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Free-form and multi-physical metamaterials with forward conformality-assisted tracing

Nature Computational Science volume 4, pages 532–541 (2024)Cite this article

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Abstract

Transformation theory, active control and inverse design have been mainstream in creating free-form metamaterials. However, existing frameworks cannot simultaneously satisfy the requirements of isotropic, passive and forward design. Here we propose a forward conformality-assisted tracing method to address the geometric and single-physical-field constraints of conformal transformation. Using a conformal mesh composed of orthogonal streamlines and isotherms (or isothermal surfaces), this method quasi-analytically produces free-form metamaterials using only isotropic media. The geometric nature of this approach allows for universal regulation of both dissipative thermal fields and non-dissipative electromagnetic fields. We experimentally demonstrate free-form thermal cloaking in both two and three dimensions. Additionally, the multi-physical functionalities of our method, including optical cloaking, bending and thermo-electric transparency, confirm its broad applicability. Our method features improvements in efficiency, accuracy and adaptability over previous approaches. This study provides an effective method for designing complex metamaterials with arbitrary shapes across various physical domains.

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Fig. 1: Fundamentals of the conformality-assisted tracing (CAT) method.
Fig. 2: Free-form diffusion metamaterials of two dimensions.
Fig. 3: Free-form diffusion metamaterials of three dimensions.
Fig. 4: Effects of ITR.
Fig. 5: Free-form multi-physical metamaterials.

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Data availability

Data for Figs. 2–4 are available at https://doi.org/10.5281/zenodo.11607658 (ref. 51). The simulated and measured data were generated by Comsol Multiphysics and an infrared camera. Source data are provided with this paper.

Code availability

Source programs are available at https://doi.org/10.5281/zenodo.11545157 (ref. 52).

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Acknowledgements

C.-W.Q. acknowledges financial support from the Singapore Ministry of Education under grant no. A-8000107-01-00. J.H. acknowledges financial support from the National Natural Science Foundation of China under grants nos. 12035004 and 12320101004 and from the Innovation Program of the Shanghai Municipal Education Commission under grant no. 2023ZKZD06. L.X. acknowledges financial support from the National Natural Science Foundation of China under grants nos. 12375040, 12088101 and U2330401. G.D. acknowledges financial support from the National Natural Science Foundation of China under grant no. 12305046. J.W. acknowledges financial support from the National Natural Science Foundation of China under grant no. 12205101.

Author information

Author notes

  1. These authors contributed equally: Liujun Xu, Gaole Dai, Fubao Yang.

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore

    Liujun Xu, Guoqiang Xu & Cheng-Wei Qiu

  2. Graduate School of China Academy of Engineering Physics, Beijing, China

    Liujun Xu & Fubao Yang

  3. School of Physics and Technology, Nantong University, Nantong, China

    Gaole Dai

  4. Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai, China

    Fubao Yang, Jinrong Liu, Yuhong Zhou & Jiping Huang

  5. School of Energy and Materials, Shanghai Polytechnic University, Shanghai, China

    Jun Wang

  6. Shanghai Engineering Research Center of Advanced Thermal Functional Materials, Shanghai, China

    Jun Wang

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Contributions

L.X., J.H. and C.-W.Q. conceived the project. L.X. performed theoretical derivations, computer simulations and experimental designs. G.D. helped with the method. F.Y. carried out experiments and analyzed the data. J.L. helped with experiments. Y.Z. helped with data plots. J.W. and G.X. participated in the discussion. J.H. and C.-W.Q. supervised the project. All authors contributed to the writing of the paper.

Corresponding authors

Correspondence to Jiping Huang or Cheng-Wei Qiu.

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Nature Computational Science thanks Shikui Chen and the other, anonymous, reviewer(s) for their contributions to the peer review of this work. Primary Handling Editor: Jie Pan, in collaboration with the Nature Computational Science team.

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Xu, L., Dai, G., Yang, F. et al. Free-form and multi-physical metamaterials with forward conformality-assisted tracing. Nat Comput Sci 4, 532–541 (2024). https://doi.org/10.1038/s43588-024-00660-1

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