在本研究中，為實現高效且可重構的光學相位調制器架構，採用連續波雷射源、光學定向耦合器、摻鉺光纖放大器（EDFA）與相位調制器等光學元件，設計出兩種不同輸出形式的相位控制相位調制器架構，分別為「直線型」與「正弦曲線型」輸出。其中，EDFA 具備高增益、低噪聲與寬頻帶等特性，能有效放大訊號光，提升系統整體性能，並廣泛應用於光纖通訊與光學計算系統中。
為精確調控光學元件參數，本研究引入雙層多層感知器（2-layer multilayer perceptron, MLP）系統，推導出光學定向耦合器的耦合率與相位調制器的相位延遲。其中相位調制器透過電光效應改變光波相位，實現高速且精確的相位控制，廣泛應用於光通訊與光學計算等領域。
在性能評估方面，透過多組模擬結果與理想值進行標準差分析。結果顯示，直線型架構的相位與功率標準差最低值分別為 1.77° 與 0.048mW；正弦曲線型架構的相位與功率標準差最低值則分別為 1.69° 與 0.014mW，顯示兩種架構皆具備良好的穩定性與準確性。此外，這些相位控制相位調制器架構可被建構於晶片上，並應用於光學計算系統的發展中。

In this study, to realize an efficient and reconfigurable optical phase modulator architecture, we employed optical components such as a continuous-wave (CW) laser source, optical directional couplers, erbium-doped fiber amplifiers (EDFAs), and phase modulators. Based on these components, two types of phase-controlled phase modulator architectures with different output forms were designed: a linear-type output and a sinusoidal-type output. Among them, the EDFA, which possesses characteristics such as high gain, low noise, and broad bandwidth, can effectively amplify the signal light and enhance overall system performance. EDFAs are widely utilized in optical fiber communication and optical computing systems.
To precisely control the parameters of the optical components, this study introduces a two-layer multilayer perceptron (2-layer MLP) system to derive the coupling ratios of the optical directional couplers and the phase delays of the phase modulators. The phase modulators, by utilizing the electro-optic effect, enable high-speed and precise phase control and are extensively applied in the fields of optical communication and optical computing.
For performance evaluation, multiple simulation datasets were analyzed using standard deviation comparisons against ideal values. The results indicate that the linear-type architecture achieves minimum phase and power standard deviations of 1.77° and 0.048 mW, respectively, while the sinusoidal-type architecture achieves minimum phase and power standard deviations of 1.69° and 0.014 mW, respectively. These results demonstrate that both architectures exhibit excellent stability and accuracy. Moreover, the proposed phase-controlled phase modulator architectures can be integrated on-chip and are suitable for future developments in optical computing systems.

1. Xue, Z., et al., Fully forward mode training for optical neural networks. Nature, 2024. 632(8024): p. 280-286.
2. Zhou, S., et al., Automating multi-task learning on optical neural networks with weight sharing and physical rotation. Scientific Reports, 2025. 15(1): p. 14419.
3. Li, B., et al., Multi-functional broadband diffractive neural network with a single spatial light modulator. APL Photonics, 2025. 10(1): p. 016115.
4. Bhuiyan, M.A.H., S.A. Mitu, and S.M. Choudhury. VO2-based All-optical Reflection Modulator for 2μm Wave Band. in 2023 IEEE Photonics Conference (IPC). 2023.
5. Fan, J., et al. An ultimate-high linear silicon modulator based on all-optical linearization method. in 2024 Optical Fiber Communications Conference and Exhibition (OFC). 2024.
6. Wang, Y., et al. Epsilon-Near-Zero Based Electro-Optical and All-Optical Modulator for Intensity and Phase Modulation. in 2023 Opto-Electronics and Communications Conference (OECC). 2023.
7. Ruan, Z., et al., All-Optical Graphene Oxide Modulator Based on Phase-Shifted FBG. Journal of Lightwave Technology, 2021. 39(17): p. 5516-5522.
8. Wu, K., et al. Two-dimension Nanomaterial Tungsten Disulfide (WS2) Integrated Fiber Device as All Optical Phase Shifter, Switch and Modulator Near 1550 nm. in Conference on Lasers and Electro-Optics. 2017. San Jose, California: Optica Publishing Group.
9. Wei, K., et al., All-optical PtSe2 silicon photonic modulator with ultra-high stability. Photonics Research, 2020. 8(7): p. 1189-1196.
10. Zhang, M., et al., Integrated lithium niobate electro-optic modulators: when performance meets scalability. Optica, 2021. 8(5): p. 652-667.
11. Li, M., et al., Lithium niobate photonic-crystal electro-optic modulator. Nature Communications, 2020. 11(1): p. 4123.
12. Gao, L., et al., Compact low-half-wave-voltage thin film lithium niobate electro-optic phase modulator fabricated by photolithography-assisted chemo-mechanical etching (PLACE). Optics Letters, 2024. 49(20): p. 5783-5786.
