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

具有确定性非周期有序光学材料的性质与晶体材料和随机无序材料的性质相同。最突出的例子是光子准晶体。虽然晶体和无序光学材料可以在自然界中大量存在，但确定性非周期材料必须在我们所知的范围内人工制造：对于这些材料，介电常数根据数学级数沿所有三维方向变化。因此，这些材料在其光势中具有几乎任意可调的相关性，并且非常适合于详细了解由此产生的输运/局部化现象以及由此产生的非线性光学性质。到目前为止，还没有关于三维确定性非周期材料的实验工作发表，仅仅是因为制造还不可能。这些材料中的开放问题是，例如，对安德森或其他光局部化现象的观察，光输运（弹道，扩散，超或次扩散）或非线性体系中的波混合现象的潜在性质。该项目的目的是缩小这一知识差距，并对这种人造材料的光学特性有一个详细的了解。我们的制造方法是三维激光光刻技术，由于最近的发展，可以在可接受的时间（几个小时）内在所有三个维度上进行块状样品扩展。我们将精力集中在基于三个数学级数的材料上，它们构成了自然界中发现的傅立叶谱的原型：斐波那契级数（纯点傅立叶谱）、Thue-Morse级数（奇异连续傅立叶谱）和Rudin-Shapiro级数（也发现了完全随机无序材料的绝对连续傅立叶谱）。样品将通过时间和空间分辨光谱以及劳埃图进行表征。多色泵浦探针实验有助于理解非线性光学性质。所有的实验工作都伴随着理论研究来分析，例如，所得模态结构、光谱特征以及这些量与潜在势之间的依赖关系。对确定性非周期结构的详细理解不仅会影响随机激光领域，而且会影响最近发展的强散射介质成像技术。

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.