Spatial correlations and optical properties in three-dimensional deterministic aperiodic structures

Photonic systems have strongly varying optical properties depending on the spatial correlations present in a given realization. In photonic crystals the correlations are spatially periodic forming Bravais lattices whereas the building blocks of an amorphous medium are randomly distributed without any long-range order. In this manuscript we study the optical properties of so-called deterministic aperiodic structures which fill the gap between the aforementioned two limiting cases. Within this group we vary the spectrum of the spatial correlations from being pure-point over singularly-continuous to absolutely-continuous. The desired correlations are created in direct-laser written three-dimensional polymer structures using one construction principle which allows us to attribute the optical behaviour solely to the encoded spectrum. Infrared reflection measurements reveal the characteristic response of each spectral type verifying the successful fabrication of large deterministic aperiodic structures. To prove the presence of the correlations in all directions we perform transmission experiments parallel to the substrate by means of micro-optical mirrors placed next to the structures. Transport measurements reveal a strong dependence of the effective beam width at the output facet on the encoded lattice type. Finally, we reproduce the lattice type dependent transport behavior in numerical calculations ruling out extrinsic experimental reasons for these findings.