FReSCo: Painting in Fourier Space

Bird feathers, butterfly wings, or flower petals are typical examples of materials that display interesting optical properties (e.g. color) due to an underlying periodic structure. In recent years, more and more attention has been devoted to aperiodic optical materials, and in particular to systems that look completely disordered to the naked eye. Such materials can achieve properties seen in periodic structures (coloration, low transmissions at specific wavelengths), as well as original properties that require disorder.

However, such properties require the disordered structure to display some sort of correlation. Even assuming that the precise type of desired correlation is known, it is in general challenging to realize it in a system.

In this talk, I present an optimization method, the Fast Reciprocal-Space Correlator (FReSCo), that enabled us to paint arbitrary correlations into the Fourier-space representation of the pair correlations of a system of points, at record speeds and up to record system sizes.

This can be exploited to generate full trajectories of points encoding movies in Fourier space, with applications to real-time rendering.

Since FReSCo is implemented as the minimization of an effective energy, it can be combined with physical constraints, for instance repulsion, to make assemblies of particles with physical sizes rather than just points.

Taking advantage of the efficiency of FReSCo, we can generate large ensembles of points with specified correlations. Such large systems pave the way to designing materials at scale. I will, as an example, describe how this allows us to "paint" photonic scattering properties directly into the correlation function of a system of small scatterers, with applications to the design of functional disordered materials.