Implementing any linear transformation matrix through the optical channels of an on-chip reconfigurable multiport interferometer has been emerging as a promising technique for various fields of study, such as information processing and optical communication systems. Recently, the use of multiport optical interferometric-based linear structures in neural networks has attracted a great deal of attention. Optical neural networks have proven to be promising in terms of computational speed and power efficiency, allowing for the increasingly large neural networks that are being created today. This paper demonstrates the experimental analysis of programming a $4\times 4$ reconfigurable optical processor using a unitary transformation matrix implemented by a single layer neural network. To this end, the Mach-Zehnder interferometers (MZIs) in the structure are first experimentally calibrated to circumvent the random phase errors originating from fabrication process variations. The linear transformation matrix of the given application can be implemented by the successive multiplications of the unitary transformation matrices of the constituent MZIs in the optical structure. The required phase shifts to construct the linear transformation matrix by means of the optical processor are determined theoretically. Using this method, a single layer neural network is trained to classify a synthetic linearly separable multivariate Gaussian dataset on a conventional computer using a stochastic optimization algorithm. Additionally, the effect of the phase errors and uncertainties caused by the experimental equipment inaccuracies and the device components imperfections is also analyzed and simulated. Finally, the optical processor is experimentally programmed by applying the obtained phase shifts from the matrix decomposition process to the corresponding phase shifters in the device. The experimental results show that the optical processor achieves 72$\%$ classification accuracy compared to the 98.9$\%$ of the simulated optical neural network on a digital computer.

中文翻译：

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由基于 4×4 MZI 的光处理器实现的单层神经网络

通过片上可重构多端口干涉仪的光通道实现任何线性变换矩阵已成为各种研究领域的有前途的技术，例如信息处理和光通信系统。最近，在神经网络中使用基于多端口光学干涉测量的线性结构引起了广泛关注。事实证明，光神经网络在计算速度和功率效率方面很有前景，可以支持当今正在创建的越来越大的神经网络。本文演示了使用由单层神经网络实现的酉变换矩阵对 $4\times 4$ 可重构光学处理器进行编程的实验分析。为此，该结构中的 Mach-Zehnder 干涉仪 (MZI) 首先经过实验校准，以规避由制造工艺变化引起的随机相位误差。给定应用的线性变换矩阵可以通过光学结构中组成 MZI 的酉变换矩阵的连续乘法来实现。通过光学处理器构建线性变换矩阵所需的相移是从理论上确定的。使用这种方法，训练单层神经网络以使用随机优化算法在常规计算机上对合成的线性可分多元高斯数据集进行分类。此外，还分析和模拟了由实验设备不准确和器件元件缺陷引起的相位误差和不确定性的影响。最后，通过将矩阵分解过程中获得的相移应用于设备中的相应移相器，对光学处理器进行实验编程。实验结果表明，与数字计算机上模拟光神经网络的 98.9$\%$ 相比，该光处理器实现了 72$\%$ 的分类精度。