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The hybrid skin-topological effect (HSTE) in non-Hermitian systems exhibits both the skin effect and topological protection, offering a novel mechanism for the localization of topological edge states (TESs) in electrons, circuits, and photons. However, it remains unclear whether the HSTE can be realized in quasicrystals, and the unique structure of quasicrystals with multi-site cells may provide novel localization phenomena for TESs induced by the HSTE. We propose an eight-site cell in two-dimensional quasicrystals and realize the HSTE with eight-site nonreciprocal intracell hoppings. Furthermore, we can arbitrarily adjust the eigenfield distributions of the TESs and discover domain walls associated with effective dissipation and their correlation with localization. We present a new scheme to precisely adjust the energy distribution in non-Hermitian quasicrystals with arbitrary polygonal outer boundaries.

The Moir\'e patterns generated by altering the structural parameters in a two or more layers of periodic materials, including single-layer structure, interlayer stacking, and twisting parameters, exhibit prosperous topological physical properties. However, the intricate characteristics of twisted nested Moir\'e patterns and their relationship with topological transitions remain unclear. In this Letter, based on the proposed twisted nested photonic crystal (TNPC), we derive its spatial geometric functions (SGFs), aperiodic-quasiperiodic-periodic properties in twisted nested Moir\'e patterns, and the SSH{\phi} Hamiltonian. We reveal the intrinsic correlation between twisted nested Moir\'e patterns and topological transitions, obtaining higher-order topological states (HOTSs) with C2z symmetry. This work will provide theoretical references for the design and application of twisted topological PC and their devices.

We report the discovery of multiple topological phase transitions induced by the photonic quantum spin Hall effect (PQSHE) in a non-Hermitian photonic crystal (PhC). When increasing the magnitude of the non-Hermitian terms, the system undergoes transitions from topological corner states to topological edge states and subsequently to topological bulk states. The angular momentum of the wave function of the out-of-plane electric field excited by the chiral source acts as the pseudospin degree of freedom in the PQSHE. Therefore, we consider the introduction of chiral sources with different circular polarizations into non-Hermitian PhCs and observe the emergence of asymmetric field responses. These results are expected to enable the multi-dimensional manipulation of topological states, offering a new avenue for the detection of chiral sources.

Recently, the studies of topological corner states (TCSs) are extended from crystals to quasicrystals, which are referred to as higher-order topological quasicrystalline insulators (HOTQIs). However, the TCSs of complete quasi-periodic structure in photonic systems have yet to be demonstrated. Moreover, there is only one TCS in each corner region in higher-order topological insulators (HOTIs). Increasing the number of TCS is expected to increase application potential of TCSs. In this work, HOTQIs in photonic systems are experimentally observed. It is found that HOTQIs possess TCS arrays, and each TCS array contains several TCSs. Furthermore, the universal theoretical framework of the multimer analysis method is improved, and the difference in the average charge density is proposed as a real-space topological index. These results will open up new ideas for investigating highly integrated, multi-region localized TCSs and are expected to provide new ways to explore topological phenomena and the applications of photonic quasicrystals.

The multifrequency quantum valley Hall effect (QVHE) with a large valley Chern number has been realized to significantly improve the transmission capacity of topological waveguides and increase the mode density of topological waveguides. However, multifrequency and multimode QVHEs have not been realized simultaneously. In this work, using tight-binding model calculations and numerical simulations, a valley photonic crystal (VPC) consisting of a Stampfli-triangle photonic crystal is constructed, and its multiple degeneracies in the low-frequency and high-frequency bands split simultaneously to realize the QVHE with multiple topological edge states (TESs). The multifrequency and multimode topological transmission with two low-frequency modes and four high-frequency modes is realized by means of simulations and experiments through a Z-shaped waveguide constructed using two VPCs with opposite valley Chern numbers to prove the realization of a large valley Chern number in the two frequency bands. The two low-frequency modes are successfully distinguished with position-dependent selective excitations, which experimentally demonstrates the occurrence of a large valley Chern number. A frequency-dependent multimode beam splitter is theoretically proposed for high-performance integrated photonic device applications. These results provide new ideas for high-efficiency and high-capacity optical transmission and communication devices and their integration; furthermore, they broaden the application range of TESs.

Topological corner state (TCS) and topological edge state (TES) have provided new approaches to control the propagation of light. The construction of topological coupled cavity-waveguide system (TCCWS) based on TCS and TES is worth looking forward to, due to its research prospects in realizing high-performance micro-nano integrated photonic devices. In this Letter, TCCWS is proposed in two-dimensional (2D) photonic crystal (PC), which possesses strong optical localization, high quality factor and excellent robustness compared with the conventional coupled cavity-waveguide system (CCCWS). This work will provide the possibility to design high-performance logic gates, lasers, filters and other micro-nano integrated photonics devices and expand their applications.