Linear geometry-frequency scalability in metamaterial absorbers

Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số 49, 06 - 2017 161
LINEAR GEOMETRY – FREQUENCY SCALABILITY IN 
METAMATERIAL ABSORBERS 
Pham Duy Tien1,2, Ly Nguyen Le3, Pham Tai Nhan1, 
Nguyen Thanh Tung1**, Nguyen Manh Thang3* 
Abstract: Linearly scaling the absorption frequency by changing its physical 
parameters is an important advance of an absorptive material for many 
applications. In this report, we numerically and experimentally investigate a simple 
but perfect absorber using metamaterials that allows a linear geometry-frequency 
scalability in a wide range of the frequency regime. Samples are fabricated by the 
standard photolithography and characterized by free-space vector network analyzer 
in the frequency band of 8-12 GHz for demonstration. Finite integration simulations 
are performed to support the experiments. 
Keywords: Metamaterial absorbers; Absorptive materials; Microwave frequency. 
1. INTRODUCTION 
Absorption is one of the most important optical properties of materials since it can find 
applicability in many aspects of life, for example, electromagnetic filter, optical and 
thermal detector, light shield, or energy storage [1]. Nevertheless, controlling the 
absorption frequency is not always simple since it rigorously depends on intrinsic 
properties of materials and formation conditions as well. In 2000, a new class of artificial 
materials, the so-called metamaterials, was introduced to tailor electromagnetic properties 
for novel applications without changing material constitutes [2]. For example, light not 
only transmits and reflects but also can negatively refract in metamaterials [3]. Specific 
metamaterials can be designed as invisible cloaks, where light can be bent around an 
object as nothing was there [4]. In 2008, a new concept of ultrathin highly-absorptive 
media using metal resonator-dielectric-metal mirror metamaterials was reported [5]. This 
work has been followed by many other scientists, and the research of metamaterial 
absorbers has been extensively developed [6-9]. 
Recently, we have investigated a metamaterial absorber composed of periodically 
arranged sub-wavelength unit cells. Each of unit cells contains a dielectric spacer 
sandwiched by a resonator and a metallic mirror [10]. The fabricated metamaterial 
absorber can exhibit a high absorption peak in microwave frequencies that would benefit 
for radar stealth applications [11]. The absorption mechanism can be explained using the 
equivalent circuit model, where the absorption is attributed to the magnetic resonant loss. 
In this report, we show that the proposed metamaterial absorber can provide not only a 
high absorptivity but also a selected absorption frequency using the geometry scalability. 
Both numerical simulations and experiments are carried out to elaborate our idea. 
2. SIMULATION AND EXPERIMENTAL SETUP 
In order to confirm the validity of our equivalent circuit model presented in the 
previous study [9,10], we design two geometrically-different metamaterial absorber 
samples that have an identical resonant frequency. The first one marked as S1 consists of a 
dielectric spacer in between a split-ring resonator and a metallic mirror while the second 
one labeled as S2 is the same as S1 except that a simple cut-wire resonator is used for the 
split-ring one. A series of simulations and experiments will be carried for both samples S1 
and S2 to show that their absorption frequency can be tuned simply by scaling their 
geometrical parameters. 
Vật lý 
P.D. Tien, L.N. Le, , “Linear geometry-frequency scalability metamaterial absorbers.” 162 
Figure 1. Computational unit cell of metamaterial absorbers and corresponding photos of 
their actual samples for (a) S1 and (b) S2. The metallic patterns and mirror are indicated 
by yellow while the dielectric material is blue. The geometrical parameters of fabricated 
samples are as follow: for S1, w= 1 mm, c = 3 mm, g = 2mm, b = 8 mm, and a = 12mm; 
for S2, w = 1 mm, l = 8.5 mm, and a = 12 mm. 
