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Cited by 67Metamaterials and Metasurfaces ApplicationsAdvanced Antenna and Metasurface TechnologiesTopology Optimization in Engineering

Meta-atom library generation via an efficient multi-objective shape optimization method

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Whiting, Eric B., Campbell, Sawyer D., Kang, Lei, Werner, Douglas H.·2020·Optics Express
DOI 10.1364/oe.398332
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Abstract

Optimizing the shape of metasurface unit cells can lead to tremendous performance gains in several critically important areas. This paper presents a method of generating and optimizing freeform shapes to improve efficiency and achieve multiple metasurface functionalities (e.g., different polarization responses). The designs are generated using a three-dimensional surface contour method, which can produce an extensive range of nearly arbitrary shapes using only a few variables. Unlike gradient-based topology optimization, the proposed method is compatible with existing global optimization techniques that have been shown to significantly outperform local optimization algorithms, especially in complex and multimodal design spaces.

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  • Local optimizers may get stuck at suboptimal designs, which is especially problematic in non-convex optimization scenarios like metasurface design.

    “However, local optimizers may get stuck at suboptimal designs which is especially problematic in non-convex optimization scenarios like metasurface design [38].”

    From Robust inverse design of all-dielectric metasurface transmission-mode color filters (2020) · cites this paper as [38]

