Grating waveguides by machine learning for augmented reality

Xi Chen; Dongfeng Lin; Tao Zhang; Yiming Zhao; Hongwei Liu; Yiping Cui; Chenyang Hou; Jingwen He; Sheng Liang

doi:10.1364/AO.486285

Applied Optics
Vol. 62,
Issue 11,
pp. 2924-2935
(2023)
•https://doi.org/10.1364/AO.486285

Grating waveguides by machine learning for augmented reality

Xi Chen, Dongfeng Lin, Tao Zhang, Yiming Zhao, Hongwei Liu, Yiping Cui, Chenyang Hou, Jingwen He, and Sheng Liang

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Xi Chen, Dongfeng Lin, Tao Zhang, Yiming Zhao, Hongwei Liu, Yiping Cui, Chenyang Hou, Jingwen He, and Sheng Liang, "Grating waveguides by machine learning for augmented reality," Appl. Opt. 62, 2924-2935 (2023)

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Table of Contents Category
- Fiber Optics, Fiber Sensors, and Optical Communications
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About this Article
History
- Original Manuscript: January 23, 2023
- Revised Manuscript: March 16, 2023
- Manuscript Accepted: March 17, 2023
- Published: April 6, 2023

Abstract

We propose a machine-learning-based method for grating waveguides and augmented reality, significantly reducing the computation time compared with existing finite-element-based numerical simulation methods. Among the slanted, coated, interlayer, twin-pillar, U-shaped, and hybrid structure gratings, we exploit structural parameters such as grating slanted angle, grating depth, duty cycle, coating ratio, and interlayer thickness to construct the gratings. The multi-layer perceptron algorithm based on the Keras framework was used with a dataset comprised of 3000–14,000 samples. The training accuracy reached a coefficient of determination of more than 99.9% and an average absolute percentage error of 0.5%–2%. At the same time, the hybrid structure grating we built achieved a diffraction efficiency of 94.21% and a uniformity of 93.99%. This hybrid structure grating also achieved the best results in tolerance analysis. The high-efficiency artificial intelligence waveguide method proposed in this paper realizes the optimal design of a high-efficiency grating waveguide structure. It can provide theoretical guidance and technical reference for optical design based on artificial intelligence.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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	Slanted Grating	Coated Grating	Interlayer Grating	Twin-Pillar Grating	U-Shaped Grating
Sample definition method	slant angle	slant angle	slant angle	pillar length	pillar length
	grating depth	grating depth	grating depth	pillar height	pillar height
	duty cycle	duty cycle	duty cycle	pillar distance	pillar distance
		coating ratio	interlayer thickness		bridge height
			interlayer position
Number of samples in the dataset	2912	9000	7776	3375	6480

	Slanted Grating	Coated Grating	Interlayer Grating	Twin-Pillar Grating	U-Shaped Grating	Hybrid Grating
MAPE	0.557%	0.945%	0.726%	2.001%	2.389%	0.5829%
${M g F}_{2}$ score	99.9946%	99.95%	99.994%	99.973%	99.95%	99.98%

	Slanted Grating	Coated Grating	Interlayer Grating	Twin-Pillar Grating	U-Shaped Grating	Hybrid Grating
Number of predicted structures	17,980	738,150	389,376	43,911	248,829	1,015,014
Estimated calculation time by FEM	${M g F}_{2}$	${T i O}_{2}$	$θ$	$a$	$e$	$b$
Calculation time by machine learning		$c$	$h = b / d$	$k = c / a$	$+ 1$	$R^{2}$

	Slanted Grating	Coated Grating	Interlayer Grating	Twin-Pillar Grating	U-Shaped Grating	Hybrid Grating
Angle of incidence (°)	0–14	0–14	0–14	−14–14	−14–14	0–14
Structure parameters	$< 1 m i n$				$< 1 m i n$	$< 1 m i n$
		$Γ = 1 - \frac{η_{m a x} - η_{m i n}}{η_{m a x} + η_{m i n}} .$	$Γ$	$η_{m a x}$	$η_{m i n}$	$+ 1$
		$+ 1$	${T i O}_{2}$	${M g F}_{2}$	${T i O}_{2}$	$\pm 2$
		${T i O}_{2}$	${M g F}_{2}$		$- 1$	$+ 1$
			$+ 1$			${M g F}_{2}$
Peak diffraction efficiency	94.16%	95.28%	84.88%	91.56%	83.03%	98.00%
Average diffraction efficiency	66.01%	86.29%	73.18%	67.35%	64.26%	94.21%
Uniformity	36.17%	82.97%	62.75%	48.99%	44.76%	94.94%

Article	Time	Structure	Condition	Performance
[20]	2021	meta grating	green light, 54 FOV	peak diffraction efficiency 86.8%
[21]	2022	slanted grating	green light, 18 FOV	peak diffraction efficiency 95.5%, average diffraction efficiency 91.5, uniformity 95.1%
[39]	2020	shining grating	green light, single-angle entry	peak diffraction efficiency 65%
[40]	2022	multi-layer grating	850 nm wavelength, single angle entry	peak diffraction efficiency 92%
[41]	2022	surface coated grating	1.05 µm wavelength, single angle entry	peak diffraction efficiency 91.9%
[42]	2022	asymmetric gratings		peak diffraction efficiency 93.1%
[43]	2020	embedded triple-layer grating	800 nm wavelength, 5.6 FOV	peak diffraction efficiency 97.04%
Our structure	2022	hybrid grating	green light, 15 FOV	peak diffraction efficiency 98.00%, average diffraction efficiency 94.21%, uniformity 94.94%

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Applied Optics