Non-Euclidean conformal devices with continuously varying refractive index profiles based on bi-spheres

Either conformal transformation optics or geodesic mapping provides a design method to bend light rays in two-dimensional space with a nonuniform refractive index profile. In this paper, we combine both methods above to design a conformal invisible cloak based on bi-spheres with a refractive index profile varying from 0 to 10.7, smaller than 24.6 for the previous case of a single sphere. Moreover, we obtain an omnidirectional retro-reflector and a specular reflector by making position adjustments to mirrors, and achieve similar invisible effect by tuning sizes of the bi-spheres. Our work expands the toolkits for designing conformal devices with continuously-varying index profile.