Two bits dual-band switchable terahertz absorber enabled by composite graphene and vanadium dioxide metamaterials

Abstract

This article presents the design of a 2-bit dual-band switchable terahertz absorber using a stacked combination of graphene and vanadium dioxide (VO₂) metamaterials. For the first time, the proposed absorber design offers four switchable states by controlling the conductivity of graphene and VO₂ metamaterial layers. The lower absorption band is produced by the graphene metamaterial, whereas the upper band is implemented by the VO₂ metamaterial pattern. The structure shows two absorption bands (State 11) at 0.745–0.775 THz and 2.3–5.63 THz, when the Fermi graphene level of graphene is 0.2 eV and the VO₂ is in the metallic phase. The lower absorption band is turned off, while keeping the upper band (State 01), when the graphene Fermi level is 0 eV and the VO₂ layer is in the metallic phase. The upper absorption band is turned off, while preserving the lower absorption band (State 10) by switching the VO₂ into the insulator phase and keeping the graphene Fermi level at 0.2 eV. Finally, both of the absorption bands are turned off by setting the graphene Fermi level to 0 eV and switching the VO₂ into the insulating phase. Equivalent circuit modelling analysis and full-wave electromagnetic simulations are used to explain the operation principle of the proposed absorber. Very good agreement is obtained between the theoretical analysis and the simulations confirming the presented design principle for the 2-bit switchable absorber.

Introduction

Absorbers are fundamental components in various telecommunication, sensing, and imaging systems operating in a broad range of spectrum from microwave up to terahertz and optical frequencies^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}. Metamaterials-inspired structures are attractive choices in many of such applications due to their thin profiles, near perfect absorption, and flexibility in designing both narrow and wideband absorption characteristics^{1,2,3,4,5,6,7}. Metamaterial absorbers are conventionally implemented in three-layer configurations made of metamaterial patterned layer, a dielectric spacer and a bottom metallic layer that acts as a perfect reflector. Such a configuration has been applied in the design of absorbers with narrowband^5,6,7, broadband^1,2,3,4, and multi-band^6,7 absorption characteristics. However, designing absorbers with tunable/reconfigurable responses still remain challenging at terahertz frequencies mainly due to the limited devices and materials that can be applied with switchable and/or tunable electromagnetic properties terahertz frequencies. Recently, tunable metamaterials using graphene^16,17,18,19, vanadium dioxide (VO₂)^20,21,22, doped silicon²³, germanium antimony telluride (GST)^24,25,26, and liquid crystals^27,28 were introduced to realize reconfigurable absorbers. However, in such structures just a single characteristic of the response such as center frequency, bandwidth, or absorption level can be tuned without any multi-functional or reconfigurable capability. Graphene is a unique thin two-dimensional (2D) material composed of carbon atoms, which exhibits exceptional electrical and optical properties such as tight field confinement, high electron mobility, and flexible tunability^29,30. The conductivity of graphene can be dynamically tuned by adjusting the Fermi energy level through chemical doping or electrostatic gating^31,32,33,34. Hence, graphene-based metamaterials are ideal candidates for tunable and switchable electromagnetic devices. On the other hand, VO₂ is a phase change material that is highly attractive for realizing switchable and tunable devices. VO₂ undergoes a reversible transition behavior from the insulator to the metallic phase on a sub-picosecond timescale triggered by electrical, thermal, or optical excitations. VO₂ shows an insulating behavior in the monoclinic phase below the transition temperature (around 340 K) and a metallic behavior at the tetragonal rutile phase above it^{35,36,37,38,39,40,41,42,43,44,45}. Thus, combination of the VO₂ and graphene properties in a single design would potentially be an appropriate approach for realizing multi-functional switchable and reconfigurable absorbers.

Recently, tunable and switchable terahertz absorbers were developed based on hybrid metamaterials of graphene and phase change materials^46,47,48,49. In Ref.⁴⁶, a switchable metamaterial absorber was designed using VO₂ and graphene. The functionality of this absorber can be switched from a broadband to a narrowband absorber by the phase transition of VO₂ from insulator to metal. A dynamically switchable dual-broadband absorber based on a hybrid metamaterial with vanadium dioxide and graphene was designed at terahertz regime in Ref.⁴⁷. When the vanadium dioxide is in the metallic phase and the Fermi energy level of graphene is set to zero, a high-frequency broadband absorption from 2.05 THz to 4.30 THz was achieved. This structure acts as a low-frequency broadband absorber from 1.10 THz to 2.30 THz if the vanadium dioxide is in the insulating phase. In addition, minimum absorption is observed by tuning the Fermi energy level. In Ref.⁴⁸, a switchable graphene-vanadium oxide metamaterial-based narrowband absorber is designed. When the VO₂ is in an insulating phase, the absorption spectrum shows a single narrowband absorption peak with near 100% absorption. When the VO₂ is in a metallic phase, the absorber shows two narrowband absorption peaks with around 90% absorptivity. Furthermore, a wide absorption band can also be achieved by tuning the Fermi energy level.

