# Single-layer silicon metalens for broadband achromatic focusing and wide field of view

Jian Cao, Sarra Salhi, Jonathan Peltier, Jean-René Coudevylle, Samson Edmond, Cédric Villebasse, Etienne Herth, Laurent Vivien, Carlos Alonso Ramos, Daniele Melati

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Jian Cao, Sarra Salhi, Jonathan Peltier, Jean-René Coudevylle, Samson Edmond, et al., Single-layer silicon metalens for broadband achromatic focusing and wide field of view. 2025. [hal-05116436](https://hal.science/hal-05116436v1)

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Preprint submitted on 21 Jul 2025

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Single-layer silicon metalens for broadband achromatic
focusing and wide field of view: supplementary
information document

Jian Cao, Sarra Salhi, Jonathan Peltier, Jean-René Coudevylle, Samson Edmond, Cédric
Villebasse, Etienne Herth, Laurent Vivien, Carlos Rasmos, Daniele Melati

Centre de Nanosciences et de Nanotechnologies, Université Paris-Saclay, CNRS, 91120
Palaiseau, France

<table><caption>Table S1. Experimental results reported in the literature for achromatic and/or wide field-of-view metalenses. FOV: Field of view. NA: Numerical aperture. Norm. relative focal shift: ratio between the change of the focal distance in the considered wavelength range and the designed focal distance. Focusing efficiency: (*) the ratio between the power in the focal spot region and the incident power; (+) the ratio between the power in the focal spot region and the transmitted power through metalens area. Reference numbers are at the end of this document.</caption><thead><tr><th>FOV(°)</th><th>Norm. relative focal shift</th><th>Wavelength</th><th>NA</th><th>Focusing efficiency</th><th>Type</th><th>Ref.</th></tr></thead><tbody><tr><td>\</td><td>~0.15%</td><td>488 - 658 nm</td><td>0.70</td><td>~15%*</td><td>Singlet</td><td>[1]</td></tr><tr><td>\</td><td>~12.9%</td><td>400 - 660 nm</td><td>0.11</td><td>30% - 67%*</td><td>Singlet</td><td>[2]</td></tr><tr><td>\</td><td>7.2%</td><td>1200 - 1600 nm</td><td>0.12</td><td>21.2%-51.4%*</td><td>Singlet</td><td>[3]</td></tr><tr><td>\</td><td>5.2%</td><td>1300 - 1600 nm</td><td>0.85</td><td>45.7%-55.7%*</td><td>Singlet</td><td>[3]</td></tr><tr><td>>170°</td><td>\</td><td>5.2 µm</td><td>0.24</td><td>32% - 45%*</td><td>Singlet (Pinhole)</td><td>[4]</td></tr><tr><td>≈180°</td><td>\</td><td>940 nm</td><td>0.2</td><td>41% - 88%*</td><td>Singlet (Pinhole)</td><td>[4]</td></tr><tr><td>>170°</td><td>\</td><td>532 nm</td><td>0.80</td><td>25%+</td><td>Singlet</td><td>[5]</td></tr><tr><td>86°</td><td>\</td><td>1500 - 1640 nm</td><td>0.83</td><td>~ 7.9%+</td><td>Singlet</td><td>[6]</td></tr><tr><td><10°</td><td>~0.1%</td><td>488 - 658 nm</td><td>0.70</td><td>~12%</td><td>Singlet</td><td>[7]</td></tr><tr><td>\</td><td>9.3%</td><td>470 - 670 nm</td><td>0.20</td><td>~20%*</td><td>Singlet</td><td>[8]</td></tr><tr><td>\</td><td>5.4%</td><td>1000 - 1800 nm</td><td>0.06</td><td>~65.6%(average)*</td><td>Hybrid</td><td>[9]</td></tr><tr><td>50°</td><td>\</td><td>632 nm</td><td>0.71</td><td>~9%*</td><td>Doublet</td><td>[10]</td></tr><tr><td>86°</td><td>1.3%</td><td>1500 - 1600 nm</td><td>0.80</td><td>~ 20%+</td><td>Singlet</td><td>This work</td></tr></tbody></table>
<figure><img src="image_2.png" /></figure>

