Physics-data-driven intelligent optimization for large-aperture metalenses

Yingli Ha; Yu Luo; Mingbo Pu; Fei Zhang; Qiong He; Jinjin Jin; Mingfeng Xu; Yinghui Guo; Xiaogang Li; Xiong Li; Xiaoliang Ma; Xiangang Luo

doi:10.29026/oea.2023.230133

Opto-Electronic Advances, Volume. 6, Issue 11, 230133(2023)

Physics-data-driven intelligent optimization for large-aperture metalenses

Yingli Ha1...2,3,†, Yu Luo1,2,3,†, Mingbo Pu1,2,3,4,*, Fei Zhang1,2,3, Qiong He1,2, Jinjin Jin1,2, Mingfeng Xu1,2,3,4, Yinghui Guo1,2,3,4, Xiaogang Li5, Xiong Li1,2,4, Xiaoliang Ma1,2,4, and Xiangang Luo1,2,34,** |Show fewer author(s)

Author Affiliations

¹National Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu 610209, China

²State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China

³Research Center on Vector Optical Fields, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China

⁴School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China

⁵Tianfu Xinglong Lake Laboratory, Chengdu 610299, China

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Figures & Tables(5)

Fig. 1. Working principle of the “intelligent optimizer”. The “intelligent optimizer” incorporates both Adj and DL methods. Data-sets of the DL network are obtained from the small-aperture metalens optimized by the Adj method. Super meta-atoms of large-aperture metalens are fed into the network one by one. Output meta-atoms are spliced together to create a new metalens with improved focusing efficiency.

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Fig. 2. Design method for the large-aperture metalens. (a) The differences in widths distribution for the meta-atoms before and after optimization. (b) The widths distribution of metalens, with the smooth region and rough region corresponding to translucent boxes I and II, respectively. (c) The optimized network framework consists of an A-network that expands the information space of sampled data, and the weak coupling strength structures are filtered by the I-network.

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Fig. 3. Simulation results of Adj and DL methods. (a) Electric field distributions in the xy and xz planes designed by DL method for x- and y-polarized light, and the Adj method for x-polarized, respectively. (b) Electric intensity profiles of the focal spot designed by theory, Adj, and DL methods, respectively. (c) Width distributions of metalenses on y=0 plane (x>0) designed by the traditional (Tra), Adj, and the proposed methods, respectively. (d) Width differences between the initial metalens and the optimized metalenses designed by the Adj method and our methods.

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Fig. 4. Experimental results of optimized metalenses. (a) The left image shows an overview of the device, with each diameter corresponding to four exposure doses. The inset is the optical microscope image. Scale bar: 100 µm. The right image is the scanning electron microscope image. Scale bar: 2 µm. (b) The first row shows the focal plane intensity distributions of the three metalenses (100.5 μm, 500 μm, and 1 mm, from left to right, respectively). The second row shows the normalized focal intensity along the x-axis at the focal plane of the three metalenses. (c) Focal intensity distributions in the xz plane at the three metalenses. (d) Relative focusing efficiencies and Strehl ratios of three metalenses. (e) Imaging results of elements #5 and #6 from group #7 of the USAF resolution target at 1 mm diameter optimized metalens (left) and 1 mm diameter ideal metalens (right). Scale bar: 5 µm.

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Table 1. Examples to show the representative parameters and performance of various methods.

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Table 1. Examples to show the representative parameters and performance of various methods.

Ref.	λ(nm)	Material	NA	D (µm)	Dimension	Efficiency	Method	Time
^a)Absolute focusing efficiency; ^b)Relative focusing efficiency; ^c)Relative focusing efficiency compared to the ideal efficiency; ^d)Simulated result; ^e)Experimental result; ^f)Predict result
Liang et al. ²⁰	532	TiO₂	0.98	-	2D	67%^a),e)	Hybrid optimization algorithm	-
Cai et al.²⁹	532	TiO₂	0.51	24	1D	60%^a),e)	Genetic algorithm	1000 s
Mansouree et al.³³	850	a-Si	0.78	52	2D	65%^a),e)	Adjoint optimization	97 min /iteration
Li et al.³⁵	RGB	TiO₂	0.3	10000	2D	15%^a),e)	Conservative convex separable approximation	few hours
An et al.⁴¹	1550	p-Si	0.72	32	1D	77.62%^b),d)	Deep learning	200 s
Phan et al.⁶⁰	640	SOI	0.5	200	1D	89%^c),e)	Topology optimization	100 h
Pestourie et al.⁶¹	RGB	TiO₂	0.3	235	1D	-	“Locally periodic” approximation	250 s
Arbabi et al.⁶²	1550	a-Si	0.37	50	2D	82%^a),e)	High- contrast gratings	-
This work	1550	SOS	0.44	50.5	2D	95.7%^c),d)	Physics-data-driven method	15 s
This work	1550	SOS	0.44	1000	2D	93.4%^c),e)	Physics-data-driven method	6 min and 45 s
This work	1550	SOS	0.44	10000	2D	~95%^c),f)	Physics-data-driven method	2 h and 54 min

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Yingli Ha, Yu Luo, Mingbo Pu, Fei Zhang, Qiong He, Jinjin Jin, Mingfeng Xu, Yinghui Guo, Xiaogang Li, Xiong Li, Xiaoliang Ma, Xiangang Luo. Physics-data-driven intelligent optimization for large-aperture metalenses[J]. Opto-Electronic Advances, 2023, 6(11): 230133

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