Paraxial optics cloak using four converging lenses with arbitrary focal lengths

In this paper, we show that cloaking region can be achieved with four converging lenses of any focal length by solving the ray transfer matrix of a four lens optical system. It has been shown before that cloaking can be achieved using four converging lenses (so-called Rochester cloaks). However, those cloaks require having 2 sets of 2 lenses with equal focal lengths, which we did not impose. We also discuss in this paper how the separation lengths between the lenses are affected by their focal lengths. In addition, we show how our formulas hold under Rochester cloak conditions.