- Email: [email protected]
Dual-band tunable terahertz perfect metamaterial absorber based on strontium titanate (STO) resonator structure
Journal Pre-proof Dual-band tunable terahertz perfect metamaterial absorber based on strontium titanate (STO) resonator structure Wangyang Li, Yongzhi Cheng
PII: DOI: Reference:
S0030-4018(20)30019-5 https://doi.org/10.1016/j.optcom.2020.125265 OPTICS 125265
To appear in:
Optics Communications
Received date : 30 October 2019 Revised date : 3 January 2020 Accepted date : 6 January 2020 Please cite this article as: W. Li and Y. Cheng, Dual-band tunable terahertz perfect metamaterial absorber based on strontium titanate (STO) resonator structure, Optics Communications (2020), doi: https://doi.org/10.1016/j.optcom.2020.125265. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
Journal Pre-proof
Dual-band tunable terahertz perfect metamaterial absorber based on strontium titanate (STO) resonator structure
pro
of
Wangyang Li, Yongzhi Cheng† School of Information Science and Engineering, Wuhan University of Science and Technology, 430081, China † Corresponding author: [email protected],[email protected] Abstract: A temperature-controlled dual-band terahertz perfect metamaterial absorber
(MMA) based on strontium titanate (STO) resonator structure is proposed and investigated numerically. This MMA is a simple periodic array, consisting of two stacked square-shaped STO resonator structures and a copper substrate. Numerical
re-
simulation results indicate that the reflectance of the proposed MMA under room temperature T = 300 K is decreased to 2.1% and 0.2% at 0.114 THz and 0.181 THz, and corresponding absorbance is up to 97.9% and 99.8 %, respectively. Further results
urn al P
show that the designed MMA is polarization-insensitive, and wide-angle to the incident waves for both transverse electric (TE) and transverse magnetic (TM) modes. The simulated distributions of electromagnetic (EM) fields and power flow reveal that the observed high-level absorption is originated from the excitations of the fundamental dipole modes. Furthermore, the absorption property can be changed by varying structural parameters of the MMA and external temperature. Due to its excellent performance, the designed tunable MMA may find useful and important applications such as thermal emitter, bolometric imaging, energy harvesting, and sensing in terahertz region.
Key words: terahertz metamaterial absorber, STO material, temperature sensing
Jo
1 Introduction
In recent years, metamaterial absorbers (MMAs) have gradually become a
research hotspot and get rapidly develop in microwave [1-3], terahertz [4-7] and even optical frequency due to their wide and potential applications [8-10]. Among them, terahertz (THz) MMAs have been paid great attention since they have potential
Journal Pre-proof
applications in many scopes, such as sensing, detection, imaging, bolometer and so on [8,11-14]. Generally, the metasurface are composed of periodic patterned metallic structure array and ground-plane layers separated by dielectric material. Metasurface can produce near unity absorption by suppressing the transmission via using a
of
ground-plane and simultaneously minimizing the reflection extremely via matching the impedance to free-space [15,16]. Up to now, various MMAs, such as narrow-band [17,18], dual-band [19.20], multi-band [21-22], and broad-band [23-30] have been
pro
widely demonstrated and investigated by exploiting approaches technologies and different models. However, most of the reported MMAs can only operate in a fixed frequency range, and the absorption property cannot be modulated as desired, which greatly limits their practical applications. Hence, high performance tunable MMAs are
re-
still needed to explore, which have received extensive attention due to their great flexibility in practical applications. At present, tunable MMAs have been proposed by introducing active materials into either the structure or the surrounding medium by
urn al P
using an external stimulus, such as machine [31], additional offset voltage [32-35], optical illumination [35,36], and thermal modulation [37]. Meanwhile, these tunable MMAs require the relative harsh working conditions, thus seriously hamper the practical application. One of the widely used media is strontium titanate (STO) material since it has the capability to integrate passive components in a module, and to achieve miniaturization easily by the enhanced low-temperature co-fired ceramic (LTCC) technology [38,39].
The STO as a typical functional ceramic dielectric material has some unique properties including high dielectric constant, low dielectric loss, superior insulation, and good chemical stability [39,40]. The most attractive property is that the high
Jo
dielectric constant of the STO can be adjusted dynamically by varying external environment temperature [41,42], which can also be applied to the tunable devices in THz region. Thus, the STO can be regarded as a promising candidate material for designing the tunable MMA due to its excellent performance [41-46]. For example, Wang et al, achieved narrow band tunable absorption by designing the STO as one of the layers in the MMA [41]. Then, Luo et al, proposed a MMA comprising a periodic
Journal Pre-proof
array of multiple metallic structure resonator fabricated on STO dielectric substrate, which can achieve tunable multiband stronger absorption in THz region [42]. However, these tunable MMAs based on STO material usually require unit-cells with complex sandwiched structure, resulting in increased difficulty and cost of fabrication.
of
Thus, the larger area applications of STO based MMAs are also limited due to the fabrication complexity of the geometries structure and high cost. Recently, MMAs based on all-dielectric resonators have been developed, which could achieve near
pro
perfect absorption through special structural designs in THz region [47-50]. The all-dielectric MMAs have the advantages that they avoid Joule heating and good temperature stability for applications [48]. Thus, it inspires us to construct a
simple geometry structure. In
this
work,
we
re-
high-performance tunable MMA using all-dielectric STO materials with a relatively
proposed
and
demonstrated
numerically
a
temperature-tunable dual-band MMA in THz region, which consists of two stacked
urn al P
square-shaped STO resonator structures and a copper ground-plane. Firstly, we theoretically investigated the dependent relationship between the dielectric constant of STO material and external environment temperature. Then, we studied the absorption properties of the proposed MMA. The results show that the proposed MMA under room temperature T = 300 K can achieve absorption peaks of 97.9% and 99.8 % at 0.114 THz and 0.181 THz, respectively. It also exhibits that the high absorption performance of the MMA can be kept stable under different polarization and incident angles for both transverse-electric (TE) and transverse-magnetic (TM) modes. An underlying physical origin is revealed by analyzing the distributions of electric and magnetic fields, and power flow power at resonances. Furthermore, the dual-band
Jo
absorption properties of the MMA are also studied systematically by varying the geometric parameters of STO-cube resonator structures and external environment temperature. The simple of the high-performance tunable MMA allows for its integration easily into on-chip systems.
2. Theory, structure design and simulation
Journal Pre-proof
In this section, we firstly study the dielectric property of the STO material dependent on the external environment temperature in the frequency range of 0.01 THz- 0.3 THz. The complex relative permittivity of STO material is related with the temperature and frequency. According to the damped harmonic oscillator model of the
r (,T )
2 i 2 0
of
bulk STO material [40-45,53,54], the complex relative permittivity can be given as:
(1)
pro
where ε∞= 9.6 is the high-frequency bulk permittivity, = 2.3×1010 m-2 is a temperature independent oscillator strength, and ω is the angular frequency of incident THz wave. In addition, ω0, γ are the soft mode frequency and soft mode damping factor, which can be respectively written as: 0 (T ) 100 a(T Tc )
re-
(2)
(T ) 100(bT c )
(3)
where a = 3.12×105 m-2K-1, Tc = 42.5 K, b = 940 m-1K-1, c= -330 m-1, c is the light
urn al P
speed of free space and T is the temperature in Kelvin. 800 700
Re()
600 500
200
T=200K T=250K T=300K T=350K T=400K T=450K T=500K
150
Im()
900
100
400
50
300 200 100
T=200K T=250K T=300K T=350K T=400K T=450K T=500K
(a)
0.05
0.10
0.15
0.20
Frequency/THz
0.25
0
(b) 0.05
0.10
0.15
0.20
0.25
Frequency/THz
Fig.1. (a,b) The temperature dependence of the relative permittivity (Re(ε), Im(ε)) of STO material in terahertz frequency region.
Obviously, the real and imaginary parts of the relative permittivity (Re(ε), Im(ε))
Jo
of STO material are changed with the different environment temperature. We can see clearly that the magnitude of the Re(ε) of the STO material gradually decreases with the increase of environment temperature T, as shown in Fig. 1(a). However, the Re(ε) of the STO material is changed slightly with the changes of the THz frequency. As shown in Fig. 1(b), in the lower frequency range (0-0.12THz), the magnitude of Im(ε) have almost no changes with the increase of temperature. In the frequency range of
Journal Pre-proof
0.12THz-0.3THz), the magnitude of Im(ε) will increase quickly with the frequency, while the one will decrease quickly with the temperature. These results indicate that the complex relative permittivity of STO material is sensitive extremely to the change of environment temperature at a given frequency range (0.01 - 0.3 THz), suggesting
of
potential applications in the temperature-tunable THz integrated devices. Meanwhile, the dispersion of STO material is slightly sensitive to a given environment temperature range (200 - 500 K). It is worth noting that the STO material can be a
pro
good candidate for designing deep sub-wavelength THz devices due to its larger Re(ε). In previous researches [47-50], the structural design of the high constant dielectric can support the surface plasmonic resonances (SPRs) for the incident THz wave [51]. It can be believed that structural designs of STO material also can response the THz
re-
wave under different environment temperature. Thus, it inspires us that the STO material also can be used to construct the high-performance temperature tunable
urn al P
MMA in THz region.
(a)
t
l
px
x
t s STO material
Jo
py
(b)
Gold substrate (c)
z y
(d)
Fig.2 Schematic of the designed temperature tunable MMA: (a) two-dimensional (2D) array structure, (b-d) front, lattice, and perspective view of the unit-cell structure.
