Electromagnetic wave propagation in a sandwich structure containing single-negative metamaterial

Tuanhui Feng, Libo Fan College of Electrical and Information Engineering, Xuchang University, Xuchang 461000, P. R. China

Email: fengtuanhui@yahoo.com.cn

Abstract—In this paper, the transmission property and

mechanism of a sandwich structure constructed by μ-negative

(MNG) material, air and ε-negative (ENG) material is

investigated. First, the transmission properties of the

MNG-Air-ENG sandwich structure is theoretically studied and it

is illustrated that, under certain condition, electromagnetic wave

can efficiently transmit through the MNG-Air-ENG sandwich

structure and the electric and magnetic field is interestingly

localized at the interface of MNG-Air and ENG-Air respectively,

Which makes the composite structure important for potential

application in free-space communication and other relative fields.

In addition, the transmission mechanism is also explored and the

results show that the MNG-Air-ENG sandwich structure can be

regarded as an air cavity resonator with single-negative

metamaterial reflectors.

Keywords-metamaterial; ε-negative material; μ-negative

material; free-space communication

Ⅰ. INTRODUCTION

Metamaterials, including double negative metamaterials and single-negative (SNG) metamaterials, have drawn intensive attention in the past few years, due to their unique electromagnetic properties and potential applications [1-20]. For double negative metamaterials, their permittivity and permeability are simultaneously negative. There are two kinds of SNG metamaterials: one is the ε-negative (ENG) material, in which the permittivity is negative but the permeability is positive; the other is the μ-negative (MNG) material, in which the permeability is negative but the permittivity is positive. In double negative materials, the propagation of electromagnetic wave exhibits lots of unusual properties and many important applications have been found, such as realization of perfect

imaging, fabrication of novel microwave devices, cloaking, and so on [3-8]. Contrasted to propagating modes in double negative metamaterials, SNG materials are opaque and support only evanescent modes. However, they also have many interesting properties and extraordinary applications [11-20]. In particular, the propagation of electromagnetic wave in some composite structures containing SNG materials has attracted many people’s attention [11-17]. It was shown that there exits tunneling phenomenon in a conjugate matched pairing structure made of ENG and MNG metamaterials in [11] and [12] and a single-mode resonator with subwavelength size has been proposed based on such an ENG-MNG pair [13]. In [14] and [15], the transparency phenomenon in the photonic heterostructure consisting of SNG materials was found and a kind of zero-phase-shift omnidirectional filter was presented. In addition, the authors demonstrated that electromagnetic waves can also transmit through a sandwich structure constructed by a slab of MNG media and two identical slabs with high permittivity in [16].

In our present work, the transmission property and mechanism of a sandwich structure including a MNG slab, air, and an ENG slab is investigated. First, we demonstrate that, under certain condition, electromagnetic waves can efficiently transmit through the MNG-Air-ENG sandwich structure and the electric and magnetic field is interestingly localized at the interface of MNG-Air and ENG-Air respectively. Then, the transmission mechanism is also studied and the results show that the MNG-Air-ENG structure can be regarded as an air cavity resonator with single-negative material reflectors. With these features, The MNG-Air-ENG sandwich structure may be important for potential applications in some fields, such as free-space communication, wireless energy transfer, and so on.

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Figure 1. The schematic of the MNG-Air-ENG sandwich structure.

Ⅱ. TRANSMISSION PROPERTIES

First we investigate the transmission properties of the sandwich structure consisting of a MNG slab, air, and an ENG slab which is shown in Fig. 1. The black, the light gray and the gray region denote the MNG medium, the air and the ENG medium respectively. We suppose a transverse electric wave, e.g., the electricfield lying in the y direction as shown in Fig. 1, is normally (along the z direction) incident on the MNG-Air-ENG sandwich structure. The media in the two sides of the sandwich structure are air. The treatment for the transverse magnetic wave is similar. In addition, Drude model are used to describe the isotropic single-negative materials, given as:

αε A = ε a − , (1) ω 2 μ A = μa

in ENG materials and

ε B = ε b ,

corresponding to the tunneling frequency f0 = 72.5 MHz is shown in Fig. 3. From Fig. 3 it can be seen that the electric field is localized at the interface of MNG layer and air but the

βμB = μb − (2) ω 2

in MNG materials. It is noted that these kinds of dispersion

forε A and μB may be realized in special metamaterials [1].

