Figure 1
From: Controlling lightwave in Riemann space by merging geometrical optics with transformation optics
Basic function of Zhukovski transformation. (a) Reference space. (b) Real space. In (a), the pink plane is the first Riemann sheet (upper space), and the cyan plane is the second Riemann sheet (lower space), corresponding to the pink part (outer of the circle) and cyan part (interior of the circle) in (b). The red line (curve) represents a light ray which touches the branch cut, and the blue line (curve) represents another ray in the orthogonal direction, which will never touch the branch cut.
