Geometrically controllable electric fields
  According to a first-principles approach, we clarify electric cloaks universality concerning a new class of phase transitions between negative pathway (NGP) and normal pathway of electric displacement fields, which are driven by the geometric shape of the cloak. We report that the NGP arises from shape-enhanced strong negative electric polarization, and that it is related to a symmetric oscillation of the paired electric permittivities, which are shown to satisfy a sum rule. The NGP does not occur for a spherical cloak, but appears up to maximum as the ratio a/b 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. Then, the cloaking efficiency is compared between different geometrical shapes. The possibility of experiments is discussed. This work has relevance to crucial control of electric fields and to general physics of phase transitions. 
C. Z. Fan, Y. Gao, and J. P. Huang