Vol. 26, No. 6 | 19 Mar 2018 | OPTICS EXPRESS 7148
Broadband tunable terahertz absorber based
on vanadium dioxide metamaterials
ZHENGYONG SONG,1,* KAI WANG,1 JIAWEN LI,1 AND QING HUO LIU2
1
Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen University,
Xiamen 361005, China
2
Department of Electrical and Computer Engineering, Duke University, Durham 27708, USA
*
zhysong@xmu.edu.cn
Abstract: An active absorption device is proposed based on vanadium dioxide metamaterials.
By controlling the conductivity of vanadium dioxide, resonant absorbers are designed to work
at wide range of terahertz frequencies. Numerical results show that a broadband terahertz
absorber with nearly 100% absorptance can be achieved, and its normalized bandwidth of
90% absorptance is 60% under normal incidence for both transverse-electric and transversemagnetic polarizations when the conductivity of vanadium dioxide is equal to 2000 Ω −1cm −1 .
Absorptance at peak frequencies can be continuously tuned from 30% to 100% by changing
the conductivity from 10 Ω −1cm −1 to 2000 Ω −1cm −1 . Absorptance spectra analysis shows a
clear independence of polarization and incident angle. The presented results may have tunable
spectral applications in sensor, detector, and thermophotovoltaic device working at terahertz
frequency bands.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
OCIS codes: (040.2235) Far infrared or terahertz; (310.3915) Metallic, opaque, and absorbing coatings.
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#320904
Journal © 2018
https://doi.org/10.1364/OE.26.007148
Received 31 Jan 2018; revised 1 Mar 2018; accepted 1 Mar 2018; published 8 Mar 2018
Vol. 26, No. 6 | 19 Mar 2018 | OPTICS EXPRESS 7149
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1. Introduction
Metamaterials (MMs) are a distinct kind of electromagnetic materials and have been
intensively studied in the past several years for some fascinating phenomenon, such as
negative refraction [1, 2], perfect lens [3, 4], and transparency [5–7]. Its properties mainly
result from subwavelength details of the metallic or dielectric element rather than their
chemical composition. Recently dynamic control of the MMs’ response attracts lots of
interest through the electric or optical methods [8–11]. It is well known that vanadium
dioxides ( VO2 ) show the transition behavior from insulator to metal at around 340 K. The
lattice structure is transformed from monoclinic to tetragonal structures as the temperature
rises, and the conductivity of VO2 increases by several orders of magnitude during the
transition. So VO2 has wide potential for temperature sensitive photonic, electronic, and
thermic devices. Thus, combining MMs with VO2 thin film or small particles is a promising
way to dynamically modulate electromagnetic properties of some practical devices [12–24].
In 2010, W. Huang et al. fabricated a composite metamaterial of
gold strip / VO2 spacer / gold strip sandwich structure to study the optical response [15].
Their results indicated that the designed nanostructure with VO2 spacers can be used as a
dynamically temperature-controlling optical switch. In 2012, M. A. Kats et al. showed perfect
absorption in a system comprising a single lossy VO2 layer with ultra-thin thickness much
smaller than the incident wavelength on the sapphire substrate [16]. The design leads to
Vol. 26, No. 6 | 19 Mar 2018 | OPTICS EXPRESS 7150
99.75% absorption at λ = 11.6 μ m in the vicinity of the VO2 insulator-to-metal phase
transition. In 2015, H. Kocer et al. demonstrated thermally tunable short-wavelength infrared
resonant absorbers by heating up hybrid gold- VO2 nanostructure arrays above the phase
transition temperature of VO2 [17]. In 2017, Z. Zhu et al. realized an efficient absorber metadevice with each unit cell consisting of a gold bow-tie antenna with a small VO2 patch placed
in its feed gap [18]. The device has an experimentally measured tuning range as large as 360
nm in the near infrared region and a modulation depth of 33% at the resonant wavelength. In
the terahertz frequency region, the dielectric constant of VO2 varies by several orders of
magnitude when the film undergoes phase transition. In this paper, we propose a composite
MM with sandwich nanostructures metal cross / SiO2 spacer / VO2 film to dynamically
modulate the absorption property.
2. Numerical calculations and discussions
Fig. 1. Schematic of the
red (cyan) part is
VO2 -based tunable terahertz MM absorber studied in this paper. The
VO2 ( SiO2 )
with the thickness of
t2 = 0.5 μ m ( t1 = 70 μ m ). The
μ m , length of 155 μ m .
yellow part is gold with the thickness of 0.02 μ m , width of 2.9
The substrate is
SiO2
which is infinite in simulation.
