Power splitters with low loss, compact footprint, and high stability are essential building blocks in modern on-chip photonic integrated systems for optical interconnection, signal routing, and dynamic optical power management. Conventional on-chip power splitters rely on phase matching and modal interference, and therefore usually suffer from splitting-ratio drift, increased loss, and enhanced crosstalk under bandwidth dispersion, fabrication errors, and bending-induced defects, making it difficult to maintain stable and consistent performance in large-scale integration. Photonic topological insulators (PTIs) exhibit remarkable advantages in suppressing backscattering, tolerating sharp bends, and maintaining robustness against defects due to their unique topologically protected edge-state transport, thus providing an effective route for the design of high-performance power splitters. However, the existing topological power splitters still regulate the splitting ratio via modifying geometric parameters, reconfiguring topological interfaces, or changing the coupling path length, so continuous dynamic tuning within a fixed structure remains difficult after fabrication, which restricts their application in reconfigurable integrated photonic systems. To overcome this limitation, this work was to propose a liquid-crystal-assisted topological power splitter based on coupled valley photonic crystal waveguides. From the perspective of functional units and ordered architectures, the device used petal-shaped VPC unit cells as the functional units and utilized zigzag topological interfaces together with backward-coupled waveguides as the ordered splitter architecture, thereby enabling continuously tunable power distribution through external-field-controlled liquid-crystal molecular reorientation, while preserving topological robustness.

A petal-shaped VPC unit cell was designed as a functional unit of the device. The spatial inversion symmetry was broken and a topolo gical bandgap was opened under transverse-magnetic (TM) polarization via changing the rotation angle from α of 0° to α of ±30°. Two topologically distinct domains (denoted as VPCA and VPCB) were then arranged into zigzag AB and BA interfaces, forming an ordered architecture that could support valley-locked edge states. On this basis, a topological power splitter consisting of two parallel topological waveguides and one rectangular coupling region was constructed. The coupling distance (d) was 4a and the coupling length (L) was 170a. A nematic liquid crystal (LC) was introduced into the air holes in the boundary waveguide and coupling regions. A line source polarized along the out-of-plane direction was placed at Port 1 to excite the edge state in WG1. The numerical simulations were conducted to calculate band structures, projected interface bands, transmission spectra, power-flow distributions, and electric-field distributions. In the numerical model, the liquid crystal was treated as a uniaxial anisotropic medium, and its optical response was described by an orientation-dependent permittivity tensor associated with director rotation in the XZ plane. The ordinary and extraordinary refractive indices were taken as n_o of 1.45 and n_e of 1.75, respectively. The LC-controlled section length was denoted by w, and its influence on the output power ratio was investigated at a fixed operating frequency of 193.4 THz. To evaluate topological robustness, six defects belonging to three representative defect types were introduced into the structure.

Based on this mechanism, effective backward coupling is realized between two adjacent topological waveguides in opposite propagation directions, and the simulated power-flow distribution shows a coupling loop consisting of forward transport in WG1, backward transport in WG2, and local vortex-mediated energy flow. To verify whether the coupling effect can be still preserved after introducing liquid crystal (LC), the transmission spectra of the two cases without and with LC filling in the boundary-waveguide and coupling regions are compared. The results show that effective coupling maintains in both cases, while the operating frequency range shifts after introducing LC. In the LC-filled case, nearly complete power transfer from WG1 to WG2 is achieved at 193.1-193.6 THz, and the total transmission efficiency reaches 93% as L=170a. When the LC orientation changes fromθ of 90° to θ of 0°, the coupling band shifts from 192.5-194.1 THz to 185.8-187.2 THz. At a fixed operating frequency of 193.4 THz, increasing the LC-controlled length w continuously reduces the effective coupling region, decreases the output power from WG2, and increases the transmitted power in WG1, thereby enabling continuously tunable power splitting in a fixed structure. In addition, the transmission spectra and output power ratios remain nearly unchanged under the representative defect types, defect numbers, and defect distributions, indicating that the proposed device maintains a good robustness against structural perturbations.

An LC-assisted topological power splitter based on coupled valley photonic crystal waveguides was proposed and numerically demonstrated from the perspective of functional-unit engineering and ordered-architecture design. The device could achieve robust edge-state transport, effective inter-waveguide coupling, and continuously tunable power distribution within a fixed structure via combining petal-shaped valley photonic crystal unit cells, zigzag topological interfaces, the ordered architecture of backward-coupled waveguides, and external-field-controlled molecular reorientation of nematic liquid crystal. The results showed that the proposed splitter could reach a total transmission efficiency of 93%, realize continuously tunable power splitting via adjusting the LC-controlled length, and maintain stable transmission and power-distribution performance under the representative defect conditions. This work could provide a feasible strategy for reconfigurable on-chip power routing, dynamic optical interconnection, and actively tunable topological photonic devices.