Mechanically tunable dual-band metamaterial absorber at ultra-high frequency - Tài liệu text (2023)

Keywords: Mechanically tunable; Dual-band; Metamaterial absorber; Ultra-high frequency.

1. INTRODUCTION
Metamaterials (MMs) are well-known as man-made structures which possess novel properties
not found in natural materials. After being experimentally proven by Smith et al. in 2000 [1],
MMs has attached much of attention and discovered interesting new effects and technologies
such as negative refractive indices [1], perfect lenses [2], backward Cherenkov radiation [3],
inverse Doppler effect [4] etc. In particular, a fascinating ability that MMs can achieve unity
absorption was the first introduced by Landy et al. in 2008 and these MMs were called
metamaterial perfect absorber (MPA) [5]. The great advancement of MPAs that are thin
thickness and high-performance efficiency, so MPA has been become an outstanding candidate
for a wide-range application areas, such as sensors [6, 7], energy harvesting [8, 9], images
[10,11], radar target stealth [12], etc. operating in various frequency ranges from the microwave
[6, 13-15] to optical range [16, 17].
In recent years, telecommunication technology has developed rapidly, the potential
application of MPA has been extended to many devices operating in lower frequency region such
as power imaging purposes [18], chipless radio-frequency identification tags [19], and sub-GHz
wireless systems [20]. However, the designing MPA for reality applications at low frequencies is
challenging. Firstly, MPA is required to have high-efficiency absorption in low frequency bands
with compact structure and light weight. To overcome this challenge, various efficient methods
have been developed. One of popular approaches is that integrating the lumped elements into the
designed structure. For example, Khuyen et al. exploited the lumped capacitors with through
interconnects, the unit-cell size of their MPA was miniaturized to be λ/816 at 102 MHz [21]. In
2018, Li et al. obtained a thin and ultra-broadband MPA with absorption over 80% for the range

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of 20.98 GHz (from 4.48 to 25.46 GHz) by using multi-layered resonators lumped with 4
resistors [22]. Beside using lumped elements, optimizing the structure was also utilized to
achieve miniaturization for MPA in low frequency band. Remarkably, Yoo et al. designed a
snake-shaped MPA to scale down the size of unit cell to be λ/30 and λ/40 for the resonant
frequency of 400 MHz [23]. In the ultra-high frequency (UHF) band, Fan et. al. obtained an
MPA with small-size unit cell by combining fractal and coupling lines [24]. Their absorber
induced an absorption peak at 442 MHz while the ratio between size of unit cell and absorption
wavelength is only 1/68. So far, the inflexibility can be regarded as the second challenge for
practical applications of recent MPAs in UHF band (300 MHz - 3 GHz). In general, MPA is
constructed with a three layered structure, in which the dielectric layer is hard, so it is limited in
practical applications, especially in the case of wrapping the rough surfaces. This problem can be
solved by replacing rigid dielectric layer by flexible substrates such as paper, polyimide, ultralam
substrates. Recently, there are several works in which flexible substrates have been exploited for
MPA [23-25], however the influence of curvature states on the absorption properties of MPA
structure have been not yet surveyed sufficiently.
In this work, we introduce a dual-band MPA using a good flexibility substrate (polyimide).
By a proper design, a dual-band absorption at UHF band was induced by the fundamental and
third-order magnetic resonance. For these both peaks, the dependence of absorption spectra on
the incident angle and polarization angle of electromagnetic (EM) waves wave was investigated
in detail. Moreover, the simulated results for curvature configuration reveal that, there are new
peaks appear at the higher frequency range.
2. STRUCTURE DESIGN AND METHODS
The unit cell of the proposed MPA is depicted in Fig. 1. Its structure includes three layers: a
periodic folded-line structure on the top, a dielectric spacer at the middle and a continuous metal
plate at the bottom. The top and bottom layers are made of copper with a thickness of tm = 0.035
mm and the electric conductivity of 5.96 x 107 S/m. To achieve the flexible property, a polyimide
substrate with a dielectric constant of 3.5 and a loss tangent of 0.0027 is chosen as the dielectric
layer. Such a three-layer material configuration has been successfully fabricated in which the

metal layers adhere very well to the polyimide dielectric layer, and they are stable in curvature
state with different bending radii [26]. The key geometrical parameters of designed structure are
the size of unit cell, the thickness of dielectric layer, the width and length of folding lines and the
gap between them. In order to obtained the best absorption performance, the values of these
parameters are optimized and illustrated in table 1.
Table 1. Optimized geometrical parameters of MPA.
Geometrical parameters a
p
t w1 w2 w3 l1
l2
l3
l4
55 54.5 4 2.8 0.6 0.5 7.2 6.5 13.5 20
Value (mm)

Figure 1. Schematic of the unit cell: (a) Top view; (b) Side view; (c) Bending model with radius R.
Our simulation is carried out by using the commercial Computer Simulation Technology (CST)
Microwave Studio [27]. In this simulation, the boundary conditions are set to be the unit cells for x( )
and y-directions and open for the z direction. The absorption is calculated by ( )