In this study, we demonstrate conductivity-tunable terahertz resonant absorbers by utilizing a
phase change material ( VO2 ) to achieve dynamic control of metadevices. As shown in Fig. 1,
the metadevice is based on the perfect absorber architecture with each unit cell consisting of a
metal cross and a VO2 film [25–27]. These two layers are separated by a SiO2 spacer layer.
The thicknesses of metal crosses, SiO2 layer, and VO2 film is 0.02 μ m , 70 μ m , and 0.5
μ m . The chosen width, length, and period of metal crosses in simulation are 2.9 μ m , 155
μ m , and 174 μ m . In order to avoid the Fabry-Perot resonance caused by the finite thickness
of the underlying SiO2 substrate, the thickness of the underlying SiO2 substrate is assumed
to be infinite in simulation. A variable conductivity of VO2 is assumed to simulate the phase
transition effect. The optical permittivity of VO2 in terahertz range can be described by Drude
ω p2 (σ )
model as follows: ε (ω ) = ε ∞ − 2
, where ε ∞ = 12 is the permittivity at high frequency,
ω + iγω
ω p (σ ) is the conductivity dependent plasma frequency and γ is the collision frequency [22–
24]. In addition, both ω p2 (σ ) and σ are proportional to free carrier density. The plasma
Vol. 26, No. 6 | 19 Mar 2018 | OPTICS EXPRESS 7151
frequency
at
σ
can
be
approximately
expressed
as
ω p2 (σ ) =
σ 2
ω (σ )
σ0 p 0
with σ 0 = 3 × 103 Ω −1cm −1 , ω p (σ 0 ) = 1.4 × 1015 rad / s , and γ = 5.75 × 1013 rad / s which is
assumed to be independent of σ . The relative permittivity of SiO2 with negligible loss is set
to 3.8 at terahertz frequencies [28, 29]. The relative permittivity of gold is described by a
Drude model ε Au = 1 − ω p2 / ω (ω + iΓ) with plasma frequency ω p = 1.37 × 1016 rad / s and
collision frequency Γ = 1.2 × 1014 rad / s [30].
Full-wave electromagnetic simulations are performed using finite-element-method
(comsol multiphysics). All simulations use extremely adaptive fine mesh settings. A unit cell
of the investigated structure is simulated using periodic boundary condition. The total
2
2
absorptance (A) in the designed structure is calculated by A = 1 − R − T = 1 − S11 − S21 ,
where R is the total reflectance and T is the transmittance. As shown in Fig. 2, the simulated
results clearly tell that the values of reflectance, transmittance, and absorptance undergoe a
noticeable shift as the conductivity increases. Figure 2(c) shows the absorptance spectra as a
function of frequency and conductivity under normal incidence. It is obvious that as the
conductivity increases, the absorptance increases without changing the operating frequency
range. The corresponding absorptance increases from 30% to nearly 100% as conductivity
increases from 10 Ω −1cm−1 to 2000 Ω −1cm −1 . In the case of σ = 2000 Ω −1cm −1 , the
absorptance can reach 100%. The perfect absorptance is realized by the interference of the
fields between metal crosses and VO2 film. From the absorptance spectra, it is observed that
90% absorptance bandwidth reaches 0.33 THz with a central frequency of 0.55 THz under
normal incidence when σ = 2000 Ω −1cm −1 . The normalized 90% bandwidth with respect to
the central frequency is 60%. From the calculated results, we can see that the conductivity of
VO2 has a remarkable impact on the absorptance properties of the designed system, which
enables the creation of terahertz absorber with dynamically flexible behaviors. As shown in
Fig. 3, The reason leading to this phenomenon is mainly caused by the variations of
permittivity of VO2 , it experiences an optical transition from dielectric to metal when the
conductivity changes from 10 Ω −1cm −1 to 2000 Ω −1cm −1 . The larger the conductivity, the
better the metallic behavior, and the absorptance becomes more striking. Therefore, such a
MM absorber with the flexible ability can be used as a terahertz broadband attenuator or
modulator in absorption or transmission mode.
Fig. 2. Simulated reflectance (a), transmittance (b), and absorptance (c) spectra of the designed
system at a series of conductivity values of VO2 under normal incidence.
Vol. 26, No. 6 | 19 Mar 2018 | OPTICS EXPRESS 7152
Fig. 3. The calculated real part of permittivity of
VO2
at a series of conductivities.
