E.M.S. Hitzer

*Advances in Applied Clifford Algebras* **10**(2), 225 (2000).

**Abstract:**
A new type of deformation for microscopic laser disks, the
*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
*closed paths* inside equiangular spirals are derived.
Third, their numerical solution is performed and found to yield two
generic types of closed light paths. *Degenerate* closed paths that
exist over large intervals of the deformation parameter, and
*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
*stable asymmetric bow-tie* shaped light trajectory was found.

[Postscript] 94k, gzip compressed

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