A formula for ray trajectories in GRIN cylindrical lenses

Graded-index rod lenses have been widely used in various optoelectronic devices such as planar waveguide lasers and external-cavity semiconductor lasers in a new way of cylindrical lenses. In this article, an analytic calculation model of ray trajectories is set up by fitting the data of ray trajectories obtained by numerical ray tracing. Then, a parabolic formula of a ray trajectory is developed by a comparing calculation results. The formula is proved to be reliable by calculation error analysis. It is demonstrated that this formula could improve efficiency of numerical calculation and could be helpful for widening their application range.