The design schematic of the proposed temperature tunable MMA is illustrated
in Fig. 2. Fig. 2(a) presents the two-dimensional (2D) array, which is composed of
Journal Pre-proof
two stackable square-shaped STO resonator structures arranged periodically on a metal substrate. Figs. 2(b-c) display the front, lattice, and perspective view of the unit-cell structure of the designed MMA. The metal substrate layers of the MMA are made of 20 μm copper with a frequency-independent conductivity of σCu=5.7×107S/m.
follows: px = py = 80 μm, l = 55 μm, t = 100 μm, ts = 35 μm.
of
The optimized geometrical parameters of the unit-cell structure of the MMA are as
To verify its efficiency of the designed MMA, full-wave simulations were
pro
performed using a frequency domain solver based on finite integration technology (FIT) in a Computer Simulation Technology (CST) Microwave Studio. In simulation, the periodic boundary conditions are applied in x-/y-axis direction in order to use the transverse boundaries to replicate an infinite array of the MMA, and the perfectly
re-
matched layer with absorbing boundary conditions is employed in z-axis direction. The absorbance is calculated by A(ω) = 1 - T(ω) - R(ω) = 1 - |S21(ω)|2 - |S11(ω)|2, where S21(ω) and S11(ω) represent the transmission coefficient and reflection
urn al P
coefficient, respectively. Since the thickness of the copper substrate is enough to avoid EM wave penetrating the MMA structure, thus T(ω) is 0. Therefore, the absorbance can be expressed by A(ω) = 1 - |S11(ω)|2 [6].
3. Results and discussion
Figure 3(a) shows the reflectance and absorbance spectra of the designed MMA at a certain environment temperature T (T= 300 K). It can be seen that two resonance frequency points are evidently: f1 = 0.114 THz, f2 = 0.183 THz. At resonances, the reflectance of the MMA is decreased to 2 % and 0.2 %, and yielding absorption rates of 98.0% and 99.8%, respectively. It closely achieves a perfect absorption to the incident THz wave at resonances. In addition, the full width at half maximum
Jo
(FWHM) bandwidth of two resonances (f1 = 0.114 THz, f2 = 0.183 THz) are only about 0.011 THz and 0.058 THz, respectively. Thus, the corresponding Q-factor of the proposed MMA is about 10.4 and 3.2, respectively. Based on the simulated S parameter S11(ω), the retrieved relative wave impedance of the proposed MMA is displayed in Fig. 3(b). It can be observed that real part of the relative impedance
Journal Pre-proof
(Re(z)) is about 0.8 and 1.09, while the imaginary part (Im(z)) is about -0.12 and 0 at resonances of f1 = 0.114 THz and f2 = 0.183 THz, respectively. Obviously, the relative impedance of the proposed MMA is nearly well matched to the free space at resonance. In another word, the real part of the relative impedance is near unity and
R,A()
0.6 0.4 0.2 0.0
(a) 0.05
0.10
0.15
0.20
3
Re(z) Im(z)
2 1 0
-1
0.25
0.05
0.10
0.15
0.20
Frequency/THz
(b) 0.25
re-
Frequency/THz
of
R A()
0.8
pro
1.0
Relative impedance,z
the imaginary part is near zero corresponding to the unity of absorption peak [54].
Fig.3. (a) The simulated reflectance and absorbance spectra of the proposed MMA when T = 300 K, (b) the corresponding real and imaginary parts of the relative impedance (Re(z), Im(z)).
Then, we studied the sensitivity of the proposed MMA to the polarization
urn al P
angle and oblique incident angle of the THz wave. Figs. 4(a,b) present the dependence of the absorbance spectrum on the polarization angles from 0° to 80° by a step of 5° under normal incident wave for both TE and TM modes. Due to the good symmetry of the proposed MMA structure, different polarization angles (0-80°) for both TE and TM modes of normal incident THz waves have no influence on the absorption performance. Thus, the absorption spectrum of MMA has nothing to do with polarization angles.
Next, the effect of different oblique incident angles from 0° to 80° by a step of 5° for both TE and TM modes on the absorbance spectrum of the designed MMA is also considered. As shown in Fig. 4(c), for TE mode oblique incidence, dual-band
Jo
strong absorption performance is nearly unchanged when the incident angle is less than 50°. When beyond 50°, the absorbance will decrease gradually accordingly since the effective area of the magnetic resonance is smaller with increase of the incident angle [55]. For TM mode oblique incidence, as shown in Fig. 4(d), with the incidence angle increase, the dual-band strong absorption level remains nearly unchanged. However, when over 45°, the dual-band absorption spectrum begins to blue shift and
Journal Pre-proof
the bandwidth of the higher frequency region will also increase. This should be due to parasitic resonance caused by the tight arrangement of STO stacks and a sharp increase in the incidence angle, where a side lobe appears at a larger incidence angle [44]. As a conclusion, the designed dual-band MMA has polarization-insensitive and
of
Incident angle (degree) Polarization angle (degree)
wide-angle absorption properties. (a)
75
(b)
0.2
45 30 15
TE mode
0
(c)
TM mode (d)
re-
75
pro
60
60 45 30
urn al P
15 0
0
TE mode
0.10
0.15
0.20
0.25
Frequency/THz
0.15
0.6 0.8 1
0 0.2 0.4 0.6 0.8
TM mode 0.10
0.4
0.20
1
0.25
Frequency/THz
Fig.4 Simulated absorbance spectrum of the designed MMA with different (a,b) polarization and (c,d) incident angles for different modes when T = 300K, (a,c) TE mode, (b, d) TM mode.
To explain the resonance absorption mechanism of MMA, we observe and analyze the distributions of the electric and magnetic fields of resonance responses at two resonance frequencies (f1 = 0.114 THz and f2 = 0.183 THz) under normal incident waves. Fig.5 presents the distributions of the electric and magnetic fields in the MMA unit-cell structure under the normal incident y-polarized wave at f1 = 0.114 THz and f2 = 0.183 THz, respectively. The solid arrows indicate the distributions of the electric
Jo
and magnetic field density. Previous researches indicate that the high-index dielectric material can excite Mie-type dipolar resonances along with other multipolar resonances [56-59]. Obviously, it can be conjectured that the proposed MMA based on STO material with high-index dielectric also can support multipolar resonances response and enhance the stronger absorption for the normal incident THz wave. At
Journal Pre-proof
the lower frequency of f1= 0.114 THz, as shown in Fig. 4(a), the induced electric field in the y-z plane of the unit-cell structure resembles an electric dipole resonance. And the magnetic field in the x-z plane of the unit-cell structure has a vortex-like shape (see Fig. 4(c)), indicative of an electric Mie resonance. While at the higher frequency
of
of f2= 0.185 THz, as shown in Fig. 4(b), the case is contrary, the induced electric field distribution in the y-z plane of the unit-cell structure exhibits a vortex-like shape, which resembles a magnetic dipole resonance. And the induced magnetic field in the
pro
x-z plane of the unit-cell structure is antiparallel to the incident magnetic field (see Fig. 4(d)), which is typical magnetic Mie resonance response [57]. Thus, the two near perfect absorption peaks are mainly resulted from the enhanced electric and magnetic resonances responses formed in the MMA structure, where the incident THz wave
urn al P
re-
energy can be effectively captured and dissipated.
(a)
(c)
(b)
(d)
Jo
Fig. 5 Distributions of the (a,b) electric (y-z plane) and (c,d) magnetic (x-z plane) fields in the of the MMA unit-cell structure under the normal incident y-polarized wave at different resonance frequencies: (a,c)f1= 0.114 THz, (b,d)f2= 0.183 THz.
It is also interesting and necessary to explore the power flow distribution since
it can provide deeper insight into the perfect absorption and detail information about how and where the absorption happens in the MMA structure. Figs. 4(a,b) present the power flow streams from a view along the x-axis direction (y-z plane) of the proposed MMA at f1= 0.114 THz and f2= 0.183 THz, respectively.
Journal Pre-proof
MAX
0
z
(b)
(a)
of
y
pro
Fig.6 Distributions of power flow in the y-z plane of the MMA unit-cell structure at (a) f1= 0.114 THz, and (b) f2= 0.183 THz.
In the space far away from the MMA structure, the input power flows are originally parallel streams at the two resonance frequencies. However, when the streams move closer to the surface of the MMA structure, most of them flow across
re-
and curl in the two stacked STO layers, and finally concentrate on the internal domain of the square-shaped STO resonator structure [60]. It is clearly that the power flows can gather on the interface of the two stacked STO layers, and they decay with the
urn al P
transmission of waves. It means that the incident THz wave power flows from the top part to the bottom of the STO layers, and finally decay completely. Obviously, the forms of the THz wave energy streams in two stacked STO layers are different at different resonance frequencies, which is consistent with the electric and magnetic field profiles (see Fig.5). Thus, the losses caused by the different mode excitations should be mainly originated from the array of two stacked STO layers in THz region. In addition, the near perfect absorption of the proposed MMA is also contributed to the dielectric loss nature of STO material.
In the flowing, we will discuss the influence of different structure parameters on absorption properties of the proposed MMA under the environment temperature of
Jo
T = 300 K. Here, only three structures parameters need to be considered: thickness ts of the bottom STO layer, and the thickness t and side length l of the top STO layer of the MMA structure. Figs. 6(a-c) present the absorbance spectra with three different parameters (ts, t and l). It can be seen that the absorbance always over 90%, which is nearly unchanged with the variations of the structure parameters of the MMA in a certain range.
