Multiband metamaterial absorber base on high - order magnetic resonance in a ring structure

 Communications in Physics, Vol.31, No. 2 (2021), pp. 199-2010
 DOI:10.15625/0868-3166/15520
 MULTIBAND METAMATERIAL ABSORBER BASE ON HIGH-ORDER
 MAGNETIC RESONANCE IN A RING STRUCTURE
 NGUYEN THI HIEN1,?, NGUYEN THI ANH HONG1, BUI XUAN KHUYEN2,†,
 BUI SON TUNG2,‡, NGUYEN XUAN CA1, NGUYEN VAN NGOC3,
 NGUYEN BA TUONG3 AND VU DINH LAM3
1Faculty of Physics and Technology, TNU- University of Sciences
 Tan Thinh Ward, Thai Nguyen City, Thai Nguyen Province, Vietnam
2Institute of Materials Science, Vietnam Academy of Science and Technology,
 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam
3Graduate University of Science and Technology, Vietnam Academy of Science and Technology
 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam
 E-mail: ?hiennt@tnus.edu.vn; †khuyenbx@ims.vast.ac.vn; ‡tungbs@ims.vast.ac.vn
 Received 18 September 2020
 Accepted for publication 21 December 2020
 Published 05 January 2020
 Abstract. We proposed a multi-band metamaterial absorber (MA) based on high-order magnetic
 resonance using ring-shaped structures. We obtained three absorption peaks at 4.71 GHz (the
 fundamental resonance), 13.39 GHz (the third-order behavior), and 19.91 GHz (the fifth-order
 behavior) with correspondent absorptions of 90%, 100%, and 99.33%, respectively. Therefore,
 these high-order perfect absorptions are the potential to make the easier fabrication for the next
 generation of MAs, especially in high-frequency regions. Particular, the obtained results are fur-
 ther controlled using the LC circuit model. Besides, by scaling down the unit-cell size, the third-
 and fifth-order absorptions are created in the THz frequency band.
 Keywords: Metamaterials, Perfect absorber, High-order resonance.
 Classification numbers: 81.05.Xj; 78.67.Pt.
 ©2021 Vietnam Academy of Science and Technology
200 MULTIBAND METAMATERIAL ABSORBER BASE ON HIGH-ORDER MAGNETIC RESONANCE ...
I. INTRODUCTION
 During the last decades, metamaterials (MMs) have emerged as one of the most potential
research field in the revolution of science and technology happening all over the world. Due to
their extraordinary properties, MMs can be regarded in the top ten breakthrough topics changing
modern science (ranked by the Materials Today journal [1]). The theoretical design of MMs was
firstly proposed by Veselago in 1968 [2], for the simultaneous combination between the negative
permeability (µ < 0) and the negative permittivity (ε < 0) material. Thenceforth, in 1996 and
1999, J. B Pendry realized these media by using the wire and split-ring resonator (SRR) struc-
ture [3, 4]. Particularly, Smith et al. demonstrated the existence of a measured negative refractive
index (NRI) structure, constructed from wires and SRRs [5]. This success opened a new brand
of artificial advanced materials- the so-call MMs. MMs are defined as artificially structured me-
dia in a size scale smaller than the wavelength of external stimulation. They are composed of
periodically arranged unit cells, which play the role of “meta-atoms” in materials. Therefore,
MMs can possess novel properties that cannot be easily attainable from natural materials. To date,
there are many different research directions as the negative refractive index (NRI) [6–8], perfect
absorption [9–11], invisible cloak [12], electromagnetically induced transparency [13, 14] and so
on. Among them, the perfect absorption feature is used for many potential applications, such as
plasmonic sensors [15, 16], solar-energy capturing [17], and camouflage. The first metamaterial
absorber (MA) has been demonstrated under the concept of MMs and a near-unity absorption
peak can be realized at the resonant frequency [18]. To date, MAs have been demonstrated in
every technologically relevant spectral range, from the microwave [10, 11, 19], the THz [15, 16],
NIR [20] to the optical range [21]. However, most recent studies focus on the fundamental absorp-
tion mechanism of MM [9–11, 22]. Moreover, one of the most interesting properties of MMs is
that we can design and fabricate them working in the desired frequency range, from GHz to THz
or even in the visible region. In recent years, THz-MAs have received the most research attention,
which might be a solution to the shortage of THz sources and devices. However, at high frequen-
cies, the small unit cell might be quite difficult for fabrication technologies. Research shows that
the unit-cell size based on the high-order resonance increases significantly compared to that based
on the first-order resonance. This can be further useful for practical manufacturing.
