AI 中文总结
该研究在飞秒激光写入的椭圆玻璃波导中，通过共同设计波导限制与扰动奇偶性，实现对称性引导的模式控制，为量子光子应用提供路径-模式联合自由度支持。
AI 中文摘要
少模光子电路无需增加波导路径即可提升功能，但弯曲和制造误差会混合其横模。我们研究一种策略，即在垂直椭圆的飞秒激光写入玻璃波导中，共同设计波导限制与扰动奇偶性。目标模式基包括偶1S模式和垂直奇2P_y模式。低限制（LC）设计未解析出窗口收敛的2P_x态，而高限制（HC）设计能引导2P_x，因此需通过对称性将其隔离。在标量光束传播计算中，1S-2P_y的传播常数分裂对垂直调制相干模式分离器的优化周期预测误差在1.0%以内。水平S形弯曲对1S↔2P_y耦合仍为奇偶不匹配，而对称性允许的HC设计下1S→2P_x转移在最大位移处仅达0.6%。位移为150μm时，HC设计保留的2P_y功率与LC设计在40μm处保留的功率大致相同。热和随机写入误差计算揭示了权衡：更强的限制提升模式功率保留，但破坏x奇偶性的写入抖动会使导模2P_x被激发。这些结果表明，模式基工程可将部分串扰控制负担从波导轨迹转移至波导对称性，为量子光子应用中的路径-模式联合自由度提供支持。
英文摘要
Few-mode photonic circuits can increase functionality without multiplying waveguide paths, but bends and fabrication errors can mix their transverse modes. We investigate a strategy in which waveguide confinement and perturbation parity are engineered together in vertically elliptical, femtosecond-laser-written glass waveguides. The intended modal basis comprises the even $1S$ mode and the vertically odd $2P_y$ mode. No window-converged $2P_x$ state is resolved for a lower-confinement (LC) design, whereas a higher-confinement (HC) design guides $2P_x$, which must therefore be isolated by symmetry. In scalar beam-propagation calculations, the $1S$-$2P_y$ propagation-constant splitting predicts the optimized periods of a vertically modulated coherent modal splitter to within $1.0\%$. Horizontal S-bends remain parity-mismatched for $1S \leftrightarrow 2P_y$ coupling, while the symmetry-allowed HC $1S \rightarrow 2P_x$ transfer reaches only $0.6\%$ at the largest displacement. At a displacement of $150~μ\mathrm{m}$, the HC design retains approximately the same $2P_y$ power as the LC design retains at $40~μ\mathrm{m}$. Thermal and stochastic writing-error calculations reveal the resulting trade-off: stronger confinement improves modal-power retention, but writing jitter that breaks $x$-parity can populate the guided $2P_x$ mode. These results demonstrate how modal-basis engineering can shift part of the crosstalk-control burden from the trajectory to waveguide symmetry, supporting joint path--mode degrees of freedom in quantum photonic applications.