The angular frequency ω/2π is in units of gigahertz. In the following calculation, the material parameters are selected as

ε μa b= =1 , μa b= =ε 1 , and α = =β 400 .The

thicknesses of MNG slab, air and ENG slab are assumed to be dA = 20 mm, dC = 1000 mm and dB = 20 mm, respectively. The transmittance of the composite structure and the field distribution can be obtained by means of the transfer-matrix method. Fig. 2 depicts the calculated transmittance of the composite structure. From Fig. 2 we can see clearly that the electromagnetic energy completely tunnels through the sandwich structure at f0 = 72.5 MHz. Moreover, the electromagnetic field distribution in the sandwich structure

Figure 2. The transmittance of the MNG-Air-ENG sandwich structure with

dA = 20 mm, dB = 20 mm and dC = 1000 mm.

magnetic field is localized at the interface between air and ENG slab. With these properties, The MNG-Air-ENG sandwich structure may be important for potential applications in some fields, such as free-space communication, wireless energy transfer, and so on. If we utilize the ENG medium as a wireless receiving device, it will benefit the

Figure 3. The electromagnetic field distribution in the MNG-Air-ENG

structure corresponding to the tunneling frequency f0 = 72.5 MHz.

people that carry it for the reason that the magnetic field localizing at the interface between air and ENG slab will not interact with common environment objects.

Ⅲ. TRANSMISSION MECHANISM

Next, the transmission mechanism will be discussed. According to [2], the MNG-Air-ENG sandwich structure may be regarded as an air cavity with SNG metamaterial reflectors and the resonant frequency can be determined by the

following formula:

4 / 0ENG MNGfd cπ φ φ− + + = , (3)

where c is the speed of light, d denotes the length of the air,

ENGφ and MNGφ is the reflection phase of the ENG and

MNG materials respectively. As the SNG materials are highly dispersive, the reflection phase of them depends on the

(a)

(b)

Figure 4. (a) The reflection phase of the ENG and MNG materials ( ENGφ

and MNGφ ), the phase shift in air ( 4 /Air fd cφ π= − ) and the sum of phase

( 4 /Sum ENG MNGfd cφ π φ φ= − + + ) with frequency; (b) The comparison

between the frequency where 0Sumφ = and the tunneling frequency with

different air length.

frequency f. For the parameters of SNG materials used in our

calculation, the ENGφ and MNGφ with f is shown in Fig. 4(a)

(the thickness of the ENG and MNG materials are both 20

mm). In addition, the phase shift in air, 4 /Air fd cφ π= − ,

and the sum of phase, 4 /Sum ENG MNGfd cφ π φ φ= − + + ,

are also depicted in Fig. 4(a). From Fig. 4(a), it can be seen that at the frequency of 1.389 GHz which is just the tunneling frequency according to the calculated transmittance of the

MNG-Air-ENG structure, the resonant condition 0sumφ =

is satisfied. In Fig. 4(b), we change the length of air to some different values, and a comparison between the frequency

where the resonant condition 0sumφ = is satisfied and the

frequency where the tunneling phenomenon occurs is given. The results illustrate clearly that the MNG-Air-ENG sandwich structure can be regarded as an air cavity resonator with SNG material reflectors.

Ⅳ. CONCLUSION

In conclusion, we investigate the propagation of electromagnetic wave in the MNG-Air-ENG sandwich composite structure. we illustrate that, by properly choosing parameters, the electromagnetic wave can tunnel through the MNG-Air-ENG sandwich structure and the electric and magnetic field is localized at the interface of MNG-Air and ENG-Air respectively. In addition, the investigation results on the transmission mechanism show that the MNG-Air-ENG sandwich structure is an unusual air cavity resonator with SNG material reflectors. Due to these features, the MNG-Air-ENG snadwich structure may be important for potential applications in some fields, such as free-space communication, wireless energy transfer, and so on.

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