Vol.3, No.4, 328-333 (2011) Natural Science

http://dx.doi.org/10.4236/ns.2011.34043

Copyright © 2011 SciRes. OPEN ACCESS

Effect of negative permittivity and permeability on the

transmission of electromagnetic waves through a

structure containing left-handed material

Muin F. Ubeid1*, Mohammed M. Shabat1, Mohammed O. Sid-Ahmed2

1Department of Physics, Faculty of Science, Islamic University of Gaza, Gaza, Palestine;

*Corresponding Author: mubeid@mail.iugaza.edu

2Department of Physics, Faculty of Science, Sudan University of Science and Technology, Khartoum, The Republic of The Sudan

Received 5 March 2011; revised 23 March 2011; accepted 27 March 2011.

ABSTRACT

We investigate the characteristics of electro-

magnetic wave reflection and transmission by

multilayered structures consisting of a pair of

left-handed material (LHM) and dielectric slabs

inserted between two semi-infinite dielectric

media. The theoretical aspect is based on

Maxwell's equations and matching the boundary

conditions for the electric and magnetic fields of

the incident waves at each layer interface. We

calculate the reflected and transmitted powers

of the multilayered structure taking into account

the widths of the slabs and the frequency de-

pendence of permittivity and permeability of the

LHM. The obtained results satisfy the law of

conservation of energy. We show that if the

semi-infinite dielectric media have the same

refractive index and the slabs have the same

width, then the reflected (and transmitted) pow-

ers can be minimized (and maximized) and the

powers-frequency curves show no ripple. On

the other hand if the semi-infinite dielectric me-

dia have different values of refractive indices

and the slabs have different widths, then under

certain conditions the situation of minimum and

maximum values of the mentioned powers will

be reversed.

Keywords: Electromagnetic Waves; Left-Handed

Materials; Frequency; Reflected and Transmitted

Powers

1. INTRODUCTION

Metamaterials (sometimes termed left-handed materi-

als (LHMs)) are materials whose permittivity

and

permeability

are both negative and consequently

have negative index of refraction. These materials are

artificial and theoretically discussed first by Veselago [1]

over 40 years ago. The first realization of such materials,

consisting of split-ring resenators (SRRs) and continuous

wires, was first introduced by Pendry [2,3]. Regular ma-

terials are materials whose

and

are both positive

and termed right handed materials (RHMs). R. A. Shelby

et al. [4] have studied negative refraction in LHMs. I. V.

Shadrivov [5] has investigated nonlinear guided waves

in LHMs. N. Garcia et al. [6] have shown that LHMs

don’t make a perfect lens. Kong [7] has provided a gen-

eral formulation for the electromagnetic wave interaction

with stratified metamaterial structures. M. M. Shabat et

al [8] have discussed Nonlinear TE surface waves in a

left-handed material and magnetic super lattice wave-

guide structure. I. Kourakis et al. [9] have investigated a

nonlinear propagation of electromagnetic waves in nega-

tive–refraction index LHM. H. Cory et al. [10] and C.

Sabah et al. [11] have estimated high reflection coatings

of multilayered structure. Oraizi et al. [12] have obtained

a zero reflection from multilayered metamaterial struc-

tures.

In this paper we consider a structure consisting of

LHM and dielectric slabs inserted between two semi-

infinite dielectric media. A plane polarized wave is

obliquely incident on it. We use Maxwell’s equations

and match the boundary conditions for the electric and

magnetic fields of the incident waves at each layer in-

terface. Then we solve the obtained equations for the

unknown parameters to calculate the reflection and

transmission coefficients. We take into account the fre-

quency dependence of permittivity and permeability of

the LHM (in contradict with [10,11]), widths of the slabs,

refractive indices of the media and angle of incidence of

the incident waves. Maximum and minimum transmitted

(minimum and maximum reflected) powers of the con-

sidered structure are proposed. The numerical results are