【摘要】 旨在探索在片上波导阵列中利用模式合成维度构建高维拓扑光子态的方法。基于传播常数调制方法，研究了模式合成维度在片上波导阵列体系中的具体实现。首先，在一维J_x和Su-Schrieffer-Heeger(SSH)阵列中成功实现了模式维度构建，并观测到光场在合成维度中的演化。然后，将拓扑波导超胞阵列与模式合成维度结合，设计出可在一维实空间波导阵列中实现的准二维SSH拓扑晶格。数值仿真结果表明，该合成晶格能够支持并清晰地展示拓扑角态、实空间与模式维度的拓扑边界态以及体态的光传输特性。本工作为在低维片上光子平台上模拟和实现高维拓扑态提供了一种有效且与现有工艺兼容的新思路。更多还原

【Abstract】 Objective Exploring high-dimensional topological photonic states in on-chip platforms provides a promising route for developing integrated photonic devices and simulating complex physical phenomena.However,conventional on-chip waveguide arrays are inherently restricted to one-dimensional or quasi-one-dimensional geometries,which limits the implementation and investigation of higher-dimensional topological phases.Synthetic dimension approaches offer an effective strategy to overcome this dimensional limitation.This work aims to construct high-dimensional topological photonic states in on-chip waveguide arrays via mode-based synthetic dimensions enabled by propagation constant modulation,a method compatible with standard fabrication processes.It focuses on demonstrating feasible device designs and characterizing the transport properties of topological states in synthetic lattices,thereby establishing a practical framework for realizing high-dimensional topological photonics on chip.Methods We propose and numerically study a mode synthetic dimension scheme using propagation constant modulation in silicon-oninsulator(SOI) waveguide arrays.This method introduces controlled perturbations to the propagation constants of individual waveguides,breaking the orthogonality between the array supermodes and inducing nearest-neighbor coupling in mode space.First,the scheme is applied to one-dimensional J_x and Su-Schrieffer-Heeger(SSH) arrays to build a synthetic mode dimension.The synthetic Hamiltonian is derived using coup ling-modulated equations and eigenmode analysis.Full-wave simulations based on COMSOL Multiphysics are performed to verify the design and visualize light evolution in both real and synthetic spaces.Furthermore,we integrate waveguide supercells with the mode synthetic dimension to construct a quasi-two-dimensional SSH lattice within a physically one-dimensional array.The inter-supercell coupling is designed to be considerably weaker than intra-supercell coupling,maintaining the independence of supermodes while extending the synthetic lattice along the real-space dimension.Numerical simulations based on coupled-mode theory are carried out to analyze the propagation of topological edge states,corner states,and bulk states in the synthetic lattice.Results and Discussions In the one-dimensional J_x array,propagation constant modulation effectively induces coupling between supermodes,converting the array into a synthetic mode lattice.Light injected into a specific supermode shows dynamic evolution in mode space,transitioning to higher-order modes and reflecting at boundaries,which validates the successful construction of the synthetic dimension.For the four-site SSH array that satisfies the real-symmetric eigenvector matrix condition,modulation generates a synthetic SSH chain in mode space.When a bulk supermode in the original array is excited,light becomes localized at the edge of the synthetic lattice,revealing a topological edge state protected by SSH topology.In contrast,exciting an original edge supermode leads to light propagation within the bulk sites of the synthetic lattice with negligible coupling to the synthetic edges.By combining SSH waveguide supercells with mode synthetic dimensions,a quasi-two-dimensional SSH lattice is realized in a one-dimensional waveguide array,supporting various high-dimensional topological states.Exciting a bulk supermode in a boundary supercell produces a real-space edge state that diffuses rapidly along the synthetic lattice boundary and couples to the opposite edge through the bulk region.Exciting an edge supermode in a boundary supercell generates a topological corner state that remains strongly localized at the synthetic lattice corner with low dispersion.Exciting an edge supermode in a bulk supercell results in a mode-dimension edge state confined to one boundary of the synthetic lattice due to propagation constant mismatch.Bulk state excitation leads to fast propagation within the synthetic bulk,isolated from edges and corners.Although the synthetic lattice deviates from an ideal two-dimensional SSH model,such as exhibiting onsite energy mismatch in the mode dimension and non-uniform inter-supercell coupling,its fundamental topological properties are preserved,allowing the observation of corner states and robust edge transport.Conclusions This work demonstrates the feasibility of constructing high-dimensional topological photonic states in on-chip waveguide arrays through mode synthetic dimensions based on propagation constant modulation.We successfully realize onedimensional synthetic mode lattices in J_x and SSH arrays and observe the characteristic dynamics of topological edge states.Furthermore,by integrating waveguide supercells with the synthetic dimension,we design and numerically validate a quasi-twodimensional SSH lattice within a physically one-dimensional array,which supports topological corner states,real-space edge states,and mode-dimension edge states.The proposed approach offers a practical and fabrication-compatible route to emulate and study highdimensional topological phenomena on low-dimensional photonic platforms,with potential applications in robust integrated photonic circuits and topological photonic devices.更多还原