Geodesics on the surface of stationary phase for a twisted light beam

The region of the stationary phase of a monochromatic light beam propagating through two twisted slits was calculated with an elementary wave theory according to Huygens together with its analytic continuation; its screw like shape was experimentally verified [1,2]. To obtain a feeling for classical particle trajectories we calculate the geodesics on this surface (H) using the tools of differential geometry for curved space-time. H is twisted but its torsion tensor is zero and we introduce a metric on H, as in the case of the hyperbolic paraboloid [3]. We found geodesics which spread out after the slits corresponding to momentum conservation and we developed a simple demonstration model for geodesics on a curved manifold using a toy engine. [1,2] E.Frins et al. DGAO-Proc. 2018,2019 [3] G.Bernacchi; Tensors made easy, Problem 43.