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arXiv · 1306.0660

Closed Light Paths in Equiangular Spiral Disks

Eckhard Hitzer
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Abstract

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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Eckhard Hitzer. 2013-06-04. Closed Light Paths in Equiangular Spiral Disks. https://doi.org/10.1007/s00006-000-0005-z

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