Fig. S1. Phase error for a metalens with a numerical aperture of 0.8, focal distance of 90 µm and radius of 120 µm at three different wavelengths in the 1.5 µm – 1.6 µm range. The phase error is calculated as the difference between the target phase delay and the meta-atom phase delay for a given wavelength and for each position along a radius of the metalens. Red solid lines refer to the broadband metalens while blue solid line to the single wavelength one.
<figure><img src="image_3.png" /><figcaption>Fig. S2. Fourier transform results for (a,d,g) ideal, (b,e,h) broadband and (c,f,i) single-wavelength metalenses, with numerical aperture of 0.8, radius of 120 µm at $\lambda = 1.55$ µm. (a) – (c) Phase profile of metalenses. (d) – (f) Normalized amplitude of the electric field after the metalenses. (g) – (i) Normalized 2D Fourier transform results in k-space. The white circle denotes the propagation region.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. S3. 1D normalized spatial spectra along the k<sub>x</sub>/k<sub>0</sub> axis for an ideal metalens implementing exactly the target phase profile shown in Fig. 9 of the manuscript for λ = 1.55 µm, a radius of 120 µm, and numerical aperture varying from 0.2 to 0.9. (a) Spatial spectrum for normal illumination θ = 0°, (b) illumination tilted at θ = 43.8°, and (c) at θ = 89°.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. S4. 1D normalized spatial spectra of the transmitted electric field for metalenses with a numerical aperture of 0.8, a radius of 120 µm, and with different sampling steps of the electric field. (a) - (c) Results for a sampling step of 650 nm, as determined by the period of the fabricated metalenses, at three different incident angles in the range 0° - 89°. The red solid lines refer to the spectra of the ideal metalens while the blue solid lines to that of the single-wavelength metalens. (d) - (f) The same series of results with a sampling step of 400 nm. and (g) - (i) for a sampling step of 160 nm. The latter are the ones reported in the manuscript.</figcaption></figure>
References

[1] Li Z, Pestourie R, Park J S, et al. Inverse design enables large-scale high-performance meta-optics reshaping virtual reality. Nature communications, 2022, 13(1): 2409.

[2] Wang S, Wu P C, Su V C, et al. A broadband achromatic metalens in the visible. Nature nanotechnology, 2018, 13(3): 227-232.

[3] Shrestha S, Overvig A C, Lu M, et al. Broadband achromatic dielectric metalenses. Light: Science & Applications, 2018, 7(1): 85.

[4] Shalaginov M Y, An S, Yang F, et al. Single-element diffraction-limited fisheye metalens. Nano Letters, 2020, 20(10): 7429-7437.

[5] Martins A, Li K, Li J, et al. On metalenses with arbitrarily wide field of view[J]. Acs Photonics, 2020, 7(8): 2073-2079.

[6] Liu Y, Zhang J, Le Roux X, et al. Broadband behavior of quadratic metalenses with a wide field of view. Optics Express, 2022, 30(22): 39860-39867.

[7] Li Z, Lin P, Huang Y W, et al. Meta-optics achieves RGB-achromatic focusing for virtual reality[J]. Science Advances, 2021, 7(5): eabe4458.

[8] Chen W T, Zhu A Y, Sanjeev V, et al. A broadband achromatic metalens for focusing and imaging in the visible. Nature nanotechnology, 2018, 13(3): 220-226.

[9] Balli F, Sultan M, Lami S K, et al. A hybrid achromatic metalens. Nature communications, 2020, 11(1): 3892.

[10] Li Z, Wang C, Wang Y, et al. Super-oscillatory metasurface doublet for sub-diffraction focusing with a large incident angle. Optics Express, 2021, 29(7): 9991-9999.