Analytical design framework for metasurface projection optics

Fan Yang; Fan Yang; Tian Gu; Tian Gu; Tian Gu; Juejun Hu; Juejun Hu

doi:10.1364/JOSAB.496653

Journal of the Optical Society of America B
Vol. 40,
Issue 8,
pp. 2211-2220
(2023)
•https://doi.org/10.1364/JOSAB.496653

Analytical design framework for metasurface projection optics

Fan Yang, Tian Gu, and Juejun Hu

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Fan Yang, Tian Gu, and Juejun Hu, "Analytical design framework for metasurface projection optics," J. Opt. Soc. Am. B 40, 2211-2220 (2023)

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Related Topics
Table of Contents Category
- Optics Modes, Structured Light, and Beam Shaping
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About this Article
History
- Original Manuscript: May 31, 2023
- Revised Manuscript: July 14, 2023
- Manuscript Accepted: July 17, 2023
- Published: July 31, 2023

Abstract

Beam steering and pattern/image projection have recently emerged as promising applications for optical metasurfaces, potentially bringing significant benefits to fields such as automotive and consumer electronics. To date, designs of metasurfaces for these applications have resorted to iterative numerical optimization. In this paper, we derive analytical solutions to enable computationally efficient design of flat optics systems for optical beam steering and pattern projection. For a single-layer metasurface, we show that a quadratic phase profile yields optimal beam quality. Doublet metasurfaces offer additional control over the beam forming characteristics, and as an example, we demonstrate on-demand distortion correction following analytically derived designs.

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Equations (21)

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$A_{1, 1}$	$A_{1, 2}$	$A_{1, 3}$	$A_{1, 4}$	$A_{1, 5}$	$A_{1, 6}$
−8.96	$- 2.58 \times 10^{4}$	$1.18 \times 10^{5}$	$- 6.52 \times 10^{5}$	$2.45 \times 10^{6}$	$- 6.18 \times 10^{6}$
$A_{1, 7}$	$A_{1, 8}$	$A_{1, 9}$	$A_{1, 10}$	$A_{1, 11}$
$1.09 \times 10^{7}$	$- 1.35 \times 10^{7}$	$1.11 \times 10^{7}$	$- 5.35 \times 10^{6}$	$1.15 \times 10^{6}$
$A_{2, 1}$	$A_{2, 2}$	$A_{2, 3}$	$A_{2, 4}$	$A_{2, 5}$	$A_{2, 6}$
$- 8.12 \times 10^{3}$	$1.36 \times 10^{4}$	$- 8.90 \times 10^{4}$	$2.06 \times 10^{6}$	$- 2.91 \times 10^{7}$	$2.60 \times 10^{8}$
$A_{2, 7}$	$A_{2, 8}$	$A_{2, 9}$	$A_{2, 10}$	$A_{2, 11}$
$- 1.48 \times 10^{9}$	$5.32 \times 10^{9}$	$- 1.17 \times 10^{10}$	$1.41 \times 10^{10}$	$- 7.14 \times 10^{9}$

$A_{1, 1}$	$A_{1, 2}$	$A_{1, 3}$	$A_{1, 4}$	$A_{1, 5}$	$A_{1, 6}$
−9.62	$- 2.58 \times 10^{4}$	$1.18 \times 10^{5}$	$- 6.52 \times 10^{5}$	$2.45 \times 10^{6}$	$- 6.17 \times 10^{6}$
$A_{1, 7}$	$A_{1, 8}$	$A_{1, 9}$	$A_{1, 10}$	$A_{1, 11}$
$1.09 \times 10^{7}$	$- 1.35 \times 10^{7}$	$1.11 \times 10^{7}$	$- 5.35 \times 10^{6}$	$1.14 \times 10^{6}$
$A_{2, 1}$	$A_{2, 2}$	$A_{2, 3}$	$A_{2, 4}$	$A_{2, 5}$	$A_{2, 6}$
$- 8.13 \times 10^{3}$	$1.36 \times 10^{4}$	$- 8.90 \times 10^{4}$	$2.06 \times 10^{6}$	$- 2.91 \times 10^{7}$	$2.60 \times 10^{8}$
$A_{2, 7}$	$A_{2, 8}$	$A_{2, 9}$	$A_{2, 10}$	$A_{2, 11}$
$- 1.48 \times 10^{9}$	$5.32 \times 10^{9}$	$- 1.17 \times 10^{10}$	$1.41 \times 10^{10}$	$- 7.14 \times 10^{9}$

$A_{1, 1}$	$A_{1, 2}$	$A_{1, 3}$	$A_{1, 4}$	$A_{1, 5}$	$A_{1, 6}$
−8.96	$- 2.58 \times 10^{4}$	$1.18 \times 10^{5}$	$- 6.52 \times 10^{5}$	$2.45 \times 10^{6}$	$- 6.18 \times 10^{6}$
$A_{1, 7}$	$A_{1, 8}$	$A_{1, 9}$	$A_{1, 10}$	$A_{1, 11}$
$1.09 \times 10^{7}$	$- 1.35 \times 10^{7}$	$1.11 \times 10^{7}$	$- 5.35 \times 10^{6}$	$1.15 \times 10^{6}$
$A_{2, 1}$	$A_{2, 2}$	$A_{2, 3}$	$A_{2, 4}$	$A_{2, 5}$	$A_{2, 6}$
$- 8.12 \times 10^{3}$	$1.36 \times 10^{4}$	$- 8.90 \times 10^{4}$	$2.06 \times 10^{6}$	$- 2.91 \times 10^{7}$	$2.60 \times 10^{8}$
$A_{2, 7}$	$A_{2, 8}$	$A_{2, 9}$	$A_{2, 10}$	$A_{2, 11}$
$- 1.48 \times 10^{9}$	$5.32 \times 10^{9}$	$- 1.17 \times 10^{10}$	$1.41 \times 10^{10}$	$- 7.14 \times 10^{9}$

$A_{1, 1}$	$A_{1, 2}$	$A_{1, 3}$	$A_{1, 4}$	$A_{1, 5}$	$A_{1, 6}$
−9.62	$- 2.58 \times 10^{4}$	$1.18 \times 10^{5}$	$- 6.52 \times 10^{5}$	$2.45 \times 10^{6}$	$- 6.17 \times 10^{6}$
$A_{1, 7}$	$A_{1, 8}$	$A_{1, 9}$	$A_{1, 10}$	$A_{1, 11}$
$1.09 \times 10^{7}$	$- 1.35 \times 10^{7}$	$1.11 \times 10^{7}$	$- 5.35 \times 10^{6}$	$1.14 \times 10^{6}$
$A_{2, 1}$	$A_{2, 2}$	$A_{2, 3}$	$A_{2, 4}$	$A_{2, 5}$	$A_{2, 6}$
$- 8.13 \times 10^{3}$	$1.36 \times 10^{4}$	$- 8.90 \times 10^{4}$	$2.06 \times 10^{6}$	$- 2.91 \times 10^{7}$	$2.60 \times 10^{8}$
$A_{2, 7}$	$A_{2, 8}$	$A_{2, 9}$	$A_{2, 10}$	$A_{2, 11}$
$- 1.48 \times 10^{9}$	$5.32 \times 10^{9}$	$- 1.17 \times 10^{10}$	$1.41 \times 10^{10}$	$- 7.14 \times 10^{9}$

Abstract

Data availability

Cited By

Figures (10)

Tables (2)

Equations (21)

Journal of the Optical Society of America B