 From this motivation, in this work, GHz- and THz-MAs are developed to create multi-band
high-order absorption. Our investigations are attempt to clarified that multi-band absorption is
simultaneously achieved by the fundamental-/third-/fifth-magnetic resonance in both the GHz and
THz ranges. In addition, the influence of absorption on geometrical parameters is also estimated
an ... the simulated results of reflection, transmission and absorption in the
frequency range from 2 to 21 GHz. We observed three absorption peaks at 4.71, 13.39, and 19.91
GHz with absorption of 90%, 100%, and 99.33%, respectively.
 Front (a) f1 = 4.71 GHz Back 
 Front (b) f3 = 13.39 GHz Back 
 Front (c) f5 = 19.91 GHz Back 
 Fig. 2. Simulated induced surface current distributions of ring-shaped structure at
 (a) f1 = 4.71 GHz, (b) f3 = 13.39 GHz, and (c) f5 = 19.91 GHz.
 As shown in Fig. 2(a), it is found that the surface-current distributions at f1 = 4.71,
f3 = 13.39 and f5 = 19.91 GHz confirm the anti-parallel currents on two metallic surfaces. This
 NGUYEN THI HIEN et al. 203
means that strong magnetic resonances are created at 4.71 GHz (fundamental mode) [25, 26].
However, from the current distribution at 13.39 GHz and 19.91 GHz, (in Figs. 2 (b) and 2(c)),
the surface currents are mainly located in the centers of three- and five-circular currents, but in
different directions since the central circular current is opposite to the others, respectively. As
a results, f3 and f5 are introduced to denote the third- and fifth-order magnetic resonances, re-
spectively [25–27]. Thus, by using only the ring-structure, we created triple-band absorption with
absorptions above 90% for f1 and f5, and absorption of 100% for f3.
 Building a formula of the absorption frequencies is extremely important to know how to
manipulate absorption frequency effectively. In addition, the formula also benefits to the explana-
tion of the deviation between simulated and measured spectra. In general, the dependence of the
first- and higher-order absorption frequencies on the structural parameters is further verified by
using the equivalent circuit model LC. According to Refs. [28, 29], the equivalent circuit diagram
LC of ring structure at first-order magnetic resonance frequency as shown in Fig. 1 (b), in which
the resistors are omitted for simplicity. In particular, the metal component on two metallic layers
can be regarded as effective inductance (L) in parallel, while the dielectric spacer acts like effective
capacitance Cm.
First- order magnetic resonance frequency
 In order to define the fundamental magnetic resonance depended on geometrical parame-
ters, we calculated effective inductance and capacitance of the ring-shaped structure. Their distri-
bution of the magnetic field density (B) at first-order magnetic resonance is shown in Fig. 3(a):
 µI
 B = , (1)
 w
where µ, I and w are the free space permeability, the current on the ring pair and the width of the
ring, respectively.
 The magnetic flux was calculated by:
 Z
 φ = BdS, (2)
 Z (ts+2tm)/2 Z R1 µI
 φ = dz ∗ 2 ∗ dy, (3)
 p 2 2
 −(ts+2tm)/2 R2 2 R1 − y
where Nφ = LI and N = 1 is denoted for the number of turns and the inductance of the ring-pair
system, respectively. The inductance L can be approximated as:
 Z (ts+2tm)/2 Z (R1−R2) µ
 L = dz dy, (4)
 p 2 2
 −(ts+2tm)/2 −(R1−R2) 2 R1 − y
   
 π R2
 L = µ (ts + 2tm) − arcsin , (5)
 2 R1
 h  i
 π R2
 L µ (ts + 2tm) 2 − arcsin R
 L = = 1 . (6)
 m 2 2
 On the other hand, when the electromagnetic (EM) wave impinges on the material, the
Lorentz force, which is caused by the magnetic field, pushes the charge on both ends of the ring.
