Method for arbitrary phase transformation by a slab based on transformation optics and the principle of equal optical path

The optical path lengths travelled by rays across a wavefront essentially determine the resulting phase front irrespective of the shape of a medium according to the principle of equal optical path. Thereupon we propose a method for the transformation between two arbitrary wavefronts by a slab, i.e. the profile of the spatial separation between the two wavefronts is taken to be transformed to a plane surface. Interestingly, for the mutual conversion between planar and curved wavefronts, the method reduce to an inverse transformation method in which it is the reversed shape of the desired wavefront that is converted to a planar one. As an application, three kinds of phase transformation are realized and it is found that the transformation on phase is able to realize some important properties such as phase reversal or compensation, focusing, and expanding or compressing beams, which are further confirmed by numerical simulations. The slab can be applied to realizing compact electromagnetic devices for which the values of the refractive index or the permittivity and permeability can be high or low, positive or negative, or near zero, depending on the choice of coordinate transformations.Comment: 8 pages, 6 figure