Introduction

In recent years, artificial absorbers that usually used in stealth field, detectors, and thermo-solar cells for their unique feature to absorb electromagnetic wave at a given frequency band such as microwave [1], terahertz [2, 3], infrared [4,5,6], and visible [7, 8] have attracted significant attention [9, 10]. The absorption characteristics of the conventional artificial absorbers are mainly dependent on the material loss and geometric structures resonance, which are generally unchanged [1,2,3,4,5,6,7,8]. Thus, these absorbers are negligibly influenced by external stimuli such as external fields, temperature, or pressure, offering no chance to tune its electromagnetic response. In order to achieve controllable absorbing characteristics, the active components, such as varactor diode and PIN diode have been reported to construct the tunable absorbers at the microwave region [11, 12]. By tuning the bias voltages applied to the loaded diodes, the absorber can dynamically change its absorbing characteristics. However, the similar method is not suitable for the higher frequency application, such as terahertz (THz) band and infrared band. To mitigate this issue, the phase change material vanadium dioxide (VO2), which can be transformed from insulator phase to metal phase at temperature above the insulator-to-metal transition (IMT) temperature (67 °C in bulk crystals) [13], has been recently reported as an active media to achieve tunable absorbers at these frequency bands [14, 15].

The permittivity of VO2 at room temperature is chosen to be 9 and the conductivity at this situation is about 200 S/m [14]. Furthermore, the conductivity can even reach at 1 × 105 S/m (about 500 times than 200 S/m) when the IMT is realized, usually induced by direct thermal control [16, 17] and photo-thermal effect [18, 19]. However, these control methods are much complex and inconvenient compared with electrically controlled technique. Liu et al. reported an electrically active absorber through Joule heating effect at infrared band [20]. In this article, a mesh-patterned Au layer is adopted to heat the VO2 thin films, leading to thermally induced IMT. The practicability is limited as the introduction of the mesh-patterned Au layer for the following two main reasons: firstly, the resonance response of the absorber mainly relies on the geometric structure of the Au layer, which limits its application in many fields. Furthermore, the sophisticated techniques, take lithography for instance, are required to fabricate the Au layer, severely increasing the cost of the absorber.

In this article, an electrically controlled resistive layer (ECRL) composed of VO2 and resistive film is proposed to achieve tunable material with predominance of large resistance tuning range and lithography-free feature. Numerical calculation and simulation results show the effective resistance of the active resistive layer can be tuned from 18 Ω/sq (at this situation, the ECRL can act as perfect electrical conductor) to 300 Ω/sq based on the electro-thermally induced insulator-to-metal transition of VO2. Besides, the ECRL can be achieved directly by the deposition of successive layers with corresponding materials without lithography. With such a large resistance tuning range and lithography-free feature, the ECRL can be flexibly applied in many fields. Here, a tunable bidirectional absorber with the absorption tuned from 98 to 18% around 1 THz and a non-planar tunable absorber with a broad band from 1.08 to 2.5 THz are designed based on the ECRL. The polarization-insensitive feature of the two absorbers is realized due to their symmetrical structures. The designed absorbers are also demonstrated to keep absorption efficiency as high as 80% under incident angle of 60°.

Results

An Electrically Controlled Resistive Layer Based on the IMT of VO2

The structure of the ECRL which consists of VO2 layer and resistive layer (a nichrome film with sheet resistance Rs = 300 Ω/sq) is shown in Fig. 1a. As the resistive layer is connected to external bias voltage, Joule heating is produced as a result of the current flow, leading to the electro-thermally induced IMT of VO2. Thus, the conductivity σVO2 of VO2 is changed, indicating that the effective sheet resistances of the VO2 layer (RVO2 = 1 ∕ (σVO2 × tVO2)) and the ECRL (Re) can be tuned as a function of the external bias voltage.

