High-Efficiency Achromatic Metalens Topologically Optimized in the Visible
Abstract
:1. Introduction
2. Materials and Methods
3. Topology Optimization of Nano-Post
4. Results and Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Luo, X. Principles of Electromagnetic Waves in Metasurfaces. Sci. China Phys. Mech. Astron. 2015, 58, 594201. [Google Scholar] [CrossRef]
- Danila, O.; Manaila-Maximean, D. Bifunctional Metamaterials Using Spatial Phase Gradient Architectures: Generalized Reflection and Refraction Considerations. Materials 2021, 14, 2201. [Google Scholar] [CrossRef]
- Yue, F.; Wen, D.; Xin, J.; Gerardot, B.D.; Li, J.; Chen, X. Vector Vortex Beam Generation with a Single Plasmonic Metasurface. ACS Photonics 2016, 3, 1558–1563. [Google Scholar] [CrossRef]
- Wu, P.C.; Zhu, W.; Shen, Z.X.; Chong, P.H.J.; Ser, W.; Tsai, D.P.; Liu, A.-Q. Broadband Wide-Angle Multifunctional Polarization Converter via Liquid-Metal-Based Metasurface. Adv. Opt. Mater. 2017, 5, 1600938. [Google Scholar] [CrossRef]
- Huang, Y.-W.; Chen, W.T.; Tsai, W.-Y.; Wu, P.C.; Wang, C.-M.; Sun, G.; Tsai, D.P. Aluminum Plasmonic Multicolor Meta-Hologram. Nano Lett. 2015, 15, 3122–3127. [Google Scholar] [CrossRef]
- Wan, W.; Gao, J.; Yang, X. Full-Color Plasmonic Metasurface Holograms. ACS Nano 2016, 10, 10671–10680. [Google Scholar] [CrossRef]
- Ni, X.; Wong, Z.J.; Mrejen, M.; Wang, Y.; Zhang, X. An Ultrathin Invisibility Skin Cloak for Visible Light. Science 2015, 349, 1310–1314. [Google Scholar] [CrossRef]
- Xie, X.; Pu, M.; Li, X.; Liu, K.; Jin, J.; Ma, X.; Luo, X. Dual-Band and Ultra-Broadband Photonic Spin-Orbit Interaction for Electromagnetic Shaping Based on Single-Layer Silicon Metasurfaces. Photon. Res. 2019, 7, 586. [Google Scholar] [CrossRef]
- Pan, M.; Fu, Y.; Zheng, M.; Chen, H.; Zang, Y.; Duan, H.; Li, Q.; Qiu, M.; Hu, Y. Dielectric Metalens for Miniaturized Imaging Systems: Progress and Challenges. Light Sci. Appl. 2022, 11, 195. [Google Scholar] [CrossRef]
- Khorasaninejad, M.; Aieta, F.; Kanhaiya, P.; Kats, M.A.; Genevet, P.; Rousso, D.; Capasso, F. Achromatic Metasurface Lens at Telecommunication Wavelengths. Nano Lett. 2015, 15, 5358–5362. [Google Scholar] [CrossRef]
- Gao, Z.; Zhang, C.; Li, H.; Li, Y. Broadband Achromatic Metalens Based on Lithium Niobite on Insulator. J. Phys. D Appl. Phys. 2021, 54, 485103. [Google Scholar] [CrossRef]
- Cheng, W.; Feng, J.; Wang, Y.; Peng, Z.; Zang, S.; Cheng, H.; Ren, X.; Shuai, Y.; Liu, H.; Wu, J.; et al. Genetic Algorithms Designed Ultra-Broadband Achromatic Metalens in the Visible. Optik 2022, 258, 168868. [Google Scholar] [CrossRef]
- Arbabi, E.; Arbabi, A.; Kamali, S.M.; Horie, Y.; Faraon, A. Multiwavelength Polarization-Insensitive Lenses Based on Dielectric Metasurfaces with Meta-Molecules. Optica 2016, 3, 628. [Google Scholar] [CrossRef] [Green Version]
- Shan, D.; Xu, N.; Gao, J.; Song, N.; Liu, H.; Tang, Y.; Feng, X.; Wang, Y.; Zhao, Y.; Chen, X.; et al. Design of the All-Silicon Long-Wavelength Infrared Achromatic Metalens Based on Deep Silicon Etching. Opt. Express 2022, 30, 13616. [Google Scholar] [CrossRef] [PubMed]
