光逻辑门作为电计算向光计算跨越的桥梁，可以进行通用计算，具有处理速度快、串扰低和吞吐量高等特点。利用轨道角动量模式无穷大和正交性的特性，将其作为光逻辑门的逻辑状态，不仅提高了逻辑门的并行处理能力，而且增强了其逻辑区分度和鲁棒性。论文提出了一种傅里叶空间与衍射深度神经网络相结合的方法实现增强型光逻辑门架构，有效降低了对逻辑门入射光束的质量和配准度的要求。主要研究内容包括：

（1）采用具有轨道角动量的涡旋光作为逻辑门输入信号，生成了完备状态的输入光波前数据集。基于光学衍射深度神经网络构建光学器件的多层衍射神经网络模型，以衍射深度神经网络输出平面上的特定光强度分布表征逻辑运算结果，训练并建立了衍射深度神经网络模型，实现“与”、“或”和“非”等基本逻辑运算。

（2）为优化衍射深度神经网络实现逻辑运算系统的性能，使之在非理想入射波前状态下依然能保证较低的误码率。论文利用频域对信号的空间域变化不敏感的特点，在衍射深度神经网络模型的基础上，提出将傅里叶空间与衍射深度神经网络相结合，构成傅里叶-衍射深度神经网络。在频域空间中采用仅振幅型调制的衍射深度神经网络，训练并建立了傅里叶透镜后端的衍射深度神经网络模型。仿真实现了“与”、“或”和“非”逻辑门运算，能够有效地降低逻辑门对入射光束的质量和配准度的要求，同时减少了模型物理制作的难度。

（3）为设计和开发具有标准功能的光学模块器件，通过级联基本逻辑门的方法构建“异或”门和“同或”门，实现衍射深度神经网络逻辑运算系统。仿真实验结果表明，基于傅里叶-衍射深度神经网络调制轨道角动量模式实现逻辑门的方法能够降低光逻辑计算的误码率，提高光逻辑门的鲁棒性，为逻辑门实际应用提供了一种潜在的解决方案，在光计算中具有潜在的应用前景。

Optical logic operations demonstrate the key role of optical digital computing, which can perform general-purpose calculations with high processing speed, low crosstalk and high throughput. Using the properties of orbital angular momentum mode infinity and orthogonality as the logic states of the optical logic gates, this not only improves parallel processing but also enhances the logic differentiation and robustness of the logic gates. The paper proposes a method based on a combination of Fourier and diffraction deep neural network to implement an enhanced optical logic gate architecture, which can effectively reduce the quality and alignment requirements of the incident beam. The main research elements include:

(1) The vortex beam with orbital angular momentum is used as the input signal of logic gate, the input votex wavefront data set with complete states is generated. The multilayer diffraction neural network model of optical device is constructed, the logic operation results are characterized by the specific light intensity distribution on the output plane of diffraction deep neural network, and the diffraction deep neural network model is trained and established to realize the basic logic operations such as ‘AND’, ‘OR’ and ‘NOT’.

(2) In order to optimize the performance of diffraction deep neural network for logic operations, a low Bit Error Bite can be guaranteed even in non-ideal incident wavefront states. Taking advantage of the insensitivity of the frequency domain to changes in the spatial domain of the signal, the thesis proposes to combine Fourier space with diffraction deep neural network on the basis of the diffraction deep neural network model to make up a Fourier-diffraction deep neural network. The amplitude-only modulated diffraction deep neural network in the frequency domain space are used to train and build the diffraction deep neural network model at the back end of the Fourier lens. The simulation implements ‘AND’, ‘OR’ and ‘NOT’ logic gates, which effectively reduces the quality and alignment requirements of the incident beam for the logic gates, while reducing the physical difficulty of the model.

(3) In order to design and develop an optical module device with standard functions, a diffraction deep neural network logic operation system is implemented by cascading basic logic gates to build ‘NOR’ and ‘XNOR’ gates. The simulation results show that the implementation of logic gates based on Fourier-diffraction deep neural network modulated orbital angular momentum patterns can reduce the Bit Error Rate of optical logic operations and improve the robustness of optical logic gates. It provides a potential solution for the practical application of logic gates and has potential application prospects in optical computing.