In all of the previous works, the operational states are limited to three, whereas by having two switchable materials (i.e. graphene and VO₂), potentially four operational states are achievable by switching the VO₂ and graphene patterns independently. Here, using the electrical tunable properties of graphene and the phase change behavior of VO₂, a 2-bit (four state) switchable THz dual-band (narrowband-wideband) absorber with polarization insensitive^{46,47,48,49,50,51,52} and high angular response stability is designed. The structure includes two layers of graphene patterned square and VO₂-patterned elements of cross strips. The resonant behavior of the graphene layers is used to realize a low-frequency narrow absorption band, while the resonant properties of VO₂ layer in the metallic phase is used to obtain a broadband absorption at the higher frequency range. Thus, the structure shows dual narrow-wide absorption bands, when the Fermi level energy of graphene is set to 0.2 eV and VO₂ is in the metallic phase (state 11). When the Fermi energy level of graphene is 0.2 eV and VO₂ is switched to the insulator phase, the absorber shows a single narrow absorption band at low frequencies (state 10). By changing the Fermi energy level to 0 eV, the lower frequency absorption band is omitted, and the absorber shows a single high frequency absorption band in metallic phase of VO₂ (state 01). In the fourth state, when the Fermi energy level of graphene is 0 eV and VO₂ is switched to the insulator phase, there is no absorption band (state 00). The design concept can also be extended to a dual wideband switchable absorber by tuning the relaxation time of graphene and change in thickness of dielectric spacer embedded at the bottom of the graphene layer. A similar switching scenario can be employed for the wideband/wideband prototype as well.

The rest of the paper is organized as follows: Section "Structural design" describes the configuration of the proposed absorber and an equivalent circuit model. The absorption performance of the designed absorber is investigated in Section "Results and discussion (dual narrowband-broadband absorber)" together with its four-state switchable behavior. In Section "Dual broadband switchable absorber", a dual wideband/wideband absorber is proposed as an extension of the presented design. Finally, Section "Conclusion" presents the main conclusions.

Structural design

A uint cell of the proposed absorber including the two layers of resonators patterns seperated by a dielectric spacer is shown in Fig. 1. From top to the bottom, the absorber composes of a graphene layer of thickness h_g, a dielectric spacer of thickness h₂, four VO₂ cross strips with a thickness of h_VO2, a dielectric spacer with a thickness of h₁, and the bottom metallic film of thickness t_m. The graphene layer is designed as an array of square patchs of width w_g, and the VO₂ layer includes an array of VO₂-patterned elements of cross strips, where the length and width of the VO₂ strips are l and w, respectively. The dielectric spacer is Polyethylene Cyclic Olefin Copolymer (COC) with a relative permittivity of ε_r = 2.3 and tanδ = 0.0006. The periodicity in both x and y directions is P. The bottom metal layer is gold. The thickness of the bottom metallic layer is larger than the skin depth. Thus, it acts as a perfect reflector and a perfect electric conductor (PEC) approximation is valid. Figure 1a also shows directions of the E and H-fields in incident electromagnetic wave for the TE mode. The E and H-fields in the TE mode are in y and x-directions, respectively. Because of the structural symmetry, the design works for the TM mode as well, where in the TM mode the E and H-fields directions are in the x and y-directions, respectively. In the absorber design, the VO₂ is placed at the bottom since the lower absorption band is produced by the graphene metamaterial layer. The graphene layer requires a thicker dielectric spacer since it produces absorption at the lower frequency band. At these frequencies, the VO₂ layer is almost transparent to the incident electromagnetic fields and thus the combination of graphene layer and the thick dielectric spacer formed by a combination of h₁ and h₂ dielectric spacers result in the lower absorption band.

Figure 1

(a) Cross-sectional view of a unit cell including: a top layer of a graphene patch, first layer of the dielectric spacer, a layer of four VO₂ cross strips, second layer of the dielectric spacer, and a bottom metallic layer. Directions of the E and H-fields are presented for the TE mode of the incident wave. Top views of (b) the graphene patch and (c) the VO₂ cross strips.