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  1. [1]1. F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient Metasurfaces: A Review of Fundamentals and Applications,” Rep. Prog. Phys. 81(2), 026401 (2018). Crossref
  2. [2]2. S. Sun, Q. He, J. Hao, S. Xiao, and L. Zhou, “Electromagnetic Metasurfaces: Physics and Applications,” Adv. Opt. Photonics 11(2), 380–479 (2019). Crossref
  3. [3]3. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011). Crossref
  4. [4]4. A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-Thick Lenses with High Numerical Apertures and Large Efficiency Based on High-Contrast Transmitarrays,” Nat. Commun. 6(1), 7069 (2015). Crossref
  5. [5]5. M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at Visible Wavelengths: Diffraction-Limited Focusing and Subwavelength Resolution Imaging,” Science 352(6290), 1190–1194 (2016). Crossref
  6. [6]6. W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A Broadband Achromatic Metalens for Focusing and Imaging in the Visible,” Nat. Nanotechnol. 13(3), 220–226 (2018). Crossref
  7. [7]7. J. Nagar, S. D. Campbell, and D. H. Werner, “Apochromatic Singlets Enabled by Metasurface-Augmented GRIN Lenses,” Optica 5(2), 99–102 (2018). Crossref
  8. [8]8. L. Zhang, J. Ding, H. Zheng, S. An, H. Lin, B. Zheng, Q. Du, G. Yin, J. Michon, Y. Zhang, Z. Fang, M. Y. Shalaginov, L. Deng, T. Gu, H. Zhang, and J. Hu, “Ultra-Thin High-Efficiency Mid-Infrared Transmissive Huygens Meta-Optics,” Nat. Commun. 9(1), 1481 (2018). Crossref
  9. [9]9. M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-Efficiency All-Dielectric Metasurfaces for Ultracompact Beam Manipulation in Transmission Mode,” Nano Lett. 15(9), 6261–6266 (2015). Crossref
  10. [10]10. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface Holograms Reaching 80% Efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). Crossref
  11. [11]11. X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D Meta-Holography by Broadband Plasmonic Modulation,” Sci. Adv. 2(11), e1601102 (2016). Crossref
  12. [12]12. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012). Crossref
  13. [13]13. V. Egorov, M. Eitan, and J. Scheuer, “Genetically Optimized All-Dielectric Metasurfaces,” Opt. Express 25(3), 2583–2593 (2017). Crossref
  14. [14]14. L. Hsu, M. Dupré, A. Ndao, J. Yellowhair, and B. Kanté, “Local Phase Method for Designing and Optimizing Metasurface Devices,” Opt. Express 25(21), 24974–24982 (2017). Crossref
  15. [15]15. M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-Efficiency Dielectric Huygens’ Surfaces,” Adv. Opt. Mater. 3(6), 813–820 (2015). Crossref
  16. [16]16. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric Metasurfaces for Complete Control of Phase and Polarization with Subwavelength Spatial Resolution and High Transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). Crossref
  17. [18]18. T. Feichtner, O. Selig, M. Kiunke, and B. Hecht, “Evolutionary Optimization of Optical Antennas,” Phys. Rev. Lett. 109(12), 127701 (2012). Crossref
  18. [19]19. F. Babaei, M. Javidnasab, and A. Rezaei, “Supershape Nanoparticle Plasmons,” Plasmonics 13(4), 1491–1497 (2018). Crossref
  19. [20]20. C. Forestiere, M. Donelli, G. F. Walsh, E. Zeni, G. Miano, and L. Dal Negro, “Particle-swarm Optimization of Broadband Nanoplasmonic Arrays,” Opt. Lett. 35(2), 133–135 (2010). Crossref
  20. [21]21. C. Forestiere, A. J. Pasquale, A. Capretti, G. Miano, A. Tamburrino, S. Y. Lee, B. M. Reinhard, and L. Dal Negro, “Genetically Engineered Plasmonic Nanoarrays,” Nano Lett. 12(4), 2037–2044 (2012). Crossref
  21. [22]22. C. Forestiere, Y. He, R. Wang, R. M. Kirby, and L. Dal Negro, “Inverse Design of Metal Nanoparticles’ Morphology,” ACS Photonics 3(1), 68–78 (2016). Crossref
  22. [23]23. P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances On-Demand for Plasmonic Nano-Particles,” Nano Lett. 11(6), 2329–2333 (2011). Crossref
  23. [24]24. J. R. Ong, H. S. Chu, V. H. Chen, A. Y. Zhu, and P. Genevet, “Freestanding Dielectric Nanohole Array Metasurface for Mid-infrared Wavelength Applications,” Opt. Lett. 42(13), 2639–2642 (2017). Crossref
  24. [26]26. Q. Zhang, X. Wan, S. Liu, J. Yuan Yin, L. Zhang, and T. J. Cui, “Shaping Electromagnetic Waves using Software-Automatically-Designed Metasurfaces,” Sci. Rep. 7(1), 3588 (2017). Crossref
  25. [27]27. D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries,” Nano Lett. 17(6), 3752–3757 (2017). Crossref
  26. [28]28. D. Sell, J. Yang, S. Doshay, and J. A. Fan, “Periodic Dielectric Metasurfaces with High-Efficiency, Multiwavelength Functionalities,” Adv. Opt. Mater. 5(23), 1700645 (2017). Crossref
  27. [29]29. Z. Lin, V. Liu, R. Pestourie, and S. G. Johnson, “Topology Optimization of Freeform Large-Area Metasurfaces,” Opt. Express 27(11), 15765–15775 (2019). Crossref
  28. [30]30. J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Free-Form Diffractive Metagrating Design Based on Generative Adversarial Networks,” ACS Nano 13(8), 8872–8878 (2019). Crossref