Journal Pre-proof
Absorbance
1.0 0.8 0.6
ts= 25 μm ts= 30 μm
0.4
ts= 35 μm
0.2
ts= 40 μm
0.6 0.4
t = 70 μm t = 85 μm
of
Absorbance
0.8
t = 100 μm t = 115 μm t = 130 μm
0.2
pro
(b)
Absorbance
0.0 1.0 0.8 0.6 0.4
l = 45 μm l = 50 μm l = 55 μm l = 60 μm l = 65 μm
0.2
(c)
0.08
0.12
0.16
0.20
re-
0.0
(a)
ts= 45 μm
0.0 1.0
Frequency/THz
0.24
Fig.7 Simulated absorbance spectra for different structural parameters of the proposed MMA under the environment temperature of T = 300 K: (a) thickness ts of the bottom STO layer, (b,c) the thickness t and side length l of the top STO layer.
urn al P
As can be seen from Fig. 7(a), with the increase of the thickness ts from 25 μm to 45 μm by a step of 5 μm, the lower frequency has a remarkable red-shift, while the higher one is red-shifted slightly. It means that the lower frequency resonance absorption is mainly determined by the bottom STO layer of the MMA. The resonance frequency of the proposed MMA can be qualitatively predicted by the LC circuit model according to the equivalent circuit theory [62-63], which is approximately given as f0
1 1 2 LC l te r
, where l is the side length of the top STO
layer, εr and te is the relative permittivity and effective thickness of the STO material. Obviously, the resonance frequency is approximately inversely proportional to l, εr
Jo
and te. Thus, the lower frequency is decreased gradually with the increase of ts of the bottom STO layer. It is because that the equivalent inductance L of the bottom STO layer increases with the increase of t, finally resulting in a red-shift of the absorption spectrum for the lower frequency region. As shown in Fig. 7(b), the case is contrary; the higher frequency is decreased gradually, while the lower one is nearly unchanged with the increase of t from 70 μm to 130 μm by a step of 15 μm. As t increases, the
Journal Pre-proof
equivalent inductance L of the top STO layer increases, resulting in a red-shift of the absorption spectrum for the higher frequency region. In Fig. 7(c), by increasing the l from 45 μm to 65 μm by a step of 5 μm, both the lower and higher resonance frequencies are decreased gradually. With the increase of l, the distance between
of
adjacent units decreases, and the equivalent capacitance C between edges increases, resulting in a red-shift of the absorption spectrum [62-64]. These results indicate that the variations of the structure parameters of the proposed MMA only influence the 1.0
Frequency/THz
0.6
0.24
T=200K T=250K T=300K T=350K T=400K T=450K T=500K
0.4 0.2 0.0
(a)
0.05
0.10
0.15
0.20
0.18
S2(Sim.) S1(Fit.) S2(Fit.)
0.15
0.25
0.12 0.09
(b)
200 250 300 350 400 450 500
Temperature/K
urn al P
Frequency/THz
0.21
S1(Sim.)
re-
Absorbance
0.8
pro
absorption spectrum, and nearly un-effect the near-perfect dual-band absorbance.
Fig.8 (a) The absorbance spectra of the designed MMA with different temperature T, (b) the simulated resonance frequencies (black squares) and the fitting curve (solid line) as a function of external temperature T.
Taking a further, we have studied the absorption property of the designed MMA by changing the external environment temperature T. Based on above analysis, the relative permittivity ε(ω) of STO material is approximately inversely proportional to T. This feature gives us a possibility to actively adjust the resonance absorption properties of the MMA by varying T. Fig. 8(a) presents absorbance spectra of the designed MMA by changing T from 200 K to 500 K by a step of 50 K. It can be seen that the dual-band absorption frequencies of MMA will gradually blue shift with the
Jo
increase of T. However, the absorption peaks are changed slightly, and always over 95%, which is mainly due to the slight change of the STO material loss resulting from the change of T. The blue-shift of the two resonance absorption frequencies can be attributed to its temperature dependent relative permittivity ε(ω) of STO material, which are proportional to the T, and agreement well with the theoretical predictions.
Journal Pre-proof
Fig. 8(b) presents the relation between the resonance frequencies shift Δf and the temperature variation ΔT of surrounding environment of the MMA. Obviously, the dual-band resonance absorption frequencies are directly proportion to T. The good linearity is demonstrated as fitted solid lines, which are agreement with the
of
dependence of the simulated two absorption peak frequencies. The slope of the fitting curve depicts the absorption peak frequencies as temperature values, and the values are about 0.174GHz/K and 0.319GHz/K, respectively. Thus, it is expected that the
pro
proposed MMA can be served as a temperature sensor/detector. 1.0
Absorbance
0.8
0.4
t2
t3
t1
x
0.2
z
l1
l2
l3
y
0.08
0.12
0.16
urn al P
0.0
re-
0.6
0.20
Frequency/THz
0.24
Fig.9 The simulated absorbance spectra of the triple-band MMA based on the tri-layered STO material, and the inset shows the single unit-cell structure with axis indicating propagation direction.
From the above discussion, one concludes the absorption peak frequencies of the proposed MMA exhibits a good linearity relation with the structure parameters. Thus, it can inspire us to construct a tunable multi-band MMA based on STO material. Here, we just give an example of a triple-band MMA based on tri-layered STO material resonator structure under the external environment temperature of 300 K, as
Jo
shown the inset of Fig. 9. The final optimized structural parameters are as follows: t1= 110 μm, t2= 60 μm, t3= 30 μm, l1= 40 μm, l2= 60 μm, l3= 80 μm. As shown in Fig.9, it can be seen that the absorption peaks are up to 96.3%, 96.7%, and 96.9% at 0.109 THz, 0.181 THz, and 0.239THz, respectively. It should be noticed that the mechanical stability of the multi-band MMA will be deteriorated when further increasing the
Journal Pre-proof
numbers of the STO material layer, and also increasing the difficulty and cost of the practical fabrication.
4. Conclusion In summary, we propose and demonstrate numerically a dual-band
of
temperature-controlled MMA based on the STO material for THz waves. The designed MMA consists of a periodically arranged two stacked square-shaped STO
pro
material resonator structures placed on a copper substrate. The MMA has two nearly perfect absorption bands, and its frequencies of two peaks is about 0.114 THz and 0.181 THz when the room temperature (T= 300 K) is considered, in which the absorption peaks can reach 98.0% and 99.9%, respectively. The simulations indicate that the MMA is polarization insensitive to the normal incident wave for both TE and
re-
TM modes due to the symmetry of the unit-cell structure. The dual-band near perfect absorption performance of the MMA also can be kept with increase of the incident angle even to 45° for both TE and TM modes, which is beneficial for practical
urn al P
application. The electric and magnetic fields, and power flow distributions of the unit-cell structure reveal that the high level dual-band absorption originates from electric and magnetic dipoles response based on Mie-resonance. Furthermore, the resonance frequencies of absorption peaks of MMA can be adjusted by varying the geometric parameters of the unit-cell structure and environment temperature, which gives a considerable freedom to change the absorption frequencies to meet different application needs in THz region. It is worth mentioning that the proposed MMA is easy to fabricate by using the current Micro and nano processing technology for practical application. Firstly, the copper substrate layer is evaporated on a handle substrate. Then, the STO material layers can be fabricated on the copper substrate by
Jo
molecular beam epitaxy (MBE), RF magnetron sputtering, chemical vapor deposition (CVD), hydrothermal-electrochemical, atomic layer deposition (ALD), chemical solution deposition (CSD), and so on [36]. Finally, the unnecessary STO material proportion can be removed by the standard electron-beam lithography (EBL) method. This work provides a new idea for the design temperature tunable terahertz MMA and
Journal Pre-proof
has potential prospects in temperature sensing, imaging, thermal emitters and so on.
Acknowledgment This work was supported by the Science and Technology Research Project of Education Department of Hubei China (No. D20181107) and University Student
of
Innovation Foundation of Wuhan University of Science and Technology (Grant No.
pro
JCX201964)
References
Jo
urn al P
re-
[1] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, Perfect metamaterial absorber, Phys. Rev. Lett. 100 (2008) 207402. [2] J. Zhang, X. Wu, L. Liu, C. Huang, X. Chen, Ultra-broadband microwave metamaterial absorber with tetramethyl urea inclusion. Opt. Express 207 (2019) 25595-25602. [3] G. Stanislav, T. Sergei, B. Pavel, K. Yuri, Metasurfaces: From microwaves to visible. Physics Reports. 634 (2016) 1-72. [4] Y. Cheng, M. Huang, H. Chen, Z. Guo, Ultrathin Six-Band Polarization Insensitive Perfect Metamaterial Absorber Based on a Cross-Cave Patch Resonator for Terahertz Waves, Materials. 10 (2017) 591. [5] H. Zou, Y. Cheng, Design of a six-band terahertz metamaterial absorber for temperature sensing application, Opt. Mater. 88 (2019) 674-679. [6] M. Huang, Y. Cheng, Z. Cheng, H. Chen. Based on graphene tunable dual-band terahertz metamaterial absorber with wide-angle, Opt. Commun. 415 (2018) 194-201. [7] Y. Cheng, H. Chen, J. Zhao, X. Mao, Z. Cheng, Chiral metamaterial absorber with high selectivity for terahertz circular polarization waves, Opt. Mater. Express 8 (2018) 1399-1409. [8] Y. Cheng, X. Mao, C. Wu, L. Wu, R. Gong. Infrared non-planar plasmonic perfect absorber for enhanced sensitive refractive index sensing, Opt. Mater. 53 (2016) 195–200. [9] Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, Critical coupling with graphene-based hyperbolic metamaterials, Scientific Reports. 4 (2014) 5483. [10] J. Wang, Y. Jiang, Infrared absorber based on sandwiched two-dimensional black phosphorus metamaterials, Opt. Express. 25 (2017) 5206-5216. [11] A. Sobhani, M.W. Knight, Y. Wang, B. Zheng, etl. Narrowband photo-detection in the near-infrared with a Plasmon-induced hot electron device, Nat. Commun. 4 (2013) 1643. [12] I. E. Carranza, J. P. Grant, J. Gough, D. Cumming, Terahertz metamaterial absorbers implemented in CMOS technology for imaging applications: Scaling to
Journal Pre-proof
Jo
urn al P
re-
pro
of
large format focal plane arrays, IEEE J. Sel. Top. Quantum Electron. 23 (2017) 4700508. [13] X. Ling, Z. Xiao, X. Zheng, Tunable terahertz metamaterial absorber and the sensing application, J. Mater. Sci. Mater. Electron. 29 (2017) 1–7. [14] P. Yu, X. Chen, Z. Yi, etl. A numerical research of wideband solar absorber based on refractory metal from visible to near infrared, Opt. Mater. 97 (2019) 109400. [15] Z. Li, J. Hao, L. Huang, etl. Manipulating the wavefront of light by plasmonic metasurfaces operating in high order modes, Opt. Express 24 (2016) 8788-8796. [16] Z. Li, X. Cai, L. Huang, H. Xu, Y. Wei, N. Dai, Controllable Polarization Rotator with Broadband High Transmission Using All-Dielectric Metasurfaces, Adv. Theory Simul. 2 (2019) 1900086. [17] S. Luo, J. Zhao, D. Zuo, X. Wang, Perfect narrow band absorber for sensing applications, Opt. Express 24 (2016) 9288-9294. [18] S. Chen, Z. Chen, J. Liu, J. Cheng, Y. Zhou, L. Xiao, K. Chen, Ultra-Narrow Band Mid-Infrared Perfect Absorber Based on Hybrid Dielectric Metasurface, Nano. 9 (2019) 2079-4991. [19] B.P. Saeedeh, K. Amin, Designing Dual-Band Absorbers by Graphene/Metallic Metasurfaces, IEEE J. Quantum Elect. 55 (2019) 1-8. [20] J. Wang, R. Yang, J. Tian, X. Chen, W. Zhang, A Dual-Band Absorber with Wide-Angle and Polarization Insensitivity, IEEE Antenn Wirel PR. 17 (2018) 1242-1246. [21] B. Mohammad, A. Somayyeh, B. Sadegh, A. M. Sadegh, Analytical design of tunable multi-band terahertz absorber composed of graphene disks, OPTIK. 182 (2019) 433-442. [22] X. Wang, Q. Wang, G. Dong, Y. Hao, M. Lei, K. Bi. Multi-band terahertz metasurface absorber. Mod phys lett B. 31 (2017)0217-9849. [23] C. Cen, Y. Zhang, X. Chen, A dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency, Physica E 117 (2020) 113840. [24] Y. Zhang, Y. Fang, Q. Cai, Broad band absorber based on cascaded metamaterial layers including graphene, Wave random complex 28 (2018) 287-299. [25] Y. Cheng, H. Zou, J. Yang, X. Mao, and R. Gong, Dual and broadband terahertz metamaterial absorber based on a compact resonator structure, Opt. Mat. Express 8 (2018) 3104-3114. [26] M. Zhang, F. Zhang, Y. Ou, J. Cai, H. Yu, Broadband terahertz absorber based on dispersion-engineered catenary coupling in dual metasurface, Nanophotonics 8 (2019) 117–125. [27] F. Hu, Y. Qian, Z. Li, J. Niu, K. Nie, etl. Design of a tunable terahertz narrowband metamaterial absorber based on an electrostatically actuated MEMS cantilever and split ring resonator array, J. Optic. 15 (2013) 055101. [28] C. Liang, Y. Zhang, Z. Yi, etl. A broadband and polarization-independent metamaterial perfect absorber with monolayer Cr and Ti elliptical disks array, Results Phys. 15 (2019) 102635. [29] M. Lia, C. Liang, Y. hang, Terahertz wideband perfect absorber based on open loop with cross nested tructure, Results Phys. 15 (2019) 102603.