Within the THz range, the relative permittivity of VO₂ can be expressed using the Drude model³⁵:

$$ \varepsilon_{{VO_{2} }} (\omega ) = \varepsilon_{\infty } - \frac{{\omega_{p}^{2} (\sigma_{{VO_{2} }} )}}{{(\omega^{2} + i\gamma \omega )}} $$

(1)

where $\varepsilon_{\infty } = 12$ is the permittivity at very high frequencies,$\omega_{p}^{2} (\sigma_{{VO_{2} }} ) = \left( {{{\sigma_{{VO_{2} }} } \mathord{\left/ {\vphantom {{\sigma_{{VO_{2} }} } {\sigma_{0} }}} \right. \kern-0pt} {\sigma_{0} }}} \right)\omega_{p}^{2} (\sigma_{0} )$ is the plasma frequency with $\omega_{p} (\sigma_{0} ) = 1.4 \times 10^{15} Rad/s$, $\gamma = 5.75 \times 10^{13} \,\,Rad/s$ is the damping rate, and $\sigma_{0} = 3 \times 10^{5} \,S/m$. VO₂ is a temperature sensitive material that transits from an insulator to metal at a critical temperature around 340 K. The variations of the VO₂ conductivity as a function of the temperature at both of the temperature rising and falling cycles are extracted from Ref.⁵¹ and plotted in Fig. 2. As observed, the temperature change drastically affects the conductivity of VO₂, especially at the phase transition point. Due to the thermal hysteresis effect, the transition curves are slightly different in the rising and falling cycles, however, it does not affect the transition between two stable phases. By using the plot in Fig. 2 and Eq. (1), one can plot the relative permittivity of VO₂ at different temperatures. Figure 3 shows the relative permittivity as function of frequency for the insulator phase ($\sigma_{{VO_{2} }} = 200\,S/m$) and the metallic phase ($\sigma_{{VO_{2} }} = 200000\,S/m$). The conductivity of VO₂ ($\sigma_{{VO_{2} }}$) can be tuned by applying thermal or electrical stimuli^{39,40,41,42,43}.

Figure 2

The conductivity of VO₂ as function of temperature extracted from data presented in Ref.⁵¹.

Figure 3

The complex permittivity of VO₂ as function of frequency for two stable phases as dielectric phase (σ_VO2 = 200 S/m) and metallic phase (σ_VO2 = 200,000 S/m). (a) Real part of the permittivity and (b) the imaginary part of the permittivity.

The surface conductivity of graphene is described by the Kubo equation⁵²:

$$ \begin{aligned} \sigma _{g} (\omega )\, & = \,\sigma _{{\text{int} er}} + \sigma _{{\text{int} ra}} \, = \\ & \frac{{2e^{2} k_{B} T}}{{\pi \,\hbar ^{2} }}\frac{j}{{ - \omega + j\tau ^{{ - 1}} }}\ln \left[ {2\cosh \left( {E_{f} /2k_{B} T} \right)} \right] \\ & - \frac{{je^{2} }}{{4\pi \,\hbar }}\ln \left[ {\frac{{2E_{f} - \hbar (\omega - j\tau ^{{ - 1}} )}}{{2E_{f} + \hbar (\omega - j\tau ^{{ - 1}} )}}} \right]\, \\ \end{aligned} $$

(2)

where e is the electron charge, E_f denotes the Fermi level, ħ refers to the reduced Plank constant, $k_{B}$ represents the Boltzmann constant, $\omega = 2\pi \,f$ is the angular frequency, T = 300 K is the temperature, and $\tau$ is the relaxation time. The surface conductivity of graphene contains intra-band conductivity (first term in (1)) and inter-band conductivity (the second term in (1)). At low frequencies, the inter-band term of conductivity is dominant and for $E_{f} > > K_{B} T$, $\sigma_{g}$ is driven as the Drude form:

$$ \sigma_{g} (\omega ) = \frac{{e^{2} E_{f} \tau }}{{\pi \,\hbar^{2} }}\frac{1}{1 + j\omega \tau }. $$

(3)

In simulations, graphene is modeled by a layer of thickness h_g = 1 nm, whose permittivity is $\varepsilon_{g} = \varepsilon_{0} - j\left( {\sigma_{g} (\omega )/h_{g} \omega } \right)$. The conductivity of graphene can be dynamically tuned by adjusting the Fermi energy level. We consider two Fermi energy levels for switching the graphene layer. For each Fermi energy level, the corresponding permittivity is extracted and then, the values are imported into the High-Frequency Structure Simulator (HFSS) software. In addition, the VO₂ layer is modelled as a layer of thickness h_vo2 whose relative permittivity is defined in (1). The permittivity of the VO₂ can be controlled through the thermal excitation. When temperature is 300 K, the VO₂ layer is in the dielectric phase and the conductivity is around 200 S/m and when temperature is 350 K, the VO₂ layer is in the metallic phase with a conductivity around 200,000 S/m. For these two phases with different conductivities, the relative permittivity is obtained from (1) and the values are imported into the simulation software. For simulation, a unit cell of the absorber is considered with the periodic boundary conditions (PBC) along x- and y-directions and the Floquet port in z-direction.

