Fundamental optics

Scattering underlies the propagation of light in non-absorbing media. This process unfolds when light interacts with inhomogeneities in the refractive index, known as scattering centers. At every scattering event, light deviates from its initial trajectory depending on the geometrical characteristics and the refractive index of the scatterer. The perceived appearance of a material is determined by a combination of factors: the properties of individual scatterers and the collective characteristics of the ensemble, including the filling fraction (the volumetric ratio of scatterers), their prevalent alignment, and the structure factor (i.e., the spatial organisation of the scatterers).

In the following, I will discuss my research both on optimising scattering in disordered media and on the optical properties of systems exhibiting short-range order.

Scattering in disordered media

The study of light propagation in materials whose microscale architecture is disordered has garned significant interest due to its implications for both fundamental and applied problems, ranging from imaging through turbid media to the fabrication of white materials. When I started my PhD, most efforts on scattering optimisation had focused on isotropic, high refractive index systems.

Using both 2D and 3D finite difference time domain (FDTD) simulations, we demonstrated that the scattering efficiency of disordered systems is mainly determined by topologically invariant features, such as the filling fraction and correlation length. Optimal scattering efficiency can thus be obtained from a broad range of disordered structures. An exception to this “invariance” is the presence of anisotropy, that marks a net increase in the scattering efficiency of a system. This finding, is crucial not only to understand the optical properties of biological networks but also for the fabrication of sustainable, white materials (read more here).

main collaborators:

• Riccardo Sapienza (Imperial College London, UK)
• Jacopo Bertolotti (University of Exeter, UK).

Short-range order media

The previous section focused on the propagation of light in disordered structures, which gives rise to white colourations. Their ordered counterpart, the so-called photonic crystals, have been extensively studied in the last decades. Their appearance depends on the periodicity of the crystal, therefore often referred to as structural colouration. Colours arising from crystalline structures are iridescent, meaning that they depend on the angle of observation, as depicted by Bragg’s law.

In my work, I demonstrated that structures with intermediate degrees of order give rise to angle-independent colours spanning the whole visible range. Combining analytical and numerical methods, I showed such isotropic colourations emerge from a delicate balance between the single-scatterer and ensemble contribution to scattering. In particular, to obtain bright and saturated colourations it is necessary to minimise the single-scatterer contribution by having scattering elements embedded in matrix with a higher refractive index. Moreover, I also showed that using core-shell structures allows for further decoupling single-scatterer and ensemble contribution and maximise the saturation of the structural colour. This balance between individual and collective scattering properties becomes particularly delicate at long wavelengths, which might be the reason why in nature, red angle-independent colours are typically achieved through chemical absorption rather than by photonic structures. The translation of these finding in the study of biological photonic structures and for the fabrication of angle-independent pigments is further discussed here.