11 - Designing correlation functions of random, fractal, and quasicrystalline disorder in complex nanostructures for tailoring linear and nonlinear optical properties: Applications to BRDF and k-space engineering

We are going to study the influence of correlation functions on disorder in plasmonic and dielectric nanostructures. We will investigate 2D as well as 3D systems, and study long- and short-range disorder as well as fractal and quasicrystalline arrangements. We will investigate experimentally the angle-dependent photonic bandstructure as well as the bidirectional reflection distribution function (BRDF) as a function of polarization, angle, and wavelength, from the visible to the mid-infrared.We are going to use additional degrees of freedom such as lateral phase distribution on metasurfaces, radiation cones and array factors, as well as a combination of dielectrics and metals to tailor the disorder correlation functions. Manufacturing will be conducted using deterministic electron-beam lithography arrangements including stacking, as well as large area fabrication techniques that allow for tunable disorder.We are going to determine the relationship between two-point correlation functions, k-dependent optical properties, and wavelength dependent BRDF, in order to tailor nanostructured disordered surfaces for generation of designer surfaces for perfect absorbers, solar harvesting layers, as well as illumination diffusors.

Furthermore, we will study the giant nonlinear optical properties which should arise near the percolation threshold of disordered and fractal metal surfaces. The sub-nm gaps occurring just before a current path through the surface is closed are supposed to lead to large localized field enhancements. Theoretically, we will develop protocols to determine which numerical approach (S-matrix, finite element, resonant state expansion) can be used most efficiently and reliably to model a certain type and a tailored degree of disorder. For this purpose, we will compare numerical results with analytical calculations for simple one-dimensional periodic structures.

Moreover, we are going to implement perturbative and semi-analytical methods, which will allow us to model the influence of disorder on the optical properties of nanostructures starting from the ideal system. Thus, we will be able to support the experimental projects of the proposal in an efficient manner and study the influence of different types of disorder as well as the two-point correlation function in relation to the optical properties of disorder structures.We are going to include Mercator-Professor Sergei Tikhodeev from the General Physics Institute of the Russian Academy of Sciences in Moscow, who is a long-standing collaborator in the field of light propagation in ordered and disordered plasmonic nanostructures. He is planning to visit us for three months every year and also foster the exchange of theoretical students between Moscow and Stuttgart.