In this paper, we investigate the theoretical models and potential applications of spatial diffractive neural network (SDNN) structures, with a particular focus on mode manipulation. Our research introduces a novel diffractive transmission simulation method that employs matrix multiplication, alongside a parameter optimization algorithm based on neural network gradient descent. This approach facilitates a comprehensive understanding of the light field manipulation capabilities inherent to SDNNs. We extend our investigation to parameter optimization for SDNNs of various scales. We achieve the demultiplexing of 5, 11 and 100 orthogonal orbital angular momentum (OAM) modes using neural networks with 4, 10 and 50 layers, respectively. Notably, the optimized 100 OAM mode demultiplexer shows an average loss of 0.52 dB, a maximum loss of 0.62 dB, and a maximum crosstalk of -28.24 dB. Further exploring the potential of SDNNs, we optimize a 10-layer structure for mode conversion applications. This optimization enables conversions from Hermite-Gaussian (HG) to Laguerre-Gaussian (LG) modes, as well as from HG to OAM modes, showing the versatility of SDNNs in mode manipulation. We propose an innovative assembly of SDNNs on a glass substrate integrated with photonic devices. A 10-layer diffractive neural network, with a size of 49 mm × 7 mm × 7 mm, effectively demultiplexes 11 orthogonal OAM modes with minimal loss and crosstalk. Similarly, a 20-layer diffractive neural network, with a size of 67 mm × 7 mm × 7 mm, serves as a highly efficient 25-channel OAM to HG mode converter, showing the potential of SDNNs in advanced optical communications.

中文翻译：

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使用深度空间衍射神经网络进行光学模式操纵

在本文中，我们研究了空间衍射神经网络（SDNN）结构的理论模型和潜在应用，特别关注模式操纵。我们的研究引入了一种新颖的衍射透射模拟方法，该方法采用矩阵乘法以及基于神经网络梯度下降的参数优化算法。这种方法有助于全面理解 SDNN 固有的光场操纵能力。我们将研究扩展到各种规模的 SDNN 的参数优化。我们分别使用 4、10 和 50 层的神经网络实现了 5、11 和 100 个正交轨道角动量 (OAM) 模式的解复用。值得注意的是，优化的 100 OAM 模式解复用器的平均损耗为 0.52 dB，最大损耗为 0.62 dB，最大串扰为 -28.24 dB。进一步探索 SDNN 的潜力，我们针对模式转换应用优化了 10 层结构。这种优化实现了从 Hermite-Gaussian (HG) 模式到 Laguerre-Gaussian (LG) 模式的转换，以及从 HG 到 OAM 模式的转换，显示了 SDNN 在模式操作方面的多功能性。我们提出了在与光子器件集成的玻璃基板上创新性地组装 SDNN。尺寸为 49 mm × 7 mm × 7 mm 的 10 层衍射神经网络可有效解复用 11 个正交 OAM 模式，同时损失和串扰最小。同样，尺寸为 67 mm × 7 mm × 7 mm 的 20 层衍射神经网络可作为高效的 25 通道 OAM 到 HG 模式转换器，显示了 SDNN 在先进光通信中的潜力。