  29. [31]31. Z. A. Kudyshev, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Machine-Learning-Assisted Metasurface Design for High- Efficiency Thermal Emitter Optimization,” arXiv 28 (2019).
  30. [32]32. S. Inampudi and H. Mosallaei, “Neural Network Based Design of Metagratings,” Appl. Phys. Lett. 112(24), 241102 (2018). Crossref
  31. [33]33. Z. Liu, D. Zhu, S. P. Rodrigues, K.-T. Lee, and W. Cai, “Generative Model for the Inverse Design of Metasurfaces,” Nano Lett. 18(10), 6570–6576 (2018). Crossref
  32. [34]34. W. Ma, F. Cheng, and Y. Liu, “Deep-Learning-Enabled On-Demand Design of Chiral Metamaterials,” ACS Nano 12(6), 6326–6334 (2018). Crossref
  33. [35]35. P. R. Wiecha and O. L. Muskens, “Deep Learning Meets Nanophotonics: A Generalized Accurate Predictor for Near Fields and Far Fields of Arbitrary 3D Nanostructures,” Nano Lett. 20(1), 329–338 (2020). Crossref
  34. [36]36. C. C. Nadell, B. Huang, J. M. Malof, and W. J. Padilla, “Deep Learning for Accelerated All-Dielectric Metasurface Design,” Opt. Express 27(20), 27523–27535 (2019). Crossref
  35. [37]37. S. An, C. Fowler, B. Zheng, M. Y. Shalaginov, H. Tang, H. Li, L. Zhou, J. Ding, A. M. Agarwal, C. Rivero-Baleine, K. A. Richardson, T. Gu, J. Hu, and H. Zhang, “A Deep Learning Approach for Objective-Driven All-Dielectric Metasurface Design,” ACS Photonics 6(12), 3196–3207 (2019). Crossref
  36. [38]38. Q. Zhang, C. Liu, X. Wan, L. Zhang, S. Liu, Y. Yang, and T. J. Cui, “Machine-Learning Designs of Anisotropic Digital Coding Metasurfaces,” Adv. Theory Simul. 2(2), 1800132 (2019). Crossref
  37. [39]39. T. Qiu, X. Shi, J. Wang, Y. Li, S. Qu, Q. Cheng, T. Cui, and S. Sui, “Deep Learning: A Rapid and Efficient Route to Automatic Metasurface Design,” Adv. Sci. 6(12), 1900128 (2019). Crossref
  38. [40]40. E. S. Harper, E. J. Coyle, J. P. Vernon, and M. S. Mills, “Inverse Design of Broadband Highly Reflective Metasurfaces Using Neural Networks,” Phys. Rev. B 101(19), 195104 (2020). Crossref
  39. [41]41. J. S. Jensen and O. Sigmund, “Topology Optimization for Nano-Photonics,” Laser Photonics Rev. 5(2), 308–321 (2011). Crossref
  40. [42]42. C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, and E. Yablonovitch, “Adjoint Shape Optimization Applied to Electromagnetic Design,” Opt. Express 21(18), 21693–21701 (2013). Crossref
  41. [43]43. M. P. Bendsøe and O. Sigmund, Topology Optimization: Theory, Methods, and Applications, Second edition, corrected printing, Engineering Online Library (Springer, 2011).
  42. [44]44. J. A. Bossard, L. Lin, S. Yun, L. Liu, D. H. Werner, and T. S. Mayer, “Near-Ideal Optical Metamaterial Absorbers with Super-Octave Bandwidth,” ACS Nano 8(2), 1517–1524 (2014). Crossref
  43. [45]45. S. Jafar-Zanjani, S. Inampudi, and H. Mosallaei, “Adaptive Genetic Algorithm for Optical Metasurfaces Design,” Sci. Rep. 8(1), 11040–16 (2018). Crossref
  44. [46]46. B. Adomanis, D. Bruce Burckel, and M. Marciniak, “3D Plasmonic Design Approach for Efficient Transmissive Huygens Metasurfaces,” Opt. Express 27(15), 20928–20937 (2019). Crossref
  45. [47]47. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-Index Meta-surfaces as a Bridge Linking Propagating Waves and Surface Waves,” Nat. Mater. 11(5), 426–431 (2012). Crossref
  46. [48]48. X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, and W. Zhang, “Broadband Terahertz Wave Deflection Based on C-shape Complex Metamaterials with Phase Discontinuities,” Adv. Mater. 25(33), 4567–4572 (2013). Crossref
  47. [49]49. M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast Optimization of Electromagnetic Design Problems Using the Covariance Matrix Adaptation Evolutionary Strategy,” IEEE Trans. Antennas Propag. 59(4), 1275–1285 (2011). Crossref
  48. [50]50. N. Hansen, S. D. Müller, and P. Koumoutsakos, “Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES),” Evolutionary Comput. 11(1), 1–18 (2003). Crossref
  49. [51]51. P. R. Wiecha, A. Arbouet, C. Girard, A. Lecestre, G. Larrieu, and V. Paillard, “Evolutionary Multi-Objective Optimization of Colour Pixels Based on Dielectric Nanoantennas,” Nat. Nanotechnol. 12(2), 163–169 (2017). Crossref
  50. [52]52. P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking Five Global Optimization Approaches for Nano-optical Shape Optimization and Parameter Reconstruction,” ACS Photonics 6(11), 2726–2733 (2019). Crossref
  51. [53]53. K. Deb and H. Jain, “An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints,” IEEE Trans. Evol. Computat. 18(4), 577–601 (2014). Crossref
  52. [54]54. C. Igel, N. Hansen, and S. Roth, “Covariance Matrix Adaptation for Multi-objective Optimization,” Evolutionary Comput. 15(1), 1–28 (2007). Crossref
  53. [55]55. D. Hadka and P. Reed, “Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework,” Evolutionary Comput. 21(2), 231–259 (2013). Crossref
  54. [56]56. S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-Efficiency Broadband Anomalous Reflection by Gradient Meta-Surfaces,” Nano Lett. 12(12), 6223–6229 (2012). Crossref