[1]Abdollahramezani S, Hemmatyar O, Adibi A. Meta-optics for spatial optical analog computing[J]. Physics Optics, 2020, 9(13): 4075-4095.

[2]Shastri B J, Tait A N, Ferreira De Lima T, et al. Photonics for artificial intelligence and neuromorphic computing[J]. Nature Photonics, 2021, 15(2): 102-114.

[3]Wetzstein G, Ozcan A, Gigan S, et al. Inference in artificial intelligence with deep optics and photonics[J]. Nature, 2020, 588(7836): 39-47.

[4]Muhammed V, Deniz M, Nezih T Y, et al. Terahertz pulse shaping using diffractive networks[C]//AI and Optical Data Sciences II. 2021: 117031G.

[5]Jianmin X, Zejun Z, Jing X. Advances and progress of diffractive deep neural networks[C]//Proc.SPIE, 2021: 120690V.

[6]Zhou T, Fang L, Yan T, et al. In situ optical backpropagation training of diffractive optical neural networks[J]. Photonics Research, 2020, 8(6): 940-953.

[7]Xiao Y-L, Li S, Situ G, et al. Unitary learning for diffractive deep neural network[J]. Optics and Lasers in Engineering, 2021, 139(1): 106499.

[8]Caulfield H J, Dolev S. Why future supercomputing requires optics? [J]. Nature Photonics, 2010, 4(5): 261-263.

[9]Sawchuk A A, Strand T C. Digital optical computing[J]. Proceedings of the IEEE, 1984, 72(7): 758-779.

[10]Brenner K-H, Huang A, Streibl N. Digital optical computing with symbolic substitution[J]. Applied Optics, 1986, 25(18): 3054-3060.

[11]Bakopoulos P, Vyrsokinos K, Fitsios D, et al. All-optical T-flip-flop using a single SOA-MZI-based latching element[J]. IEEE Photonics Technology Letters, 2012, 24(9): 748-750.

[12]Westlund M, Andrekson P A, Sunnerud H. High performance all-optical waveform sampling for fiber communication systems[C]//European Conference on Optical Communication. IET, 2005, 4: 937-940.

[13]Dagenais M, Geunmin R, Simarjeet S, et al. Semiconductor optical amplifier switch matrices for optical header recognition[C]//Proceedings of SPIE - The International Society for Optical Engineering, 2008, 6897: 68970X-68970X-13.

[14]Teimoori H, Topomondzo J D, Ware C, et al. Optical packet header processing using time-to-wavelength mapping in semiconductor optical amplifiers[J]. Journal of Lightwave Technology, 2007, 25(8): 2149-2158.

[15]Rendón-Salgado I, Ramírez-Cruz E, Gutiérrez-Castrejón R. 640 Gb/s all-optical AND gate and wavelength converter using bulk SOA turbo–switched Mach–Zehnder interferometer with improved differential scheme[J]. Optics & Laser Technology, 2019, 109: 671-681.

[16]Soto H, Diaz C A, Topomondzo J, et al. All-optical AND gate implementation using cross-polarization modulation in a semiconductor optical amplifier[J]. IEEE Photonics Technology Letters, 2002, 14(4): 498-500.

[17]Kobayashi M. More than Moore[J]. The Journal of The Institute of Image Information and Television Engineers, 2016, 70(3): 324-327.

[18]Xu X, Tan M, Corcoran B, et al. Photonic perceptron based on a kerr microcomb for high-speed, scalable, optical neural networks[J]. Laser & Photonics Reviews, 2020, 14(10): 2000070.

[19]Liu J, Huang Y, Wang F, et al. Numerical simulation of all-optical logic gates based on hybrid-cavity semiconductor lasers[J]. Journal of the Optical Society of America. A, Optics, 2021, 38(6): 808-816.