Journal Pre-proof
Jo
urn al P
re-
pro
of
[30] M. Huang, Y. Cheng, Z. Cheng, H. Chen, X. Mao, R. Gong, Design of a Broadband Tunable Terahertz Metamaterial Absorber Based on Complementary Structural Graphene, materials 11 (2018) 540. [31] Q. Zhou, P. Liu, C. Liu, Y. Zhou, S. Zha, Graphene-Based THz Absorber with a Broad Band for Tuning the Absorption Rate and a Narrow Band for Tuning the Absorbing Frequency, Nanomaterials 8 (2019) 2079-4991. [32] F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, Ken Broadband wave absorption in single-layered and nonstructured graphene based on far field interaction effect, Opt. Express 25 (2017) 9579. [33] L. Ye, Y. Chen, G. Cai, N. Liu, J. Zhu, Z. Song, Q. Liu, Broadband absorber with periodically sinusoidally-patterned graphene layer in terahertz range, Opt. Express 25 (2017) 11223-11232. [34] C. Liu, L. Qi, X. Zhang, Broadband graphene-based metamaterial absorbers, Aip Adcances. 8 (2018) 2158-3226. [35] Y. Cheng, R. Gong, J. Zhao, A photoexcited switchable perfect metamaterial absorber/reflector with polarization-independent and wide-angle for terahertz waves, Opt. Mater, 62 (2016) 28–33. [36] X. Zhao, Y. Wang, J. Schalch, G. Duan, K. Cremin, J. Zhang, C. Chen, R. D. Averitt, X. Zhang, Optically Modulated Ultra-Broadband All-Silicon Metamaterial Terahertz Absorbers, ACS Photonics 6 (2019) 830-837. [37] H. Liu, G. Ren, Y. Gao, B. Zhu, B. Wu, H. Li, S. Jian, Tunable Terahertz Plasmonic Perfect Absorber Based on T-Shaped InSb Array, Plasmonics 11 (2016) 411-17. [38] C. Tang, Harmonic-suppression LTCC filter with the step-impedance quarter-wavelength open stub, IEEE T Microw Theory, 52 (2004) 617-624. [39] F. M. Pontes, E.J.H Lee, E.R. Leite, E. Longo, High dielectric constant of SrTiO3 thin films prepared by chemical process, Mater. Sci. 35 (2000) 4783–7. [40] K. Benthem, C. Elsässer, Bulk electronic structure of SrTiO3: experiment and theory, Appl. Phys. 90 (2001) 6156–64. [41] B. Wang, X. Zhai, G. Wang, W. Huang, L. Wang, Frequency tunable metamaterial absorber at deep-subwavelength scale, Opt. Mater. Express 5 (2015) 227-235. [42] C. Luo, D. Li, Q. Luo, J. Yue, P. Gao, J. Yao, F. Ling, Design of a tunable multiband terahertz waves absorber, Journal of Alloys and Compounds 652 (2015) 18-24. [43] X. Ling, Z. Xiao, X. Zheng, Tunable terahertz metamaterial absorber and the sensing application, Journal of Materials Science: Materials in Electronics, 29 (2018) 1497–1503. [44] J. Zhang, J. Tian, L. Li, Pantoscopic and temperature-controlled dual-band perfect absorber based on strontium titanate material, Mater. Res. Express 5 (2018) 065802. [45] D. Li, H. Huang, H. Xia, J. Zeng, H. Li, D. Xie, Temperature-dependent tunable terahertz metamaterial absorber for the application of light modulator, Results Phys. 11 (2018) 659-664.
Journal Pre-proof
Jo
urn al P
re-
pro
of
[46] X. Huang, W. He, F. Yang, J. Ran, Q. Yang, S. Xie, Thermally tunable metamaterial absorber based on strontium titanate in the terahertz regime, Opt. Mater. Express 9 (2019) 1377-1385. [47] K. Fan, J. Y Suen, X. Liu, W. J. Padilla, All-dielectric metasurface absorbers for uncooled terahertz imaging, Opt. 4 (2017) 601. [48] X. Liu, K. Fan, I.V. Shadrivov, W. Padilla, Experimental realization of a terahertz all-dielectric metasurface absorber, Opt. express 25 (2017) 191. [49] J. Gao, C. Lan, Q. Zhao, B. Li, J. Zhou, Experimental realization of Mie-resonance terahertz absorber by self-assembly method, Opt. Express 26(10) (2018) 13001-13011. [50] H. Luo, Y. Cheng, Dual-band terahertz perfect metasurface absorber based on bi-layered all dielectric resonator structure, Opt. Mater. 96 (2019) 109279. [51] Y. Wang, F. Qin, Z. Yi, X. Chen, Effect of slit width on surface plasmon resonance, Results Phys. 15 (2019) 102711. [52] M. Lia, C. Liang, Y. hang, Terahertz wideband perfect absorber based on open loop with cross nested tructure, Results Phys. 15 (2019) 102603. [53] Y. Esipov, V. Mukhortov, S. Biryukov, A. Mamatov, S. Masychev, Modified relations for calculating the dielectric constant of barium–strontium titanate nanofilms, Tech. Phys. 61 (2016) 1220-1224. [54] A. Yamanaka, M. Kataoka, Y. Inaba, K. Inoue, B. Hehlen, E. Courtens, Evidence for competing orderings in strontium titanate from hyper-Raman scattering spectroscopy, Europhys. Lett. 50 (2000) 688–94. [55] N. Wu, D. Xu, F. Yang, Porous Fe Hollow Structures with Optimized Impedance Matching as Highly Efficient, Ultrathin, and Lightweight Electromagnetic Wave Absorbers, Ind. Eng. Chem. Res. 58 (2019) 6446-6455. [56] J.W. Park, X.R. Jin, P.V. Tuong, J.Y. Rhee, K.W. Kim, D. Kim, Y.P. Lee, Magnetic resonance of a highly symmetric metamaterial at microwave frequency, Phys. Status Solidi B 249 (2012) 858–61. [57] Q. Zhao, J. Zhou, F. Zhang, D. Lippens, Mie resonance-based dielectric metamaterials, Mater. Today 12 (2009) 60-69. [58] J. Gao, C. Lan, Q. Zhao, B. Li, J. Zhou, Experimental realization of Mie-resonance terahertz absorber by self-assembly method, Opt. Express 26 (2018) 13001-13011. [59] M. Abdelsalam, A.M. Mahmoud, M.A. Swillam, Polarization independent dielectric metasurface for infrared beam steering applications, Sci. Rep.9 (2019) 10824. [60] Y. Cheng, H. Zou, J. Yang, X. Mao, R. Gong, Dual and broadband terahertz metamaterial absorber based on a compact resonator structure, Opt. Mater. Express 8 (2018) 3104-3114. [61] A. Forouzmand, H. Mosallaei, Dynamic beam control via Mie-resonance based phase-change metasurface: a theoretical investigation, Opt. Express 26 (2018) 17948-17963. [62] K. R. Carver, J.W. Mink, Microstrip antenna technology, IEEE Trans. Antennas Propag. 29 (1981) 2–24.
Journal Pre-proof
Jo
urn al P
re-
pro
of
[63] J. Zhou, E.N. Economon, T. Koschny, C, M, Soukoulis, Unifying approach to left-handed material design, Opt. Lett. 31 (2006) 3620–2. [64] Y. Cheng, Y. Nie, R. Gong, A polarization-insensitive and omnidirectional broadband terahertz metamaterial absorber based on coplanar multi-squares films, Opt. Laser Technol. 48 (2013) 415–421.