Figure 1 illustrates the schematic drawing of S1 and S2 with polarization and geometric 
parameters. The incident wave is normal to the structure plane while the electric and the 
magnetic directions are defined to be parallel to y-axis and x-axis respectively. In both 
experiments and simulations, the metal is chosen as copper while FR-4 is selected for 
dielectric material. The thicknesses of copper and dielectric components are tc=0.036 mm 
and td=0.4 mm, respectively. The electromagnetic simulations are performed by CST 
software using the finite-integration-simulation technique [12]. The unit cell is placed 
between two waveguide ports, which act like transmitter and also receiver antennas. 
For experiments, the metamaterial samples are fabricated using commercial FR4 
printed circuit board (PCB) following unit-cell parameters aforementioned. Undergoing 
photo-lithography and chemical etching steps, the metamaterial perfect absorber is formed. 
During measurements, the samples are distanced between two horn antennas in a 
reflection mode and held by a homemade plastic sample holder. The reflection signal is 
recorded by a Vector Network Analyzer MS2028B. Since the transmission is prohibited 
by the metallic mirror, the absorption intensity is obtained via the corresponding 
reflection. 
3. RESULTS AND DISCUSSIONS 
It has been agreed that the origin of metamaterial absorption associated with a magnetic 
resonance and its corresponding antiparallel current distribution [9]. The magnetic 
resonant frequency can be described by a LC equivalent circuit model f=1/[2 .sqrt(LC)], 
where C is the induced capacitance between two metallic layers, and L is the induced 
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số 49, 06 - 2017 163
inductance of metallic resonators. In general, for each shape of the front resonator, i.e. 
split-ring [5], disk [13], ring, or cut-wire [14], the approximate values of C and L can be 
calculated from their geometrical parameters. 
Figure 2. Absorption spectra of (a) sample S1 and (b) S2. 
Figures 2(a) and 2(b) present the simulated absorption spectra of samples S1 and S2. 
With the given set of parameters, the working frequency of metamaterial absorbers is 
about 8-12 GHz. In particular, an absorption peak of more than 97% appears at 10.5 GHz 
in both spectra. Their high absorption is in line with previous results [10,11], validating 
the magnetic origin of their absorptivity. Despite their geometrical difference, the 
absorption behavior is very similar to each other as expected, confirming the effectiveness 
of the equivalent circuit model. Nevertheless, not only the absorption intensity but also the 
information about their frequency scalability is important for practical applications. The 
geometry-frequency scalability refers to the behavior of metamaterial absorption 
frequency once we shrink down/up all geometrical parameters of the original design. For 
this purpose, the absorption behavior of selected counterparts of the proposed S1 and S2 
absorbers, which operate at different frequency regime, are numerically examined 
according to different scaling factors relative to the sizes defined in Figs. 2(a) and 2(b). 
The results are presented in Fig. 3, where all the geometrical parameters are scaled down 
simultaneously by a factor s of 1, 0.1, 0.01, and 0.001. For the sake of simplicity, the 
dielectric constant of the substrate is assumed as 4+i0.008 during the simulation. It is 
obvious that for both S1 and S2 the ratio between the original absorption frequency (f0 = 
10.5 GHz at s = 1) and scaled absorption frequency f decreases linearly with the decrease 
of scaling factor from 1 to 0.001. It means that geometrically scaling down a metamaterial 
absorber will scale up its operating frequency proportionally GHz to THz. Meanwhile, the 
high absorption intensity of metamaterial absorbers remains unchanged up to few tens 
THz (not shown here). It is even more optimistic for higher-frequency absorbers since the 
optical loss is more significant with used dielectric materials. 
