光子晶体薄膜中倒空间拓扑涡旋的研究

作为空间矢量场的一类面内构型，涡旋被认为是最基本的拓扑激发并与诸多稳定的拓扑性质相关。尽管涡旋已经被发现存在于诸多物理体系，比如流体动力学和超流超导体系之中，但可被直接观测到的涡旋大多存在于实空间。对于倒空间中的涡旋，至今难以被直接观测。.本课题拟利用自主开发的显微角分辨光谱测量技术实现对光子晶体薄膜倒空间中的拓扑涡旋进行直接的实验观测研究。由于光场偏振矢量的紧致性和光子晶体在实空间和倒空间的对称性，光子晶体薄膜在倒空间中可能广泛的存在偏振矢量涡旋。而这些涡旋的奇点又和具有高品质因子的连续谱中束缚态紧密的联系在一起。通过直接观测这类倒空间中的涡旋态，有利于深入理解拓扑的物理含义以及连续谱中束缚态的拓扑本质。进一步研究倒空间涡旋态随对称性等结构参数的依赖关系，分析涡旋的产生和湮灭机理，可以最终实现对倒空间涡旋的调控和相关方面应用，比如高品质光学微腔和低阈值激光器等。

Vortex, a fundamental topological excitation featuring the in-plane winding of a vector field, is directly related with lots of robust topological properties. Although vortices are widely observed in various areas such as fluid dynamics and superconductors, they were almost found exclusively in the real space. Directly observing vortices in reciprocal space is still challenging. .Here, we plan to experimentally observation and study of reciprocal space topological vortices in photonic crystal slabs by using home-made angle-resolved micro-spectroscopic techniques. Due to the compactness of the polarization vectors in optics and the symmetry properties of photonic crystals in real and reciprocal spaces, there could be vortices as the winding of far-field polarization vectors in the Brillouin zone of photonic crystal slabs. And the Bloch state at the vortex singularity is trapped in the slab, so called bound states in the continuum. By direct observing those vortices in reciprocal space, it could help us to deeply understand the topological nature in optics. Further researching on the relationship between those vortices and the structure parameters of photonic crystal slabs, such as symmetries and filling fraction etc., we could analyze and mimic the generation and annihilation of vortices, leading to control those vortices as will. Our proposal could help us to finally realize high Q factor cavity and low threshold lasers.