94 D. T. Ha, …, V. D. Lam, “Mechanically tunable dual-band metamaterial … ultra-high frequency.”

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( ), where ( ) | | and ( ) | | are the reflection and the transmission coefficient,
respectively. Due to the appearance of continuous metallic plane at the bottom, the transmission is
( ).
vanished, and then the absorption can be simplified as: A( )
3. RESULTS AND DISCUSSION

Firstly, we simulate the absorption of the proposed MPA for normal incidence of EM wave in
the planar configuration. The simulated results are presented in Fig. 2. It is clear that, two nearlyperfect absorption peaks are obtained at 450 MHz and 1.47 GHz with absorptions of 99.4% and
99.8%, respectively. It is noteworthy that the thickness of MPA is miniaturized to be only
, in which is the longest absorption wavelength (in mm). This value is smaller than those of
previous works [24, 28-30]. The mechanism of perfect absorption can be explicated using the
impedance-matching theory, where the effective impedance of the proposed MPA can be
calculated based on the extracted S-parameters as following expression [31]:
( )

√

(

( ))

( )

(

( ))

( )

(1)

Fig. 2(b) shows the real and the imaginary parts of the effective impedance in the MHz range.
Obviously, the real part is about 1.08 and the imaginary part is zero at 450 MHz, which reveals
that the effective impedance is nearly equal to the free space impedance. We also calculate the
effective impedance of MPA in the GHz range as plotted in Fig. 2(d). Similarly, at the absorption
frequency of 1.47 GHz, the values of imaginary and real parts of the effective impedance are

zero and approximate 1.0, respectively. These values confirm that the effective impedance of
MPA is matched well with free space. Consequently, at 450 MHz and 1.47 GHz, there is no
reflection wave and the incoming wave can be captured inside the MPA.

Figure 2. (a) Absorption spectrum and (b) effective impedance of the MPA in MHz range,
(c) Absorption spectrum and (d) effective impedance of the MPA in GHz range.
To investigate the physical mechanism of perfect absorption, the distributions of induced
surface current on the meta-surfaces are simulated at 450 MHz and 1.47 GHz, as shown in Fig. 3.
At 450 MHz, the top- and bottom-induced surface currents are opposite directions, as presented
in Fig. 3(a), which confirm that the absorption mechanism is ruled by the fundamental magnetic
resonance [32]. Meanwhile, at higher absorption peak (1.47 GHz), the induced surface currents
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are divided into three separated regions and these currents in each region are anti-parallel, as
indicated in Fig. 3(b). Therefore, there are three current loops, which are all created between the
top and bottom copper layers. These phenomena confirm that, the second perfect absorption (at
1.47 GHz) is originated from the third-order magnetic resonance [33].

Figure 3. Distributions of induced-surface-currents on the metallic layers of MPA
at (a) 450 MHz and (b) 1.47 GHz.
The influence of incidence angle of EM wave on absorption feature of flat MPA is
investigated and illustrated in Fig. 4. For the case of absorption peak at 450 MHz, since the
incident angle is increased from 0o to 60o, the absorptions maintain above 90% and slightly shifts
to the higher frequency for both TE and TM polarization wave, as shown in Figs. 4(a) and 4(b),
reflectively. As the incident angle is increased up to 75o, the absorption falls to below 65% for

the TE polarization and to 83% for the TM case. At 1.47 GHz, for both TE and TM
polarizations, the absorption is still remained to be over 90%, when the incident angle is
increased from 0o to 60o. However, at larger incident angles, the absorption peak is shifted to
lower frequency range (for the case of TE polarization), whereas it is shifted towards high
frequencies (for the case of TM polarization). Besides, our MPA is designed with high
symmetry, so it is polarization-insensitive, as has been shown in previous works [25, 34].
It can be noted that, one advantage of using flexible substrate over stiff dielectric material is
that we can simply wrap or attach MPA on a rough surface (for example cylindrical surface).
Secondary, for practical uses, the proposed absorber should be mechanically flexible to be able
to bend with bending radii in the range from 100 mm to 500 mm. In this simulation, a full
structure of MPA is constructed and simulated for the TE polarization of the EM wave. The plan
wave propagates along the z-direction while the electric field and magnetic field are set to be
along the y- and x-directions, respectively. Firstly, the influence of curvature on absorption
performance of MPA structure in the MHz frequency range is studied and shown in Fig. 5(a). As
the bending radius of 500 mm, there is a new absorption peak raised at 556 MHz with the
absorption of 73% while the absorption of original absorption peak at 450 MHz falls to below
28%. The absorption of initial peak reduces to only about 10% when the bending radius is
decreased to be 200mm, whereas the absorption at 556 MHz is reached to be nearly 90%.