- Fan, Z.-B.; Qiu, H.-Y.; Zhang, H.-L.; Pang, X.-N.; Zhou, L.-D.; Liu, L.; Ren, H.; Wang, Q.-H.; Dong, J.-W. A Broadband Achromatic Metalens Array for Integral Imaging in the Visible. Light Sci. Appl. 2019, 8, 67. [Google Scholar] [CrossRef] [Green Version]
- Shrestha, S.; Overvig, A.C.; Lu, M.; Stein, A.; Yu, N. Broadband Achromatic Dielectric Metalenses. Light Sci. Appl. 2018, 7, 85. [Google Scholar] [CrossRef] [Green Version]
- Zhao, F.; Jiang, X.; Li, S.; Chen, H.; Liang, G.; Wen, Z.; Zhang, Z.; Chen, G. Optimization-Free Approach for Broadband Achromatic Metalens of High-Numerical-Aperture with High-Index Dielectric Metasurface. J. Phys. D Appl. Phys. 2019, 52, 505110. [Google Scholar] [CrossRef]
- Zhou, H.; Chen, L.; Shen, F.; Guo, K.; Guo, Z. Broadband Achromatic Metalens in the Midinfrared Range. Phys. Rev. Appl. 2019, 11, 024066. [Google Scholar] [CrossRef]
- Chen, W.T.; Zhu, A.Y.; Sanjeev, V.; Khorasaninejad, M.; Shi, Z.; Lee, E.; Capasso, F. A Broadband Achromatic Metalens for Focusing and Imaging in the Visible. Nat. Nanotechnol. 2018, 13, 220–226. [Google Scholar] [CrossRef] [Green Version]
- Balthasar Mueller, J.P.; Rubin, N.A.; Devlin, R.C.; Groever, B.; Capasso, F. Metasurface Polarization Optics: Independent Phase Control of Arbitrary Orthogonal States of Polarization. Phys. Rev. Lett. 2017, 118, 113901. [Google Scholar] [CrossRef] [Green Version]
- Zhou, Y.; Kravchenko, I.I.; Wang, H.; Nolen, J.R.; Gu, G.; Valentine, J. Multilayer Noninteracting Dielectric Metasurfaces for Multiwavelength Metaoptics. Nano Lett. 2018, 18, 7529–7537. [Google Scholar] [CrossRef] [PubMed]
- Tang, D.; Chen, L.; Liu, J.; Zhang, X. Achromatic Metasurface Doublet with a Wide Incident Angle for Light Focusing. Opt. Express OE 2020, 28, 12209–12218. [Google Scholar] [CrossRef]
- Wang, S.; Wu, P.C.; Su, V.-C.; Lai, Y.-C.; Chen, M.-K.; Kuo, H.Y.; Chen, B.H.; Chen, Y.H.; Huang, T.-T.; Wang, J.-H.; et al. A Broadband Achromatic Metalens in the Visible. Nat. Nanotechnol. 2018, 13, 227–232. [Google Scholar] [CrossRef] [PubMed]
- Lin, R.J.; Su, V.-C.; Wang, S.; Chen, M.K.; Chung, T.L.; Chen, Y.H.; Kuo, H.Y.; Chen, J.-W.; Chen, J.; Huang, Y.-T.; et al. Achromatic Metalens Array for Full-Colour Light-Field Imaging. Nat. Nanotechnol. 2019, 14, 227–231. [Google Scholar] [CrossRef]
- Michell, A.G.M. LVIII. The Limits of Economy of Material in Frame-Structures. Lond. Edinb. Dublin Philos. Mag. J. Sci. 1904, 8, 589–597. [Google Scholar] [CrossRef] [Green Version]
- Shen, B.; Wang, P.; Polson, R.; Menon, R. An Integrated-Nanophotonics Polarization Beamsplitter with 2.4 × 2.4 Μm2 Footprint. Nat. Photonics 2015, 9, 378–382. [Google Scholar] [CrossRef]
- Xiao, T.P.; Cifci, O.S.; Bhargava, S.; Chen, H.; Gissibl, T.; Zhou, W.; Giessen, H.; Toussaint, K.C.; Yablonovitch, E.; Braun, P.V. Diffractive Spectral-Splitting Optical Element Designed by Adjoint-Based Electromagnetic Optimization and Fabricated by Femtosecond 3D Direct Laser Writing. ACS Photonics 2016, 3, 886–894. [Google Scholar] [CrossRef]