The absorption is expressed as $A(\omega ) = 1 - R(\omega ) - T(\omega )$ where $R\left(\upomega \right)={\left|{S}_{11}\right|}^{2}$ and $T\left(\omega \right)={\left|{S}_{21}\right|}^{2}$ describe the reflectance and transmittance respectively, and S denotes the scattering parameter. The bottom metallic film is considered sufficiently thick (larger than the skin depth) with near zero transmittance. Thus, in order to achieve maximum absorption, the reflectance must be minimum. To reach this goal, it is necessary to match the input impedance of the proposed structure with the free space characteristic impedance.

The designed metasurface can be fabricated using the micro/nano fabrication technology. The fabrication process can be described as the following. In the first step, the ground plane is realized by gold coating (with 200 nm thickness) of a silicon wafer using an electron beam evaporator. Then the COC dielectric spacer will be spin coated on the gold layer. In the third step, we deposit the VOx film on the COC polymer layer through DC magnetron sputtering technique^53,54. Then annealing in low O2 pressure will be used to convert the VOx into VO₂. Next, the VO₂ resonator array will be realized by a photolithography process followed by chemical etching. Again the layers of COC and polysilicon should be spin coated on VO₂ layer. The polysilicon layers can be deposited using Low Pressure Chemical Vapor Deposition (LPCVD) process. The graphene layer can be prepared using chemical vapour deposition techniques and it will be transferred to the surface of polysilicon layer by the wet transfer technology^55,56,57. In experiments, a hot plate heater placed on the back side of the ground plane can be used to heat up the VO₂ and a laser thermometer can be used to precisely monitor the temperature. However, this results in a bulky structure. Alternatively, Platinum (Pt) resistive heater can be deposited under the VO₂ patterns in the microfabrication process. The VO₂ temperature can be precisely controlled by applying bias voltage to the resistive heaters⁵⁸.

Equivalent circuit model

An equivalent circuit model is developed and analyzed for the designed absorber in this section as plotted in Fig. 4.

Figure 4

The circuit model equivalent to the proposed absorber.

In the circuit model, the VO₂ layer including the array of cross strips is modelled as a surface admittance. For the metallic phase of the VO₂ layer, the surface admittance can be modelled as the lumped elements in the form of a series R₁-L₁-C₁. In this model, the gap between two adjacent strips is modeled as a capacitor, whereas the vertical strips for TE polarization and horizontal strips for TM polarization are modelled as inductor. The resistance is associated with the finite conductivity of the VO₂ layer in the metallic phase. The values of the lumped elements corresponding to the surface admittance of VO₂ cross strips are C₁ = 0.19 fF, L₁ = 9.13 pH, R₁ = 226 Ω. Therefore, the surface admittance corresponding to VO₂ layer can be computed as

$$ Y_{{VO_{2} }} = \left( {R_{1} + jL_{1} \omega + \frac{1}{{jC_{1} \omega }}} \right)^{ - 1} . $$

(4)

For insulator phase of VO₂, the surface admittance equivalent to VO₂ patterned layer ($Y_{{VO_{2} }}$) defined in Eq. (4) would be zero. Therefore, the R₁-L₁-C₁ branch will be deleted in the circuit model for insulator phase of VO₂. For more accuracy, the VO₂ layer can be modelled as a transmission line equivalent a dielectric medium with relative permittivity obtained from Eq. (1) in insulator phase. However, since the thickness of VO₂ layer is very thin, this equivalent transmission line don’t have the considerable effects on the obtained results.

The graphene layer made of square patches array is modelled as an equivalent admittance surface admittance² defined as:

$$ Y_{g} = \left( {\sigma_{g}^{ - 1} (\omega ) + \frac{{q_{11} }}{{j\omega \varepsilon_{eff} }}} \right)^{ - 1} \left( {\frac{{S^{2} }}{{P^{2} K}}} \right), $$

(5)

in which

$$ K = 1.1634\,w_{g}^{2} ,\,\,S = 1.015\,w_{g}^{2} ,\,\,q = 0.2\,\pi /w_{g} ,\,\,\varepsilon_{eff} = \varepsilon_{0} (1 + \varepsilon_{r} )/2. $$

(6)

According to (3) that can be used for each non-zero Fermi energy level, Eq. (5) can be modelled as the lumped elements in the form of a series R₂-L₂-C₂². The lumped element values corresponding to the surface admittance of graphene patches are

$$ R_{2} = \frac{{P^{2} K}}{{S^{2} }}\frac{{\pi \hbar^{2} }}{{e^{2} E_{f} \tau }},\,L_{2} = \tau R_{2} ,\,C_{2} = \frac{{S^{2} }}{{P^{2} K}}\frac{{\varepsilon_{eff} }}{q}. $$

