Perturbative analysis of optical microdisk cavities with boundary deformation

近十年来，光学微腔的研究已成为物理学研究的一个重要课题。最突出的是低语通道腔，如微盘腔，其中光被限制在微米尺度上，通过腔边界的全内反射。变形这种空腔的边界已经导致了各种各样的应用和有趣的物理。在这个项目中，我们将采用微扰理论来分析变形微盘腔的几个重要方面。我们将介绍并研究远场发射方向图已知且需要确定相应空腔变形的反问题。此外，我们将使用微扰理论推导出频率分裂和q干扰的简便公式。我们计划研究模式耦合对衰减率的影响，并将微扰理论与近可积量子系统中的共振辅助隧穿理论联系起来。最后，我们将使用微扰理论来分析表面粗糙度的影响。

In the recent decade, the study of optical microcavities has become an important subject of research in physics. Most prominent are whispering-gallery cavities, e.g. microdisk cavities, where light is confined on a micrometer scale by total internal reflection at the boundary of the cavity. Deforming the boundary of such cavities has led to a variety of applications and interesting physics. In this project, we are going to employ a perturbation theory to analyze several important aspects of deformed microdisk cavities. We will introduce and study the inverse problem where the far-field emission pattern is given and the corresponding cavity deformation has to be determined. Moreover, we will use the perturbation theory to derive handy formulas for frequency splitting and Q-spoiling. We plan to study the effect of mode coupling on decay rates and relate the perturbation theory to the theory of resonance-assisted tunneling in nearly-integrable quantum systems. Finally, we will use the perturbation theory to analyze the effects of surface roughness.