基于光学“准角态”和“准轨道角动量态”的通用线性变换

Linear optical transformations of high-dimensional vectors is a fundamental and powerful tool for both quantum mechanics and classical technologies. Typically, arbitrary linear operators can be achieved with the Reck scheme, in which the N-dimensional transformation matrix is achieved by a specific triangular mesh of 2ⅹ2 beam splitters (or directional coupler) and phase shifters. Thus, as the dimensionality (N) increased, the complexity in terms of system arrangement and parameter control would grow significantly as the square of the dimension(N^2). In order to avoid the cascaded multi-stage mesh in the Reck structure, we have proposed the concept of "quasi OAM state" and "quasi angular state" of finite dimension. Although the characteristics of the infinite dimension of OAM state is cut off, quasi angular state and quasi OAM state have guaranteed the practical implementation. Recently, we have realized the 7-dimensional arbitrary linear transformation matrix, which exceeds the reported 6-dimensional arbitrary coefficient matrix. In this project, the research target is to perform optical linear transformation matrix of arbitrary dimension coefficients with dimensionality more than 20. The contents of this project include: (1) further optimizing the high dimensional optical linear transform scheme based on "quasi angle state" and "quasi OAM" state with improved the matrix dimension, transform fidelity and conversion efficiency; (2) validating the optical linear transformation of more than 20-dimension; (3) application of high dimensional optical linear transformation, including OAM sorting and topological charge detection in classical optics as well as quantum state detection and multi-photon boson sampling in quantum optics.

对高维向量的线性变换是光学信息处理中一个基础而又功能强大的工具，在量子光学和经典光学领域都有重要的应用。目前实现高维线性变换的方案是通过级联2ⅹ2矩阵变换单元的Reck结构，但是器件数目将随着维度的平方增加。为了避免Reck结构中多级级联结构，我们提出了有限维“准OAM态”和“准角态”概念。“准角态”和“准OAM态”，虽然牺牲了OAM态无限维度的特性，但保证了物理的可实现性。我们已经实现了7维的任意线性变换矩阵，超过了已有报道的6维任意系数光学变换矩阵。本项目研究目标：实现维度超过20的任意复系数的光学线性变换矩阵，研究内容：(1)进一步优化基于“准角态”和“准OAM态”高维光学态线性变换方案，提高矩阵维度、变换保真度和变换效率；(2)超过20维的光学态线性变换的实验论证；(3)高维光学态线性变换的应用研究，包括经典光学中的OAM分类与拓扑荷检测以及量子光学中量子态的检测和光子玻色采样等。

对高维向量进行线性变换是光学信息处理一个基础而又功能强大的工具，在量子光学和经典光学领域都有着广泛而重要的应用。项目的研究目标：实现维度超过20的任意系数的光学线性变换矩阵，研究内容包括：(1) 进一步优化基于“准角态”和“准OAM态”高维光学态线性变换方案，提高矩阵维度、变换保真度和变换效率；(2) 超过20维的光学态线性变换的实验论证；(3) 高维光学态线性变换的应用研究。经过4年的研究，本项目按照原定计划顺利完成了原定的研究目标，项目负责人冯雪作为通信作者累计发表期刊论文8篇，其中SCI收录论文7篇，获得专利授权一项，取得的成果主要包括三方面：（1）高维光学模态的线性变换架构方面：实现了基于离散相干空间模式的24维可编程任意线性变换，而已有报道最高值为6维（Journal of Optics 21, 104003, (2019)）；提出并验证了一种用于光学线性变换的矩阵变换方案，实现了路径域和轨道角动量(OAM)域酉变换架构的统一（National Science Open, 1(3): 20220019 (2022)）。（2）高维光学线性变换的应用：在量子光学领域，基于离散空间相干模式实现了15维量子态层析矩阵的变换（Physical Review Applied, 14(2), 024027, (2020)）；提出了基于“采样—复矩阵变换—平方检波”的单层全光神经网络架构，并进行了手写数字识别和物体图像识别实验（Optics Express, 29 (17): 26474-26485 (2021)）。 （3）新型集成器件方面：实现了一种偏振控制产生单向传输局域余弦高斯光束（LCGB）的耦合器（Optics Express, 27 (16): 22053-22073, (2019)），进一步还实现了带有相位调制的复合光学角动量分束器（ACS Photonics, 7(1): 212-220, (2020)）；优化硅基集成光学轨道角动量（OAM）发射器，实现11阶OAM模式动态切换，是已有报道中可调阶次范围最大的（Photonics Research, 9 (9): 1865-1870 (2021)），进一步实现了国际上首个室温工作、硅基集成、阶次可调的OAM可预报单光子源（Laser Photonics Review, 16(12), 2270059)。

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