Journal Pre-proof
Declaration of interest statement Dear Editor, We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or
of
other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the
re-
on strontium titanate (STO) resonator structure”
pro
manuscript entitled, “Dual-band tunable terahertz perfect metamaterial absorber based
Jo
urn al P
Jan.,03th,2020
PII: DOI: Reference:
S0030-4018(20)30019-5 https://doi.org/10.1016/j.optcom.2020.125265 OPTICS 125265
To appear in:
Optics Communications
Received date : 30 October 2019 Revised date : 3 January 2020 Accepted date : 6 January 2020 Please cite this article as: W. Li and Y. Cheng, Dual-band tunable terahertz perfect metamaterial absorber based on strontium titanate (STO) resonator structure, Optics Communications (2020), doi: https://doi.org/10.1016/j.optcom.2020.125265. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
Journal Pre-proof
Dual-band tunable terahertz perfect metamaterial absorber based on strontium titanate (STO) resonator structure
pro
of
Wangyang Li, Yongzhi Cheng† School of Information Science and Engineering, Wuhan University of Science and Technology, 430081, China † Corresponding author: [email protected],[email protected] Abstract: A temperature-controlled dual-band terahertz perfect metamaterial absorber
(MMA) based on strontium titanate (STO) resonator structure is proposed and investigated numerically. This MMA is a simple periodic array, consisting of two stacked square-shaped STO resonator structures and a copper substrate. Numerical
re-
simulation results indicate that the reflectance of the proposed MMA under room temperature T = 300 K is decreased to 2.1% and 0.2% at 0.114 THz and 0.181 THz, and corresponding absorbance is up to 97.9% and 99.8 %, respectively. Further results
urn al P
show that the designed MMA is polarization-insensitive, and wide-angle to the incident waves for both transverse electric (TE) and transverse magnetic (TM) modes. The simulated distributions of electromagnetic (EM) fields and power flow reveal that the observed high-level absorption is originated from the excitations of the fundamental dipole modes. Furthermore, the absorption property can be changed by varying structural parameters of the MMA and external temperature. Due to its excellent performance, the designed tunable MMA may find useful and important applications such as thermal emitter, bolometric imaging, energy harvesting, and sensing in terahertz region.
Key words: terahertz metamaterial absorber, STO material, temperature sensing
Jo
1 Introduction
In recent years, metamaterial absorbers (MMAs) have gradually become a
research hotspot and get rapidly develop in microwave [1-3], terahertz [4-7] and even optical frequency due to their wide and potential applications [8-10]. Among them, terahertz (THz) MMAs have been paid great attention since they have potential
Journal Pre-proof
applications in many scopes, such as sensing, detection, imaging, bolometer and so on [8,11-14]. Generally, the metasurface are composed of periodic patterned metallic structure array and ground-plane layers separated by dielectric material. Metasurface can produce near unity absorption by suppressing the transmission via using a
of
ground-plane and simultaneously minimizing the reflection extremely via matching the impedance to free-space [15,16]. Up to now, various MMAs, such as narrow-band [17,18], dual-band [19.20], multi-band [21-22], and broad-band [23-30] have been
pro
widely demonstrated and investigated by exploiting approaches technologies and different models. However, most of the reported MMAs can only operate in a fixed frequency range, and the absorption property cannot be modulated as desired, which greatly limits their practical applications. Hence, high performance tunable MMAs are
re-
still needed to explore, which have received extensive attention due to their great flexibility in practical applications. At present, tunable MMAs have been proposed by introducing active materials into either the structure or the surrounding medium by
urn al P
using an external stimulus, such as machine [31], additional offset voltage [32-35], optical illumination [35,36], and thermal modulation [37]. Meanwhile, these tunable MMAs require the relative harsh working conditions, thus seriously hamper the practical application. One of the widely used media is strontium titanate (STO) material since it has the capability to integrate passive components in a module, and to achieve miniaturization easily by the enhanced low-temperature co-fired ceramic (LTCC) technology [38,39].
The STO as a typical functional ceramic dielectric material has some unique properties including high dielectric constant, low dielectric loss, superior insulation, and good chemical stability [39,40]. The most attractive property is that the high
Jo
dielectric constant of the STO can be adjusted dynamically by varying external environment temperature [41,42], which can also be applied to the tunable devices in THz region. Thus, the STO can be regarded as a promising candidate material for designing the tunable MMA due to its excellent performance [41-46]. For example, Wang et al, achieved narrow band tunable absorption by designing the STO as one of the layers in the MMA [41]. Then, Luo et al, proposed a MMA comprising a periodic
Journal Pre-proof
array of multiple metallic structure resonator fabricated on STO dielectric substrate, which can achieve tunable multiband stronger absorption in THz region [42]. However, these tunable MMAs based on STO material usually require unit-cells with complex sandwiched structure, resulting in increased difficulty and cost of fabrication.
of
Thus, the larger area applications of STO based MMAs are also limited due to the fabrication complexity of the geometries structure and high cost. Recently, MMAs based on all-dielectric resonators have been developed, which could achieve near
pro
perfect absorption through special structural designs in THz region [47-50]. The all-dielectric MMAs have the advantages that they avoid Joule heating and good temperature stability for applications [48]. Thus, it inspires us to construct a
simple geometry structure. In
this
work,
we
re-
high-performance tunable MMA using all-dielectric STO materials with a relatively
proposed
and
demonstrated
numerically
a
temperature-tunable dual-band MMA in THz region, which consists of two stacked
urn al P
square-shaped STO resonator structures and a copper ground-plane. Firstly, we theoretically investigated the dependent relationship between the dielectric constant of STO material and external environment temperature. Then, we studied the absorption properties of the proposed MMA. The results show that the proposed MMA under room temperature T = 300 K can achieve absorption peaks of 97.9% and 99.8 % at 0.114 THz and 0.181 THz, respectively. It also exhibits that the high absorption performance of the MMA can be kept stable under different polarization and incident angles for both transverse-electric (TE) and transverse-magnetic (TM) modes. An underlying physical origin is revealed by analyzing the distributions of electric and magnetic fields, and power flow power at resonances. Furthermore, the dual-band
Jo
absorption properties of the MMA are also studied systematically by varying the geometric parameters of STO-cube resonator structures and external environment temperature. The simple of the high-performance tunable MMA allows for its integration easily into on-chip systems.
2. Theory, structure design and simulation
Journal Pre-proof
In this section, we firstly study the dielectric property of the STO material dependent on the external environment temperature in the frequency range of 0.01 THz- 0.3 THz. The complex relative permittivity of STO material is related with the temperature and frequency. According to the damped harmonic oscillator model of the
r (,T )
2 i 2 0
of
bulk STO material [40-45,53,54], the complex relative permittivity can be given as:
(1)
pro
where ε∞= 9.6 is the high-frequency bulk permittivity, = 2.3×1010 m-2 is a temperature independent oscillator strength, and ω is the angular frequency of incident THz wave. In addition, ω0, γ are the soft mode frequency and soft mode damping factor, which can be respectively written as: 0 (T ) 100 a(T Tc )
re-
(2)
(T ) 100(bT c )
(3)
where a = 3.12×105 m-2K-1, Tc = 42.5 K, b = 940 m-1K-1, c= -330 m-1, c is the light
urn al P
speed of free space and T is the temperature in Kelvin. 800 700
Re()
600 500
200
T=200K T=250K T=300K T=350K T=400K T=450K T=500K
150
Im()
900
100
400
50
300 200 100
T=200K T=250K T=300K T=350K T=400K T=450K T=500K
(a)
0.05
0.10
0.15
0.20
Frequency/THz
0.25
0
(b) 0.05
0.10
0.15
0.20
0.25
Frequency/THz
Fig.1. (a,b) The temperature dependence of the relative permittivity (Re(ε), Im(ε)) of STO material in terahertz frequency region.
Obviously, the real and imaginary parts of the relative permittivity (Re(ε), Im(ε))
Jo
of STO material are changed with the different environment temperature. We can see clearly that the magnitude of the Re(ε) of the STO material gradually decreases with the increase of environment temperature T, as shown in Fig. 1(a). However, the Re(ε) of the STO material is changed slightly with the changes of the THz frequency. As shown in Fig. 1(b), in the lower frequency range (0-0.12THz), the magnitude of Im(ε) have almost no changes with the increase of temperature. In the frequency range of
Journal Pre-proof
0.12THz-0.3THz), the magnitude of Im(ε) will increase quickly with the frequency, while the one will decrease quickly with the temperature. These results indicate that the complex relative permittivity of STO material is sensitive extremely to the change of environment temperature at a given frequency range (0.01 - 0.3 THz), suggesting
of
potential applications in the temperature-tunable THz integrated devices. Meanwhile, the dispersion of STO material is slightly sensitive to a given environment temperature range (200 - 500 K). It is worth noting that the STO material can be a
pro
good candidate for designing deep sub-wavelength THz devices due to its larger Re(ε). In previous researches [47-50], the structural design of the high constant dielectric can support the surface plasmonic resonances (SPRs) for the incident THz wave [51]. It can be believed that structural designs of STO material also can response the THz
re-
wave under different environment temperature. Thus, it inspires us that the STO material also can be used to construct the high-performance temperature tunable
urn al P
MMA in THz region.
(a)
t
l
px
x
t s STO material
Jo
py
(b)
Gold substrate (c)
z y
(d)
Fig.2 Schematic of the designed temperature tunable MMA: (a) two-dimensional (2D) array structure, (b-d) front, lattice, and perspective view of the unit-cell structure.
