Apparently Negative Electric Polarization in Shaped Graded Dielectric Materials

@article{Chunzhen2010ApparentlyNE,
  title={Apparently Negative Electric Polarization in Shaped Graded Dielectric Materials},
  author={Fan Chun-zhen and Gao Yin-hao and Gao Yong and Huang Ji-ping},
  journal={Communications in Theoretical Physics},
  year={2010},
  volume={53},
  pages={913-919}
}
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… 
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