204 MULTIBAND METAMATERIAL ABSORBER BASE ON HIGH-ORDER MAGNETIC RESONANCE ...
 Fig. 3. (a) Distribution of the magnetic field density of the ring-shaped structure at the
 first-order magnetic resonance, (b) View of ring-structure on (left) (k, H) plane and and
 (c) (right) (E, H) plane.
Then, the charge of the ring focuses only on the two ends of the ring, forming two flat capacitors.
The capacitance value of the capacitors may be determined by the equation:
  2 2

 πc1 R1 − R2
 Cm = ε , (7)
 ts
where C1 is a geometrical factor 0.2 ≤ c1 ≤ 0.3 [30] and ε is the permittivity of FR-4. Conse-
quently, we can obtain the magnetic resonance frequency as
 √
 1 2t
 ω = √ = s . (8)
 L C r   
 m m  2 2
 π R2
 πc εµ (ts + 2tm) R − R − arcsin
 1 1 2 2 R1
 √
 1 2ts
 fm1 = √ = . (9)
 2 L C r   
 π m m  2 2
 π R2
 2π πc εµ (ts + 2tm) R − R − arcsin
 1 1 2 2 R1
 NGUYEN THI HIEN et al. 205
 If R2<<R1, the ring shape will transform into a disk shape and the magnetic resonance
frequency is approximately as:
 √
 1 2 ts
 ω = √ = p . (10)
 LmCm πR1 c1εµ (ts + 2tm)
 √
 1 ts
 fm1 = √ = . (11)
 2 p
 2π LmCm π R1 c1εµ (ts + 2tm)
Third-order magnetic resonance frequency
 In Fig. 2(b), the current distribution at the third-order resonant frequency ( f3 = 13.39 GHz),
there are three pairs of anti-parallel surface current and alternate directions. Therefore, the nature
of the resonance at this frequency is magnetic resonance [25, 26]. The electric field distribution
shows that the electric field focuses on four positions of the structure, as plotted in Fig. 4(a).
 Fig. 4. (a) Distributions of induced charges and surface current at 13.39 GHz (b) Ef-
 fective radius at third-order resonance frequency, which has properties as the first-order
 resonance frequency.
 From Fig. 4(b), a specific area corresponding to the effective radius Rhd is considered. In
this effective area, it can be noted that the induced surface current distributions are similar in
comparison with the case of first-order magnetic resonance. Thus, to calculate the third-order
resonance, instead of studying all of the structure, the radius R1 is equivalently transformed to the
effective radius.
 R1
 The effective radius value will be taken approximately by Rhd ≈ 2 . By using Rhd instead
of R1, the third-order magnetic resonance frequency can be estimated as:
 √
 1 2ts
 fm3 = √ = . (12)
 2 L C r   
 π m m  2 2
 π R2
 2π πc εµ (ts + 2tm) Rhd − R − arcsin
 2 2 2 Rhd
206 MULTIBAND METAMATERIAL ABSORBER BASE ON HIGH-ORDER MAGNETIC RESONANCE ...
In Eq. (9), the total charge of the ring focuses only on two regions. However, in Eq. (12), which
determines the third-order resonant frequency, the charges are concentrated in four areas (as shown
in Fig. 4). Substituting the structural parameters (R1 = 8.2 mm, R2 = 2 mm, td = 0.8 mm,
ts = 0.036 mm, ε = 4.3, C1 = 0.2) into Eq. (9), fm1 was obtained to be 4.36 GHz and into Eq.
(12), fm3 was obtained to be 14.5 GHz. The deviation between simulated and calculated results
for f3 can be explained because Rhd and C2 have been approximately applied.
 Fig. 5. Influence of (a) lattice constant a, (b) dielectric thickness td, (c) radius R1, (d)
 radius R2 on absorption spectrum.
 Understanding the dependence of resonance on structural parameters are very necessary to
optimize the structure. Figure 5 shows the dependence of simulated absorption on the structural
parameters. It can be noticed that the absorption frequencies at first- and third-order resonances are
strongly influenced by the parameters R1 and R2, but not by the lattice constant a or the dielectric
thickness ts. The dependence of the resonant frequency on the structural parameters is perfectly
matched by Eqs. (9) and (12). Fig. 5 presents the dependence of the triple-band absorption ( f1, f3
and f5) on structural parameters, which are optimized to be a = 18 mm, ts = 0.8 mm, R1= 8.2 mm,
and R2 = 2.0 mm.
