Abstract
This paper proposes a novel and perfect absorber based on patterned graphene and vanadium dioxide hybrid metamaterial, which can not only achieve wide-band perfect absorption and dual-channel absorption in the terahertz band, but also realize their conversion by adjusting the temperature to control the metallic or insulating phase of VO2. Firstly, the absorption spectrum of the proposed structure is analyzed without graphene, where the absorption can reach as high as 100% at one frequency point (f = 5.956 THz) when VO2 is in the metal phase. What merits attention is that the addition of graphene above the structure enhances the almost 100% absorption from one frequency point (f = 5.956 THz) to a wide frequency band, in which the broadband width records 1.683 THz. Secondly, when VO2 is the insulating phase, the absorption of the metamaterial structure with graphene outperforms better, and two high absorption peaks are formed, logging 100% and 90.7% at f3 = 5.545 THz and f4 = 7.684 THz, respectively. Lastly, the adjustment of the Fermi level of graphene from 0.8 eV to 1.1 eV incurs an obvious blueshift of the absorption spectra, where an asynchronous optical switch can be achieved at fK1 = 5.782 THz and fK2 = 6.898 THz. Besides, the absorber exhibits polarization sensitivity at f3 = 5.545 THz, and polarization insensitivity at f4 = 7.684 THz with the shift in the polarization angle of incident light from 0° to 90°. Accordingly, this paper gives insights into the new method that increases the high absorption width, as well as the great potential in the multifunctional modulator.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials, as an artificially designed electromagnetic medium, exhibit extraordinary physical properties absent from natural materials [1,2], and have attracted widespread attention in recent years. The amplitude, phase, and polarization of light can be controlled in the THz band through a special design, which effectively manipulates electromagnetic waves. The mature development and proven feasibility of metamaterials in the past few decades prompt their application in fields like wave absorbing materials [3–5], biological detection [6,7], stealth technology [8], communication antennas [9], etc. In addition, metamaterials perform excellent optical properties, such as electromagnetic induced transparency (EIT) [10,11], perfect absorption [12,13], negative refractive index [14], etc., among which the perfect absorber is a vital research branch. Landy, N. I, et al. first initiated the perfect absorber in 2008 [15], proposed a metal plasma structure, and achieved perfect absorption at a single frequency point, which grabbed the attention of researchers. Pu, Mingbo, et al. put forward a metal-dielectric-metal structure in 2011, and achieved a multi-band perfect absorption [16]. Pu, Mingbo, et al. further used metal films to broaden the absorption width and achieve broadband absorption in the next year, which was a landmark for communication and sensing research [17]. The traditional absorbers, however, are generally composed of metals, and are difficult to change once the design is completed, limiting further modulation and absorption width. Researchers accordingly found many excellent materials to solve this problem, such as graphene and vanadium dioxide.
Graphene [18] is equipped with a two-dimensional crystalline structure, and is considered a revolutionary material of the future. Thanks to its metal-like properties, it can excite the surface plasma polaritons (SPPs) [19–21]. Compared with metals, the graphene-based SPPs are superior with excellent optical properties, such as dynamic tunability [22–24], strong localization [25], strong dispersion [26], etc., which explains the extensive application of graphene in designing electromagnetic absorbers [27–29] in the THz band. In 2012, R. Alaee et al. proposed a graphene-dielectric-gold metamaterial, and realized a perfect absorption at multi-frequency points by controlling the Fermi level of graphene [30]. Another paper published in the same year also proved 100% absorption in the patterned graphene structure [28]. Benefiting from the excellent optical properties of graphene, these absorbers perform better absorption capacity, and are adjustable. Given the limited current application of narrow-band or fixed frequency range absorption, another noteworthy metamaterial, vanadium dioxide (VO2), is proposed to achieve perfect broadband absorption. Extensive attention has been paid to VO2 [31,32], a monoclinic crystal structure with phase change properties [33]. The phase transition temperature is 68 °C, that is, the VO2 is the insulating phase at T < 68oC, while the metallic phase at T > 68oC. Due to this unique property, VO2 has been widely employed in tunable devices such as optical switches [34], terahertz absorbers [35,36], and sensors [37]. In 2021, Z. Run et al. proposed a VO2 absorber that achieved a more than 90% absorption with a width of 0.65 THz by varying the temperature [38], which manifested that VO2 could improve the performance of absorber, and realize broadband absorption. In 2022, Zeng. et al. proposed a graphene and VO2 hybrid structure to achieve dynamic absorption and multifunctional modulators [39]. Therefore, considering the excellent properties of the two metamaterials mentioned above, this paper attempts to combine graphene and VO2, which provides a new approach to achieve multiple modulations, and to improve absorption capacity and width [34,40,41].
