Advances in Condensed Matter Physics

Volume 2017 (2017), Article ID 1216867, 4 pages

https://doi.org/10.1155/2017/1216867

## Geometrically Tunable Transverse Electric Field in Multilayered Structures

^{1}Institute of Nanoscience and Nanotechnology, NCSR “Demokritos”, Neapoleos & Patriarchou Grigoriou, 15310 Athens, Greece^{2}Institute of Radiophysics & Electronics, NAS of Armenia, 0203 Ashtarak, Armenia

Correspondence should be addressed to Roland H. Tarkhanyan

Received 4 December 2016; Accepted 6 March 2017; Published 15 March 2017

Academic Editor: Jörg Fink

Copyright © 2017 Roland H. Tarkhanyan and Dimitris G. Niarchos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Appearance of a transverse component in dc electric field with respect to the applied current is investigated in periodic multilayer composite structures made of nanometer-to-micrometer scale alternating layers of two different homogeneous and isotropic conducting materials. Dependence of the transverse electric field on geometrical orientation of the layers is examined using the coordinate transformation approach. Electric field bending angle as a function of the layers’ resistivity ratio is studied in detail. It is shown that both the direction and the magnitude of the field can be changed using orientation angle of the layers as a tuning parameter.

#### 1. Introduction

Recent realization of metamaterial devices based on cloaking and concentration effects for a static magnetic field [1–5] became one of the most up-to-date applications of transformation electrodynamics [6–9]. Analogous methods have been widely used to design devices of various type controlling manipulation of heat [10–13], acoustic [14], and material [15] waves. In [16], an analytical design of a multilayered composite structure allowing redirection (bending) of dc magnetic induction vector with respect to the applied external magnetic field has been presented. The aim of this paper is an investigation of dc electric field redirection relative to the direction of the applied electric current in stratified structures. Using coordinate transformation approach analogous to that in [16], we will show the possibility for the appearance of transverse (with respect to the current) component of the field in such a periodic multilayer structure. The ratio of the transverse and longitudinal components is very sensitive to geometrical orientation of the alternating isotropic layers. It means that both the direction and magnitude of the field can be changed using orientation angle of the layers as a tuning parameter. We hope that geometrically tunable anisotropic resistivity in multilayered structures predicted in this paper can find use in various devices based on the control and manipulations of dc electric field.

#### 2. Model and Theory

Consider a periodic multilayer structure consisting of alternating layers of two different materials with isotropic resistivity and , static dielectric permittivity , , and thickness , in micrometer-to-nanometer scale, as both and are much larger than the lattice constant of the constituent components of the medium. The structure in the presence of dc electric current can be considered as an effective anisotropic homogeneous medium (a metamaterial) with electric field vector where is the applied electric current density, is the effective resistivity tensor, and is the effective conductivity tensor of the composite structure. In the coordinate system with the -axis perpendicular to the plane of the layers, tensor and effective permittivity tensor have the formwhereand is the period of the structure. Note that parallel to the plane of the layers components and are always less than the transverse component

An additional anisotropy in the resistivity and permittivity can be introduced rotating the layers in the structure around the -axis on an angle (see Figure 1). Such a rotation can be realized using coordinate transformations [16]where is the reference coordinate system fixed to the sample of rectangular parallelepiped form while system of the coordinate axes is connected with the layers which are arranged in the direction perpendicular to the -axis. The angle is assumed to be positive if the rotation is in counterclockwise direction.