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

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 bispheres 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 retroreflector and a specular reflector by making position adjustments to mirrors, and achieve a similar invisible effect by tuning sizes of the bispheres. Our work expands the toolkits for designing conformal devices with a continuously varying index profile.