The design schematic of the proposed temperature tunable MMA is illustrated
in Fig. 2. Fig. 2(a) presents the two-dimensional (2D) array, which is composed of
Journal Pre-proof
two stackable square-shaped STO resonator structures arranged periodically on a metal substrate. Figs. 2(b-c) display the front, lattice, and perspective view of the unit-cell structure of the designed MMA. The metal substrate layers of the MMA are made of 20 μm copper with a frequency-independent conductivity of σCu=5.7×107S/m.
follows: px = py = 80 μm, l = 55 μm, t = 100 μm, ts = 35 μm.
of
The optimized geometrical parameters of the unit-cell structure of the MMA are as
To verify its efficiency of the designed MMA, full-wave simulations were
pro
performed using a frequency domain solver based on finite integration technology (FIT) in a Computer Simulation Technology (CST) Microwave Studio. In simulation, the periodic boundary conditions are applied in x-/y-axis direction in order to use the transverse boundaries to replicate an infinite array of the MMA, and the perfectly
re-
matched layer with absorbing boundary conditions is employed in z-axis direction. The absorbance is calculated by A(ω) = 1 - T(ω) - R(ω) = 1 - |S21(ω)|2 - |S11(ω)|2, where S21(ω) and S11(ω) represent the transmission coefficient and reflection
urn al P
coefficient, respectively. Since the thickness of the copper substrate is enough to avoid EM wave penetrating the MMA structure, thus T(ω) is 0. Therefore, the absorbance can be expressed by A(ω) = 1 - |S11(ω)|2 [6].
3. Results and discussion
Figure 3(a) shows the reflectance and absorbance spectra of the designed MMA at a certain environment temperature T (T= 300 K). It can be seen that two resonance frequency points are evidently: f1 = 0.114 THz, f2 = 0.183 THz. At resonances, the reflectance of the MMA is decreased to 2 % and 0.2 %, and yielding absorption rates of 98.0% and 99.8%, respectively. It closely achieves a perfect absorption to the incident THz wave at resonances. In addition, the full width at half maximum
Jo
(FWHM) bandwidth of two resonances (f1 = 0.114 THz, f2 = 0.183 THz) are only about 0.011 THz and 0.058 THz, respectively. Thus, the corresponding Q-factor of the proposed MMA is about 10.4 and 3.2, respectively. Based on the simulated S parameter S11(ω), the retrieved relative wave impedance of the proposed MMA is displayed in Fig. 3(b). It can be observed that real part of the relative impedance
Journal Pre-proof
(Re(z)) is about 0.8 and 1.09, while the imaginary part (Im(z)) is about -0.12 and 0 at resonances of f1 = 0.114 THz and f2 = 0.183 THz, respectively. Obviously, the relative impedance of the proposed MMA is nearly well matched to the free space at resonance. In another word, the real part of the relative impedance is near unity and
R,A()
0.6 0.4 0.2 0.0
(a) 0.05
0.10
0.15
0.20
3
Re(z) Im(z)
2 1 0
-1
0.25
0.05
0.10
0.15
0.20
Frequency/THz
(b) 0.25
re-
Frequency/THz
of
R A()
0.8
pro
1.0
Relative impedance,z
the imaginary part is near zero corresponding to the unity of absorption peak [54].
Fig.3. (a) The simulated reflectance and absorbance spectra of the proposed MMA when T = 300 K, (b) the corresponding real and imaginary parts of the relative impedance (Re(z), Im(z)).
Then, we studied the sensitivity of the proposed MMA to the polarization
urn al P
angle and oblique incident angle of the THz wave. Figs. 4(a,b) present the dependence of the absorbance spectrum on the polarization angles from 0° to 80° by a step of 5° under normal incident wave for both TE and TM modes. Due to the good symmetry of the proposed MMA structure, different polarization angles (0-80°) for both TE and TM modes of normal incident THz waves have no influence on the absorption performance. Thus, the absorption spectrum of MMA has nothing to do with polarization angles.
Next, the effect of different oblique incident angles from 0° to 80° by a step of 5° for both TE and TM modes on the absorbance spectrum of the designed MMA is also considered. As shown in Fig. 4(c), for TE mode oblique incidence, dual-band
Jo
strong absorption performance is nearly unchanged when the incident angle is less than 50°. When beyond 50°, the absorbance will decrease gradually accordingly since the effective area of the magnetic resonance is smaller with increase of the incident angle [55]. For TM mode oblique incidence, as shown in Fig. 4(d), with the incidence angle increase, the dual-band strong absorption level remains nearly unchanged. However, when over 45°, the dual-band absorption spectrum begins to blue shift and
Journal Pre-proof
the bandwidth of the higher frequency region will also increase. This should be due to parasitic resonance caused by the tight arrangement of STO stacks and a sharp increase in the incidence angle, where a side lobe appears at a larger incidence angle [44]. As a conclusion, the designed dual-band MMA has polarization-insensitive and
of
Incident angle (degree) Polarization angle (degree)
wide-angle absorption properties. (a)
75
(b)
0.2
45 30 15
TE mode
0
(c)
TM mode (d)
re-
75
pro
60
60 45 30
urn al P
15 0
0
TE mode
0.10
0.15
0.20
0.25
Frequency/THz
0.15
0.6 0.8 1
0 0.2 0.4 0.6 0.8
TM mode 0.10
0.4
0.20
1
0.25
Frequency/THz
Fig.4 Simulated absorbance spectrum of the designed MMA with different (a,b) polarization and (c,d) incident angles for different modes when T = 300K, (a,c) TE mode, (b, d) TM mode.
To explain the resonance absorption mechanism of MMA, we observe and analyze the distributions of the electric and magnetic fields of resonance responses at two resonance frequencies (f1 = 0.114 THz and f2 = 0.183 THz) under normal incident waves. Fig.5 presents the distributions of the electric and magnetic fields in the MMA unit-cell structure under the normal incident y-polarized wave at f1 = 0.114 THz and f2 = 0.183 THz, respectively. The solid arrows indicate the distributions of the electric
Jo
and magnetic field density. Previous researches indicate that the high-index dielectric material can excite Mie-type dipolar resonances along with other multipolar resonances [56-59]. Obviously, it can be conjectured that the proposed MMA based on STO material with high-index dielectric also can support multipolar resonances response and enhance the stronger absorption for the normal incident THz wave. At
Journal Pre-proof
the lower frequency of f1= 0.114 THz, as shown in Fig. 4(a), the induced electric field in the y-z plane of the unit-cell structure resembles an electric dipole resonance. And the magnetic field in the x-z plane of the unit-cell structure has a vortex-like shape (see Fig. 4(c)), indicative of an electric Mie resonance. While at the higher frequency
of
of f2= 0.185 THz, as shown in Fig. 4(b), the case is contrary, the induced electric field distribution in the y-z plane of the unit-cell structure exhibits a vortex-like shape, which resembles a magnetic dipole resonance. And the induced magnetic field in the
pro
x-z plane of the unit-cell structure is antiparallel to the incident magnetic field (see Fig. 4(d)), which is typical magnetic Mie resonance response [57]. Thus, the two near perfect absorption peaks are mainly resulted from the enhanced electric and magnetic resonances responses formed in the MMA structure, where the incident THz wave
urn al P
re-
energy can be effectively captured and dissipated.
(a)
(c)
(b)
(d)
Jo
Fig. 5 Distributions of the (a,b) electric (y-z plane) and (c,d) magnetic (x-z plane) fields in the of the MMA unit-cell structure under the normal incident y-polarized wave at different resonance frequencies: (a,c)f1= 0.114 THz, (b,d)f2= 0.183 THz.
It is also interesting and necessary to explore the power flow distribution since
it can provide deeper insight into the perfect absorption and detail information about how and where the absorption happens in the MMA structure. Figs. 4(a,b) present the power flow streams from a view along the x-axis direction (y-z plane) of the proposed MMA at f1= 0.114 THz and f2= 0.183 THz, respectively.
Journal Pre-proof
MAX
0
z
(b)
(a)
of
y
pro
Fig.6 Distributions of power flow in the y-z plane of the MMA unit-cell structure at (a) f1= 0.114 THz, and (b) f2= 0.183 THz.
In the space far away from the MMA structure, the input power flows are originally parallel streams at the two resonance frequencies. However, when the streams move closer to the surface of the MMA structure, most of them flow across
re-
and curl in the two stacked STO layers, and finally concentrate on the internal domain of the square-shaped STO resonator structure [60]. It is clearly that the power flows can gather on the interface of the two stacked STO layers, and they decay with the
urn al P
transmission of waves. It means that the incident THz wave power flows from the top part to the bottom of the STO layers, and finally decay completely. Obviously, the forms of the THz wave energy streams in two stacked STO layers are different at different resonance frequencies, which is consistent with the electric and magnetic field profiles (see Fig.5). Thus, the losses caused by the different mode excitations should be mainly originated from the array of two stacked STO layers in THz region. In addition, the near perfect absorption of the proposed MMA is also contributed to the dielectric loss nature of STO material.
In the flowing, we will discuss the influence of different structure parameters on absorption properties of the proposed MMA under the environment temperature of
Jo
T = 300 K. Here, only three structures parameters need to be considered: thickness ts of the bottom STO layer, and the thickness t and side length l of the top STO layer of the MMA structure. Figs. 6(a-c) present the absorbance spectra with three different parameters (ts, t and l). It can be seen that the absorbance always over 90%, which is nearly unchanged with the variations of the structure parameters of the MMA in a certain range.
Journal Pre-proof
Absorbance
1.0 0.8 0.6
ts= 25 μm ts= 30 μm
0.4
ts= 35 μm
0.2
ts= 40 μm
0.6 0.4
t = 70 μm t = 85 μm
of
Absorbance
0.8
t = 100 μm t = 115 μm t = 130 μm
0.2
pro
(b)
Absorbance
0.0 1.0 0.8 0.6 0.4
l = 45 μm l = 50 μm l = 55 μm l = 60 μm l = 65 μm
0.2
(c)
0.08
0.12
0.16
0.20
re-
0.0
(a)
ts= 45 μm
0.0 1.0
Frequency/THz
0.24
Fig.7 Simulated absorbance spectra for different structural parameters of the proposed MMA under the environment temperature of T = 300 K: (a) thickness ts of the bottom STO layer, (b,c) the thickness t and side length l of the top STO layer.
urn al P
As can be seen from Fig. 7(a), with the increase of the thickness ts from 25 μm to 45 μm by a step of 5 μm, the lower frequency has a remarkable red-shift, while the higher one is red-shifted slightly. It means that the lower frequency resonance absorption is mainly determined by the bottom STO layer of the MMA. The resonance frequency of the proposed MMA can be qualitatively predicted by the LC circuit model according to the equivalent circuit theory [62-63], which is approximately given as f0
1 1 2 LC l te r
, where l is the side length of the top STO
layer, εr and te is the relative permittivity and effective thickness of the STO material. Obviously, the resonance frequency is approximately inversely proportional to l, εr
Jo
and te. Thus, the lower frequency is decreased gradually with the increase of ts of the bottom STO layer. It is because that the equivalent inductance L of the bottom STO layer increases with the increase of t, finally resulting in a red-shift of the absorption spectrum for the lower frequency region. As shown in Fig. 7(b), the case is contrary; the higher frequency is decreased gradually, while the lower one is nearly unchanged with the increase of t from 70 μm to 130 μm by a step of 15 μm. As t increases, the
Journal Pre-proof
equivalent inductance L of the top STO layer increases, resulting in a red-shift of the absorption spectrum for the higher frequency region. In Fig. 7(c), by increasing the l from 45 μm to 65 μm by a step of 5 μm, both the lower and higher resonance frequencies are decreased gradually. With the increase of l, the distance between
of
adjacent units decreases, and the equivalent capacitance C between edges increases, resulting in a red-shift of the absorption spectrum [62-64]. These results indicate that the variations of the structure parameters of the proposed MMA only influence the 1.0
Frequency/THz
0.6
0.24
T=200K T=250K T=300K T=350K T=400K T=450K T=500K
0.4 0.2 0.0
(a)
0.05
0.10
0.15
0.20
0.18
S2(Sim.) S1(Fit.) S2(Fit.)
