Apparently Negative Electric Polarization in Shaped Graded Dielectric Materials

By using a first-principles approach, we investigate the pathway of electric displacement fields in shaped graded dielectric materials existing in the form of cloaks with various shapes. We reveal a type of apparently negative electric polarization （ANEP）, which is due to a symmetric oscillation of the paired electric permittivities, satisfying a sum rule. The ANEP does not occur for a spherical cloak, but appears up to maximum as a/b （the ratio between the long and short principal axis of the spheroidal cloak） is about 5/2, and eventually disappears as a/b becomes large enough corresponding to a rod-like shape. Further, the cloaking efficiency is calculated for different geometrical shapes and demonstrated to closely relate to the ANEP. The possibility of experiments is discussed. This work has relevance to dielectric shielding based on shaped graded dielectric materials.