13. Wu, J., et al., Epsilon-near-zero photonics: infinite potentials. Photonics Research, 2021. 9(8): p. 1616-1644.
14. Li, W., et al., Ultrafast All-Optical Graphene Modulator. Nano Letters, 2014. 14(2): p. 955-959.
15. Liu, Z.-B., et al., Broadband all-optical modulation using a graphene-covered-microfiber. Laser Physics Letters, 2013. 10(6): p. 065901.
16. Zhang, H., et al., Enhanced all-optical modulation in a graphene-coated fibre with low insertion loss. Scientific Reports, 2016. 6(1): p. 23512.
17. Gao, H., et al., Relief-Surface-Based On-Chip Hybrid Diffraction Neural Network Enabled by Authentic All-Optical Fully Connected Architecture. ACS Photonics, 2024. 11(11): p. 4818-4829.
18. Xiang, S., et al., Computing Primitive of Fully VCSEL-Based All-Optical Spiking Neural Network for Supervised Learning and Pattern Classification. IEEE Transactions on Neural Networks and Learning Systems, 2021. 32(6): p. 2494-2505.
19. Rani, D., R.S. Kaler, and B. Painam, All-optical NOR gate based on cross structures in 2D photonic crystal using logic NOT and OR gates. Journal of Optical Technology, 2017. 84(12): p. 851-857.
20. Fernandes, C.A.R., et al., Design of Optical Logic Gates Using Mach–Zehnder Interferometers and Machine Learning. Journal of Lightwave Technology, 2022. 40(18): p. 6240-6248.
21. Rao, D.G.S., S. Swarnakar, and S. Kumar, Design of all-optical reversible logic gates using photonic crystal waveguides for optical computing and photonic integrated circuits. Applied Optics, 2020. 59(35): p. 11003-11012.
22. Lin, C.-E., et al., Reconfigurable electro-optical logic gates using a 2-layer multilayer perceptron. Scientific Reports, 2022. 12(1): p. 14203.
23. Pal, A., et al. All-optical Switch and Logic Gates Using Phase Asymmetries in High-Q Resonators. in Advanced Photonics Congress 2024. 2024. Québec City: Optica Publishing Group.
24. Keshtkar, P., M. Miri, and N. Yasrebi, Low power, high speed, all-optical logic gates based on optical bistability in graphene-containing compact microdisk resonators. Applied Optics, 2021. 60(24): p. 7234-7242.
25. Sethi, P. and S. Roy, All-Optical Ultrafast Switching in 2 × 2 Silicon Microring Resonators and its Application to Reconfigurable DEMUX/MUX and Reversible Logic Gates. Journal of Lightwave Technology, 2014. 32(12): p. 2173-2180.
26. Xu, J., et al., Reconfigurable All-Optical Logic Gates for Multi-Input Differential Phase-Shift Keying Signals: Design and Experiments. Journal of Lightwave Technology, 2009. 27(23): p. 5268-5275.
27. Kim, J.-Y., et al., All-Optical Multiple Logic Gates With XOR, NOR, OR, and NAND Functions Using Parallel SOA-MZI Structures: Theory and Experiment. Journal of Lightwave Technology, 2006. 24(9): p. 3392.
28. Xie, R.-R., et al., Phase-controlled dual-wavelength resonance in a self-coupling whispering-gallery-mode microcavity. Optics Letters, 2021. 46(4): p. 773-776.
29. Ren, W., et al., Direct phase control method for binary phase-shift keying spacecoherent laser communication. Chinese Optics Letters, 2022. 20(6): p. 060601.
30. Sun, W., et al., Adaptive respiratory signal prediction using dual multi-layer perceptron neural networks. Phys Med Biol, 2020. 65(18): p. 185005.
31. Barbosa, B.S.d.S., et al. Application of Artificial Neural Networks for Prediction of Received Signal Strength Indication and Signal-to-Noise Ratio in Amazonian Wooded Environments. Sensors, 2024. 24, DOI: 10.3390/s24082542.
32. Yan, H., Prototype optimization for nearest neighbor classifiers using a two-layer perceptron. Pattern Recognition, 1993. 26(2): p. 317-324.
33. Dudul, S.V., Prediction of a Lorenz chaotic attractor using two-layer perceptron neural network. Applied Soft Computing, 2005. 5(4): p. 333-355.
34. Hu, Z., et al. Two-Layer Perceptron for Voice Recognition of Speaker’s Identity. in Advances in Computer Science for Engineering and Education III. 2021. Cham: Springer International Publishing.
35. Fu, T., et al., Optical neural networks: progress and challenges. Light: Science & Applications, 2024. 13(1): p. 263.
36. Aleksic, S., Energy and Entropy Flow in Erbium-Doped Fiber Amplifiers: A Thermodynamic Approach. Journal of Lightwave Technology, 2012. 30(17): p. 2832-2838.