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Diffraction gratings with high upward diffraction efficiency and largeeffective length are required for chip-scale light detection and ranging. Inthis paper, we propose a diffraction grating based on a multilayer siliconnitride waveguide, which theoretically achieves an upward diffractionefficiency of 92$\%$, a near-field effective length of 376 $\mu m$ and afar-field divergence angle of 0.105$^{\circ}$ at a wavelength of 850 nm. Thediffraction grating has a high tolerance to process variations based on MonteCarlo Analysis. When the conditions are $\pm$5$\%$ layer thickness variation,$\pm$50 nm lithographic variation and $\pm$20 nm wavelength drift, more than71$\%$ of the grating samples have a diffraction efficiency higher than 80$\%$,and 100$\%$ of the samples have an effective length larger than 200 $\mu m$(corresponding to a far-field divergence <0.2$ ^{\circ}$). Furthermore, thenear-field effective length of the grating with an upward diffractionefficiency above 90$\%$ can be adjusted from hundreds of microns to centimetersby changing the etching layer thickness and the grating duty cycle. Thisdiffraction grating has potential application in optical sensing and imagingfrom visible to near-infrared wavelengths.

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