Fig. 2: Double-layer lenses with foci at infinity.

The Generalized Maxwell Fish Eye profile can be used as a double-layer lens, with one homogeneous layer and foci at infinity. We show four examples, with ray turning angle Δϕ of π plus a π/4; b π/2; c π; and d 3π/2. When M is an odd integer, the lens provides the functionality of an ordinary Eaton lens; when M is an even integer, it acts as an invisible lens where the rays travel in loops in the lens. Note that in Fig. 2 and the following figures the mirror coupling into lower waveguide is indicated as a red solid line, and the color of the rays (blue/green) indicates in which waveguide the propagation occurs (upper inhomogeneous index/lower homogeneous index).