# 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

**Source**: https://www.cs.tum.de/spp1839/projects/1st-period-2015-2018/11.html
**Parent**: https://www.cs.tum.de/spp1839/projects.html

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.

## Contributors

- [Prof. Harald Gießen](http://www.pi4.uni-stuttgart.de/home/members)
- [Prof. Thomas Weiss](http://www.pi4.uni-stuttgart.de/home/institute/junior_research_groups/physical_optics)

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