Dual controlled cross-shaped broadband terahertz absorber based on vanadium oxide—liquid crystal metamaterial

A low terahertz broadband tunable absorber was proposed, which composed of vanadium oxide (VO2) film and nematic liquid crystal layer. The simulation results show that the absorption is great than 90% in the frequency range of 0.458–1.1492 THz. The tuning absorber was realized by increasing the temperature to modulate the VO2 transited into metal state. Since the dielectric constant of the nematic liquid crystal can be adjusted by bias voltage, without changing the intensity of absorption, however, a shift in the bandwidth was observed. In addition, the designed structure is insensitive to incident light polarization and still remained high absorption at 60°. The tunable broadband metamaterial absorber can be used for attenuator and energy harvesting.


Introduction
Metamaterial absorbers have always attracted the tremendous attention owing to their significant roles in various practical applications such as sensing [1,2], solar energy harvesting [3], thermal emission [4] and stealth technology [5,6].Currently, the research on narrow-band and semiconductors [26,27], liquid crystals and vanadium dioxide (VO 2 ) [28][29][30][31].The methods of modulation can be listed as thermal control [32], photoexcitation [33] and external voltage [34].Among these materials, as a phase change material, the electrical conductivity can be increased by orders of magnitude [35].Nematic liquid crystals have agile dielectric constants and relatively low dielectric losses over a wide frequency range [36].
In this study, we proposed a broadband dual tunable metamaterial absorber in terahertz range.The different geometrical dimensions VO 2 films tiled on the top and middle parts were composed of nematic liquid crystal (LC) and dielectric layer.Based on the insulator-metal phase change of VO 2 and the orientation of the liquid crystal molecules can be controlled by an external bias voltage [37][38][39], the operation frequency was chosen from 0.4150 to 1.1492 THz and the shift resonant frequency could be observed.

Materials and methods
We proposed a low terahertz broadband metamaterial absorber, which schematic diagram is presented in Fig. 1.As shown in Fig. 1a, the absorber has five layers which composed top layer of VO 2 , dielectric layer of polyimide, LC layer, dielectric layer of polyimide and bottom layer of metal.The first layer of VO 2 is made up of four proportional cross-shapes, and in the insulator phase, the permittivity of VO 2 was ε = 9 [40]; each resonator is located in the center of the corresponding portion.In the original proportional starting from the first cross-shape on the left, the proportions are 0.9, 0.8 and 0.7 in clockwise direction.The middle layer is separated by polyimide between the liquid crystal and the metal substrate with the dielectric permittivity ε d = 3.1.The structure of metal base plate makes the transmission is 0. The nature of metal in terahertz (THz) range is described by the Drude model with the plasma frequency ω p = 1.37 × 1016 s −1 , Here, the frequency of the scattering γ = 4.08 × 10 13 s −1 [41].It is periodic in the x and y directions with the length of P x = P y = 350 μm, l 1 = 165 μm, d 1 = 55 μm.The side view of the structure in Fig. 1c shows the thickness of the structure, respectively h 1 = 0.08 μm, h 2 = 1.625 μm, h 3 = 50 μm, h 4 = 0.2 μm.We used the finite difference time domain (FDTD) method, where x, y is the unit cell boundary condition and in the z direction is open add space.According to the electromagnetic wave propagation theory on the medium interface, the amount of reflection and transmission depends on the electromagnetic wave impedance in free space and the intrinsic impedance equivalent degree of the medium.Considering the periodic structure of sub-wavelength, through the reflection and transmission of electromagnetic waves, absorption can be expressed by 2 |, respectively.S 11 (ω) is the reflection and S 21 (ω) is the transmission.Due to the zero transmission from the absorber, absorption ultimately equals to 1 − R(ω).On the other hand, LCs are another promising material for practical applications in the terahertz range as the permittivity can be controlled by an external bias voltage.In here, the up layer and the metal ground plane are used as two electrodes and liquid crystals 4'-n-pentyl-4-cyanobiphenyl (5CB) were filled into the middle gap [42,43].The LC material is composed of anisotropic molecules and initial alignment direction of 5CB without bias voltage should be parallel to the electrical field direction.Therefore, the effective refractive index of 5CB could be changed with the different angles of the LC arrangement.When the closer the orientation of LC is to the direction of the external electric field, the higher the refractive index of liquid crystal is.The magnitude of the extraordinary and ordinary refractive indices are given as follows: n e = 1.77 and n o = 1.58, in which the birefringence is equal to 0.20 ± 0.02 [31].