(7)

It is known that an array of metallic patches shows capacitive behavior⁵⁹. When we use graphene for realization of the patches, it contributes an additional resistive-inductive surface admittance because of the real and imaginary parts of graphene surface conductivity. The relations of (5) and (7) show that the surface admittance equivalent to graphene patterned layer are corresponding to the parameters of graphene (the Fermi energy level and the relaxation time). In the following, we will consider two cases according to the Fermi energy level as E_f = 0.2 eV and E_f = 0 eV for graphene layer. For case of E_f = 0.2 eV, the lumped elements corresponding to graphene layer can be computed using (4). While for case of E_f = 0 eV, since we can’t use Eq. (3) for computation of the conductivity of the graphene, so the equivalent surface admittance should be computed by (5) where the conductivity is computed by (2).

As shown in the equivalent circuit model of Fig. 4, the dielectric spacers are modeled as transmission line stubs, where $\beta_{d} = k_{0} \sqrt {\varepsilon_{r} }$ and $Y_{d} = \sqrt {\varepsilon_{r} } /\eta_{0}$ are the propagation constant and the characteristic admittance of the transmission lines corresponding to the dielectric spacers respectively, where ${\eta }_{0}=120\pi$ is the free-space impedance and ${k}_{0}=\omega /c$ (c is the speed of light in vacuum) is the free space wave number. The metallic back reflector is considered as a short circuit. The input admittance of the proposed structure is obtained as:

$$ \begin{aligned} Y_{{in}} \, & = Y_{g} + \left( {Y_{d} \frac{{Y_{1} + jY_{d} \tan (\beta _{d} h_{2} )}}{{Y_{d} + jY_{1} \tan (\beta _{d} h_{2} )}}} \right), \\ Y_{1} \, & = Y_{{VO_{2} }} - jY_{d} \cot (\beta _{d} h_{1} ), \\ \end{aligned} $$

(8)

where

$$ \begin{gathered} Y_{g} = \left( {R_{2} + jL_{2} \omega + \frac{1}{{jC_{2} \omega }}} \right)^{ - 1} , \hfill \\ Y_{{VO_{2} }} = \left( {R_{1} + jL_{1} \omega + \frac{1}{{jC_{1} \omega }}} \right)^{ - 1} . \hfill \\ \end{gathered} $$

(9)

Finally, the absorption values can be calculated as:

$$ A(\omega ) = 1 - R(\omega ) = 1 - \left| {\frac{{\left( {{{Z_{in} } \mathord{\left/ {\vphantom {{Z_{in} } {Z_{0} }}} \right. \kern-0pt} {Z_{0} }}} \right) - 1}}{{\left( {{{Z_{in} } \mathord{\left/ {\vphantom {{Z_{in} } {Z_{0} }}} \right. \kern-0pt} {Z_{0} }}} \right) + 1}}} \right|^{2} $$

(10)

where $Z_{in} = Y_{in}^{ - 1}$ and $Z_{0}$ is the free-space impedance. When the real part of the normalized impedance ($Z_{in} /Z_{0}$) is approximately 1, and the imaginary part approaches near zero, the impedance matching condition occurs resulting in the maximum absorption. Comparisons between the results obtained from the circuit model and full-wave EM simulations of the absorber in HFSS are investigated in the next section.

Results and discussion (dual narrowband-broadband absorber)

This section presents the simulation results of the switchable absorber. The multifunctinality of the proposed structure is due to the switching behavior of the VO₂ layer from a metal phase to an insulator through the temperature transition and the electrical tunable property of the graphene surface conductivity. The geometrical parameters of the proposed structure are presented in Table 1. These parameters are designed to realize a dual-band absorber. The unit cell and the dielectric spacer dimensions are designed and optimized based on the impedance matching condition through the full-wave electromagnetic simulations in the Ansys HFSS. The process is started by designing each metamaterial layer separately and then putting them together. First, dimensions of the graphene patch unit cell and the dielectric spacer of h₁ + h₂ thickness is optimized to obtain a narrowband impedance matching at 0.76 THz resulting in a narrow absorption band. In the second step, dimensions of the cross-shaped VO₂ unit cell and h₁ are optimized through a separate full-wave simulation to achieve a wideband impedance matching and absorption within 2.3–5.63 THz. By optimizing h₁ dimension in this step, the h₂ value is automatically obtained by knowing h₁ + h₂ from the previous step. In the last step, the final dual-band absorber is designed by putting the two layers together and performing small dimensional optimizations to fix the absorption bands (narrow absorption at 0.76 THz and wide absorption band within 2.3–5.63 THz.

