Diffraction gratings based on a multilayer silicon nitride waveguide with high upward efficiency and large effective length

Wen-Ling Li; Wen-Ling Li; Jing-Wei Liu; Guo-An Cheng; Qing-Zhong Huang; Rui-Ting Zheng; Xiao-Ling Wu

doi:10.1364/AO.452651

Applied Optics
Vol. 61,
Issue 10,
pp. 2604-2609
(2022)
•https://doi.org/10.1364/AO.452651

Diffraction gratings based on a multilayer silicon nitride waveguide with high upward efficiency and large effective length

Wen-Ling Li, Jing-Wei Liu, Guo-An Cheng, Qing-Zhong Huang, Rui-Ting Zheng, and Xiao-Ling Wu

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Wen-Ling Li, Jing-Wei Liu, Guo-An Cheng, Qing-Zhong Huang, Rui-Ting Zheng, and Xiao-Ling Wu, "Diffraction gratings based on a multilayer silicon nitride waveguide with high upward efficiency and large effective length," Appl. Opt. 61, 2604-2609 (2022)

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Abstract

Diffraction gratings with high upward diffraction efficiency and large effective length are required for chip-scale light detection and ranging. We propose a diffraction grating based on a multilayer silicon nitride waveguide, which theoretically achieves an upward diffraction efficiency of 92%, a near-field effective length of 376 µm, and a far-field divergence angle of 0.105° at a wavelength of 850 nm. The diffraction grating has a high tolerance to process variations based on Monte Carlo analysis. When the conditions are ${\pm}5\%$ layer thickness variation, ${\pm}50\;{\rm nm}$ lithographic variation, and ${\pm}20\;{\rm nm}$ wavelength drift, more than 71% of the grating samples have a diffraction efficiency higher than 80%, and 100% of the samples have an effective length larger than 200 µm (corresponding to a far-field divergence ${\lt}{0.2}^\circ$). Furthermore, the near-field effective length of the grating with an upward diffraction efficiency above 90% can be adjusted from hundreds of microns to centimeters by changing the etching layer thickness and the grating duty cycle. This diffraction grating has a potential application in optical sensing and imaging from visible to near-IR wavelengths.

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Parameters	Standard Values	Variation
Thickness of $S i O_{2}$ bottom cladding $h_{b o t t o m}$	3.39 µm	Gaussian, $3 σ \pm 5 %$
Thickness of first $S i_{3} N_{4}$ layer $t_{1}$	107 nm	Gaussian, $3 σ \pm 5 %$
Thickness of first $S i O_{2}$ layer $g_{1}$	148 nm	Gaussian, $3 σ \pm 5 %$
Thickness of second $S i_{3} N_{4}$ layer $t_{2}$	107 nm	Gaussian, $3 σ \pm 5 %$
Thickness of second $S i O_{2}$ layer $g_{2}$	120 nm	Gaussian, $3 σ \pm 5 %$
Thickness of third $S i_{3} N_{4}$ layer $t_{3}$	50 nm	Gaussian, $3 σ \pm 5 %$
Thickness of top cladding $S i O_{2}$ $h_{t o p}$	3.07 µm	Gaussian, $3 σ \pm 5 %$
Grating etching tooth width	232 nm	Gaussian, $3 σ \pm$ 50 nm
Grating etching depth	70 nm	Gaussian, $3 σ \pm$ 5 nm
Side-wall angle $α$	82°	Gaussian, $3 σ \pm 2^{\circ}$
Wavelength	850 nm	Uniform, $\pm 20 n m$

Structure	Wavelength (nm)	Upward Efficiency	Effective Length ( $µ m$ )	Far-field Divergence (°)
offset dual-layer $S i_{3} N_{4}$ [7]	1550	93.2%	3000	—
offset single-layer $S i_{3} N_{4}$ [18]	1550	95%	3000	—
single-layer $S i_{3} N_{4}$ [11]	905	—	90	0.6
this work (multilayer $S i_{3} N_{4}$ )	850	92%	376	0.105

Parameters	Standard Values	Variation
Thickness of $S i O_{2}$ bottom cladding $h_{b o t t o m}$	3.39 µm	Gaussian, $3 σ \pm 5 %$
Thickness of first $S i_{3} N_{4}$ layer $t_{1}$	107 nm	Gaussian, $3 σ \pm 5 %$
Thickness of first $S i O_{2}$ layer $g_{1}$	148 nm	Gaussian, $3 σ \pm 5 %$
Thickness of second $S i_{3} N_{4}$ layer $t_{2}$	107 nm	Gaussian, $3 σ \pm 5 %$
Thickness of second $S i O_{2}$ layer $g_{2}$	120 nm	Gaussian, $3 σ \pm 5 %$
Thickness of third $S i_{3} N_{4}$ layer $t_{3}$	50 nm	Gaussian, $3 σ \pm 5 %$
Thickness of top cladding $S i O_{2}$ $h_{t o p}$	3.07 µm	Gaussian, $3 σ \pm 5 %$
Grating etching tooth width	232 nm	Gaussian, $3 σ \pm$ 50 nm
Grating etching depth	70 nm	Gaussian, $3 σ \pm$ 5 nm
Side-wall angle $α$	82°	Gaussian, $3 σ \pm 2^{\circ}$
Wavelength	850 nm	Uniform, $\pm 20 n m$

Structure	Wavelength (nm)	Upward Efficiency	Effective Length ( $µ m$ )	Far-field Divergence (°)
offset dual-layer $S i_{3} N_{4}$ [7]	1550	93.2%	3000	—
offset single-layer $S i_{3} N_{4}$ [18]	1550	95%	3000	—
single-layer $S i_{3} N_{4}$ [11]	905	—	90	0.6
this work (multilayer $S i_{3} N_{4}$ )	850	92%	376	0.105

Abstract

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Applied Optics