Fabrication and characterization of three-dimensional deterministic aperiodic structures - optical transport and localization in structures between order and disorder

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The properties of optical materials with deterministic aperiodic order share properties known from crystalline as well as from randomly disordered materials. Most prominent examples are photonic quasi-crystals. While crystalline and disordered optical materials can be found amass in nature, deterministic aperiodic materials have to be artificially fabricated to the best of our knowledge: For these materials the dielectric permittivity varies along all three-dimensions according to mathematical series. Hence, these materials possess almost arbitrarily tunable correlations in their optical potential and are perfectly suited for a detailed understanding of resulting transport/localization phenomena as well as resulting non-linear optical properties. To date no experimental work has been published on three dimensional deterministic aperiodic materials simply because fabrication has not been possible. Open questions in these materials are, e.g., the observation of Anderson- or other light-localization phenomena, the underlying nature of optical transport (ballistic, diffusive, super- or sub-diffusive) or wave-mixing phenomena in the non-linear regime.The aim of this project is to close this knowledge gap and to develop a detailed understanding of the optical properties of such artificial materials. Our fabricational approach is the technique of three-dimensional laser lithography, allowing due to recent developments for bulk-like sample extensions in all three dimensions in acceptable times (few hours). We concentrate our efforts on materials based on the three mathematical series, which form the archetypes of Fourier-spectra found in nature: The Fibonacci series (pure point Fourier-spectra), the Thue-Morse series (singular continuous Fourier-spectra), and the Rudin-Shapiro series (absolute continuous Fourier-spectra also found for perfectly randomly disordered materials). The samples will be characterized via time and spatially-resolved spectroscopy as well as with Laue-diagrams. Multi-color pump-probe experiments will help in understanding the non-linear optical properties. All experimental work is accompanied by theoretical investigations to analyze, e.g., resulting mode structures, spectral features and dependencies between these quantities and the underlying potential. A detailed understanding of deterministic aperiodic structure will influence not only the field of random-lasing but also the recently developing imaging through strongly scattering media.