Retroreflector approximation of a generalized Eaton lens

We extended a previous study of the Eaton lens at specific refraction angles to the Eaton lens at any refraction angle. The refractive index of the Eaton lens is complicated and has no analytical form except at a few specific angles. We derived a more accessible form of the refractive index for any refraction angle with some accuracy using the retroreflector approximation. The finding of this study will be useful for a rapid estimation of the refractive index, and the the design of various Eaton lenses.