 Recently, most MAs have been proposed based on conventional structures such as SRRs
and cut-wires. Therefore, their absorption feature is strongly depended on the polarization of EM
 NGUYEN THI HIEN et al. 207
wave, which limits practical applications in some areas. This drawback can be overcome by taking
advantage of the proposed ring-shaped structure. The independent absorption on the polarization
of the EM wave is confirmed in Fig. 6 (a). The simulation shows that the absorption magnitudes
 o
at f1, f3 and f5 are unchanged as the polarization angle is increased from 0 to 90 . Besides,
the impacts of incident angles on the absorption is also shown in Fig. 6(b). From Fig. 6(b), the
absorption responses a low sensitivity to the incident angles between 0◦ and 20◦. The absorption
 o o
magnitudes at f1 and f3 are unchanged as the incident angles is increased from 0 to 60 . However,
 o
the absorption magnitudes at f5 changed as the incident angles is increased from 40 and appears
some new absorption peaks. The appearance of the new peaks can be explained that increasing
the incident angles will change the effective impedance of the front and back sides (creating an
asymmetric structure) [31, 32].
 Fig. 6. Absorption spectra according to (a) polarization angles and (b) incident angles.
III.2. Absorption behavior at THz frequencies
 The exploitation of the ring-structure to multiband absorber is investigated in the THz
regime, as shown in Fig. 7. By reducing the structural parameter values by scale factors of 0.001,
the resonance frequency of MMs can be increased from GHz to THz bands. It is noted that we
fix the dielectric loss tangent to 0.025 in order to keep the nature of MA unchanged. Figure 7
 0 0 0
shows that three absorption peaks are activated at f1 = 4.71, f3 = 13.39 and f5 = 19.91 THz with
absorption of 98%, 90%, and 80%, respectively. This presence of multiple absorption peaks opens
the possibility for electronic devices using multiband metamaterial absorbers not only in the GHz
 0 0
but also in the THz range. The surface-current distributions of the ring-shaped structure at f1, f3
 0
and f5 in Fig. 8 completely similar in Fig. 2. This demonstrates that these resonances are also
due to the first-, third-, and fifth-order magnetic resonances (see the anti-parallel surface currents
 0 0
at all absorption peaks). However, it can be realized that the magnitudes of absorption at f3 and f5
are significantly reduced. This phenomenon can be explained through the contributed role of the
Ohmic loss in the higher frequency regime, leading to a remarkable decrease in the magnitude of
absorption in the higher frequency regime.
208 MULTIBAND METAMATERIAL ABSORBER BASE ON HIGH-ORDER MAGNETIC RESONANCE ...
 Fig. 7. Simulated absorption spectrum of the single ring-shaped structure at THz
 frequency absorption spectrum.
 Front f1 = 4.71 THz Back 
 Front (b) f3 = 13.39 GHz Back 
 Front (c) f5 = 19.91 GHz Back 
 Fig. 8. Numerical surface current distributions of ring-shaped structure at (a) f1=
 4.71THz, (b) f3 = 13.39 THz, (b) f5 = 19.91 THz.
 NGUYEN THI HIEN et al. 209
IV. CONCLUSION
 We numerically investigated the absorption feature of a simple MA in the state of high-order
magnetic resonances. By using the ring-shaped structure triple-band absorption is obtained at
4.71, 13.39, and 19.91 GHz, corresponding to the fundamental mode, the third- and the fifth-order
resonant frequencies, with absorption of 90%, 100%, and 99.33%, respectively. In addition, the
obtained results can be predicted theoretically by exploiting the LC-circuit model. Furthermore, by
scaling down the unit-cell size, these high-order perfect absorption behaviors are also effectively
well maintained in the THz band. This strong advantage confirms that we can challenge for high-
frequency applications using a larger-size sample, which is fabricated in easier and cheaper way
in reality.
ACKNOWLEDGMENT
 This research was funded by Vietnam National Foundation for Science and Technology
Development (NAFOSTED) under Grant No. “103.99-2018.35” and by Vietnam Academy of
Science and Technology, under Grant No. NCVCC42.03/20-20.
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