=

f

m

1

Physical sciences | Physics

The effect of the dielectric layer thickness

on the negative permeability in metamaterials

Thi Trang Pham1,2, Ba Tuan Tong1,2, Thi Giang Trinh1, Hoang Tung Nguyen1, Minh Tuan Dang3, Dinh Lam Vu1*

1Institute of Materials Science, Vietnam Academy of Science and Technology (VAST)

2Hanoi University of Mining and Geology (HUMG)

3Hanoi - Amsterdam High School for the gifted

Received 20 April 2017; accepted 18 August 2017

Abstract:

the

thickness

of

the

dielectric

layer

In this work, we investigate the influences of the dielectric layer on the

has

been

concluded

to

be

extremely

magnetic resonance of the cut-wire pair structure (CWP). The interaction

significant.

However,

no

systematic

between the cut-wires is modeled through a LC circuit, based on which, the

magnetic resonant frequency is calculated. Furthermore, the dependence of

the resonant bandwidth on the structure parameters is also determined. By

tuning the dielectric layer thickness, we obtained a noticeable broadening of

the negative permeability regime of 17%, which represents the enhancement

of the magnetic resonance. A good agreement between the theory, simulation,

and practical experiment has been demonstrated. We believe that our results

should be consequential with regard to the determination of the mechanism

behind the wave-matter interaction in the GHz frequency regime.

Keywords: dielectric layer thickness, metamaterials, negative permeability

broadening.

study on the influences of the dielectric

layer thickness currently exists.

In this work, we report the effects

of dielectric layer thickness on the

negative permeability bandwidth of

the conventional cut-wire pair (CWP)

structure from 12 to 18 GHz. The

negative permeability region is observed

to be broadened as a result of the

increased dielectric layer thickness. The

phenomenon is interpreted theoretically

by calculations on the LC circuit

Classification number: 2.1

model

and

verified

by

simulations

and

experiments

with

considerable

consistency.

Theoretical model

The

CWP

structure

includes

two

Introduction

In recent years, the revolution in

science and technology with regard

to seeking novel materials has gained

tremendous popularity throughout the

world. Metamaterials (MMs) have been

one of the most prominent candidates

in this regard due to their extraordinary

properties. Numerous potential

applications of MMs have been proposed

and demonstrated, such as biological

sensor [1], superlens [2], hi-low pass

filtering [3], antennas [4], invisible

[7-9]. Whereas, the permeability and

permittivity of MMs are simultaneously

negative in a common frequency

regime [10-13]. This unique property

of MMs is known to be arbitrarily

tuned in terms of the arrangement or

design of their compositions. In fact,

the negative permittivity region can be

obtained on a wide scale through the

periodic continuous-wire structure [14],

but the negative permeability region is

restricted due to the resonant conditions.

Therefore, the realistic applications of

metal patterns on two sides of the

dielectric layer (Fig. 1A). Due to Zhou, et

al.’s great work [18], the CWP structure

can be modeled by an equivalent LC

circuit (Fig. 1B) by considering the CWs

as the inductors and the spaces between

the ends of the CW as the capacitors.

Furthermore, the resonant frequency

can be theoretically predicted as shown

below:

c (1)

l 2 c

cloaking

[5],

and

wireless

power

MMs are limited by the narrow negative

Since Eq. 1, the resonant frequency

transfer [6]. Most of these applications

permeability bandwidth. From the large

depends

on

the

CW

length

and

the

are based on the unique optical property

amount of efforts made to expand the

dielectric constant of the middle layer.

of negative refractive index in MMs

negative permeability of MMs [15-17],

However,

some

experimental

results

*Corresponding author: Email:lamvd@ims.vast.vn

December 2017 Vol.59 Number 4

Vietnam Journal of Science,

Technology and Engineering

3

� ��

=

0 1

C

�

d

0 d

s

d

1 1

�

� �

=

�

�

� =

Physical sciences | Physics

Simulation and experiment

The

proposed

CWP

structure

is

composed

of

a

dielectric

layer

FR4

with the dielectric constant as 4.3 and

copper patterns with ts = 0.036 mm, l

= 5.5 mm, w = 1 mm. The structure is

periodic along the x and y axis; the

(A) (B)

Fig. 1. (A) Unit cell and (B) the corresponding LC circuit of the CWP structure.

lattice constant for each direction is ax

= 3.6 mm and ay = 7.2 mm respectively.

The thickness of the dielectric layer is

reveal that dielectric thickness also

influences the resonant frequency [19,

20]. In our study, we propose a new

equation to calculate the inductance

and capacitance in the equivalent

LC circuit, in which the dielectric

thickness is considered according to the

hybridization model:

clw

� = 2(� + ��)� (�� 2��) td (2)

Since t is considered to fall in the

range between 0.2 to 1.0 mm, F is

always greater than 0 and smaller than 1.

Hence, Eq. 4 is positive and identifiable.

The relation between the dielectric layer

thickness and the negative permeability

bandwidth can be realized in Eq. 4 and

Eq. 5 or more clearly in Fig. 2, where

the evolution of Δf/f according to t is

presented.

tuned from 0.2 mm to 1.0 mm by a step

of 0.2 mm. The samples are prepared

on the standard printed circuit boards

(PCB) through the application of the

conventional photolithography method

(Fig. 3). The simulations are operated

on the simulation program CST [21],

and the measurements are performed by

the vector network analyzer system to

obtain the scattering parameters.

where: l is the length, w constitutes the

width, and t forms the thickness of a

CW; t represents the dielectric layer

thickness and c is a constant 0.2 c

0.3.

Hence, the resonant frequency of the

equivalent LC circuit becomes.

� = �

���2�� �1 ����/(1 + ��)

�

(3)

In Eq. 3, the resonant frequency is

shown to depend on the the width of the

CW and the dielectric layer thickness.

It is worth noting that in the case where

(ts ≪ w) and (ts ≪ td), Eq. 3 assumes the

same form as Eq. 1 of J. Zhou, et al. [18].

td (mm)

Fig. 2. The dependence of the negative permeability fractional bandwidth on

the dielectric layer thickness presented by theoretical model.

In

other

words,

the

mutual

coupling

effect between the CWs has not been

included in the calculations of J. Zhou,

et

al.

[18].

Therefore,

the

fractional

bandwidth of the negative permeability

can be expressed as follows:

� 1

� √1 �

1

(4)

where: F is defined as:

� (� + ��)� ��

������ � �� 2��

(5)

Fig. 3. Fabricated sample with the presented structure parameters.

4

Vietnam Journal of Science,

Technology and Engineering

December 2017 Vol.59 Number 4

Δf/f0