  55. [58]58. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative Index of Refraction in Optical Metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). Crossref
  56. [60]60. Z. Guo, L. Zhu, F. Shen, H. Zhou, and R. Gao, “Dielectric Metasurface Based High-efficiency Polarization Splitters,” RSC Adv. 7(16), 9872–9879 (2017). Crossref
  57. [1](1) Optics Express Siddharth Ramachandran, Editor-in-Chief Journal Home About Issues in Progress Current Issue All Issues Feature Issues Table 1. Comparison of different meta-atom topology design strategies Dielectric/ Metallic Materials Optimization Strategy Number of Function Evaluations Shape Diversity Unit-cell/Supercell Design Simple shapes Yes/Yes Parametric Sweep a Hundreds Low Yes/Yes Pixelated designs ??? b /Yes Genetic Algorithm Thousands High Yes/??? c Border defined shapes Yes/Yes Global Thousands Medium d Yes/Yes Adjoint based topology optimization Yes/Yes e Local Hundreds Very High ??? f /Yes Surface contour method Yes/Yes Global – Multi Obj. Thousands Very High Yes/Yes The common method is to perform a parametric sweep, although optimization approaches have been used as well [13–14]. Pixelated designs would lead to high aspect ratios and sharp corners, which would be unsuitable for thick dielectric materials at optical frequencies. Theoretically it would be possible to optimize a pixelated supercell design. However, the sheer number of variables would make it very difficult. Because these shapes are defined by the radial position as a function of angle, these methods cannot achieve multiple inclusions or simple shapes like the “H-shape.” While topology optimization can handle metals, the prevailing implementation is for dielectrics only. The current methods in the literature are not compatible with unit cell design, which requires the optimizer to achieve a specified phase. Confirm Citation Alert Please login to set citation alerts. MathJax Help Equations displayed with MathJax. Right click equation to reveal menu options. Field Error Select as filters Select Topics Cancel Publishing Home Journals Conferences Preprints (Optica Open) Information for Authors Reviewers Librarians Open Access Information Open Access Statement and Policy Terms for Journal Article Reuse Other Resources Optica AI Optica Open Optica Publishing Group Bookshelf Optics ImageBank Optics & Photonics News Spotlight on Optics Optica Home Accessibility Information OPG Accessibility Statement About About Optica Publishing Group About My Account Sign up for Alerts Contact Us Send Us Feedback My Favorites Go to My Account Login to access favorites Recent Pages Meta-atom library generation via an efficient multi-objective shape optimization method Clear History © Copyright 2026 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies. Privacy | Terms of Use Login or Create Account Sign in by: Please wait... Don't have an account? Create an Account. Institutional Login (Optica Publishing Group participates in eduGAIN) China CARSI Member Access China CAoS Member Access Privacy Policy Need help? Our website uses cookies In order to remember your preferences (“Functional”), to measure traffic to our site (“Analytics”), and to personalise content and ads and enable social media features (“Marketing & Social Media”), we use cookies and similar technologies. We also share information about your use of our website with our social media, analytics, and advertising partners, who may combine it with other information they have collected from your use of their services. You can change or withdraw your consent at any time. More information about the use of cookies on our website can be found in our privacy policy. Opg.optica.org Functional Cookies and similar technologies that are strictly necessary for the website to work, such as remembering your preferences, security, enabling log-in or processing forms. Consent Studio Consent Studio consent-studio__consent-id ID of the proof of consent storage within the Consent Studio platform.

Authors
Whiting, E. B., Campbell, S. D., Kang, L., & Werner, D. H.
ORCID
Venue
Optics Express
Publisher
Optica Publishing Group
Published
2020-07-31
Volume
28
Issue
16
Pages
24229
ISSN
1094-4087 (ISSN-L)
DOI
10.1364/oe.398332
OpenAlex
W3045181008
Cited by
67
References
60
Citations by year
2026: 4 · 2025: 12 · 2024: 8 · 2023: 12 · 2022: 16 · 2021: 13 · 2020: 2
FWCI
7.41
Type
journal article
Language
en
Open access
Licence
Locations
  • Optics Express (publishedVersion)
  • PubMed (publishedVersion)
Funders
Defense Advanced Research Projects Agency (HR00111720032)
Topics
  • Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
  • Physical Sciences › Engineering › Aerospace Engineering › Advanced Antenna and Metasurface Technologies
  • Physical Sciences › Engineering › Civil and Structural Engineering › Topology Optimization in Engineering
Keywords
metasurface unit cell, multi-objective shape optimization, polarization response, global optimization, derivative-free optimization

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