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

具有确定性非周期性次序的光学材料的性质与已知的晶体材料以及随机无序材料的性质相同。最突出的例子是光子准晶体。虽然晶体和无序的光学材料可以在自然界中大量发现，但确定性的非周期性材料必须根据我们的知识人工制造：对于这些材料，介电常数沿着所有三维根据数学级数变化。因此，这些材料在其光学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所产生的传输/局域化现象以及所产生的非线性光学特性。到目前为止，没有实验工作已经发表的三维确定性非周期性材料，只是因为制造一直是不可能的。这些材料中的开放性问题有，例如，观察安德森或其他光局部化现象，光学传输（弹道，扩散，超或亚扩散）的基本性质或非线性区域中的波混合现象。该项目的目的是弥合这一知识差距，并对此类人工材料的光学特性进行详细了解。我们的制造方法是三维激光光刻技术，由于最近的发展，允许在可接受的时间内（几个小时）在所有三个维度上批量样样品扩展。我们集中我们的努力，材料的基础上的三个数学系列，形成原型的傅立叶光谱在自然界中发现：斐波那契系列（纯点傅立叶光谱），Thue-Morse系列（奇异连续傅立叶光谱），和Rudin-Shapiro系列（绝对连续傅立叶光谱也发现完全随机无序的材料）。样品将通过时间和空间分辨光谱以及劳厄图进行表征。多色泵浦探测实验将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，得到的模式结构、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深入理解不仅将影响随机激光的研究领域，而且将影响最近发展起来的强散射介质成像。

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.