[20]王俊，杨晓飞．光子芯片研究进展及展望[J]．世界科学，2020，12．

[21]Sun Z, Xie L, Hu D, et al. An artificial neural network model for accurate and efficient optical property mapping from spatial-frequency domain images[J]. Computers and Electronics in Agriculture, 2021, 188: 106340.

[22]Kaur S, Prakash A. All-optical comparator using logic operations based on nonlinear properties of semiconductor optical amplifier[J]. Journal of Optics, 2018, 47(1): 104-109.

[23]Mukherjee K, Kumbhakar D. Simulation of two photon absorption in silicon wire waveguide for implementation of all optical logic gates[J]. Optik, 2012, 123(6): 489-493.

[24]Wang D, Zhang M, Lu G-W, et al. Multifunctional all-optical signal processing scheme for simultaneous multichannel WDM multicast and XOR Logic gates based on FWM in QD-SOA[C]//Optical Fiber Communication Conference, 2015: 1-3.

[25]Zhang X, Thapa S, Dutta N K. All-optical logic gates based on quantum-dot semiconductor optical amplifier[J]. International Journal of High Speed Electronics and Systems, 2018, 27(12): 131-141.

[26]Katumba A, Yin X, Dambre J, et al. A neuromorphic silicon photonics nonlinear equalizer for optical communications with intensity modulation and direct detection[J]. Journal of Lightwave Technology, 2019, 37(10): 2232-2239.

[27]Sui X, Wu Q, Liu J, et al. A review of optical neural networks[J]. IEEE Access, 2020, 8(99): 70773-70783.

[28]Zuo Y, Cao C, Cao N, et al. Optical neural network quantum state tomography[J]. Advanced Photonics, 2022, 4(2): 91-97.

[29]Yang F T. Deep belief network-hidden Markov model based nonlinear equalizer for VCSEL based optical interconnect[J]. Science China Information Sciences, 2020, 63(6): 151-159.

[30]Xu F. A survey of approaches for implementing optical neural networks[J]. Optics & Laser Technology, 2021, 136(1): 106768.

[31]Lin X, Rivenson Y, Yardimci N T, et al. All-optical machine learning using diffractive deep neural networks[J]. Science, 2018, 361(6406): 1004-1008.

[32]Zhao Q, Hao S, Wang Y, et al. Orbital angular momentum detection based on diffractive deep neural network[J]. Optics Communications, 2019, 443: 245-249.

[33]Yan T, Wu J, Zhou T, et al. Fourier-space diffractive deep neural network[J]. Physical Review Letters, 2019, 123(2): 023901.

[34]Xiong W, Huang Z, Wang P, et al. Optical diffractive deep neural network-based orbital angular momentum mode add–drop multiplexer[J]. Optics Express, 2021, 29(22): 36936-36952.

[35]Franke-Arnold S. 30 years of orbital angular momentum of light[J]. Nature Reviews Physics, 2022, 4(6): 361-361.

[36]Qian C, Lin X, et al. Performing optical logic operations by a diffractive neural network[J]. Light : Science & Applications, 2020, 9(1):1448-1454.

[37]Wang P, Xiong W, Huang Z, et al. Orbital angular momentum mode logical operation using optical diffractive neural network[J]. Photonics Research, 2021, 9(10): 2116-2124.

[38]Zarei S, Khavasi A. Realization of optical logic gates using on-chip diffractive optical neural networks[J]. Scientific Reports, 2022, 12(1): 15747.

[39]Yao A M, Padgett M J. Orbital angular momentum: origins, behavior and applications[J]. Advances in Optics and Photonics, 2011, 3(2): 161-204.

[40]Molina-Terriza G, Torres J P, Torner L. Twisted photons[J]. Nature Physics, 2007, 3(5): 305-310.

[41]Willner A E, Huang H, Yan Y, et al. Optical communications using orbital angular momentum beams[J]. Advances in Optics and Photonics, 2015, 7(1): 66-106.

[42]Albarqouni S, Baur C, Achilles F, et al. AggNet: Deep learning from crowds for mitosis detection in breast cancer histology images[J]. IEEE Transactions on Medical Imaging, 2016, 35(5): 1313-1321.

