Topological phases and the bulk-edge correspondence in 2D photonic microring resonator lattices

Topological phases and non-Hermitian topology in tunable nonreciprocal cyclic three-mode optical systems

We propose a method for simulating a 1D non-Hermitian Su-Schrieffer-Heeger model with modulated nonreciprocal hopping using a cyclic three-mode optical system. The current system exhibits different localization of topologically nontrivial phases, which can be characterized by the winding number. We find that the eigenenergies of such a system undergo a real-complex transition as the nonreciprocal hopping changes, accompanied by a non-Bloch parity-time symmetry breaking. We explain this phase transition by considering the evolution of saddle points on the complex energy plan and the ratio of complex eigenenergies. Additionally, we demonstrate that the skin states resulting from the non-Hermitian skin effect possess higher-order exceptional points under the critical point of the non-Bloch parity-time phase transition. Furthermore, we investigate the non-Hermitian skin phase transition by the directional mean inverse participation ratio and the generalized Brillouin zone. This work provides an alternative way to investigate the novel topological and non-Hermitian effects in nonreciprocal optical systems.

Broadband frequency generation by four-wave mixing in an all-bands-flat Floquet-Lieb topological insulator

All-bands-flat topological photonic insulators are photonic lattices with all dispersionless bulk bands separated by nontrivial bandgaps. A distinct feature of these systems is that the edge modes can be excited across the flatband frequencies without scattering into the localized bulk modes, thus allowing the edge mode spectrum to extend beyond the gap size. Here we exploit the wide edge mode spectrum of a Floquet-Lieb topological insulator with all flatbands to achieve broadband frequency generation by four-wave mixing on a topological silicon photonic platform. Our all-bands-flat Floquet insulator is based on a Lieb lattice of microring resonators with perfect couplings, which provides a wide frequency generation bandwidth spanning more than six microring's free spectral ranges. The all-bands-flat microring lattice can also serve as a robust topological platform for other broadband nonlinear processes such as stimulated Raman scattering, frequency comb generation, supercontinuum generation, and soliton propagation based on topologically protected edge modes.

N-band photonic Hopf insulators based on 2D microring lattices

Hopf insulators are topological insulators whose topological behavior arises from the nontrivial mapping from a 3D sphere to a 2D sphere, known as the Hopf map. The Hopf map, typically encountered in the study of spinor and Skyrmion systems, is classified topologically by an integer invariant called the Hopf index. Here we show that, owing to the periodic circulation of light inside each microring, a 2D lattice of microring resonators can emulate an N-band photonic Hopf insulator with nontrivial Hopf index. In particular, we show by numerical computation and direct analytical proof that the N-band Hopf index of the microring lattice is identical to its winding number. The result shows that the Hopf index is an alternative topological invariant for classifying 2D microring photonic lattices and establishes a correspondence between the Hopf insulator phase and the anomalous Floquet insulator phase of the lattice. More generally, our work shows that 2D microring lattices can provide a versatile nanophotonic platform for studying non-Abelian topological photonic systems.

Conjugated topological interface-states in coupled ring resonators

The optical properties of topological photonics have attracted much interest recently because its potential applications for robust unidirectional transmission that are immune to scattering at disorder. However, researches on topological series coupled ring resonators (T-SCRR) have been much less discussed. The existence of topological interface-states (TIS) in the T-SCRR is described for the first time in this article. An approach has been developed to achieve this goal via the band structure of dielectric binary ring resonators and the Zak phase of each bandgap. It is found that an ultra-high-Q with complete transmission is obtained by the conjugated topological series coupled ring resonators due to the excitation of conjugated topological interface-states, which is different from those in conventional TIS. Furthermore, the problem of transmission decreases resulting from high-Q increases in the traditional photonic system is significantly improved by this approach. These findings could pave a novel path for developing advanced high-Q filters, optical sensors, switches, resonators, communications and quantum information processors.

Realization of Anomalous Floquet Insulators in Strongly Coupled Nanophotonic Lattices

We experimentally realized Floquet topological photonic insulators using a square lattice of direct-coupled octagonal resonators. Unlike previously reported topological insulator systems based on microring lattices, the nontrivial topological behaviors of our system arise directly from the periodic evolution of light around each octagon to emulate a periodically driven system. By exploiting asynchronism in the evanescent coupling between adjacent octagonal resonators, we could achieve strong and asymmetric couplings in each unit cell, which are necessary for realizing anomalous Floquet insulator behaviors. Direct imaging of scattered light from fabricated samples confirmed the existence of chiral edge states as predicted by the topological phase map of the lattice. In addition, by exploiting the frequency dispersion of the coupling coefficients, we could also observe topological phase changes of the lattice from a normal insulator to Chern and Floquet insulators. Our lattice thus provides a versatile nanophotonic system for investigating 2D Floquet topological insulators.