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拓扑泵浦模型可以在光学波导阵列体系中调控光场,有望实现高抗干扰能力的片上光子器件。本文从Rice-Mele拓扑泵浦模型出发,分析了当系统绝热演化条件随结构长度缩短被破坏后的光场演化过程,利用能带理论研究了其物理本质。发现受绝热属性调控,在特定参数下光场模式会经历非绝热演化但最终以边界态输出。该演化结果与绝热演化一致,可被称为等效绝热演化过程,后利用微扰理论证明了该特殊现象的物理本质是能带干涉。同时表明了绝热属性可以有效调控系统演化末态与边界态的一致程度,实现完全一致或完全相异的两种输出结果。该工作补充了拓扑泵浦非绝热演化的理论分析方法,拓展了拓扑泵浦模型的光场调控能力,可以作为光学波导阵列体系的基础设计理论,有望设计高抗干扰且小型化的片上光子器件。Topological pumping based on Thouless pumping can be effectively applied to optical waveguide array systems to achieve robust light manipulation with strong disturbance resistance. One of its typical models, the Rice-Mele (R-M) model, enables directional light field transmission from the leftmost (rightmost) waveguide to the rightmost (leftmost) waveguide, which can be utilized to realize fabrication-tolerant optical couplers. Adiabatic evolution is a critical factor influencing the transport of topological eigenstates. However, it requires the system’s parameter variation to be sufficiently slow, which leads to excessively long waveguide lengths, limiting device compactness. To reduce size, non-adiabatic evolution offers a feasible alternative. Meanwhile, the adiabatic properties of topological pumping models introduce new degrees of freedom, expanding possibilities for light manipulation. Based on the R-M model, this work analyzes the relationship between adiabatic property and structure length L, investigates light field evolution behavior when adiabatic condition is violated, and explores transition from adiabatic to non-adiabatic regimes. When adiabatic condition is satisfied (L1=1000μm), the light field evolution aligns with the eigen edge state. The output mode presents as the edge state, localized at the edge waveguide. As length shortens (L2=250μm and L4=30μm), the deviations between light field and eigen edge state arise, and the eigen bulk states get involved in the light field. The output modes present as the superposition of edge and bulk states, and energy spread to other waveguides. At the specific length (L3=110μm), the light-field undergoes non-adiabatic evolution, initially deviating from the edge state and later returning to it—a phenomenon termed adiabatic equivalent evolution. The output mode is localized at the edge waveguide, as same as the adiabatic evolution. By analyzing the fidelity between output mode and eigen edge state, we demonstrate that adiabaticity can effectively regulate fidelity, achieving signal on/off at the edge waveguide. As structural length decreases, fidelity gradually declines and exhibits oscillating behavior. When fidelity approach 1, adiabatic equivalent evolution emerges. First-order perturbation approximation reveals that these oscillations stem from destructive interference between edge and bulk states, confirming their intrinsic origin in band interference. This mechanism enables eigen edge state output at shorter lengths than adiabatic requirements, offering a reliable approach to miniaturize devices. Furthermore, the fabrication tolerance is analyzed. Within the whole waveguides width deviation range of -35~+30nm (relative deviation range of -7~+6%), the transmission of edge waveguide is larger than 0.9 through the adiabatic equivalent evolution. This work analyses light-field evolution process and underlying physics for topological pumping in non-adiabatic regimes, supplements theoretical methods for analyzing non-adiabatic evolution, and provides strategies to achieve eigen edge state output at reduced lengths. This work provides feasible design principles for topological optical waveguide arrays, guiding the development of compact and robust on-chip photonic devices such as optical couplers and splitters, with broad application prospects in integrated photonics.
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