Table 1 The geometrical dimensions of the proposed absorber in Fig. 1 to realize a 2-bits switchable absorber.

Figure 5a presents the absorption response of the structure with parameters presented in Table 1, when the graphene Fermi energy level is E_f = 0.2 eV and the VO₂ material is in the metallic phase ($\sigma_{{VO_{2} }} = 200000\,\,S/m$). The relaxation time of graphene is considered as $\tau = 2.5\,ps$. We consider this state as 11.

Figure 5

The absorption spectra of the narrowband-broadband absorber prototype, when the Fermi energy level of graphene and the phase of VO₂ material considered as (a) State 11: E_f = 0.2 eV and metallic phase of VO₂, (b) State 10: E_f = 0.2 eV and insulator phase of VO₂, (c) State 01: E_f = 0 eV and metallic phase of VO₂, and (d) State 00: E_f = 0 eV and insulator phase of VO₂.

As seen, the response shows two absorption bands with the fractional bandwidths (FBW) of 4 and 84% for the low frequency (0.745–0.775 THz) and high frequency (2.3–5.63 THz) bands, respectively. FBW is defined as $FBW = 2\left( {f_{h} - f_{l} } \right)/\left( {f_{h} + f_{l} } \right)$ (where $f_{h}$ and $f_{l}$ are the high and low frequencies with 90% absorption). If we consider, the absorption band above 90% as an “ON” state and the absorptivity below 20% as “OFF” state. This case represents the “ON-ON” state. In this state, the absorption spectra includes a narrow absorption band at low frequencies, where the surface plasmons of graphene play the main role to create resonant behavior (Fermi energy level of graphene is set to 0.2 eV). The broad upper absorption band is obtained at the higher frequencies due to the resonant behavior of VO₂ layer in the metallic phase. In 10 state, we switch the VO₂ material to an insulator, whereas the graphene Fermi energy level is unchanged. As plotted in Fig. 5b, in this case the high frequency absorption band produced by the resonance of the VO₂ material in the metallic state is omitted and the absorber shows a single narrow absorption band at low frequencies due to the resonant behavior of graphene. In 01 state, the Fermi energy level of graphene is set to zero and the VO₂ material is switched to the metallic phase. As expected, the low frequency absorption band is eliminated and only the high frequency absorption band remains. Finally, when the Fermi energy level is set to zero and the VO₂ material is in insulator phase (state 00) and the absorption values are reduced to below 12% for both of the operation bands. Table 2 lists a summary of the proposed absorber functionality at four different states. Furthermore, the simulated results plotted in Fig. 5 are compared against the results obtained from the equivalent circuit model for all of the four operational states of the absorber. A very good agreement between the full-wave and the circuit model simulation results verifies the presented circuit model analysis.

Table 2 Summary of the absorption performance for low and high frequency bands at different operational states.

It is worth to describe that the conductivity of graphene can be tuned by controlling the Fermi level through applying a DC bias voltage. For electrostatic biasing of patterned graphene layer, one may use polysilicon DC gating sheets^{33,60,61,62,63} or ion-gel layer^64,65. We present a way of implementation utilizing polysilicon DC gating sheets. An example of DC biasing using two polysilicon DC gating sheets of distance t = 50 nm is shown in Fig. 6. The bias voltage is applied to the polysilicon sheets to modulate the Fermi level of the graphene patches. Since the graphene in the proposed structure includes a non-continuing pattern, it is required to use two polysilicon sheets as reported in Ref.⁵². The graphene layer should be deposited on the top polysilicon sheet. To suppress the effect of polysilicon sheets on the electromagnetic response of the device, the polysilicon sheets should be very thin (20 nm)³³. The approximate relation between the graphene Fermi level and the extra bias voltage (V_g) can be expressed as $E_{f} = \hbar v_{f} \sqrt {\frac{{\pi \varepsilon_{0} \varepsilon_{r} V_{g} }}{et}}$, where $v_{f}$ is the Fermi velocity.

Figure 6

Electrostatic biasing of graphene using two polysilicon DC gating sheets. The bias voltage applied between the two ultra-thin polysilicon sheets tunes the Fermi level of the graphene patches. t = 50 nm is the distance between two polysilicon sheets, and t_p = 20 nm is the thicknesses of the polysilicon sheets.

Now, we study the stability of the absorption spectra under oblique incidences of the electromagnetic waves. The scan angle performance of an absorber is very critical in practical applications. Figure 7 indicates the absorption spectra under the oblique incident angles up to 60° for both of the TE and TM polarizations. It is expected that the absorber would have excellent stability under different polarization angles from 0° to 90° due to the geometrical symmetry of the absorber unit cell. The absorption level remains larger than 90% in the TE polarization for low absorption band up to 55° incidence angle, whereas this is the case for the high frequency absorption band up to 50°. This can be explained due to a decrease in the electric dipole resonance of the VO₂ layer due to the reduction of the tangential component of the electric field for larger incidence angles. For TM polarization, the absorptivity remains larger than 90% up to 60° oblique incidence for both of the absorption bands.

