发表机构
MESA+ Institute for Nanotechnology, University of Twente; Institute of Photonics and Quantum Electronics (IPQ), Karlsruhe Institute of Technology (KIT)（特文特大学 MESA+ 纳米技术研究所; 卡尔斯鲁厄理工学院光子与量子电子学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出在单个集成多模波导中利用分布式热光扰动实现可重构线性光学变换，通过可微分模型和梯度优化，实现高保真度波前整形与矩阵运算，为集成光子处理提供新途径。
AI 中文摘要
波前整形能够实现对光场的控制，其应用范围从成像到光子信息处理不等。虽然传统的波前整形依赖于由体光学元件组成的自由空间系统，但紧凑且完全集成的方法相对而言尚未得到充分探索。在此，我们提出一种基于单个多模波导并带有分布式热光扰动的概念，用于控制多模传播。我们开发了一个可微分的物理模型，并利用基于梯度的优化，数值演示了出射波前的整形和可编程的线性光学变换。我们实现了20个空间模式的衍射极限聚焦，并表明在保持超过输入光功率99%的情况下，可以维持理论聚焦极限。我们将此方法扩展到完整的输入-输出变换，并实现了维度高达32×32的Sylvester-Hadamard矩阵运算，其相关性超过99%。减少可调元件的数量需要更强的个体扰动，这导致更强且更广泛的模式耦合，超出了目标模式。为减轻此效应，我们考虑了辅助模式，并实现了一个4×4变换，仅用5N^2个可调元件（其中N=4表示空间模式数）即达到93.8%±4.8%的相关性。性能最佳的实现达到了与目标98.3%的相关性。我们的结果表明，多模波导的热光控制为全集成波前整形和可编程线性光学变换提供了一种方法，在经典和量子光子处理中具有潜在应用。
英文摘要
Wavefront shaping enables control over optical fields for applications ranging from imaging to photonic information processing. While conventional wavefront shaping relies on free-space systems comprising bulk optical components, compact and fully integrated approaches are comparatively unexplored. Here, we introduce a concept based on a single multimode waveguide with distributed thermo-optic perturbations for controlling multimode propagation. We develop a differentiable physical model and numerically demonstrate shaping the outgoing wavefront and programmable linear optical transformations, using gradient-based optimization. We achieve diffraction-limited focusing with 20 spatial modes and show that the theoretical focusing limit can be retained while maintaining more than $99\%$ of the input optical power. We extend this approach to complete input--output transformations and implement Sylvester--Hadamard matrix operations with dimensions up to $32\times32$ with correlations exceeding $99\%$. Reducing the number of tunable elements requires stronger individual perturbations, resulting in stronger and broader mode coupling that extends beyond the target modes. To mitigate this effect, we consider ancillary modes and realize a $4\times4$ transformation that reaches $93.8\%\pm4.8\%$ correlation with only $5N^2$ tunable elements, where $N=4$ denotes the number of spatial modes. The best-performing realization reaches $98.3\%$ correlation with the target. Our results demonstrate that thermo-optic control of multimode waveguides offers an approach to fully-integrated wavefront shaping and programmable linear optical transformations, with potential applications in classical and quantum photonic processing
