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摘要:
基于马赫-曾德尔干涉仪（Mach-Zehnder Interferometer, MZI）级联拓扑结构的线性光学处理器被证明是实现光学神经网络（Optical Neural Network, ONN）的重要途径，但还有不少实际问题有待解决。针对芯片制造、测试过程中可能导致的相位误差和插入损耗等问题，通过实验和理论仿真分析了几种基于MZI结构的可重构光学处理器。发现可以通过单个
N ×N 的Clements阵列结构来实现任意酉矩阵的权重，构建稀疏连接的全复值光学神经网络，将光学深度大大降低，以实现较高的插入损耗鲁棒性。此外，对于多层光学神经网络来说，由于构建该任意酉矩阵的自由度有限，故在每一层Clements结构前面加一个相移器层，有助于将分类数据映射到更高的数据维度，能使神经网络更快速的收敛。Abstract:Linear optical processors based on the cascaded topology of Mach-Zehnder Interferometer (MZI) have been demonstrated to be an important way of implementing Optical Neural Networks (ONN), but several practical challenges still need resolution. Concerning issues arising from chip manufacturing and testing processes that could lead to phase errors and insertion losses, we conducted experiments and theoretical simulations for various reconfigurable optical processors. We found that the weights of any arbitrary unitary matrix can be realized through some single
N×N Clements units, that can substantially reduce the optical depth and enhance robustness against insertion losses. This approach allows for the construction of fully complex optical neural networks. Additionally, In multi-layer ONN, due to the limited degrees of freedom in constructing this arbitrary matrix, we introduced a phase-shift layer before each layer of the Clements unit. This design aids in mapping classification data to higher-dimensional spaces, facilitating faster neural network convergence. -
图 1 单个2×2 的MZI器件（a）结构示意图及（b）双端口输出功率响应曲线
Figure 1. (a) Structural diagram and (b) dual port output power response curves of single 2×2 MZI device
图 3 两种MZI阵列拓扑结构的插损与相位敏感性
Figure 3. Insertion-loss and phase sensitivity of two types of MZI array topologies
图 4 一种快速收敛的拓扑架构和对应的神经网络示意图
Figure 4. The rapidly converging topology architecture and the corresponding neural network diagram
图 5 多维聚类高斯分布数据的分类任务
Figure 5. Classification tasks for multidimensional clustering Gaussian-distribution data
图 6 两种双层光学神经网络芯片的训练过程
Figure 6. The training processes of two double-layer optical neural network chips
图 7 Iris数据在双层光学神经网络中的训练及分类结果
Figure 7. Training and classification results of Iris data in double-layer optical neural networks
表 1 第一层Clements结构中相移器的相位值
Table 1. The value of the phase shifter in the first layer Clements structure
MZI (1) (2) (3) (4) (5) (6) θ(rad) 1.354 2.518 1.683 2.614 2.614 6.248 φ(rad) 1.064 4.881 0.995 2.175 1.535 0.130 
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表 2 第二层Clements结构中相移器的相位值
Table 2. The value of the phase shifter in the second layer Clements structure
MZI (1) (2) (3) (4) (5) (6) θ(rad) 0.393 1.452 0.270 0.505 5.662 1.250 φ(rad) 5.447 3.434 2.740 0.700 5.416 5.690
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