Geometrically controllable electric fields

TL;DR

This paper investigates how the geometric shape of electric cloaks influences phase transitions between negative and normal electric displacement pathways, revealing shape-dependent phenomena and potential experimental applications.

Contribution

It introduces a first-principles analysis of shape-driven phase transitions in electric cloaks, highlighting the role of geometry in controlling electric field behavior.

Findings

Negative pathway arises from shape-enhanced negative polarization.

NGP appears in spheroidal cloaks with a/b ratio around 2.5.

Cloaking efficiency varies with geometric shape.

Abstract

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.