Fig. 1
figure 1

a Three-dimensional (3D) sketch and the transmission spectrum as a function of σVO2 for ECRL. b 3D sketch and the transmission spectrum as a function of the effective sheet resistance Re for ERM. tVO2 = 500 nm, tRs = 50 nm, and tRe = 550 nm

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Using the transmission line theory, the effective sheet resistance of the ECRL can be expressed by:

$$ {R}_{\mathrm{e}}=\frac{R_{\mathrm{VO}2}\times {R}_{\mathrm{S}}}{R_{\mathrm{VO}2}+{R}_{\mathrm{S}}} $$
(1)

The effective sheet resistance Re = 18 Ω/sq, 120 Ω/sq, and 300 Ω/sq can be obtained when the conductivity σVO2 values of VO2 are 1 × 105 S/m, 1 × 104 S/m, and 2 × 102 S/m, respectively. Thus, a large tunable range of Re is realized by changing the conductivity of VO2. To support this resistance effective theory, an effective resistance model (ERM) shown in Fig. 1b is investigated. The thickness and permittivity of the ERM are set as tRe = tVO2 + tRs and 9, respectively. The transmission spectrums of the ECRL and the ERM are respectively shown in Fig. 1a, b. It is seen that the transmission spectrums of the ERM in the case of Re = 300 Ω/sq, 120 Ω/sq, and 18 Ω/sq are almost identical to those of the ECRL as σVO2 values are 1 × 105 S/m, 1 × 104 S/m, and 2 × 102 S/m, respectively. That means the calculated effective resistance is perfectly matched to the proposed ECRL, and thus a large tuning rang of Re (from 18 to 300 Ω/sq) is demonstrated in our design. In addition, there is almost no transmission when the effective sheet resistance Re = 18 Ω/sq, and so the ECRL can act as a perfect electric conductor (PEC) layer at this situation. The maximal effective sheet resistance only depends on the chosen resistive film, that is to say, a larger tunable range of Re can be expected for a larger sheet resistance of the resistive film.

A Tunable Bidirectional Absorber

To better explain the potential application of the ECRL, a tunable bidirectional absorber composed of two ECRLs spaced by a 37.5-μm thick quartz is investigated, as shown in Fig. 2. The permittivity of quartz is chosen to be 3.8 supported by [21]. In our design, the two ECRLs displayed in Fig. 2a are the same as the ECRL discussed above. When the normal incident wave illuminates the proposed absorber as situation I, the conductivity of the bottom VO2 is tuned to be σVO2down = 1 × 105 S/m so that ECRL2 can act as a PEC layer. Then, the absorption of the absorber can be enhanced from 18 to 98% at 1 THz with the conductivity σVO2up deducing from 1 × 105 to 200 S/m, as seen in Fig. 2b. For the situation II, the ECRL1 is set as a PEC layer by switching the conductivity of top VO2 to 1 × 105 S/m, and thus, the identical absorption spectrum is obtained when the conductivity of the bottom VO2 (σVO2down) is tuned. Figure 2c shows the power loss density distributions of our absorber at 1 THz when the conductivity σVO2up is respectively set as 200 S/m, 5 × 103 S/m, and 1 × 105 S/m. It is seen that the strong power loss density is localized around the ECRL1 when the conductivity of σVO2up is 200 S/m, which means that almost all the incident wave energy is dissipated on the ECRL1. As the σVO2up is increased to 1 × 105 S/m, the ECRL1 would behave as a PEC layer, reflecting most of the incident wave. Therefore, the power loss density is very weak in our absorber at this case.

Fig. 2
figure 2

a 3D sketch of the tunable bidirectional absorber. b The absorption spectrum of the proposed absorber as a function of σVO2up under situation I when σVO2down = 1 × 105 S/m and situation II when σVO2up = 1 × 105 S/m. c The power loss density distributions under situation I of the absorber at 1 THz when the conductivity σVO2up is 200 S/m, 5 × 103 S/m, and 1 × 105 S/m. d = 37.5 μm

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The wide-angle absorbing properties of the designed tunable bidirectional absorber are also investigated under oblique incidence at situation I when σVO2up = 200 S/m. In the case of TE mode, as shown in Fig. 3a, an obvious absorption band can be observed around 1 THz. High-absorption efficiency about 80% is still kept over the incident angle of 60°. The similar wide-angle absorbing performance of the proposed absorber in TM mode can be also observed in Fig. 3c, and its absorption efficiency is still kept above 80% even at a large oblique incident angle of 80°. In our design, the use of dielectric spacer can decrease the angle sensitivity of the absorber, because the refracted angle in the high-index material will be reduced according to Snell’s law [22, 23]. Therefore, the wide-angle absorbing property is achieved.