[43]Young T, Hazarika D, Poria S, et al. Recent trends in deep learning based natural Language Processing [Review Article][J]. IEEE Computational Intelligence Magazine, 2018, 13(3): 55-75.

[44]马婷，李万杰，冯佳楠，等．光脉冲神经网络研究进展[J]．光学与光电技术，2022，20(4)：96-111．

[45]蒋昂波，王维维，等．ReLU激活函数优化研究[J]．传感器与微系统，2018，37(2)：50-53．

[46]Mustapha A, Mohamed L, Ali K. An Overview of gradient descent algorithm optimization in machine learning: application in the ophthalmology field[C]//Smart Applications and Data Analysis, 2020: 349-359.

[47]Lihua L. Simulation physics-informed deep neural network by adaptive Adam optimization method to perform a comparative study of the system[J]. Engineering with Computers, 2022, 38(2): 1111-1130.

[48]Cherri A K, Alam M S. Non-conventional joint-transform correlations for pattern recognition by use of grating filters and heterodyne scanning[J]. Optics & Laser Technology, 2008, 40(2): 261-269.

[49]Zhou Y, Chen R, Chen W-J, et al. Advances in spatial analog optical computing devices[J]. Acta Physica Sinica, 2020, 69(15): 157803.

[50]王静，陈波，王帅，等．无波前传感自适应光学神经网络控制方法[J]．激光杂志，2021，42(2)：102-105．

[51]卢艺帆，张松海．基于卷积神经网络的光学遥感图像目标检测[J]．中国科技论文，2017，12(14)：1583-1589．

[52]孙一宸，董明利，于明鑫，等．基于10.6微米波长的小型化非线性全光衍射深度神经网络建模方法[J]．激光与光电子学进展，2021，58(8)：395-406．

[53]Zuo Y, Li B, Zhao Y, et al. All-optical neural network with nonlinear activation functions[J]. Optica, 2019, 6(9): 1132-1137.

[54]Sun Y, Dong M, Yu M, et al. Nonlinear all-optical diffractive deep neural network with 10.6μm wavelength for image classification[J]. International Journal of Optics, 2021, 2021: 6667495.

[55]牛海莎，于明鑫，祝博飞，等．基于10.6微米全光深度神经网络衍射光栅的设计与实现[J]．红外与毫米波学报，2020，39(1)：1-13．

[56]Hong W, Hongxing X. Plasmonic logic gates and devices in silver nanowire networks[C]//Plasmonics Metallic Nanostructures, 2011, 8096(8096): 215-232.

[57]Miller D a B. Are optical transistors the logical next step?[J]. Nature Photonics, 2010, 4(1): 3-5.

[58]Huggins E, Introduction to fourier optics [J]. The Physics Teacher, 2007, 45(6): 364– 368.

[59]Nan Z, Xiao Y W, Nan C. Effects of the atmospheric turbulence on the single photon transmission in quantum channel[C]//2018 International Conference on Computing, Networking and Communications (ICNC). 2018: 432-436.

[60]Ren Y, Huang H, Xie G, et al. Experimental turbulence effects on crosstalk and System Power penalty over a free space optical communication Link using Orbital angular momentum multiplexing[C]//CLEO: 2013, 2013: CM2G.4.

[61]Li Y, Cui Z, Han Y, et al. Channel capacity of orbital-angular-momentum-based wireless communication systems with partially coherent elegant Laguerre-Gaussian beams in oceanic turbulence[J]. Journal of the Optical Society of America A, 2019, 36(4): 471-477.

[62]Sang X, Chu P L, Yu C. Applications of nonlinear effects in highly nonlinear photonic crystal fiber to optical communications[J]. Optical and Quantum Electronics, 2005, 37(10): 965-994.

[63]Kotb A, Guo C. 100Gb/s all-optical multifunctional AND, NOR, XOR, OR, XNOR, and NAND logic gates in a single compact scheme based on semiconductor optical amplifiers[J]. Optics & Laser Technology, 2021, 137(1): 106828.