A paraxial cloak with four lenses of different focal lengths

We demonstrate cloaking with four lenses of different focal lengths. To achieve this, we compute the separation distances between lenses such that the effective ABCD matrix is equal to just a propagation in free space. Previously, calculations using this method are restricted to 2 pairs of lenses with equal focal lengths. Our computations, on the other hand, had no such restrictions: we generalize even with an asymmetric case. We derive expressions that show the dependence of the distances on the lenses and their focal lengths. Furthermore, we propose a way to minimize the length of this cloak. Our equations reduce to the Rochester cloak when its restriction is imposed. A general paraxial cloak could be useful in advanced undergraduate experiments in optics because: 1) the limit imposed by the focal length has been lifted; and 2) there is a pedagogical benefit of doing experiments with lenses beyond the usual imaging experiments such as reinforcing concepts in Gaussian optics.
Comment: 10 pages, 4 figures