Equivalence between positive and negative refractive index materials in electrostatic cloaks

We investigate, both theoretically and numerically, the equivalence relationship between the positive and negative refraction index dielectric materials in electrostatic invisibility cloak. We have derived an analytical formula that enables fast calculate the corresponding positive dielectric constant from the negative refraction index material. The numerical results show that the negative refraction index material can be replaced by the positive refractive index materials in the static field cloak. This offers some new viewpoints for designing new sensing systems and devices in physics, colloid science, and engineering applications.