Dielectric response of graded composites having general power-law-graded cylindrical inclusions

Abstract

The dielectric response of graded composites having general power-law-graded cylindrical inclusions under a uniform applied electric field is investigated. The dielectric profile of the cylindrical inclusions is modeled by the equation i ͑r͒ = c͑b + r͒ k ͑where r is the radius of the cylindrical inclusions and c , b and k are parameters͒. Analytical solutions for the local electrical potentials are derived in terms of hypergeometric functions and the effective dielectric response of the graded composites is predicted in the dilute limit. Moreover, for a simple power-law dielectric profile i ͑r͒ = cr k and a linear dielectric profile i ͑r͒ = c͑b + r͒, analytical expressions of the electrical potentials and the effective dielectric response are derived exactly from our results by taking the limits b → 0 and k → 1, respectively. For a higher concentration of inclusions, the effective dielectric response is estimated by an effective-medium approximation. In addition, we have discussed the effective response of graded cylindrical composites with a more complex dielectric profile of inclusion, i ͑r͒ = c͑b + r͒ k e ␤r .

Effective properties of spherically anisotropic piezoelectric composites

“…Furthermore, the spherically anisotropic properties of piezoelectric inclusions imply gradient profiles of properties in Cartesian coordinates. Thus, based on our results, one can also study the graded piezoelectric composites having graded inclusion materials, [26][27][28][29][30] so that the effective elastic, dielectric, and piezoelectric properties are controllable by changing the external electric field or the gradient profile of the materials. Furthermore, the nonlinear piezoelectric composites can be investigated because the electroelastic interactions are related to the nonlinear dielectric responses.…”

Localization of the electric-field distribution in graded core-shell metamaterials

“…The precise and flexible positioning of the enhanced field may have many applications in optical design, for example, in displaying and printing technologies. Furthermore, it is also instructive to extend our method to the three-dimensional spherical core-shell system for various graded profile by using established analytical solutions of graded spherical composites [20][21][22][23], the differential effective dipole approximation [26][27][28] and the transformation field method for complex structures [25].…”

“…Motivated by the above work, we consider the problem of controlling electric field distribution in the case of graded cylindrical core-shell metamaterials. The extension of different graded metamaterial models is related to a few theoretical methods for discussing the effective response and analytical solutions of general graded materials, such as using the special function [20][21][22][23][24], the transformation field method [25] and the differential effective dipole approximation [26][27][28]. In this paper, with an applied optical field, we consider a coated cylindrical structure, which consists of a homogeneous dielectric core, a shell of graded metamaterial having a complex permittivity given by the graded Drude model [18,29] , where In Sec II, we will establish the general formalism of a graded cylindrical core-shell structure in the quasi-static limit when the optical electric field is applied along the x -direction, and obtain the equivalent permittivity of such structure.…”