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

在本计画中，我们研究二维及三维准无序结构，它可以被视为一种新的分布光子准晶体。我们设想这些有一个完整的光子带隙，即使是任意小的折射率对比。虽然这些结构看起来完全无序，缺乏任何可辨别的对称性，但它们实际上具有长程有序性，沿着具有高度对称性，从而赋予它们独特的性质。该材料的介电分布是通过具有随机取向和随机相位的正弦光栅的叠加在数学上获得的。如果用于产生结构的光栅的数量被优化，则光栅的各个带隙可以重叠以形成完整且各向同性的光子带隙。此外，各向同性带隙的形成导致在其边缘处的所有方向的低群速度。因此，一个强大的增强的源浸没在结构化介质的发射可以观察到在这些frequency.The主要目标的这个项目是表明，即使非常低的折射率对比度可以找到一个完整的光子带隙与我们提出的结构化计划。我们希望展示一个结论性的理论，如何获得最佳的结构参数（折射率对比度，光栅的数量，尺寸）的最大开口的带隙。该理论将通过2D和3D结构的模拟来证明。在一个系统的数值模拟研究中，还应该揭示各种缺陷上的完整光子带隙所需的折射率对比度的敏感性，从而表明实际的限制比理论的更强。基于我们的方法，我们设想实现一个完整的三维带隙的折射率对比度低至1.55：1（聚合物/空气）或1.43：1（玻璃/空气）。准无序结构将在2D和3D中制造，并表征其透射和反射特性。我们的方法可以用来控制自发辐射和受激辐射在二维和三维结构与低折射率对比度。因此，我们的新型分布式准晶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。结果也将是有趣的光子社区以外，所提出的方法扩展了准晶体理论和局域化现象在电子，机械和其他波系统。

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.