Closed light paths in equiangular spiral disks
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Publication:5947319
DOI10.1007/S00006-000-0005-ZzbMATH Open0990.81170arXiv1306.0660OpenAlexW3103407695MaRDI QIDQ5947319
Publication date: 16 October 2001
Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)
Abstract: A new type of deformation for microscopic laser disks, the extit{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 extit{closed paths} inside equiangular spirals are derived. Third, their numerical solution is performed and found to yield two generic types of closed light paths. extit{Degenerate} closed paths that exist over large intervals of the deformation parameter, and extit{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 extit{stable asymmetric bow-tie} shaped light trajectory was found.
Full work available at URL: https://arxiv.org/abs/1306.0660
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