Fig. 3
figure 3

Absorption spectrum of the proposed tunable bidirectional absorber as a function of frequency and the incident angle under different polarizations. a TE mode and b TM mode

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The ECRLs can be regarded as infinitesimally thin resistive sheet for its thickness of 0.55 μm is only about λ/500 at the frequency of 1 THz. Therefore, the theory of impedance matching is suitable here to explain the absorption mechanism (the situation I when σVO2up = 200 S/m and σVO2down = 1 × 105 S/m) of the tunable bidirectional absorber. The reflectivity efficiency (R1 = 1 – A − T, see Fig. 2b) of the proposed absorber under normal incidence is about zero when σVO2up = 200 S/m and σVO2down = 1 × 105 S/m; thus, the boundary conditions for the sheet can be obtained (1 and 2 denote the left side and the right side of the ECRL1, as seen in Fig. 4a) [24, 25]:

Fig. 4
figure 4

A schematic to explain the absorption mechanism at 1 THz. a The sketch map of the electromagnetic wave transmission. b The absorption spectrum as a function of the quartz thickness d

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$$ {\displaystyle \begin{array}{c}{E}^1={E}^2:{I}_1{e}^{-{ik}_1d}+{R}_1{e}^{ik_1d}={I}_2{e}^{-{ik}_2d}+{R}_2{e}^{ik_2d}\\ {}{H}^1={H}^2+J:\kern1em {Y}_1\left({I}_1{e}^{-{ik}_1d}-{R}_1{e}^{ik_1d}\right)={Y}_2\left({I}_2{e}^{-{ik}_2d}-{R}_2{e}^{ik_2d}\right)\kern0.75em +J\\ {}J={GE}^{L(R)}=G\left({I}_2{e}^{-{ik}_2d}+{R}_2{e}^{ik_2d}\right)\end{array}} $$
(2)

where I and R represent the amplitudes of incident and reflective electromagnetic wave. Y1 = 1 and k1 = 2π/λ are the admittance and the wavenumber of the free space while \( {Y}_2={Y}_1\sqrt{\varepsilon_r} \) and \( {k}_2={k}_1\sqrt{\varepsilon_r} \) are the admittance and the wavenumber of the dielectric spacer. G is conductance of the ECRL1. Therefore, the reflectivity of the absorber can be expressed as:

$$ {R}_1=\frac{e^{-{ik}_1d}}{2{Y}_1}\left[{I}_2\left({Y}_1-{Y}_2-G\right){e}^{-{ik}_2d}+{R}_2\left({Y}_1+{Y}_2-G\right){e}^{ik_2d}\right] $$
(3)

In this situation, the reflectivity R2 = I2 for the ECRL2 is regarded as a PEC layer. The normalized admittance G is nearly equal to Y1 for the effective resistance of the ECRL1 (300 Ω/sq) which is matched with free space impedance. Then, the reflectivity R1 can be further written as:

$$ {R}_1={R}_2{Y}_2{e}^{-{ik}_1d}\frac{e^{ik_1\sqrt{\varepsilon_r}d}-{e}^{-{ik}_1\sqrt{\varepsilon_r}d}}{2}={R}_2{Y}_2{e}^{-{ik}_1d}\cos \left(\frac{2\pi \sqrt{\varepsilon_r}d}{\lambda}\right) $$
(4)

The consequence of \( \cos \left(\frac{2\pi \sqrt{\varepsilon_rd}}{\lambda}\right)=0 \) can be obtained as R1 = 0, which indicates that

$$ \sqrt{\varepsilon_r}d=\lambda /4+\left( n\lambda \right)/2,n=0,1,2,\dots $$
(5)

In our design, the calculated thickness of the absorber is 38.73 μm (n = 0) at 1 THz, which is in a good agreement with the numerical result of d = 37.5 μm. To further support this conclusion, the absorption spectrum as a function of the quartz thickness d is investigated as shown in Fig. 4b. There is obvious red shift of the resonance wavelength with the increase of quartz thickness d, which is perfectly matched to the formula above.

