Topological photonics, a novel method for controlling light flow, exploits topologically protected photonic states at interfaces between topologically trivial and non-trivial structures. These states can maintain robust light transmission even in the presence of structural defects. An ideal integrated optical platform for realizing topological photonics is lithium niobate on insulator (LNOI). However, the challenges in etching lithium niobate pose a hurdle to achieving mass production. Recently, a new type of LNOI that requires no etching has been proposed. This technology, by avoiding complex etching steps, shows tremendous potential to become the next-generation optical integration platform. Nevertheless, research on topological devices using this platform is still rare. Here, we report the design of a one-dimensional waveguide array using the concept of synthetic dimensions. This design enables the coherent coupling of topological interface states between multiple layers of three-dimensional Weyl lattices by adjusting the relative twist angles between different Weyl lattices. We aim to flexibly control light output by designing waveguide arrays of different lengths, thereby enriching the freedom of light control. This approach provides new design ideas for the integration of large-scale photonic devices on chips, particularly in the fields of optical switches and logic devices.

We employ a combination of experimental and theoretical methods to investigate the topological characteristics of Weyl points in thin film unetched lithium niobate waveguide arrays. Theoretically, a tight-binding model is employed to design different waveguide spacings, which are considered synthetic dimensions. This approach aims to realize three-dimensional Weyl points within a one-dimensional waveguide array system. Multiple layers of Weyl lattices are crafted, and by adjusting the relative twist angles between different layers, the coherent coupling of topological interface states is achieved. Experimentally, unetched waveguides are fabricated using electron-beam lithography, which simplifies the production process while still leveraging the nonlinear advantages of lithium niobate. A continuous-wave laser acts as the light source and is transmitted to the waveguide array through optical fibers. Waveguide arrays of varying lengths are tested, and a power meter is utilized to scan the output grating, verifying the coherent coupling of topological interface states.

Using the concept of synthetic dimensions, the theoretical design of a one-dimensional waveguide array confirms that coherent coupling of topological interface states can be achieved by controlling the relative twist angles between multiple layers of three-dimensional Weyl lattices [Fig. 6(a)]. Theoretical calculations indicate that different interface state modes at the output end vary with different propagation lengths, confirming the presence of coherent coupling (Fig. 7). Experimentally, the theoretical design is validated by measuring the output gratings of waveguide arrays of varying lengths (Fig. 9).

We employ a novel thin film unetched lithium niobate system that integrates the concepts of topological photonics and synthetic dimensions to design a large-scale, sub-wavelength scale waveguide array system. By adjusting the waveguide spacing and introducing additional parameter dimensions, a three-dimensional Weyl lattice is constructed within a one-dimensional waveguide array system. This structure exhibits Fermi arc boundary states that extend to the parameter space boundary, enabling the connection of two layers of Weyl lattices through rotational mapping techniques. The relative twist direction determines whether topologically protected interface states exist at the stitching interface. Moreover, the stitching of three-layer twisted Weyl lattices is achieved, and by controlling the twist angles between different layers, coherent coupling of interface states at two interfaces is realized. Using different lengths of waveguide arrays facilitates directional output effects, which have been experimentally validated. Compared to traditional single topological interface states, coherently coupled topological interface states demonstrate greater potential in optical switches and logic devices, thereby opening new avenues for the integration of large-scale photonic devices on chips.