High Power Laser Science and Engineering, Volume. 13, Issue 4, 04000e62(2025)
Efficient phase locking in massive laser arrays with deep learning from structured data
Figures & Tables(12)
Fig. 1. Experimental setup for implementing the phase control for CBC based on our deep learning method.
Fig. 2. Details of the constructed CNN. (a) Overview architectures of ResNet-18 and ResNet-50. (b) Bottleneck structure of ResNet-50. (c) Basic block structure of ResNet-18.
Fig. 3. (a) Phase distributions of the 20 subsets generated through ladder sampling. Each arc represents a subset. (b)–(d) Non-focal-plane, focal-plane and source-plane visualization in different phase distributions in a 1027-channel laser array. (b1)–(b3) Non-focal plane patterns in the phase ranges of 
0.3
, 
0.7
and 
, respectively. (c1)–(c3) The corresponding intensity profiles at the focal plane. (d1)–(d3) The corresponding near-field phase distributions to the above far-field patterns. (e) Comparison of ladder sampling and random sampling strategies.
Fig. 4. Phase-locking results of the 1027-channel CBC system. (a) Normalized PIB variation of the system with dynamic phase noise in open and closed loops. (b) Phase-locking performances of networks with and without cuDNN and TensorRT accelerations (phase noise: 5000 Hz, 
0.2 rad).
Fig. 5. Phase-locking performances of the DL method and SPGD algorithm in the 1027-channel CBC system with dynamic phase noise from real high-power fiber amplifiers.
Fig. 6. Phase-locking results of the 61-channel system with dynamic phase noise under different data generation and volume. (a)–(d) PIB variation in a closed loop with ResNet-18 trained on 5000, 10,000, 100,000 and 200,000 samples for each generating strategy, respectively. (e)–(h) PIB distributions of the corresponding training samples for (a)–(d).
Fig. 7. Local correlation between far-field patterns and near-field phase distributions. (a1)–(a5) Five near-field phase maps containing locally equal phase distributions within the hexagonal areas. (b1)–(b5) The corresponding far-field patterns of (a1)–(a5) with similar intensity profiles in the rectangular areas.
Fig. 8. 1000-channel CBC system for multi-mode OAM superpositions. (a) The phase distribution of the laser array. (b) The focal pattern of (a). (c) The variation of far-field mode purities in phase-locked and unlocked states. (d) The comparison of far-field OAM spectra under different states.
Table 1. Average normalized PIB of the 1027-channel CBC system with dynamic phase noise of different levels.
View tableView in ArticleTable 1. Average normalized PIB of the 1027-channel CBC system with dynamic phase noise of different levels.
PIB $\pm 0.1\vphantom{A^{A^1}}$ $\pm 0.2$ $\pm 0.3$ $\pm 0.4$ $\pm 0.5$ $\mathrm{Frequency\ (Hz)}$ rad rad rad rad rad 1000 0.997 0.990 0.979 0.963 0.943 2000 0.994 0.979 0.954 0.920 0.878 5000 0.983 0.942 0.870 0.783 0.678
Table 2. RMS values for the intensity stability of the 1027-channel CBC system with dynamic phase noise of different levels.
View tableView in ArticleTable 2. RMS values for the intensity stability of the 1027-channel CBC system with dynamic phase noise of different levels.
RMS for intensity stability $\pm 0.1\vphantom{A^{A^1}}$ $\pm 0.2$ $\pm 0.3$ $\pm 0.4$ $\pm 0.5$ $\mathrm{Frequency\ (Hz)}$ rad rad rad rad rad 1000 0.15% 0.61% 1.39% 2.49% 3.92% 2000 0.17% 0.67% 1.51% 2.70% 4.22% 5000 0.38% 1.51% 3.39% 6.12% 9.48%
Table 3. Time consumption and phase-locking performance of networks under different acceleration strategies (phase noise: 5000 Hz,
0.2 rad).View tableView in ArticleTable 3. Time consumption and phase-locking performance of networks under different acceleration strategies (phase noise: 5000 Hz,
0.2 rad).Acceleration strategies GPU GPU+cuDNN GPU+cuDNN +TensorRT GPU+cuDNN +TensorRT+FP16 Response time (ms) 6.80 5.23 1.48 0.62 Normalized PIB 0.491 0.577 0.862 0.942
Table 4. Average normalized PIB of CBC systems with different network structures (phase noise: 5000 Hz,
0.2 rad).View tableView in ArticleTable 4. Average normalized PIB of CBC systems with different network structures (phase noise: 5000 Hz,
0.2 rad).PIB 127 channels 397 channels 1027 channels (10,000 (100,000 (350,000 $\mathrm{Network}$ samples) samples) samples) ResNet–18 0.943 0.962 0.552 ResNet–50 0.047 0.928 0.943
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Haoyu Liu, Jun Li, Kun Jin, Jian Wu, Yanxing Ma, Rongtao Su, Xiaolin Wang, Jinyong Leng, Pu Zhou. Efficient phase locking in massive laser arrays with deep learning from structured data[J]. High Power Laser Science and Engineering, 2025, 13(4): 04000e62
Paper Information
Category: Research Articles
Received: Feb. 7, 2025
Accepted: Jun. 20, 2025
Posted: Jun. 23, 2025
Published Online: Sep. 22, 2025
The Author Email: Jun Li (lijun_gfkd@nudt.edu.cn), Pu Zhou (zhoupu203@163.com)
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