AI 中文总结
该研究利用片上斯托克斯层析成像实现了相干矩阵的对角化，验证了其在多模结构化相干中的有效性，还纠正了相干矩阵重构的步数认知，仅需O(N)步即可完成。
AI 中文摘要
结构化相干（由有限个模式张成的部分相干光）正成为光通信、计算、密码学和光谱学领域的强大工具。这些应用前景的关键在于片上结构化相干处理的最新进展，其中大型干涉仪网络对代表多模部分相干光的厄米相干矩阵执行幺正和非幺正变换。结构化相干应用的两个相关关键任务是未知相干矩阵的重构及其对角化。斯托克斯层析成像已被用于重构相干矩阵，而变分处理则被用于其对角化。本文表明，斯托克斯层析成像也可被用于未知相干矩阵的片上对角化，我们在集成六角形马赫-曾德尔干涉仪网络中对双模和四模结构化相干验证了这一点。该光子电路执行一系列预定配置以估计广义斯托克斯参数，最终步骤将据此重新配置光子电路，使相干矩阵对角化。由此，该场处于包含不相关正交模式的相干模式表示中，其权重对应于原始相干矩阵的本征值。此外，该集成光子电路可被配置为在电路输出端提供原始场及其对角化对应物。我们针对不同相干秩、熵和结构的相干矩阵验证了该对角化过程。最后，我们纠正了“重构N×N相干矩阵需要O(N²)步”的普遍观念，表明仅需O(N)步即可完成。
英文摘要
Structured coherence -- partially coherent light spanned by a finite number of modes -- is emerging as a powerful tool in optical communications, computation, cryptography, and spectroscopy. Key to these prospects is the recent development of on-chip processing of structured coherence, in which large meshes of interferometers implement unitary and non-unitary transformations on the Hermitian coherence matrix representing multimode partially coherent light. Two related critical tasks for the applications of structured coherence are the reconstruction of an unknown coherence matrix and its diagonalization. Stokes tomography has been utilized in reconstructing the coherence matrix, whereas variational processing has been employed in its diagonalization. We show here that Stokes tomography can also be exploited in the on-chip diagonalization of an unknown coherence matrix, which we verify for two-mode and four-mode structured coherence in an integrated hexagonal mesh of Mach-Zehnder interferometers. This photonic circuit implements a predetermined sequence of configurations to estimate the generalized Stokes parameters, which -- in a final step -- inform a reconfiguration of the photonic circuit that diagonalizes the coherence matrix. The field is thus left in a coherent-mode representation comprising uncorrelated, orthogonal modes whose weights correspond to the eigenvalues of the original coherence matrix. Moreover, the integrated photonic circuit can be configured to provide the original field alongside its diagonalized counterpart at the circuit output. We verify the diagonalization procedure for coherence matrices of different coherence rank, entropy, and structure. Finally, we dispel the common notion that O(N^2) steps are required for reconstructing an N x N coherence matrix and show that only O(N) steps are needed.
