结构化相干性：将光学相干作为一种资源的现代视角
Structured coherence: A modern perspective on optical coherence as a resource
AI总结：
该研究提出将结构化相干性作为光学资源，通过相干矩阵构建其理论框架，揭示部分相干性的相干优势，为集成光子平台的光信息处理应用提供新途径。
AI中文摘要：
光学相干是物理光学中一个成熟的分支，该领域通过连续空间和时域自由度（DoFs）上的关联函数来描述波动光场的统计特性。然而，在任何实际场景中，仅能获取离散的自由度。在这些场景中，模式是固定、稳定且确定的，部分相干性源于随机的相对复振幅，这种构型被称为“结构化相干性”。结构化相干性的最新进展揭示了光通信和信息处理领域的新概念基础，其中部分相干性可能比完全相干性更具优势，我们将这种情况称为“相干优势”。我们通过相干矩阵来构建结构化相干性，以研究这些近期的理论和实验突破。我们首先通过2×2厄米相干矩阵表征具有二元自由度的光场，并引入对更大维度模态集具有新重要性的关键概念。接着，我们研究两个二元自由度的结构化相干性，其可通过4×4相干矩阵描述。我们引入了相干秩、熵交换和光学交叉纯度的概念。在此概述的视角中，相干被视为一种“资源”，可在自由度之间交换、集中到某一自由度或特定模式中，或分散到多个自由度上。随后，我们研究更大维度的模态集，其可在光信息处理中实现更通用的应用。此处提出的构建方法尤其适用于集成光子平台中部分光学相干性的操控，从而为结构化相干性的新型基础研究开辟了众多途径，并为光通信和信息处理中的相干优势开发提供了可能。
英文摘要：
Optical coherence is a well-established branch of physical optics in which the statistical properties of fluctuating optical fields are described in terms of correlation functions over continuous spatial and temporal degrees of freedom (DoFs). Nevertheless, in any practical setting, only discrete DoFs are ever accessible. In these scenarios, the modes are fixed, stable, and deterministic, and partial coherence arises from random relative complex amplitudes, a configuration we refer to as 'structured coherence'. Advances in structured coherence have recently unveiled new conceptual ground in optical communications and information processing in which partial coherence may be preferable to full coherence, which we call a 'coherence advantage'. We formulate structured coherence in terms of coherence matrices to investigate these recent theoretical and experimental breakthroughs. We first review optical fields characterized by a binary DoF via 2x2 Hermitian coherence matrices and introduce key concepts that take on new significance for larger-dimensional modal sets. Next, we examine the structured coherence of two binary DoFs, which can be described by 4x4 coherence matrices. We introduce the concept of coherence rank, entropy swapping, and optical cross-purity. In the perspective outlined here, coherence is viewed as a 'resource', which can be exchanged between DoFs, concentrated into a DoF or into particular modes, or spread over the DoFs. We then examine larger-dimensional modal sets, which allow for more versatile applications in optical information processing. The formulation presented here lends itself particularly to the manipulation of partial optical coherence in integrated photonic platforms, thereby opening myriad avenues for novel fundamental investigations of structured coherence and exploiting the coherence advantage in optical communications and information processing.
