等角螺旋线中的闭合光路
Closed Light Paths in Equiangular Spiral Disks
摘要：
本文提出了一种新的微激光盘变形形式--\textit{equiangular spiral deformation}。首先简要回顾了在真正的二维几何微积分语言的等角螺旋光路的几何。其次，推导了等角螺线内\textit{closed paths}的构成方程。第三，他们的数值解进行，并发现产生两个通用类型的封闭光路。\textit{Degenerate}闭合路径存在于变形参数的大间隔上，以及\textit{nondegenerate}闭合路径仅存在于跨越小于1%的非退化间隔的相对小的变形参数间隔上。第四，在非简并路径中，发现了\textit{stable asymmetric bow-tie}形状的光轨迹。
英文摘要：
A new type of deformation for microscopic laser disks, the \textit{equiangular spiral deformation} is proposed. First a short review of the geometry of light paths in equiangular spirals in the language of real two-dimensional geometric calculus is given. Second, the constituting equations for \textit{closed paths} inside equiangular spirals are derived. Third, their numerical solution is performed and found to yield two generic types of closed light paths. \textit{Degenerate} closed paths that exist over large intervals of the deformation parameter, and \textit{nondegenerate} closed paths which only exist over relatively small deformation parameter intervals spanning less than 1% of the nondegenerate intervals. Fourth, amongst the nondegenerate paths a \textit{stable asymmetric bow-tie} shaped light trajectory was found.
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