Furthermore, the dependence of absorptance of the proposed absorber on the thickness
( t2 ) of VO2 is investigated. To briefly present this property, we only discuss the absorptance
analysis under normal incidence. Figure 4 illustrates the relation between absorptance and t2
with the conductivity of VO2 fixed as σ = 2000 Ω −1cm −1 . The calculated results tell that
absorptance of the designed system under normal incidence is closely depend on t2 when it is
smaller than 0.5 μ m . As t2 increases from 0.01 μ m to 0.5 μ m , absorptance gradually
enhances. When the thickness of VO2 is larger than 0.5 μ m , absorptance becomes stable
because VO2 is enough thick to prevent transmission.
Fig. 4. Thickness dependence of absorptance under normal incidence when σ = 2000 Ω −1cm −1 .
To easily and clearly understand the effect of perfect absorption when σ = 2000 Ω −1cm −1 ,
the effective electromagnetic parameters of MM absorber are retrieved [31]. The magnetic
component of incident wave couples to this system and thus generates antiparallel currents
between metal crosses and VO2 film, resulting in resonant μ response. By changing the
conductivity of VO2 , we can simultaneously tune ε and μ such that it is possible to
approximately match the impedance ( z = μ ε ) to free space, and then minimize the
reflectance at a specific frequency. From Fig. 5, it is found that at the frequency of the
resonant absorption peak, the permittivity and permeability is approximately equal which
means that the impedance of the designed system is almost matched to that of free space, so
the reflectance is negligible. Meanwhile, the large imaginary part of the refractive index
would generate high absorption.
Vol. 26, No. 6 | 19 Mar 2018 | OPTICS EXPRESS 7153
Fig. 5. Retrieved effective physical parameters (a) permittivity, (b) permeability, (c) refractive
index, and (d) impedance in the case of perfect absorption when σ = 2000 Ω −1cm −1 .
Figure 6 gives the absorptance evolution of the structure by tuning of polarization angle
from 0° to 90° in steps of 5° . With increasing polarization angle, the absorptance is
completely unchanged. The symmetry of the designed system leads to the polarizationinsensitive behavior, and this polarization-insensitive absorber would be helpful in numerous
applications. Angular independence is very important for an absorber since incident wave in
general case is randomly oblique. Figure 7 plots the spectral absorptance of the MM absorber
as a function of incident angle and frequency. As shown in Fig. 7, it is found that the designed
absorber shows excellent performances with the stable absorptance and working bandwidth
over a wide range of oblique incident angle for both transverse electric (TE) and transverse
magnetic (TM) polarizations. The absorptance is almost insensitive to incident angle
variations up to 60° for both TE and TM polarizations, which is beneficial to practical
application over a wide range of incident angle. With increasing angles of TE polarization,
beyond 60° there is a noticeable decrease in the absorptance as the incident magnetic field
can no longer efficiently drive circulating currents between metal crosses and VO2 film. For
TM polarization, the maximum absorptance remains great even for the angle of 75° . This is
because the direction of magnetic field of the incident wave is unchanged with various
incident angles and it can efficiently drive the circulating currents at all angles of incidence,
which is important to maintain impedance matching. The incident angle- and polarizationroust characteristics could have great potential applications in terahertz sensing, detecting,
and optoelectronic devices.
Vol. 26, No. 6 | 19 Mar 2018 | OPTICS EXPRESS 7154
Fig. 6. Simulated absorptance spectrum of perfect absorption phenomenon with tuning of
polarization angles when σ = 2000 Ω −1cm −1 under normal incidence.
Fig. 7. Incident angular dependence of perfect absorptance phenomenon for TE polarization (a)
and TM polarization (b) when σ = 2000 Ω −1cm −1 .
3. Conclusions
To summarize, we propose a broadband conductivity-tunable absorber by utilizing VO2 in the
terahertz range. A terahertz-tunable absorptance involving the large shift in resonant peak
absorptance has been observed from 30% to 100% at a wide band, and 60% normalized
bandwidth of 90% absorptance can be obtained. The absorption of the proposed MM absorber
is insensitive to the incident angle of both TE and TM polarizations. And the absorber design
in our work can be easily scalable to other terahertz and infrared regions. This work may
provide the potential of highly active and tunable MM devices in the terahertz regime. A wide
range of applications such as modulator, sensor, and active filter can be expected.
Funding
This work was supported by the National Natural Science Foundation of China (NSFC) under
Grant No. 11504305.