On-chip measurement of the modal Stokes-Gell-Mann parameters for partially coherent three-mode light
部分相干三模光场的模态Stokes-Gell-Mann参数片上测量
Amin Hashemi, Abbas Shiri, Bahaa E. A. Saleh, Andrea Blanco-Redondo, Ayman F. Abouraddy
AI总结 提出并实验演示了在光子集成平台上首次直接测量部分相干三模光场的Stokes-Gell-Mann参数,通过重构3×3相干矩阵探索等熵场空间。
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Stokes参数是三个实数参数,完全表征由两个模式(无论是偏振模式对还是空间模式对)张成的部分相干光场,因此在光学中无处不在。由于Stokes参数是通过Pauli矩阵展开$2\ imes2$相干矩阵定义的,它们不能应用于包含三个模式的光场,这些光场由$3\ imes3$相干矩阵描述。此类光场的例子包括非傍轴场的偏振(由三个正交偏振模式张成)以及包含三个空间或时间模式的光场。理论上早已提出,高能粒子物理学中发展的$3\ imes3$ Gell-Mann矩阵可以作为$3\ imes3$光学相干矩阵的基,其8个展开系数称为Stokes-Gell-Mann (SGM)参数,但测量过程艰巨,且SGM参数至今未在光学中被直接测量。在这里,我们首次在包含六边形马赫-曾德尔干涉仪网格的光子集成平台上测量了部分相干三模光场的SGM参数。在芯片上测量SGM参数,并由此重构$3\ imes3$相干矩阵,有助于探索可以通过幺正变换相互转换的等熵场的完整空间,以及那些具有相同熵值但无法通过幺正变换相互转换的场。这些结果为在光通信、传感和信息处理等应用中利用多模部分相干光铺平了道路。
The Stokes parameters are three real parameters that completely characterize partially coherent optical fields spanned by two modes -- whether a pair of polarization or spatial modes -- and their use is thus ubiquitous in optics. Because the Stokes parameters are defined through an expansion of the $2\times2$ coherence matrix in terms of the Pauli matrices, they cannot be applied to optical fields comprising three modes, which are described by a $3\times3$ coherence matrix. Examples of such fields include the polarization of non-paraxial fields (spanned by three orthogonal polarization modes), and fields comprising three spatial or temporal modes. It has long been theorized that the $3\times3$ Gell-Mann matrices -- developed in high-energy particle physics -- can serve as a basis for $3\times3$ optical coherence matrices, with 8~expansion coefficients known as the Stokes-Gell-Mann (SGM) parameters, but the measurement procedure is daunting, and the SGM parameters have not been measured directly to date in optics. Here we present the first measurements of the SGM parameters for partially coherent three-mode light in a photonic integrated platform comprising a hexagonal mesh of Mach-Zehnder interferometers. Measuring the SGM parameters on chip, from which we reconstruct the $3\times3$ coherence matrix facilitates exploring the full space of iso-entropy fields that can be inter-converted into each other unitarily, and those that share the same value of entropy and yet cannot be inter-converted unitarily. These results pave the way to utilizing multimode partially coherent light in applications involving optical communications, sensing, and information processing.