Curved anisotropic polaritons

The curved surface has emerged as new research platform for understanding and manipulating novel electromagnetic behaviors in complex media. In this paper, we explore the anisotropic polaritons on the spherical surface based on Maxwell’s fish-eye metric through stereographic projection. Additionally, this phenomenon can be extended to spindle surface by conformal mapping. Our calculations and simulations demonstrate the elliptic and hyperbolic polaritons, excited by an electric dipole on the sphere, will self-focus or focus on the poles on the sphere affected by anisotropic permittivity. Furthermore, we reveal the optical singularity nature of the curved hyperbolic polaritons from the perspective of transformation optics by obtaining the equivalent optical refractive index profiles and the particle potential energy. Based on natural anisotropic materials and metamaterials, the curved polaritons have potential applications in curved surface focusing and chaos regulation. This work not only bridges the transformation optics and anisotropic polaritons at curved surface, but also provides a new route to surface optical field manipulation.