Towards macroscopic optical invisibility devices: geometrical op- tics of complex materials

Recently, a path towards macroscopic, transparent optical cloaking devices that may conceal objects spanning millions of wavelengths has been proposed [1]. Such devices are designed using transformation optics (TO) [2,3]. In this paper, we offer further analysis and improvements to the concept using the method of geometrical optics extended to complex photonic media with an arbitrary dispersion relation. A technique for solving the highly nonlinear partial differential equation of the eikonal using the finite element method is presented. Aberrations caused by the non-quadratic part of the dispersion relation are demonstrated quantitatively in a numerical experiment. An analytical argument based on the scalability of the eikonal phase is presented, which points towards a solution that removes this type of aberration in each order of the k-perturbation theory, thus restoring the perfect cloaking solution.