A Tunable Broadband Absorber

The ECRL discussed above can also be used to realize non-planar tunable broadband absorber as shown in Fig. 5. The structure of the absorber indicated in Fig. 5a, b is composed of an ECRL and a gold hemisphere particle spaced by a layer of 16-μm thick quartz and backed by a 200-nm thick gold reflecting layer. In this situation, the sheet resistance of the resistive film in the ECRL is optimized as Re = 200 Ω/sq, and the radius of the gold hemisphere particle is 45 μm. The conductivity of gold is set as 4.561 × 107 S/m [14]. Our structure can be realized by the deposition of successive layers with corresponding materials on the nanopatterned Al substrate [26]. The order of the deposited materials is VO2, nichrome, quartz, and gold. Then, the proposed absorber can be achieved by polishing the deposited gold and corroding the nanopatterned Al substrate. As the structure of the target absorber is symmetrical, the absorption spectrums of the absorber under TE mode and TM mode are the same at normal incidence as illustrated in Fig. 5c. Two obvious absorption peaks can be observed at 1.19 THz and 2.43 THz when the VO2 is at insulator phase (σVO2 = 200 S/m). The corresponding absorption efficiencies reach as high as 99.0 and 99.91% at the above two absorption peaks, respectively. Besides, the absorption efficiency is realized above 90% in a broad band ranging from 1.08 to 2.5 THz, and it can be dynamically controlled by further increasing the conductivity (σVO2).

Fig. 5
figure 5

a 3D view and b cross-section view of the designed tunable broadband absorber. c Absorption spectrum of the target absorber as a function of VO2 conductivity (σVO2) under TE mode and TM mode. p = 120 μm, Rg = 45 μm, Rq = 61 μm, Rs = 61.05 μm, Rv = 61.55 μm

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When the VO2 is at insulator phase, the absorption properties of the designed tunable broadband absorber under oblique incidence are also discussed. As Fig. 6a shows, there is an obvious absorption band from 1.08 to 2.5 THz under TE mode, and the high absorption (70–80%) is still kept at large incidence angle of 60°. For the TM mode, the wide-angle absorbing property is much better, and the absorption efficiency of our absorber is above 90% from 1.05 to 2.5 THz at the oblique incidence of 60°, as seen in Fig. 6b. The angle-insensitive property of the sphere shape in our absorber makes contribution to its wide-angle absorbing capability.

Fig. 6
figure 6

Absorption spectrum of the designed tunable broadband absorber as a function of frequency and the incident angle under a TE mode and b TM mode

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To understand the absorption mechanism at 1.19 THz, the magnetic field and electrical field distributions are studied, as shown in Fig. 7a, b, respectively. The magnetic field is mostly distributed between the neighboring gold hemisphere particles, while the electrical field is enhanced at the area between the units. This phenomenon is caused by the surface plasmon polaritons (SPP) excited at the interface between the gold and dielectric layers due to the additional wave vector originated from the periodic 2D gold hemisphere arrays [27]. Therefore, the incident wave is strongly localized around the resonator, resulting in the perfect absorption peak at 1.19 THz.

Fig. 7
figure 7

Sketch map investigating the absorption at 1.19 THz by the distributions of a magnetic field and b electric field. Side view of c magnetic field distribution and d electrical field distribution at 2.43 THz

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At the other absorption peak, part of the magnetic field energy is localized in the area between the neighboring gold hemisphere particles, as seen in Fig. 7c, which is much analogous to the magnetic field distribution at 1.19 THz, indicating that the SPP also makes contribution to the perfect absorption here. In addition, there is another strong magnetic field localized between the ECRL and the golden hemisphere, resulting in the enhanced electric field around the magnetic distribution as shown in Fig. 7d, which indicates the presence of magnetic resonance (MR) [28]. Thus, due to the combination of the SPP and MR, the incident wave energy is finally dissipated on our absorber.

Conclusion

In conclusion, we have proposed and demonstrated a novel electrically controlled resistive layer (ECRL) based on the electro-thermal induced insulator-to-metal transition of VO2. Thanks to the predominance of large resistance tuning range and lithography-free feature, the ECRL has been utilized to realize a tunable bidirectional absorber and a non-planar tunable broadband absorber here. The polarization-insensitive feature and the wide-angle absorbing property of the above two absorbers support that the ECRL has a wide range applications and profound implications in many fields.