AI 中文总结
研究多模波导弯曲设计，将其表述为依赖曲率的变分问题，通过构建品质因数推导绝热最优条件，引入SPC和SPCh弯曲，在特定平台上实现低损耗、宽带宽、制造宽容，为光互连和微波光子系统提供新设计策略。
AI 中文摘要
多模光子集成电路实现了超低损耗的片上光互连和微波光子处理，但波导弯曲在芯片尺寸和额外损耗方面占主导地位。高性能多模波导弯曲（MWB）必须在抑制模式间耦合的同时以低损耗传输工作模式，这在弯曲半径、工作带宽和制造公差之间形成了权衡。本文将等宽MWB设计表述为一个依赖曲率的变分问题。通过构建一个包含高阶模激发、基模失配和侧壁场强的品质因数，我们推导出绝热最优性的必要条件：曲率分布在整个弯曲区域，包括与输入和输出直波导的连接处，必须接近无穷可微性。这个条件解释了圆形和欧拉弯曲的局限性，并激发了具有封闭形式β函数表示的平滑多项式曲率（SPC）族。我们进一步引入了一种优化的SPC混合（SPCh）弯曲，它平衡了连接处的平滑度和内部曲率梯度。在220nm绝缘体上硅平台上，SPCh弯曲在16μm的有效半径下，从1500 - 1600nm实现了低于 - 37dB的模式消光比，在相同半径下比代表性的欧拉弯曲提供了超过22dB更强的模式抑制。模拟响应对于±60nm的波导宽度偏差仍然稳健。基于SPCh制造的微环谐振器通过标准硅制造工艺达到了高达7.53×10^6的固有品质因数和高达100GHz的自由光谱范围。所得的设计策略为高密度光互连和微波光子系统提供了紧凑、宽带且制造宽容的多模弯曲。
英文摘要
Multimode photonic integrated circuits enable ultralow-loss on-chip optical interconnects and microwave-photonic processing, yet waveguide bends dominate both chip footprint and excess loss. A high-performance multimode waveguide bend (MWB) must transmit the working mode with low loss while suppressing intermodal coupling, forcing a trade-off among bending radius, operating bandwidth, and fabrication tolerance. Here we formulate constant-width MWB design as a curvature-dependent variational problem. By constructing a figure of merit that incorporates higher-order-mode excitation, fundamental-mode mismatch, and sidewall field intensity, we derive a necessary condition for adiabatic optimality: the curvature profile must approach infinite differentiability throughout the bend, including its junctions with the input and output straight waveguides. This condition explains the limitations of circular and Euler bends and motivates a smooth polynomial curvature (SPC) family with a closed-form beta-function representation. We further introduce an optimized SPC hybrid (SPCh) bend that balances junction smoothness and the interior curvature gradient. On the 220 nm silicon-on-insulator platform, SPCh bends achieve a mode extinction ratio below $-37$ dB from 1500-1600 nm at an effective radius of $16\,μ\mathrm{m}$, providing more than 22 dB stronger mode suppression than a representative Euler bend at the same radius. The simulated response remains robust to $\pm 60$ nm waveguide-width deviations. Fabricated SPCh-based microring resonators reach an intrinsic quality factor of up to $7.53 \times 10^6$ and a free spectral range of up to 100 GHz through a standard silicon foundry process. The resulting design strategy provides compact, broadband, and fabrication-tolerant multimode bends for high-density optical interconnects and microwave-photonic systems.
