Coherent beam combining (CBC) of fiber lasers has great potential in breaking through the power limitation of a single laser beam while maintaining good beam quality – a topic that has been widely studied during the past decades[
High Power Laser Science and Engineering, Volume. 7, Issue 4, 04000e59(2019)
Deep-learning-based phase control method for tiled aperture coherent beam combining systems On the Cover
We incorporate deep learning (DL) into tiled aperture coherent beam combining (CBC) systems for the first time, to the best of our knowledge. By using a well-trained convolutional neural network DL model, which has been constructed at a non-focal-plane to avoid the data collision problem, the relative phase of each beamlet could be accurately estimated, and then the phase error in the CBC system could be compensated directly by a servo phase control system. The feasibility and extensibility of the phase control method have been demonstrated by simulating the coherent combining of different hexagonal arrays. This DL-based phase control method offers a new way of eliminating dynamic phase noise in tiled aperture CBC systems, and it could provide a valuable reference on alleviating the long-standing problem that the phase control bandwidth decreases as the number of array elements increases.
1 Introduction
Coherent beam combining (CBC) of fiber lasers has great potential in breaking through the power limitation of a single laser beam while maintaining good beam quality – a topic that has been widely studied during the past decades[
To further improve the control bandwidth, a fast and accurate phase extraction method is always necessary. As a result of their excellent real-time performance, machine learning and artificial intelligence algorithms may offer a route to further improve the phase control speed in CBC systems, which needs to be investigated carefully. In fact, this new technique has been successfully applied to many optical research fields, such as mode-locked lasers, optical microscopy and laser mode decomposition[
In this paper, we present a DL-based phase control method for tiled aperture coherent beam combining systems. To avoid the data collision mentioned above, non-focal-plane intensity profiles of the combined beam are used as training samples. We construct and train a convolutional neural network (CNN) for real-time estimation of the relative phases of the array elements, and the estimated phase error could be compensated by a servo phase control system. Such a direct phase compensation method does not cause an increase in complexity of the CBC system as the number of array elements increases, and it is compatible with optimization algorithms and dithering techniques. Our simulations are performed in detail to demonstrate the feasibility and extensibility of the proposed phase control technique, which has potential in improving the phase control bandwidth of CBC systems.
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2 Principle and method
Figure
The electric field of an
The CNN performing in our phase control scheme is modified from the VGG-16 model[
In the training procedure, the input images pass through the layers of the CNN and are regressed into an output vector with
When the network reaches convergence after several training epochs, it can be used to estimate the relative phase of each array element. Taking an intensity pattern image as input, the CNN outputs a vector with
3 Numerical simulation results and discussion
In order to demonstrate the feasibility and extensibility of the DL-based phase control method, we investigate the coherent combining of 7-element and 19-element hexagonal arrays as examples, and numerical simulations are performed in detail. The arrangements of the beam arrays are shown in Figures
First, the necessity of constructing the CNN at the non-focal-plane should be illustrated. In training a DL network, if the input image corresponds to multiple labels, it would cause data collision, which means that the constructed DL network would lose its efficiency. In our previous work, we have indicated that the same far-field intensity profile of a symmetrical beam array could correspond to different phase distributions in the near field[
Without loss of generality, we take the 7-element hexagonal array shown in Figure
To further evaluate the performances of the CNNs trained after 30 training epochs, we have tested the far-field intensity profiles of the combined beams using the 1000 testing samples mentioned above. Figure
Then, to demonstrate the feasibility of the DL-based phase control method, we simulate the far-field intensity profiles of the hexagonal beam arrays displayed in Figure
Figure
To further illustrate the extensibility of the DL-based phase control method, the CNN for the 19-element hexagonal array is constructed and the phase control performance is studied by simulation, as shown in Figure
In summary, the phase error in the CBC system could be efficiently estimated and compensated based on the DL network. Compared to the case of incoherent combining, the DL-based phase control method for coherent combining could improve the far-field energy concentration of the combined beam significantly. The most significant advantage of the DL-based phase control method is time efficiency. It can perform non-iterative phase control with a pre-trained CNN. When more array elements are involved, the DL-based phase control method consumes the same amount of time as the fewer-elements-involved cases. Although a slight decrease in the accuracy of the CNN along with the increasing number of array elements could be observed, which is caused by the increase in complexity of the non-focal-plane intensity profile, this difficulty is expected to be solved by optimizing the CNN structure, increasing the number of training samples, and the assistance of optimization algorithms (such as SPGD algorithm)[
4 Conclusion
In this paper, we have shown that the DL-based phase control method could be implemented into CBC systems to directly compensate the phase error. Comprehensively considering simulation results for the convergence of the training process and the accuracy of the trained CNN, we have shown that, different from conventional active phase control methods, the DL-based servo phase control system should be fed at the non-focal-plane. Using key metrics of the combined beams of 7-element and 19-element hexagonal arrays to evaluate the phase control performance, we have demonstrated that the DL-based phase control method is feasible and could be extended. With an increase in the number of array elements, the complexity of the DL-based phase control system and the computing time of the CNN did not increase; thus the DL-based phase control method offers an opportunity to improve the phase control bandwidth of CBC systems. By optimizing the network structure, and in conjunction with optimization algorithms, the difficulty of a slight decrease in accuracy as the number of array elements is increased is expected to be solved – a topic which deserves further study.
