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35. G. (2010). Phys. Rev. G. (2011). Phys. Rev. A, 84, 049902. 36. , and Lipson, M. (2011). J. , 13, 024010. 37. , and Sahebdivan, S. (2015). Phys. Rev. A, 92, 053848. 38. , and Zhang, X. (2011). Nature, 480, 42. ˜ ´ ´ 39. , and Ahmadpanahi, H. (2014). New J. , 16, 033015. 40. Plebanski, J. (1960). Phys. , 118, 1396. 41. , and Sihvola, A. (2001). Electromagnetics of Bi-anisotropic Materials (Gordon and Breach, Amsterdam). 42. M. (1957). C. R. Acad. Sci. (Paris), 242, 465. 43. M. (1957/1958). Archive Rat.

24) has the transformation matrix = diag (dx/dx , 1, 1) and we find from the recipe (Eq. 23): dx dx dx , , . 25) ε = μ = diag dx dx dx Inside the device, that is, inside the fold in the transformation of Fig. 4, the derivative dx /dx becomes negative and the coordinate system changes handedness. The electromagnetic left-handedness of such a material appears through a transformation to a left-handed coordinate system; the material is called a left-handed material and also a material with negative refraction.

The two reasons are connected, because Maxwell’s fish eye represents the geometry of a finite space, the virtual hypersphere, in an infinitely extended space. There the speed of light must go to infinity for keeping propagation times finite. However, there is a remedy [34, 35] that solves both problems in one stroke. Imagine we place a mirror around the equator of the virtual sphere. The mirror would create the illusion that the light propagates in the entire virtual sphere, whereas in reality it is confined to one of the Hemispheres, say the Southern Hemisphere.

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