Silicon Nitride Metalenses for Close-to-One Numerical Aperture and Wide-Angle Visible Imaging

Zhi-Bin Fan, Zeng-Kai Shao, Ming-Yuan Xie, Xiao-Ning Pang, Wen-Sheng Ruan, Fu-Li Zhao, Yu-Jie Chen, Si-Yuan Yu, and Jian-Wen Dong

Phys. Rev. Applied 10, 014005 – Published 10 July 2018

Abstract

Silicon nitride ( $Si N$ ) is one of the emerging semiconductor materials that are used in both linear and nonlinear all-optical integrated devices. Its excellent dielectric properties, high material stability, and dispersion controllability are attractive to on-chip optical communications, optical signal processing, and even imaging devices. However, a large-aperture $Si N$ metalens with high numerical aperture (NA) is limited by the low refractive index and nanofabrication technologies, particular in the visible spectrum. Here, we experimentally realize the visible-spectrum $Si N$ divergent metalenses by fabricating the 695-nm-thick hexagonal arrays with a minimum space of 42 nm between adjacent nanopillars. A micro-size divergent metalens with $NA \sim 0.98$ and subwavelength resolution enables objects to be shrunk as small as a single-mode fiber core. Another centimeter-size $Si N$ divergent metalens with over half a billion nanopillars, made by using the mature CMOS-compatible fabrication process, exhibits high-quality wide-angle imaging. Our findings may open a new door for the miniaturization of optical lenses in the fields of optical fibers, microendoscopes, and smart phones, as well as the applications in all-sky telescopes, large-angle beam shaping, and near-eye imaging.

Received 5 February 2018
Revised 11 May 2018

DOI:https://doi.org/10.1103/PhysRevApplied.10.014005

Physics Subject Headings (PhySH)

Mie scattering Nanophotonics

Metamaterials Nanostructures Semiconductor compounds

Imaging & optical processing Optical microscopy Optical nanoscopy

Atomic, Molecular & Optical

Authors & Affiliations

Zhi-Bin Fan^1,2, Zeng-Kai Shao^1,3, Ming-Yuan Xie^1,2, Xiao-Ning Pang^1,2, Wen-Sheng Ruan^1,2, Fu-Li Zhao^1,2, Yu-Jie Chen^1,3,*, Si-Yuan Yu^1,3,4, and Jian-Wen Dong^1,2,†

¹State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China
²School of Physics, Sun Yat-sen University, Guangzhou 510275, China
³School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510275, China
⁴Photonics Group, Merchant Venturers School of Engineering, University of Bristol, Bristol BS8 1UB, United Kingdom

^*chenyj69@mail.sysu.edu.cn
^†dongjwen@mail.sysu.edu.cn

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Vol. 10, Iss. 1 — July 2018

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Images

Figure 1
Simulation results of $Si N$ periodic gratings. (a) Schematic of the grating constructed by a low-refractive-index $Si N$ array with circular nanopillars on a fused silica substrate. The hexagonal lattice constant is $a = 416 nm$ , and the thickness of nanopillars is 695 nm. (b) Top and side views of the normalized magnetic field intensity at the nanopillar diameter of 200 nm. The white dashed frame depicts the boundaries of the $Si N$ nanopillars. A plane wave with $y$ polarization is normally incident onto the $Si N$ nanopillars from the bottom of the substrate. Scale bar, 200 nm. (c),(d) Calculated transmission and its phase as a function of the refractive index and the post diameter at $λ = 633 nm$ . (e),(f) Calculated transmission and its phase as a function of the wavelength and the post diameter with refractive index $n = 2$ . (g) The profile of the vertical dashed lines in panels (c)–(f), showing the full $2 π$ phase coverage and the close-to-one transmission spectrum for a family of $Si N$ periodic gratings at $λ = 633 nm$ . (h) The profile of the horizontal dashed lines in panels (e) and (f), illustrating the spectral response for $Si N$ periodic gratings with the nanopillar diameter of 200 nm and the high efficiency in broadband visible region.
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Figure 2
Schematic diagram, SEM images and measurement setup of the $100 − μ m$ -diameter micro metalens. (a) Schematic diagram of a divergent metalens operating in the transmission mode. (b) Top-view SEM image of a portion of the fabricated micro metalens. Scale bar, 400 nm. (c) Side-view SEM image with high magnification. Scale bar, 200 nm. (d) Measurement setup for characterizing the chromatic dispersion features of the micro metalens.
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Figure 3
The virtual focal planes of the micro metalens. (a),(b) Measurement and simulation of intensity patterns in the virtual focal planes at five different wavelengths of 480, 532, 633, 730, and 780 nm. Three kinds of pseudocolors are used for color bars. Scale bar, 400 nm. (c)–(e) The $x$ -direction cross sections of the measured and simulated intensity profiles at three wavelengths. The red solid curve denotes the simulated results while the blue solid curve is Airy fit of measured data (black square point). The green text gives the full widths at half-maximums (FWHMs) of the fitting measured data, showing the subwavelength virtual focus spots.
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Figure 4
The $x$ - $z$ planes of the micro metalens in different wavelengths. (a),(b) Normalized measured and simulated intensity distributions in $x$ - $z$ planes at different wavelengths. Three kinds of pseudocolors are used for color bars. Scale bar, $2 μ m$ . (c) The $z$ -direction cross sections at 633 nm. The red solid curve is the simulated data and the blue points are measured data, showing no significant difference with simulated data except for a little deviation of focus point. (d) Measured and simulated virtual focal lengths of the micro metalens as a function of wavelength. The black dashed curve represents the dispersion of diffraction optical element with an expression of $f = λ_{center} \times f_{center} / λ$ , where the subscript stands for the center wavelength. It notes that the chromatic dispersion of the metalens is mainly due to the diffraction dispersion. The pink curve demonstrates the measured transmission spectrum, which comes up to as high as $\sim 80 %$ . The error bars represent the standard deviation for three measurement repetitions.
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Figure 5
Image demonstrations of the micro metalens. (a) Measurement configuration for image demonstrations of the micro metalens. (b) A simple schematic diagram of the imaging mechanism among the logo, the 40× objective, and the micro metalens. (c) The object illuminated by inserting narrow-band (10 nm) filters of 635 nm between the lamp and pinhole. Scale bar, $4 μ m$ . (d) The corresponding image of (c) observed by the micro metalens and its enlarged view of the red dashed circular area. The whole object has been reduced to the small circular field-of-view, implying a wide field-of-view potential for imaging. (e)–(h) The corresponding results at wavelengths of 485 and 542 nm.
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Figure 6
Image demonstrations of the macro metalens. (a) Photograph of the macroscopic metalens with a focal length of −4 mm, in which the ruler is used to emphasize its 1-cm-diameter size. The number of nanopillars in such macroscopic metalens is over half a billion. (b) The central parts of object logos observed by the 10× objective without the macroscopic metalens at three different wavelengths, respectively. Scale bar, $100 μ m$ . (c) The entire logo in the same areas of (b) on the CCD camera, showing the wider field of view.
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