Two series of differently-scaled samples correponding to S1 and S2 are fabricated to 
elaborate the linear geometry-frequency of metamaterial absorbers. For demonstration, the 
absorber samples S1 and S2 operating at 10.5 GHz are chosen as the original one with s 
=1. Due to the limitation of measured frequency range, other samples correspond to 
s=1.1 (f = 9.5 GHz) and s=0.9 (f = 11.5 GHz) are prepared and characterized as shown in 
Fig. 4. It can be seen that for both series of the samples the absorption frequency shifts 
linearly with the scaling factor s, in a good agreement with the prediction in Fig. 3. In 
particular, the absorption frequencies (and the bandwidth) of S1 are f=9.6 (±0.4), 10.4 
Vật lý 
P.D. Tien, L.N. Le, , “Linear geometry-frequency scalability metamaterial absorbers.” 164 
(±0.5), and 11.4 (±0.3) GHz for s = 1.1, 1.0, and 0.9, respectively. For the sample S2, the 
absorption frequencies (and the bandwidth) are f=9.5 (±0.4), 10.5 (±0.4), and 11.4 (±0.4) 
GHz for s = 1.1, 1.0, and 0.9, correspondingly. 
Figure 3. Linear geometry-frequency scalability of sample S1 and S2. 
Figure 4. Experimental and simulated absorption spectra of sample S1 and S2 
according to s= 0.9, 1.0, and 1.1. 
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số 49, 06 - 2017 165
The experimental geometry-frequency scalability of sample S1 and S2 for s = 0.9, 1.0, 
and 1.1 is plotted in Fig. 5 for comparison. The error bars indicate the corresponding 
fractional bandwidth of each sample. Within the examined frequency range (8-12 GHz), 
both S1 and S2 exhibit their linearity in geometry-frequency dependence. A small 
discrepancy at s = 0.9 and 1.1 could be caused by the fabrication imperfectness. 
0.9 1.0 1.1
0.9
1.0
1.1
 S1
 S2
f 0
/f
s
Figure 5. Geometry - frequency dependence of sample S1 and S2. 
4. CONCLUSIONS 
In this report, we presented a study on the geometry-frequency scalability of 
metamaterial absorbers. The results show that i) the absorption frequency can be precisely 
designed using the equivalent circuit structure, ii) the absorption frequency can be linearly 
scaled by geometrically shrinking up/down the metamaterial structure, and iii) the linearity 
of geometry-frequency scalability in metamaterial structure is experimentally examined in 
the range of 8-12 GHz. It is believed that the linear geometry-frequency scalability of 
proposed metamaterial absorbers would be useful for advanced electromagnetic probing 
applications. 
Acknowledgements: This work was supported by Academy of Military Science and Technology 
and by Institute of Materials Science, Vietnam Academy of Science and Technology under grant 
number HTTĐ 03.16. 
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TÓM TẮT 
TƯƠNG THÍCH HÌNH HỌC - TẦN SỐ TUYẾN TÍNH 
CỦA VẬT LIỆU HẤP THỤ MEATMATERIALS 
Tương thích tuyến tính của tần số với sự thay đổi của các thông số vật lý là một 
ưu điểm quan trọng của vật liệu hấp thụ trong nhiều ứng dụng. Trong báo cáo này, 
chúng tôi nghiên cứu khả năng hấp thụ đơn giản nhưng hiệu suất cao của siêu vật 
liệu metamaterials, cho phép biến đổi tương cấu trúc - tần số một cách tuyến tính 
trong dải tần số rộng. Mẫu vật liệu hấp thụ được chế tạo bằng phương pháp quang 
khắc truyền thống, sau đó, đặc trưng hấp thụ được kiểm tra bằng phương pháp 
phân tích mạng vector trong giải tần 8-12 GHz. Kỹ thuật mô phỏng tích phân hữu 
hạn cũng được áp dụng để khẳng định các giá trị đo thực nghiệm. 
Từ khóa: Siêu vật liệu hấp thụ; Vật liệu hấp thụ; Tần số mỉcrowave. 
Nhận bài ngày 16 tháng 08 năm 2016 
Hoàn thiện ngày 06 tháng 11 năm 2016 
Chấp nhận đăng ngày 20 tháng 6 năm 2017 
Địa chỉ: 1Institute of Materials Science, Vietnam Academy of Science and Technology, Vietnam; 
 2Hanoi University of Science and Technology, Vietnam; 
 3Academy of Military Science and Technology, Vietnam. 
 *Email: thangnm@jmst.info; 
 **Email: tungnt@ims.vast.ac.vn