Closed Light Paths in Equiangular Spiral Disks
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.
Cite
@article{arxiv.1306.0660,
title = {Closed Light Paths in Equiangular Spiral Disks},
author = {Eckhard Hitzer},
journal= {arXiv preprint arXiv:1306.0660},
year = {2013}
}
Comments
36 pages, 18 figures