No abstract

The rational design of photonic nanostructures consists in anticipating their optical response from simple models and their systematic variations. 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 to design photonic nanostructures with optical properties optimised along several arbitrary objectives. We combine evolutionary multiobjective algorithms with frequency-domain electro-dynamical simulations to optimise the design of colour pixels based on silicon nanostructures that resonate at two user-defined, polarisationdependent wavelengths. The scattering spectra of optimised 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.Over the last decade, the field of nanophotonics or nano-optics has been rapidly increasing, mainly driven by plasmonics, since noble metal nanoparticles allow to spectrally tune plasmon resonances 1 and tailor several optical properties like directional scattering, 2 polarisation conversion, 3 optical chirality 4 or nonlinear effects 5 . Recently, high-index dielectric nanostructures have gained increasing interest thanks to their ability to provide exceptionally strong electric 6,7 and magnetic [8][9][10] resonances, tunable from the UV to the near IR. [11][12][13] In analogy to plasmonics, it is possible to design functionalities like transmissive metasurfaces, 14 enhanced nonlinear effects 15,16 or directional scattering. 17 When designing photonic nanostructures, a particular geometry is usually selected from qualitative considerations and its properties are subsequently studied systematically. As it comes to applications, a more convenient approach is to define the requested properties and design a nanostructure that optimally exhibits the desired features. For the latter approach, a structure model has to be developed, which, based on a certain set of parameters, can describe a large variety of particle geometries. However, this leads to huge parameter spaces which usually cannot be explored systematically. Also trial-and-error is not an efficient search strategy. More promising techniques are evolutionary optimisation strategies which, by mimicking natural selection, are able to find fittest parameter sets to a complex non-analytical problem. 18 In the field of nanophotonics, evolutionary algorithms have been applied to the maximisation * e-mail : peter. These studies were limited to the maximisation of one target property at a specific wavelength and polarisation. Such single-objective scenarii represent the simplest case of an optimisatio...