Figure 7

The Absorption spectra of the proposed absorber in state 11 as function of different incident angles for (a) TE polarization, (b) TM polarization.

In the following, we compare the proposed multifunctional absorber with other absorbers composed of hybrid metamaterial of graphene and VO₂. Although the various absorbers composed of graphene or VO₂ metamaterials are presented in the literature. Here, we just survey the absorbers that are composed of both graphene and VO₂. Hence the switchable behavior of the absorbers is obtained by means of two control factors being (i) the switching behavior of the VO₂ layer from a metal phase to an insulator through the temperature transition and (ii) the electrical tunable property of the graphene surface conductivity by changing the Fermi energy level. Comparisons between the absorbers in Refs.^46,47,48 and the proposed absorber are presented in Table 3. Based on the table, all of the previous designs show three switchable states, whereas the proposed absorber offers four switchable operational states.

Table 3 Comparison of the proposed absorber to other absorbers composed of hybrid metamaterial of graphene and VO₂.

Dual broadband switchable absorber

In this section, we show that the proposed absorber configuration can also be optimized to achieve dual broadband absorption response. Generally, impedance matching condition can be used for designing absorbers meaning that the input impedance of the absorber should match the free-space impedance within the bandwidth of the absorber (Im(Z_in) = 0, and Re{Z_in} = 377 Ω). In order to achieve broadband absorption, in addition to the impedance matching condition, the derivative of the imaginary part of the impedance is also set to zero within the absorption band⁶⁶. This is performed by optimizing the thickness of the dielectric spacer between the graphene and the VO₂ layers and the relaxation time of graphene. In the dual broadband absorber, the thickness of the top dielectric spacer and the relaxation time of graphene are h₂ = 50 µm and τ = 0.25 ps, whereas all of the other parameters are unchanged compared with the initial design.

Figure 8 shows the absorption spectra of the new design for the four states. According to Fig. 8a, in state 11, the absorption spectra includes two absorption bands, where the surface plasmons of graphene play the main role in creating resonant behavior of the low absorption band (Fermi energy level of graphene is set to 0.2 eV) and upper absorption band is due to the resonant behavior of VO₂ layer in the metallic phase. The fractional bandwidths (FBWs) are 69% and 93.5% for low frequency (0.55–1.12 THz) and high frequency (2.15–5.93 THz) bands, respectively. Similar to the previous design, the absorption can be switched by adjusting the Fermi energy level of graphene to zero and switching the VO₂ material to the insulating phase. The absorption responses for the other three operational states of the absorber are plotted in Fig. 8b–d confirming four state switching performance of the absorber. In addition, very good agreements between the full-wave and circuit model simulation results in all four states verify the developed circuit model. The derived values of the lumped elements for this design are similar to the previous section except the value of the resistance corresponding to the surface admittance of graphene that is different because of the change in the graphene relaxation time.

Figure 8

The absorption spectra of the proposed structure, where the Fermi energy level of graphene and the phase of VO₂ material considered as (a) state 11: E_f = 0.2 eV and metallic phase of VO₂, (b) State 10: E_f = 0.2 eV and insulator phase of VO₂, (c) State 01: E_f = 0 eV and metallic phase of VO₂, and (d) State 00: E_f = 0 eV and insulator phase of VO₂.

As seen, the absorption of level in State 00 (Fig. 8d) is larger in comparison to Fig. 5d. In the second design we changed two parameters (relaxation time of graphene and the thickness of the dielectric spacer between the VO₂ and graphene layers (h₂)). According to the circuit model presented in Section "Equivalent circuit model", these parameters mainly effect the surface admittance corresponding to the graphene and the characteristic admittance of the transmission line corresponding to the dielectric spacer, respectively. Thus, the input impedance of the structure is modified resulting in higher absorption values respect to the first design in Sate 00. In addition, increasing the thickness of the dielectric spacer between the VO₂ and graphene layers in the second design excites the higher order Fabry–Pérot resonances. Indeed, the Fabry–Perot resonances formed between the graphene at the top layer and the VO₂ at the bottom layer results in significant changes as seen in Fig. 8b, while small thickness of dielectric spacer in first design suppresses these resonances.

