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Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas

Nature Nanotechnology volume 12, pages 163–169 (2017)Cite this article

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Abstract

The rational design of photonic nanostructures consists of anticipating their optical response from systematic variations of simple models. This strategy, however, has limited success when multiple objectives are simultaneously targeted, because it requires demanding computational schemes. To this end, evolutionary algorithms can drive the morphology of a nano-object towards an optimum through several cycles of selection, mutation and cross-over, mimicking the process of natural selection. Here, we present a numerical technique that can allow the design of photonic nanostructures with optical properties optimized along several arbitrary objectives. In particular, we combine evolutionary multi-objective algorithms with frequency-domain electrodynamical simulations to optimize the design of colour pixels based on silicon nanostructures that resonate at two user-defined, polarization-dependent wavelengths. The scattering spectra of optimized pixels fabricated by electron-beam lithography show excellent agreement with the targeted objectives. The method is self-adaptive to arbitrary constraints and therefore particularly apt for the design of complex structures within predefined technological limits.

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Figure 1: Illustration of EMO.
Figure 2: Structure model for EMO.
Figure 3: Results of EMO for identical target wavelengths λX = λY = 630 nm.
Figure 4: Pareto front example of an optimization run with λX = 550 nm and λY = 450 nm.
Figure 5: Experimental demonstration of several dual-resonant silicon structures based on EMO.
Figure 6: Polarization-filtered dark-field images of micrometre-scale pictures designed by EMO.

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Acknowledgements

The authors thank P. Salles and G.-M. Caruso for technical assistance. This work was partly supported under a ‘Campus Gaston Dupouy’ grant by the French government, Région Midi-Pyrénées, and the European Union (ERDF), by the computing facility centre CALMIP of the University of Toulouse (grant no. P12167) and by the LAAS-CNRS micro and nanotechnologies platform, a member of the French RENATECH network.

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Authors and Affiliations

  1. CEMES-CNRS, Université de Toulouse, CNRS, UPS, 29 rue Jeanne Marvig, Toulouse, 31055, France

    Peter R. Wiecha, Arnaud Arbouet, Christian Girard & Vincent Paillard

  2. LAAS-CNRS, Université de Toulouse, CNRS, INP, 7 avenue du Colonel Roche, Toulouse, 31031, France

    Aurélie Lecestre & Guilhem Larrieu

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  1. Peter R. Wiecha
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Contributions

P.R.W., V.P. and A.A. designed the research. C.G., A.A. and P.R.W implemented the codes and performed the simulations. A.L. and G.L. fabricated the samples by EBL. P.R.W and V.P. performed the dark-field scattering experiments. All authors contributed to the data analysis, figure preparation and manuscript writing.

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Correspondence to Peter R. Wiecha, Arnaud Arbouet or Vincent Paillard.

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Wiecha, P., Arbouet, A., Girard, C. et al. Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas. Nature Nanotech 12, 163–169 (2017). https://doi.org/10.1038/nnano.2016.224

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