effective dimensionality of a system along “synthetic” dimensions. Here, the authors demonstrate this by modulating a ring resonator at frequencies commensurate with its mode spacing, and are able to directly measure its synthetic band structure.

Synthetic dimensions have garnered widespread interest for implementing high dimensional classical and quantum dynamics on low-dimensional geometries. Synthetic frequency dimensions, in particular, have been used to experimentally realize a plethora of bulk physics effects. However, in synthetic frequency dimension there has not been a demonstration of a boundary which is of paramount importance in topological physics due to the bulk-edge correspondence. Here we construct boundaries in the frequency dimension of dynamically modulated ring resonators by strongly coupling an auxiliary ring. We explore various effects associated with such boundaries, including confinement of the spectrum of light, discretization of the band structure, and the interaction of boundaries with one-way chiral modes in a quantum Hall ladder, which exhibits topologically robust spectral transport. Our demonstration of sharp boundaries fundamentally expands the capability of exploring topological physics, and has applications in classical and quantum information processing in synthetic frequency dimensions. The exploration of topological boundary effects is one of the important aspects that could foster the development of future topological photonics devices. Here the authors propose a straightforward method to construct sharp boundaries in synthetic dimensions using a modulated ring resonator strongly coupled to an auxiliary ring.

Engineering the topological properties of the system has been a longstanding subject in physics. Here, we propose a scheme to simulate topological materials with a non-Abelian gauge field in synthetic space-frequency dimensions where the symmetry between spin-flipped hoppings can be levitated by using coupled photonic molecules under dynamic modulations. The frequency-split supermodes in these photonic molecules can serve the pseudospin degree of freedom, which can further be connected along the frequency axis in an independent way, offering the unique opportunity to explore topological physics with imbalanced spin-flipped hoppings leading to a complex generalization of the conventional SU(2) non-Abelian gauge field, i.e., an SL ( 2 , C ) gauge field. By varying the spin-flipped hopping terms, we theoretically show the existence of a variety of Dirac semimetal transitions and the rotation of the pseudospin projection for the edge states throughout the Brillouin zone. Our proposal is experimentally feasible and therefore provides a versatile platform for the study of topological materials under non-Abelian gauge fields in photonics. Artificial gauge fields offer a powerful tool for engineering the topological phase of matter. Here, the authors propose a scheme to simulate an SL ( 2 , C ) non-Abelian gauge field by coupled photonic molecules in synthetic space-frequency dimensions, which enables various Dirac semimetal transitions.

The differences in critical times and critical momenta between self-normal and biorthogonal dynamical quantum phase transitions are revealed. The theoretical analysis is experimentally validated through multiple quench processes using a one-dimensional discrete-time non-Hermitian quantum walks.

Temporal modulation recently draws great attentions in wave manipulations, with which one can introduce the concept of temporal multilayer structure, a temporal counterpart of spatially multilayer configurations. This kind of multilayer structure holds temporal interfaces in the time domain, which provides additional flexibility in temporal operations. Here we take this opportunity and propose to simulate a non-Abelian gauge field with a temporal multilayer structure in the discrete physical system. Two basic temporal operations, i.e., the folding/unfolding operation and the phase shift operation are used to design such a temporal multilayer structure, which hence can support noncommutative operations to realize the non-Abelian Aharonov-Bohm interference in the time domain. A two-/three-dimensional non-Abelian gauge field can be built, which may be further extended to higher dimensions. Our work therefore provides a unique platform enabling generalization of non-Abelian physics to arbitrary dimensions and offers a method for wave manipulations with temporal band engineering. The authors proposed a method for simulating non-Abelian Aharonov Bohm interferences with a temporal multilayer structure in the discrete physical system. Such a method for studying non-Abelian physics can be generalized to arbitrary dimensions.

The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of nonequilibrium topological invariants is a central issue and usually necessitates the information of quantum dynamics in both the time and momentum dimensions. Here, we propose the topological holographic quench dynamics in synthetic dimension, and also show it provides a highly efficient scheme to characterize photonic topological phases. A pseudospin model is constructed with ring resonators in a synthetic lattice formed by frequencies of light, and the quench dynamics is induced by initializing a trivial state, which evolves under a topological Hamiltonian. Our key prediction is that the complete topological information of the Hamiltonian is encoded in quench dynamics solely in the time dimension, and is further mapped to lower-dimensional space, manifesting the holographic features of the dynamics. In particular, two fundamental time scales emerge in the dynamical evolution, with one mimicking the topological band on the momentum dimension and the other characterizing the residue time evolution of the state after the quench. For this, a universal duality between the quench dynamics and the equilibrium topological phase of the spin model is obtained in the time dimension by extracting information from the field evolution dynamics in modulated ring systems in simulations. This work also shows that the photonic synthetic frequency dimension provides an efficient and powerful way to explore the topological nonequilibrium dynamics.Topological holographic quench dynamics in a synthetic frequency dimension studied in modulated ring system shows the universal bulk-surface duality with complete topological information being encoded in the single time variable.

Topologically protected edge states based on valley photonic crystals (VPCs) have been widely studied, from theoretical verification to technical applications. However, research on integrated tuneable topological devices is still lacking. Here, we study the phase-shifting theory of topological edge modes based on a VPC structure. Benefiting from the phase vortex formed by the VPC structure, the optical path of the topological edge mode in the propagation direction is approximately two-fold that of the conventional optical mode in a strip waveguide. In experiments, we show a 1.57-fold improvement in π-phase tuning efficiency. By leveraging the high-efficiency phase-shifting properties and the sharp-turn features of the topological waveguide, we demonstrate an ultracompact 1 × 2 thermo-optic topological switch (TOTS) operating at telecommunication wavelengths. A switching power of 18.2 mW is needed with an ultracompact device footprint of 25.66 × 28.3 μm in the wavelength range of 1530–1582 nm. To the best of our knowledge, this topological photonic switch is the smallest switch of any dielectric or semiconductor 1 × 2/2 × 2 broadband optical switches, including thermo-optic and electro-optic switches. In addition, a high-speed transmission experiment employing the proposed TOTS is carried out to demonstrate the robust transmission of high-speed data. Our work reveals the phase-shifting mechanism of valley edge modes, which may enable diverse topological functional devices in many fields, such as optical communications, nanophotonics, and quantum information processing.An ultracompact 1 × 2 thermo-optic topological switch is demonstrated by leveraging the high-efficiency phase-shifting property and the sharp-turn feature of the topological waveguides.