Based on the results in Fig. 8, there are ripples in the upper absorption band. Note that the dielectric spacer between graphene and VO₂ (h₂ thickness) is thicker in the second design. The ripples are artifacts of the graphene layer and the thick h₂ dielectric spacer. In fact, the combination of the graphene layer and the dielectric spacer produces higher order Fabry–Perot resonances causing ripples in the upper absorption band. This is confirmed by removing the top graphene layer from the absorber and simulating it with just VO₂. We also considered the case, where the VO₂ layer is removed and just the graphene layer is included. The full wave simulated absorptions for these cases are presented in Fig. 9. It is clear from the curves in Fig. 9 that the VO₂ absorption band is almost flat if the graphene and the upper dielectric spacer are removed from the structure. Furthermore, the plot shows the higher-order resonances for the graphene only absorber, when the VO₂ is removed.

Figure 9

Full-wave simulated absorption, when the graphene layer is removed, when the VO₂ layer is removed, and when both of the VO₂ and graphene layers are included.

The stability of the absorption spectra under the oblique incident angles (up to 60°) is studied in Fig. 10 for the TE and TM polarizations. As observed, the absorptivity remains larger than 90% up to 50° oblique incidence for both TE and TM polarization in both the absorption bands.

Figure 10

The absorption spectra of the proposed absorber in state (11) as function of different incident angles for (a) TE polarization, (b) TM polarization.

Finally, to better understand the performance of proposed structure, the E-field and surface current distributions in four different operational states of the absorber are obtained and plotted in Figs. 11 and 12. The field distributions are plotted at 0.76 THz and 3.96 THz that are the center frequencies of the first and second absorption bands for the TE excitation mode.

Figure 11

Electric field distributions on the VO₂ cross resonators and graphene patches in four operational states. (a) State 11, (b) sate 10, (c) state 01, and (d) state 00. The field distributions are plotted at 0.76 THz and 3.96 THz that are the central frequencies of the lower and upper absorption bands.

Figure 12

Surface current distributions on the VO₂ cross resonators and graphene patches in four operational states. (a) State 11, (b) sate 10, (c) state 01, and (d) state 00. The field distributions are plotted at 0.76 THz and 3.96 THz that are the central frequencies of the lower and upper absorption bands.

Based on the Results in Fig. 11, the E-field distribution is maximum at the edges of the VO₂ cross-shaped resonators at 3.96 THz in States 11 and 01 meaning that the VO₂ mainly contributes to the upper absorption band. The E-field distribution is maximum at the top and bottom edges of the graphene patches at 0.76 THz in States 11 and 10 meaning that the graphene patches mainly contribute to the first absorption band. In addition, there is no significant E-field distribution on the edges of the VO₂ crosses at 0.76 THz in any of the states meaning that VO₂ does not contribute to the lower absorption band. Also, there is no significant E-field distribution on the graphene patches at 3.96 THz in any of the states meaning that the graphene patches do not contribute to the upper absorption band. The surface current distributions in Fig. 12 agrees with the results in Fig. 11 meaning that the surface current is maximum on the VO₂ cross resonators at 3.96 THz in Sates 11 and 01, while there is no significant current distribution on the VO₂ pattern at 0.76 THz in any of the operational states. Furthermore, the surface current is maximum on the graphene patches at 0.76 THz in States 11 and 10, while there is no significant current distribution on the graphene layer at 3.96 THz in any other states.

Conclusion

Dual narrowband-wideband and dual wideband switchable absorbers based on a hybrid metamaterial formed by a combination of graphene-vanadium dioxide have been investigated in this paper. The proposed absorbers are composed of two stacked resonator arrays, including graphene patches and VO₂ cross strips. The stacked resonator arrays were placed on a dielectric spacer terminated by a metallic film as a back reflector for the EM waves. The proposed structures offer dual absorption bands, where the lower absorption band is produced by the resonance of the graphene layer and the high frequency absorption band is realized by the resonance behavior of the VO₂ layer in the metallic phase. Two different designs were studied in this paper. The first design produces narrow-wide absorption bands, and the second prototype offers dual wide absorption bands. It was shown that the absorption spectra of the structures can be switched by controlling the Fermi energy level of graphene and the operational phase of VO₂ layers. Such a characteristic creates four different operational states for the designed absorbers: dual-band absorption, single-band low frequency absorption, single-band high frequency absorption, and no absorption states. Such a device would be a potential candidate for application in the switchable and reconfigurable terahertz measurement and communication systems. The designed absorbers are polarization insensitive and provide high stability over a wide range of incident angles and offer advantages such as simple structure, high absorption, both narrow and wide bandwidth characteristics. The proposed four state switchable absorber may have promising application in spectrum multiplexing for the reconfigurable communication, sensing or imaging systems within the terahertz regime, where a special frequency band can be selectively absorbed (filtered) using the proposed absorber and the spectrum selection can be switched by controlling the VO₂ and graphene patterns.