Quasi-disordered structures with 2D and 3D complete photonic bandgaps with arbitrarily small refractive-index contrast

在这个项目中，我们研究了二维和三维准无序结构，它们可以被认为是一种新的分布式光子准晶体。我们设想即使对于任意小的折射率对比，它们也具有完整的光子带隙。虽然这些结构看起来完全是无序的，缺乏任何可识别的对称性，但它们实际上具有长程有序和高度对称性，赋予它们独特的性质。这种材料的介电分布是由随机方向和随机相位的正弦光栅叠加得到的。如果优化用于生成结构的光栅数量，则光栅的单个带隙可以重叠形成完整的各向同性光子带隙。此外，各向同性带隙的形成导致其边缘在各个方向上的群速度都很低。因此，在这些频率上可以观察到浸没在结构介质中的源的强增强发射。这个项目的主要目的是表明，即使在非常低的折射率对比下，我们提出的结构方案也可以找到一个完整的光子带隙。我们想展示一个结论性的理论如何获得最佳的结构参数（折射率对比，光栅的数量，尺寸）的最大开放的带隙。这一理论将通过对二维和三维结构的模拟来证明。在系统的数值研究中，模拟还应该揭示各种缺陷上完整光子带隙所需的最低折射率对比度的灵敏度，从而表明实际限制比理论限制更强。基于我们的方法，我们设想实现一个完整的3D带隙，折射率对比度低至1.55:1（聚合物/空气）或1.43:1（玻璃/空气）。准无序结构将在二维和三维中制造，并表征其透射和反射特性。我们的方法可以用于控制低折射率对比度的二维和三维结构中的自发和受激辐射。因此，我们的新型分布式准晶体可以拓宽可用于实现光子带隙的材料范围，从而为新的应用铺平道路。结果也将在光子界之外引起人们的兴趣，因为所提出的方法扩展了准晶体理论和电子、机械和其他波系统中的局域现象。

In this project we investigate 2D and 3D quasi-disordered structures which can be considered as a new kind of distributed photonic quasicrystals. We envisage these to have a complete photonic bandgap even for arbitrarily small refractive-index contrasts. While the structures appear completely disordered and lack any discernible symmetry, they actually possess a long-range order along with a high degree of symmetry giving them unique properties. The dielectric distribution of this material is mathematically obtained by a superposition of sinusoidal gratings with random orientation and random phase. If the number of gratings used for the generation of the structure is optimized, the individual bandgaps of the gratings can overlap to form a complete and isotropic photonic bandgap. Additionally, the formation of the isotropic bandgap leads to low group velocities at its edges for all directions. Therefore, a strong enhancement of the emission of a source immersed in the structured medium can be observed at these frequencies.The main objective of this project is to show that even for very low refractive-index contrasts a complete photonic bandgap can be found with the structuration scheme we propose. We want to show a conclusive theory how to obtain the optimal structure parameters (refractive-index contrast, number of gratings, size) for the maximal opening of the bandgap. This theory is to be proven by simulations of 2D and 3D structures. In a systematic numerical study simulations should also reveal the sensitivity of the refractive-index contrast minimally required for a complete photonic bandgap on various kinds of defects, thus indicate practical limitations stronger than the theoretical ones. Based on our approach, we envisage realizing a complete 3D bandgap for a refractive-index contrast as low as 1.55:1 (polymer/air) or 1.43:1 (glass/air). The quasi-disordered structures will be manufactured in 2D and 3D and characterised for their transmission and reflection properties. Our approach can be used to control spontaneous and stimulated emission in 2D and 3D structures with a low refractive-index contrast. Our novel distributed quasicrystals can therefore widen the range of materials available for the realization of photonic bandgaps and thus can pave the way for new applications. The results will also be interesting beyond the photonic community, as the proposed approach extends the theory of quasicrystals and localisation phenomena in electronic, mechanical and other wave systems.