Exact transformation optics by using electrostatics

Abstract

We present a novel method for designing transformation optical devices based on electrostatics. An arbitrary transformation of electrostatic field can lead to a new refractive index distribution, where wavefronts and energy flux lines correspond to equipotential surfaces and electrostatic flux lines, respectively. Owing to scalar wave propagating exactly following an eikonal equation, wave optics and geometric optics share the same solutions in the devices. The method is utilized to design multipole lenses derived from multipoles in electrostatics. The source and drain in optics are considered as corresponding to positive charge and negative charge in the static field. By defining winding numbers in virtual and physical spaces, we explain the reason for some multipole lenses with illusion effects. Besides, we introduce an equipotential absorber to replace the drain to correspond to a negative charge with a grounded conductor. Therefore, it is a very general platform to design intriguing devices based on the combination of electrostatics and transformation optics.