- Borel, P.I.; Harpøth, A.; Frandsen, L.H.; Kristensen, M.; Shi, P.; Jensen, J.S.; Sigmund, O. Topology Optimization and Fabrication of Photonic Crystal Structures. Opt. Express 2004, 12, 1996. [Google Scholar] [CrossRef]
- Sigmund, O.; Hougaard, K. Geometric Properties of Optimal Photonic Crystals. Phys. Rev. Lett. 2008, 100, 153904. [Google Scholar] [CrossRef] [Green Version]
- Diaz, A.R.; Sigmund, O. A Topology Optimization Method for Design of Negative Permeability Metamaterials. Struct. Multidisc. Optim. 2010, 41, 163–177. [Google Scholar] [CrossRef]
- Zhou, S.; Li, W.; Sun, G.; Li, Q. A Level-Set Procedure for the Design of Electromagnetic Metamaterials. Opt. Express 2010, 18, 6693–6702. [Google Scholar] [CrossRef]
- Lin, Z.; Liu, V.; Pestourie, R.; Johnson, S.G. Topology Optimization of Freeform Large-Area Metasurfaces. Opt. Express 2019, 27, 15765. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Phan, T.; Sell, D.; Wang, E.W.; Doshay, S.; Edee, K.; Yang, J.; Fan, J.A. High-Efficiency, Large-Area, Topology-Optimized Metasurfaces. Light Sci. Appl. 2019, 8, 48. [Google Scholar] [CrossRef] [Green Version]
- Chung, H.; Miller, O.D. High-NA Achromatic Metalenses by Inverse Design. Opt. Express 2020, 28, 6945. [Google Scholar] [CrossRef] [Green Version]
- Wang, S.; Wu, P.C.; Su, V.-C.; Lai, Y.-C.; Hung Chu, C.; Chen, J.-W.; Lu, S.-H.; Chen, J.; Xu, B.; Kuan, C.-H.; et al. Broadband Achromatic Optical Metasurface Devices. Nat. Commun. 2017, 8, 187. [Google Scholar] [CrossRef] [PubMed]
- Bendsøe, M.P. Optimal Shape Design as a Material Distribution Problem. Struct. Optim. 1989, 1, 193–202. [Google Scholar] [CrossRef]
- Lazarov, B.S.; Sigmund, O. Filters in Topology Optimization Based on Helmholtz-Type Differential Equations. Int. J. Numer. Meth. Eng. 2011, 86, 765–781. [Google Scholar] [CrossRef]
- Guest, J.K.; Prévost, J.H.; Belytschko, T. Achieving Minimum Length Scale in Topology Optimization Using Nodal Design Variables and Projection Functions. Int. J. Numer. Methods Eng. 2004, 61, 238–254. [Google Scholar] [CrossRef]
- Wang, F.; Lazarov, B.S.; Sigmund, O. On Projection Methods, Convergence and Robust Formulations in Topology Optimization. Struct. Multidisc. Optim. 2011, 43, 767–784. [Google Scholar] [CrossRef]
- Chen, W.T. A Broadband Achromatic Polarization-Insensitive Metalens Consisting of Anisotropic Nanostructures. Nat. Commun. 2019, 7, 355. [Google Scholar] [CrossRef] [Green Version]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhang, L.; Wang, C.; Wei, Y.; Lin, Y.; Han, Y.; Deng, Y. High-Efficiency Achromatic Metalens Topologically Optimized in the Visible. Nanomaterials 2023, 13, 890. https://doi.org/10.3390/nano13050890
Zhang L, Wang C, Wei Y, Lin Y, Han Y, Deng Y. High-Efficiency Achromatic Metalens Topologically Optimized in the Visible. Nanomaterials. 2023; 13(5):890. https://doi.org/10.3390/nano13050890
Chicago/Turabian StyleZhang, Lijuan, Chengmiao Wang, Yupei Wei, Yu Lin, Yeming Han, and Yongbo Deng. 2023. "High-Efficiency Achromatic Metalens Topologically Optimized in the Visible" Nanomaterials 13, no. 5: 890. https://doi.org/10.3390/nano13050890