96 D. T. Ha, …, V. D. Lam, “Mechanically tunable dual-band metamaterial … ultra-high frequency.”

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Figure 4. Dependence of absorption spectra on different oblique incident angles
with (a)-(c) TE polarization and (b)-(d) TM polarization, in MHz and GHz regions.

Figure 5. Dependence of the simulated absorption spectrum on bending radius
for (a) fundamental absorption peak and (b) high-order one.

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For the GHz range, the impact of curvature to the absorption characteristics of MPA structure
is also considered and shown in Fig. 5(b). When the MPA is bent, the initial high-order
absorption peak at 1.47 GHz is divided into two absorption peaks, where a new absorption peak
is formed at higher frequency (1.48 GHz). The bending radius is tuned to be decrease, the
absorption at 1.48 GHz is increased to be nearly 79%, while the absorption of initial high-order
peak is still remained. The appearance of new high-order absorption peaks can be explained by
the asymmetric structure at different bending states.
The distribution of induced surface current for the case of the radius bending R = 200 mm is
presented in Fig. 6. At 450 MHz and 1.47 GHz, strong surface currents are induced at the position
of unit cells around the center of the semi-cylinder. Whereas, at 556 MHz and 1.48 GHz, strong
surface currents are induced at the position of the unit cells on the edges of the semi-cylinder. This
phenomenon indicates that, differently from the dependence of oblique incidence, the bending
state of the MPA structure makes the distribution of electric- and magnetic-fields on the MPA
surface to be inhomogeneous, which induces new resonance absorption peaks [35, 36]. The
observed of new peak in bending configuration is similar to previous works, which have shown
that, additional absorption peaks appeared due to the severe asymmetry of bent structure [26].

Figure 6. Surface-current distribution on the metallic layers of MPA with bending radius
R = 200 mm, for the case of TE polarization at different frequencies.
4. CONCLUSIONS
In this work, a dual-band flexible MPA operating in the UHF band is investigated
numerically. The MPA structure consisted of a periodic array of a folding line to obtain two
resonant peaks at 450 MHz and 1.47 GHz. The ratios of the periodicity of unit cells and thickness

to the fundamental absorption wavelength are 1/12 and 1/114, respectively. The MPA shows
absorptivity above 90% at 450 MHz and 1.47 GHz remained relatively stable under wide range of
incident angles from 0o to 60o for both TE and TM polarizations. The new two absorption peaks are

98 D. T. Ha, …, V. D. Lam, “Mechanically tunable dual-band metamaterial … ultra-high frequency.”

Nghiên cứu khoa học công nghệ

tuned when MPA is bent with different bending radius. The physical mechanism of the MPA
structure is clarified from magnetic-resonance and impedance-matching phenomena. These
achieved results could be useful for future marketable applications of flexible, polarization/obliqueincidence insensitive, low-cost and ultrathin-wearable modern electronic devices.
Acknowledgement: This research was funded by the Vietnam National Foundation for Science and
Technology Development (NAFOSTED) under grant number 103.99–2020.23. Duong Thi Ha was funded
by Vingroup JSC and supported by the Master, PhD Scholarship Programme of Vingroup Innovation
Foundation (VINIF), Institute of Big Data, code VINIF.2021.TS.092.

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TĨM TẮT
Điều khiển vật liệu biến hóa hấp thụ sóng điện từ dải kép
trong vùng tần số UHF bằng tác động cơ học
Chúng tôi nghiên cứu mô phỏng một cấu trúc vật liệu biến hóa hấp thụ sóng tuyệt đối
sóng điện từ (MPA) băng tần kép hoạt động trong vùng tần số thấp, dựa trên đế polyimide
có đặc tính đàn hồi. Khi vật liệu ở dạng phẳng, hai cực đại hấp thụ thu được tại tần số
450 MHz và 1,47 GHz với độ hấp thụ đạt trên 90%. Kích thước của ô cơ sở và độ dày của
MPA tương ứng bằng 1/12 và 1/114 bước sóng tại tần số hấp thụ thấp nhất. Đặc biệt,
MPA được đề xuất không nhạy với góc phân cực và hoạt động ổn định dưới góc tới rộng
của sóng điện từ (duy trì độ hấp thụ cao hơn 90% khi góc tới lên đến 60o). Bên cạnh đó,
khi cấu trúc được uốn cong (bán kính uốn cong khác nhau thay đổi từ 200 đến 500 mm)
bằng tác động cơ học, các đỉnh hấp thụ mới được hình thành do sự bất đối xứng của cấu
trúc. Đối với cả trạng thái phẳng và uốn cong, cơ chế hấp thụ được giải thích thơng qua

hiệu ứng cộng hưởng từ và sự phối hợp trở kháng hoàn hảo.
Từ khoá: Điều khiển cơ học; Hấp thụ dải kép; Vật liệu biến hóa hấp thụ sóng điện từ; Vùng tần số UHF.

100 D. T. Ha, …, V. D. Lam, “Mechanically tunable dual-band metamaterial … ultra-high frequency.”