[1] T. Y. Fan. IEEE J. Sel. Top. Quant. Elect., 11, 567(2005).
[2] J. R. Leger. Conference on Lasers and Electro-Optics 2010(2010).
[3] G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, M. Wickham. IEEE J. Sel. Top. Quant. Elect., 13, 460(2007).
[4] P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu. IEEE J. Sel. Top. Quant. Elect., 15, 248(2009).
[5] C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, T. Y. Fan. Opt. Lett., 36, 2686(2011).
[6] E. Seise, A. Klenke, J. Limpert, A. Tünnermann. Opt. Express, 18, 27827(2010).
[7] A. Flores, I. Dajani, R. Holten, T. Ehrenreich, B. Anderson. Opt. Eng., 55(2016).
[8] Z. Liu, P. Ma, R. Su, R. Tao, Y. Ma, X. Wang, P. Zhou. J. Opt. Soc. Am. B, 34, A7(2017).
[9] J. Bourderionnet, C. Bellanger, J. Primot, A. Brignon. Opt. Express, 19, 17053(2011).
[10] D. Kabeya, V. Kermène, M. Fabert, J. Benoist, J. Saucourt, A. Desfarges-Berthelemot, A. Barthélémy. Opt. Express, 25, 13816(2017).
[11] D. Zhi, T. Hou, P. Ma, Y. Ma, P. Zhou, R. Tao, X. Wang, L. Si. High Power Laser Sci. Eng., 7, e33(2019).
[12] J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, M. Wickham. Proc. SPIE, 6102(2006).
[13] T. M. Shay. Opt. Express, 14, 12188(2006).
[14] A. Azarian, P. Bourdon, L. Lombard, Y. Jaouën, O. Vasseur. Appl. Opt., 53, 1493(2014).
[15] Y. Ma, X. Wang, J. Leng, H. Xiao, X. Dong, J. Zhu, W. Du, P. Zhou, X. Xu, L. Si, Z. Liu, Y. Zhao. Opt. Lett., 36, 951(2011).
[16] X. Tang, Z. Huang, D. Zhang, X. Wang, J. Li, C. Liu. Opt. Commun., 321, 198(2014).
[17] M. Jiang, R. Su, Z. Zhang, Y. Ma, X. Wang, P. Zhou. Appl. Opt., 56, 4255(2017).
[18] M. Antier, J. Bourderionnet, C. Larat, E. Lallier, E. Lenormand, J. Primot, A. Brignon. IEEE J. Sel. Top. Quant. Elect., 20(2014).
[19] D. Kabeya, V. Kermene, M. Fabert, J. Benoist, A. Desfarges-Berthelemot, A. Barthelemy. Opt. Express, 23, 31059(2015).
[20] M. A. Vorontsov, V. P. Sivokon. J. Opt. Soc. Am. A, 15, 2745(1998).
[21] H. Ahn, H. Kong. Opt. Express, 23, 12407(2015).
[22] X. Fu, S. L. Brunton, J. N. Kutz. Opt. Express, 22, 8585(2014).
[23] T. Baumeister, S. L. Brunton, J. N. Kutz. J. Opt. Soc. Am. B, 35, 617(2018).
[24] Y. Rivenson, Z. Göröcs, H. Günaydin, Y. Zhang, H. Wang, A. Ozcan. Optica, 4, 1437(2017).
[25] Y. An, L. Huang, J. Li, J. Leng, L. Yang, P. Zhou. Opt. Express, 27, 10127(2019).
[26] H. Tünnermann, A. Shirakawa. Opt. Express, 27, 24223(2019).
[27] T. Hou, Y. Zhang, Q. Chang, P. Ma, R. Su, J. Wu, Y. Ma, P. Zhou. Opt. Express, 27, 4046(2019).
[28] K. Simonyan, A. Zisserman. International Conference on Learning Representations (ICLR)(2015).
[29] M. A. Vorontsov, S. L. Lachinova. J. Opt. Soc. Am. A, 25, 1949(2008).
[30] S. L. Lachinova, M. A. Vorontsov. J. Opt. Soc. Am. A, 25, 1960(2008).
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Tianyue Hou, Yi An, Qi Chang, Pengfei Ma, Jun Li, Dong Zhi, Liangjin Huang, Rongtao Su, Jian Wu, Yanxing Ma, Pu Zhou. Deep-learning-based phase control method for tiled aperture coherent beam combining systems[J]. High Power Laser Science and Engineering, 2019, 7(4): 04000e59
Category: Research Articles
Received: Jun. 16, 2019
Accepted: Sep. 20, 2019
Published Online: Nov. 12, 2019
The Author Email: Pengfei Ma (shandapengfei@126.com), Pu Zhou (zhoupu203@163.com)