Fig. 4: Double-layer lenses with both foci r = 1.
From an initial point source at rs = 1, ϕ = π we trace the ray motion through the profiles defined through the implicit Eq. (30). To aid visualization we plot the rays launched in the +y direction as dashed lines, and those launched in the −y direction as solid lines. We give four examples, where the turning angle Δϕ is π plus a π/2; b 3π/4; c π; and d 3π/2. When M is integer, the lens has the functionality of a ordinary (for even numbers) or double-layer (for odd numbers) Maxwell Fish Eye lens, while otherwise, it acts as a Generalized Fish Eye, where two foci appear on the rim.