0.15
0.25
0.12 0.09
(b)
200 250 300 350 400 450 500
Temperature/K
urn al P
Frequency/THz
0.21
S1(Sim.)
re-
Absorbance
0.8
pro
absorption spectrum, and nearly un-effect the near-perfect dual-band absorbance.
Fig.8 (a) The absorbance spectra of the designed MMA with different temperature T, (b) the simulated resonance frequencies (black squares) and the fitting curve (solid line) as a function of external temperature T.
Taking a further, we have studied the absorption property of the designed MMA by changing the external environment temperature T. Based on above analysis, the relative permittivity ε(ω) of STO material is approximately inversely proportional to T. This feature gives us a possibility to actively adjust the resonance absorption properties of the MMA by varying T. Fig. 8(a) presents absorbance spectra of the designed MMA by changing T from 200 K to 500 K by a step of 50 K. It can be seen that the dual-band absorption frequencies of MMA will gradually blue shift with the
Jo
increase of T. However, the absorption peaks are changed slightly, and always over 95%, which is mainly due to the slight change of the STO material loss resulting from the change of T. The blue-shift of the two resonance absorption frequencies can be attributed to its temperature dependent relative permittivity ε(ω) of STO material, which are proportional to the T, and agreement well with the theoretical predictions.
Journal Pre-proof
Fig. 8(b) presents the relation between the resonance frequencies shift Δf and the temperature variation ΔT of surrounding environment of the MMA. Obviously, the dual-band resonance absorption frequencies are directly proportion to T. The good linearity is demonstrated as fitted solid lines, which are agreement with the
of
dependence of the simulated two absorption peak frequencies. The slope of the fitting curve depicts the absorption peak frequencies as temperature values, and the values are about 0.174GHz/K and 0.319GHz/K, respectively. Thus, it is expected that the
pro
proposed MMA can be served as a temperature sensor/detector. 1.0
Absorbance
0.8
0.4
t2
t3
t1
x
0.2
z
l1
l2
l3
y
0.08
0.12
0.16
urn al P
0.0
re-
0.6
0.20
Frequency/THz
0.24
Fig.9 The simulated absorbance spectra of the triple-band MMA based on the tri-layered STO material, and the inset shows the single unit-cell structure with axis indicating propagation direction.
From the above discussion, one concludes the absorption peak frequencies of the proposed MMA exhibits a good linearity relation with the structure parameters. Thus, it can inspire us to construct a tunable multi-band MMA based on STO material. Here, we just give an example of a triple-band MMA based on tri-layered STO material resonator structure under the external environment temperature of 300 K, as
Jo
shown the inset of Fig. 9. The final optimized structural parameters are as follows: t1= 110 μm, t2= 60 μm, t3= 30 μm, l1= 40 μm, l2= 60 μm, l3= 80 μm. As shown in Fig.9, it can be seen that the absorption peaks are up to 96.3%, 96.7%, and 96.9% at 0.109 THz, 0.181 THz, and 0.239THz, respectively. It should be noticed that the mechanical stability of the multi-band MMA will be deteriorated when further increasing the
Journal Pre-proof
numbers of the STO material layer, and also increasing the difficulty and cost of the practical fabrication.
4. Conclusion In summary, we propose and demonstrate numerically a dual-band
of
temperature-controlled MMA based on the STO material for THz waves. The designed MMA consists of a periodically arranged two stacked square-shaped STO
pro
material resonator structures placed on a copper substrate. The MMA has two nearly perfect absorption bands, and its frequencies of two peaks is about 0.114 THz and 0.181 THz when the room temperature (T= 300 K) is considered, in which the absorption peaks can reach 98.0% and 99.9%, respectively. The simulations indicate that the MMA is polarization insensitive to the normal incident wave for both TE and
re-
TM modes due to the symmetry of the unit-cell structure. The dual-band near perfect absorption performance of the MMA also can be kept with increase of the incident angle even to 45° for both TE and TM modes, which is beneficial for practical
urn al P
application. The electric and magnetic fields, and power flow distributions of the unit-cell structure reveal that the high level dual-band absorption originates from electric and magnetic dipoles response based on Mie-resonance. Furthermore, the resonance frequencies of absorption peaks of MMA can be adjusted by varying the geometric parameters of the unit-cell structure and environment temperature, which gives a considerable freedom to change the absorption frequencies to meet different application needs in THz region. It is worth mentioning that the proposed MMA is easy to fabricate by using the current Micro and nano processing technology for practical application. Firstly, the copper substrate layer is evaporated on a handle substrate. Then, the STO material layers can be fabricated on the copper substrate by
Jo
molecular beam epitaxy (MBE), RF magnetron sputtering, chemical vapor deposition (CVD), hydrothermal-electrochemical, atomic layer deposition (ALD), chemical solution deposition (CSD), and so on [36]. Finally, the unnecessary STO material proportion can be removed by the standard electron-beam lithography (EBL) method. This work provides a new idea for the design temperature tunable terahertz MMA and
Journal Pre-proof
has potential prospects in temperature sensing, imaging, thermal emitters and so on.
Acknowledgment This work was supported by the Science and Technology Research Project of Education Department of Hubei China (No. D20181107) and University Student
of
Innovation Foundation of Wuhan University of Science and Technology (Grant No.
pro
JCX201964)
References
Jo
urn al P
re-
[1] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, Perfect metamaterial absorber, Phys. Rev. Lett. 100 (2008) 207402. [2] J. Zhang, X. Wu, L. Liu, C. Huang, X. Chen, Ultra-broadband microwave metamaterial absorber with tetramethyl urea inclusion. Opt. Express 207 (2019) 25595-25602. [3] G. Stanislav, T. Sergei, B. Pavel, K. Yuri, Metasurfaces: From microwaves to visible. Physics Reports. 634 (2016) 1-72. [4] Y. Cheng, M. Huang, H. Chen, Z. Guo, Ultrathin Six-Band Polarization Insensitive Perfect Metamaterial Absorber Based on a Cross-Cave Patch Resonator for Terahertz Waves, Materials. 10 (2017) 591. [5] H. Zou, Y. Cheng, Design of a six-band terahertz metamaterial absorber for temperature sensing application, Opt. Mater. 88 (2019) 674-679. [6] M. Huang, Y. Cheng, Z. Cheng, H. Chen. Based on graphene tunable dual-band terahertz metamaterial absorber with wide-angle, Opt. Commun. 415 (2018) 194-201. [7] Y. Cheng, H. Chen, J. Zhao, X. Mao, Z. Cheng, Chiral metamaterial absorber with high selectivity for terahertz circular polarization waves, Opt. Mater. Express 8 (2018) 1399-1409. [8] Y. Cheng, X. Mao, C. Wu, L. Wu, R. Gong. Infrared non-planar plasmonic perfect absorber for enhanced sensitive refractive index sensing, Opt. Mater. 53 (2016) 195–200. [9] Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, Critical coupling with graphene-based hyperbolic metamaterials, Scientific Reports. 4 (2014) 5483. [10] J. Wang, Y. Jiang, Infrared absorber based on sandwiched two-dimensional black phosphorus metamaterials, Opt. Express. 25 (2017) 5206-5216. [11] A. Sobhani, M.W. Knight, Y. Wang, B. Zheng, etl. Narrowband photo-detection in the near-infrared with a Plasmon-induced hot electron device, Nat. Commun. 4 (2013) 1643. [12] I. E. Carranza, J. P. Grant, J. Gough, D. Cumming, Terahertz metamaterial absorbers implemented in CMOS technology for imaging applications: Scaling to
Journal Pre-proof
Jo
urn al P
re-
pro
of
large format focal plane arrays, IEEE J. Sel. Top. Quantum Electron. 23 (2017) 4700508. [13] X. Ling, Z. Xiao, X. Zheng, Tunable terahertz metamaterial absorber and the sensing application, J. Mater. Sci. Mater. Electron. 29 (2017) 1–7. [14] P. Yu, X. Chen, Z. Yi, etl. A numerical research of wideband solar absorber based on refractory metal from visible to near infrared, Opt. Mater. 97 (2019) 109400. [15] Z. Li, J. Hao, L. Huang, etl. Manipulating the wavefront of light by plasmonic metasurfaces operating in high order modes, Opt. Express 24 (2016) 8788-8796. [16] Z. Li, X. Cai, L. Huang, H. Xu, Y. Wei, N. Dai, Controllable Polarization Rotator with Broadband High Transmission Using All-Dielectric Metasurfaces, Adv. Theory Simul. 2 (2019) 1900086. [17] S. Luo, J. Zhao, D. Zuo, X. Wang, Perfect narrow band absorber for sensing applications, Opt. Express 24 (2016) 9288-9294. [18] S. Chen, Z. Chen, J. Liu, J. Cheng, Y. Zhou, L. Xiao, K. Chen, Ultra-Narrow Band Mid-Infrared Perfect Absorber Based on Hybrid Dielectric Metasurface, Nano. 9 (2019) 2079-4991. [19] B.P. Saeedeh, K. Amin, Designing Dual-Band Absorbers by Graphene/Metallic Metasurfaces, IEEE J. Quantum Elect. 55 (2019) 1-8. [20] J. Wang, R. Yang, J. Tian, X. Chen, W. Zhang, A Dual-Band Absorber with Wide-Angle and Polarization Insensitivity, IEEE Antenn Wirel PR. 17 (2018) 1242-1246. [21] B. Mohammad, A. Somayyeh, B. Sadegh, A. M. Sadegh, Analytical design of tunable multi-band terahertz absorber composed of graphene disks, OPTIK. 182 (2019) 433-442. [22] X. Wang, Q. Wang, G. Dong, Y. Hao, M. Lei, K. Bi. Multi-band terahertz metasurface absorber. Mod phys lett B. 31 (2017)0217-9849. [23] C. Cen, Y. Zhang, X. Chen, A dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency, Physica E 117 (2020) 113840. [24] Y. Zhang, Y. Fang, Q. Cai, Broad band absorber based on cascaded metamaterial layers including graphene, Wave random complex 28 (2018) 287-299. [25] Y. Cheng, H. Zou, J. Yang, X. Mao, and R. Gong, Dual and broadband terahertz metamaterial absorber based on a compact resonator structure, Opt. Mat. Express 8 (2018) 3104-3114. [26] M. Zhang, F. Zhang, Y. Ou, J. Cai, H. Yu, Broadband terahertz absorber based on dispersion-engineered catenary coupling in dual metasurface, Nanophotonics 8 (2019) 117–125. [27] F. Hu, Y. Qian, Z. Li, J. Niu, K. Nie, etl. Design of a tunable terahertz narrowband metamaterial absorber based on an electrostatically actuated MEMS cantilever and split ring resonator array, J. Optic. 15 (2013) 055101. [28] C. Liang, Y. Zhang, Z. Yi, etl. A broadband and polarization-independent metamaterial perfect absorber with monolayer Cr and Ti elliptical disks array, Results Phys. 15 (2019) 102635. [29] M. Lia, C. Liang, Y. hang, Terahertz wideband perfect absorber based on open loop with cross nested tructure, Results Phys. 15 (2019) 102603.
