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. 2023 Oct 6;14(1):6249.
doi: 10.1038/s41467-023-41775-9.

Morphogenetic metasurfaces: unlocking the potential of turing patterns

Thomas Fromenteze  1 , Okan Yurduseven  2 , Chidinma Uche  3 , Eric Arnaud  3 , David R Smith  4 , Cyril Decroze  3
Affiliations

Morphogenetic metasurfaces: unlocking the potential of turing patterns

Thomas Fromenteze et al. Nat Commun. .

Erratum in

Abstract

The reaction-diffusion principle imagined by Alan Turing in an attempt to explain the structuring of living organisms is leveraged in this work for the procedural synthesis of radiating metasurfaces. The adaptation of this morphogenesis technique ensures the growth of anisotropic cellular patterns automatically arranged to satisfy local electromagnetic constraints, facilitating the radiation of waves controlled in frequency, space, and polarization. Experimental validations of this method are presented, designing morphogenetic metasurfaces radiating far-field circularly polarized beams and generating a polarization-multiplexed hologram in the radiative near-field zone. The exploitation of morphogenesis-inspired models proves particularly well suited for solving generative design problems, converting global physical constraints into local interactions of simulated chemical reactants ensuring the emergence of self-organizing meta-atoms.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Fig. 1
Fig. 1. Constrained generation of anisotropic Turing patterns.
The Gray-Scott model is based on the simulation of virtual, antagonistic chemical compounds referred to by A. Turing as “morphogens''. Following simple reaction (a) and diffusion (b) mechanisms, these morphogens, separated into two categories U and V, form a system of preys and predators, providing the opportunity to establish population equilibria generating spatial patterns, known as Turing patterns (c). The diffusion constants du and dv control the dimensions of the patterns generated, while the pair of parameters f and k influence their type. This model is modified to offer a new degree of freedom with anisotropic characteristics (d). Each point in space is thus associated with a diffusion tensor whose eigenaxes determine preferred directions influencing the local orientation of the synthesized patterns.
Fig. 2
Fig. 2. Morphogenetic metasurface characterization and synthesis.
a Characterization of the surface reactance controlled by morphogenetic parameters: A first characterization phase enables generation parameters to be associated with the electromagnetic properties synthesized. The study is restricted to the growth of cellular patterns whose ellipticity, dimensions and orientation are controlled by local constraints influencing morphogen self-structuring. The parameters are identical in space, which is defined with periodic boundary conditions to obtain spatial distributions enabling continuous tessellation of the plane. Finite element simulation is used to extract the electromagnetic characteristics associated with each set of morphogenetic parameters. Numerical processing is then applied to derive the reactance tensors required to convert surface waves into radiated waves. b Morphogenetic metasurface synthesis: the definition of radiation objectives enables the desired electromagnetic characteristics to be derived at the surface of a parallel plate waveguide excited by a monopole. Conversion of these targets into local morphogenetic parameters is required for metasurface generation. An iterative resolution of the anisotropic Gray-Scott model ensures the growth of elliptical patterns undergoing a series of successive divisions until they occupy the entire permitted space. Under the influence of the morphogenetic parameters, the Turing patterns self-structure to synthesize the desired electromagnetic tensors.
Fig. 3
Fig. 3. Demonstrations of procedural generation of morphogenetic metasurfaces.
a Metasurface radiating a broadside LHCP beam. b Dual-polarized metasurface radiating LHCP and RHCP beams simultaneously in two different directions. c Colormap representing orientation and anisotropy of objective tensors.
Fig. 4
Fig. 4. Experimental validations of two morphogenetic metasurfaces measured in far-field.
The realized gains are measured at 20.3GHz for the single-polarized (a) and dual-polarized (b) metasurfaces and presented according to orthographic projections and for two cutting planes.
Fig. 5
Fig. 5. Experimental demonstration of a polarization-multiplexed hologram at 20.2 GHz.
a Field scan of a morphogenetic metasurface. b Measured electric field distributions represented according to a left-hand circular polarization (∣EL∣) and a right-hand circular polarization (∣ER∣).
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References

    1. Turing AM. The chemical basis of morphogenesis. Bull. Math. Biol. 1990;52:153–197. - PubMed
    1. Kondo S, Miura T. Reaction-diffusion model as a framework for understanding biological pattern formation. Science. 2010;329:1616–1620. - PubMed
    1. Sheth R, et al. Hox genes regulate digit patterning by controlling the wavelength of a turing-type mechanism. Science. 2012;338:1476–1480. - PMC - PubMed
    1. Economou AD, et al. Periodic stripe formation by a turing mechanism operating at growth zones in the mammalian palate. Nat. Genet. 2012;44:348. - PMC - PubMed
    1. Garvie MR. Finite-difference schemes for reaction–diffusion equations modeling predator–prey interactions in matlab. Bull. Math. Biol. 2007;69:931–956. - PubMed