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