Journal Pre-proof
Jo
urn al P
re-
pro
of
[30] M. Huang, Y. Cheng, Z. Cheng, H. Chen, X. Mao, R. Gong, Design of a Broadband Tunable Terahertz Metamaterial Absorber Based on Complementary Structural Graphene, materials 11 (2018) 540. [31] Q. Zhou, P. Liu, C. Liu, Y. Zhou, S. Zha, Graphene-Based THz Absorber with a Broad Band for Tuning the Absorption Rate and a Narrow Band for Tuning the Absorbing Frequency, Nanomaterials 8 (2019) 2079-4991. [32] F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, Ken Broadband wave absorption in single-layered and nonstructured graphene based on far field interaction effect, Opt. Express 25 (2017) 9579. [33] L. Ye, Y. Chen, G. Cai, N. Liu, J. Zhu, Z. Song, Q. Liu, Broadband absorber with periodically sinusoidally-patterned graphene layer in terahertz range, Opt. Express 25 (2017) 11223-11232. [34] C. Liu, L. Qi, X. Zhang, Broadband graphene-based metamaterial absorbers, Aip Adcances. 8 (2018) 2158-3226. [35] Y. Cheng, R. Gong, J. Zhao, A photoexcited switchable perfect metamaterial absorber/reflector with polarization-independent and wide-angle for terahertz waves, Opt. Mater, 62 (2016) 28–33. [36] X. Zhao, Y. Wang, J. Schalch, G. Duan, K. Cremin, J. Zhang, C. Chen, R. D. Averitt, X. Zhang, Optically Modulated Ultra-Broadband All-Silicon Metamaterial Terahertz Absorbers, ACS Photonics 6 (2019) 830-837. [37] H. Liu, G. Ren, Y. Gao, B. Zhu, B. Wu, H. Li, S. Jian, Tunable Terahertz Plasmonic Perfect Absorber Based on T-Shaped InSb Array, Plasmonics 11 (2016) 411-17. [38] C. Tang, Harmonic-suppression LTCC filter with the step-impedance quarter-wavelength open stub, IEEE T Microw Theory, 52 (2004) 617-624. [39] F. M. Pontes, E.J.H Lee, E.R. Leite, E. Longo, High dielectric constant of SrTiO3 thin films prepared by chemical process, Mater. Sci. 35 (2000) 4783–7. [40] K. Benthem, C. Elsässer, Bulk electronic structure of SrTiO3: experiment and theory, Appl. Phys. 90 (2001) 6156–64. [41] B. Wang, X. Zhai, G. Wang, W. Huang, L. Wang, Frequency tunable metamaterial absorber at deep-subwavelength scale, Opt. Mater. Express 5 (2015) 227-235. [42] C. Luo, D. Li, Q. Luo, J. Yue, P. Gao, J. Yao, F. Ling, Design of a tunable multiband terahertz waves absorber, Journal of Alloys and Compounds 652 (2015) 18-24. [43] X. Ling, Z. Xiao, X. Zheng, Tunable terahertz metamaterial absorber and the sensing application, Journal of Materials Science: Materials in Electronics, 29 (2018) 1497–1503. [44] J. Zhang, J. Tian, L. Li, Pantoscopic and temperature-controlled dual-band perfect absorber based on strontium titanate material, Mater. Res. Express 5 (2018) 065802. [45] D. Li, H. Huang, H. Xia, J. Zeng, H. Li, D. Xie, Temperature-dependent tunable terahertz metamaterial absorber for the application of light modulator, Results Phys. 11 (2018) 659-664.
Journal Pre-proof
Jo
urn al P
re-
pro
of
[46] X. Huang, W. He, F. Yang, J. Ran, Q. Yang, S. Xie, Thermally tunable metamaterial absorber based on strontium titanate in the terahertz regime, Opt. Mater. Express 9 (2019) 1377-1385. [47] K. Fan, J. Y Suen, X. Liu, W. J. Padilla, All-dielectric metasurface absorbers for uncooled terahertz imaging, Opt. 4 (2017) 601. [48] X. Liu, K. Fan, I.V. Shadrivov, W. Padilla, Experimental realization of a terahertz all-dielectric metasurface absorber, Opt. express 25 (2017) 191. [49] J. Gao, C. Lan, Q. Zhao, B. Li, J. Zhou, Experimental realization of Mie-resonance terahertz absorber by self-assembly method, Opt. Express 26(10) (2018) 13001-13011. [50] H. Luo, Y. Cheng, Dual-band terahertz perfect metasurface absorber based on bi-layered all dielectric resonator structure, Opt. Mater. 96 (2019) 109279. [51] Y. Wang, F. Qin, Z. Yi, X. Chen, Effect of slit width on surface plasmon resonance, Results Phys. 15 (2019) 102711. [52] M. Lia, C. Liang, Y. hang, Terahertz wideband perfect absorber based on open loop with cross nested tructure, Results Phys. 15 (2019) 102603. [53] Y. Esipov, V. Mukhortov, S. Biryukov, A. Mamatov, S. Masychev, Modified relations for calculating the dielectric constant of barium–strontium titanate nanofilms, Tech. Phys. 61 (2016) 1220-1224. [54] A. Yamanaka, M. Kataoka, Y. Inaba, K. Inoue, B. Hehlen, E. Courtens, Evidence for competing orderings in strontium titanate from hyper-Raman scattering spectroscopy, Europhys. Lett. 50 (2000) 688–94. [55] N. Wu, D. Xu, F. Yang, Porous Fe Hollow Structures with Optimized Impedance Matching as Highly Efficient, Ultrathin, and Lightweight Electromagnetic Wave Absorbers, Ind. Eng. Chem. Res. 58 (2019) 6446-6455. [56] J.W. Park, X.R. Jin, P.V. Tuong, J.Y. Rhee, K.W. Kim, D. Kim, Y.P. Lee, Magnetic resonance of a highly symmetric metamaterial at microwave frequency, Phys. Status Solidi B 249 (2012) 858–61. [57] Q. Zhao, J. Zhou, F. Zhang, D. Lippens, Mie resonance-based dielectric metamaterials, Mater. Today 12 (2009) 60-69. [58] J. Gao, C. Lan, Q. Zhao, B. Li, J. Zhou, Experimental realization of Mie-resonance terahertz absorber by self-assembly method, Opt. Express 26 (2018) 13001-13011. [59] M. Abdelsalam, A.M. Mahmoud, M.A. Swillam, Polarization independent dielectric metasurface for infrared beam steering applications, Sci. Rep.9 (2019) 10824. [60] Y. Cheng, H. Zou, J. Yang, X. Mao, R. Gong, Dual and broadband terahertz metamaterial absorber based on a compact resonator structure, Opt. Mater. Express 8 (2018) 3104-3114. [61] A. Forouzmand, H. Mosallaei, Dynamic beam control via Mie-resonance based phase-change metasurface: a theoretical investigation, Opt. Express 26 (2018) 17948-17963. [62] K. R. Carver, J.W. Mink, Microstrip antenna technology, IEEE Trans. Antennas Propag. 29 (1981) 2–24.
Journal Pre-proof
Jo
urn al P
re-
pro
of
[63] J. Zhou, E.N. Economon, T. Koschny, C, M, Soukoulis, Unifying approach to left-handed material design, Opt. Lett. 31 (2006) 3620–2. [64] Y. Cheng, Y. Nie, R. Gong, A polarization-insensitive and omnidirectional broadband terahertz metamaterial absorber based on coplanar multi-squares films, Opt. Laser Technol. 48 (2013) 415–421.
Journal Pre-proof
Declaration of interest statement Dear Editor, We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or
of
other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the
re-
on strontium titanate (STO) resonator structure”
pro
manuscript entitled, “Dual-band tunable terahertz perfect metamaterial absorber based
Jo
urn al P
Jan.,03th,2020