Results and discussion
In order to demonstrate the absorption characteristics of the proposed structure, the numerical simulation results are as follows: the transverse magnetic (TM) wave and the transverse electric (TE) wave have been studied and the simulation result is presented in Fig. 2. It is clear that they have the similar absorption in TE and TM mode.We can also see that about 97% absorption is achieved between 0.4150 THz and 1.1492 THz.Considering the periodic structure of sub-wavelength and then the electromagnetic wave incident from free space to the structure, its equivalent impedance Z can be expressed as [44]: With perfectly normalized impedance, the real part of Z is close to 1 and the imaginary part of the impedance is close to 0 in the range of 0.415-1.1492THz, thus resulting in minimal reflection and very high wideband absorption.
To further illustrate the absorption mechanism, the absolute of E-field distributions of electric and magnetic fields is studied at the resonant frequencies of 0.4150 THz and 1.1492 THz, shown in Fig. 3, in which absorption values are larger than 0.9.The electrical field distributions of the frequencies of 0.4150 THz and 1.1492 THz are demonstrated in Fig. 3a, b.It is described that VO 2 films display the different resonant frequencies, and exist coupling of different sizes in a plane, and multiple absorption bands overlap to expand the absorption band.And the magnetic field distributions are shown the similar results in Fig. 3c, d.
We also demonstrate the absorption of the broadband absorber that the corresponding simulation of a crossshaped unit structure is shown in Fig. 4. It can be seen that the absorption spectrum is more than 80% from 0.312 THz to 1.226 THz.By reducing the size of the top layer, from Fig. 4b, c, d, the bandwidth of the absorption is also reduced.
Owing to the properties of the VO 2 transition from insulating to metallic states at high temperature, the tunable absorption characteristics of a broadband absorber can be realized and we set the conductivity variable from 500 S/m to 1 × 10 5 S/m. Figure 5 shows the absorption spectrum of VO 2 with different electrical conductivity under normal incidence.The results indicate that with the electrical conductivity of cruciform patches 2 and 4 changes, the corresponding absorption spectrum changes accordingly.It can be seen from that the position of the bandwidth is almost constant and the intensity of the absorption spectrum changes significantly and the absorption is above 97% in the low THz frequency range.Specially, the absorption decreases gradually at 0.95 THz with the conductivity decreases.Meanwhile, VO 2 is in conductor state, and broadband tuning can also be achieved by adjusting the temperature.
We give the effective dielectric constant of aligned nematic LC and the arrangement angle of it [45].
When the orientation of the LC molecules is θ = 0°, the direction of the electric field is perpendicular to the LC molecules.As liquid crystals are anisotropic medium and the n 2 e sin 2 + n 2 o cos 2 electric field becomes higher, its molecule direction tends to be oriented in the z direction.Through calculating the direction of the LC under 0°, 30°, 45°, 60°, 90° corresponding to the n eff = 1.58, 1.62, 1.67, 1.72, 1.77.Figure 6 shows that the absorption spectrum of tunable bandwidth is achieved as bias voltage is applied to the LC cell.In Fig. 6, it was shown that broadband absorption as the LC molecule is orientated from 0° to 90°, which can be attributed to the high absorption and adjust within a relatively small range.To validate the effect of the thickness of the VO 2 on absorption, it is obvious from Fig. 7 that the absorption of the broadband absorber gradually decreases with the thickness of the VO 2 increases.The absorption reaches an optimum at h 1 = 0.08 μm.
We also provide additional performance validation of the proposed absorber under different polarization angles in TM mode.It can be seen from Fig. 8 that the absorption level is Fig. 4 The absorption spectra are obtained and the corresponding geometrical structure is shown as follows: the ratio of single cross-shapes is 1, 0.9, 0.8 and 0.7, respectively nearly unchanged with the increasing polarized angle, while the resonant frequency range is changed.Thus, we provide a characteristic of broadband absorber with flexible tunability, and it maintains about 95% absorption above from 0.6 THz to 1.1 THz over relatively wide angles.

Conclusions
In this paper, we proposed a broadband metamaterial absorber combining two active materials, vanadium oxide and nematic liquid crystal.The simulation results show that the resonant region of the broadband absorber over 90% in which the relative bandwidth reaches 57.6%.In the electric field distribution of the metamaterial absorber in the absorption wave of 0.418 THz and 1.1492 THz and the equivalent impedance of the structure response, a cross-shaped unit structure is given, and then, the simulation results show the analogous high bandwidth absorption.It is also verified that the absorber has the allied absorption for TM and TE waves, besides the absorbance is maintained at 80% when the incident angle increases to 60° in the TM mode.Additionally, the metamaterial absorber achieves tunability at lower terahertz frequencies which compared to previous metamaterial absorbers that can just achieve fixed bandwidth absorption.The vanadium oxide can be transited from an insulator to a metal at different operating temperatures, and the absorbance and bandwidth are relatively enhanced as the temperature increases.Based on the dielectric constant of nematic liquid crystal which is affected by the rotation of liquid crystal molecules, thus adjusting the bias voltage can achieve another tuning performance.Benefiting from these advantages, the properties of the device provided a way for energy harvesting, imaging and other fields.

Fig. 1
Fig. 1 (a) 3-D THz broadband tunable absorber, (b) Unit structure schematic of the absorber and (c) The side view of the structure

Fig. 2 Fig. 3
Fig. 2 (a)Absorption spectrum of terahertz broadband tunable absorber and (b) the matching impedance (Z) of the wideband absorber

Fig. 5 Fig. 6 Fig. 7 Fig. 8
Fig. 5 Resonant absorption of the broadband absorber in the lower terahertz region tuned by the conductivity of the VO 2 film