This paper proposes a hybrid metamaterial based on patterned graphene and VO2 to achieve a broadband 100% absorption or a high dual-channel absorption, which exhibits excellent performance and prospects in multifunctional modulators. Firstly, the absorption spectrum of the proposed structure in the absence of graphene is investigated, revealing that as VO2 gradually changes from the insulating phase to the metallic phase, the absorption grows. Most importantly, when the graphene is applied above the structure, the absorption (≈100%) is strengthened from one frequency point to an ultra-wide frequency band. Secondly, when the VO2 is the insulating phase and graphene is added, two high absorption peaks are observed. The absorption under such situation is greatly enhanced compared with the absence of graphene, which demonstrates the role of graphene in absorption enhancement, and achieving dual-channel absorption. Finally, the Fermi level of graphene and the polarization angle of incident light are controlled to explore the applications of the structure, and an asynchronous optical switch can be realized at fK1 = 5.782 THz and fK2 = 6.898 THz. Besides, the absorber shows the polarization sensitivity at f3 = 5.545 THz while the polarization insensitivity at f4 = 7.684 THz, which is vital for realizing polarizers and other modulators. In summary, this paper presents a new method to improve the performance of the absorber, and realizes an ultra-wide nearly 100% absorption, which guides the multifunctional application.
2. Model design and methods
Figure 1(a) illustrates the schematic diagram of the periodic structure based on a patterned graphene and ring-shaped VO2 hybrid metamaterial, which enables the interconversion between broadband absorption and dual-channel absorption. Unlike most absorber structures, the proposed structure utilizes the excellent metal-like and the graphene-based SPPs properties of graphene to enhance absorption, exhibiting a broadband perfect absorption. The proposed structure is composed of six layers (Au-VO2-SiO2-VO2-SiO2-graphene): the bottom layer is a gold layer, which acts as a reflector to reflect most of the light; the 2 μm-thickness VO2 film, which can also serve as a reflector to reflect most incident light at metal phase VO2; the first SiO2 layer; the ring-shaped VO2 layer with a thickness of 0.1 µm; the second SiO2 layer, and the top layer, that is, the patterned graphene layer. The graphene layer is deposited with an ionic gel layer, and a metal gate contact is provided on the top graphene structure to connect the gate voltage Vg as shown in the cell structure in Fig. 1(b). The ionic gel, 2.56 in relative permittivity and 1 nm in thickness, connects the graphene together to facilitate the application of gate voltage. Figure 1(c) shows the top view of the graphene layer, which consists of two graphene strips and a graphene square block (referred to as TGSs and GSB for convenience). Figure 1(d) indicates the top view of the ring-shaped VO2 layer, with Rout and Rin denoting the inner and outer radius of the ring, respectively. In addition, the geometrical parameters of the structure are as follows: tAu = 2 µm, tVO2 = 2 µm, tSiO2 = 5.2 µm, dVO2 = 0.1 µm, dSiO2 = 0.6 µm, l1 = 4 µm, l2 = 1.5 µm, l3 = 1.75 µm, l4 = 3 µm, p = 10 µm, Rin = 2.5 µm, and Rout = 4 µm.
The x, y, and z directions are set as the periodic boundary, the periodic boundary, and the perfect matching layer (PML), respectively, in simulation. Furthermore, the surface current model of graphene is employed, and the graphene is equivalent to a surface current J, satisfying the differential form of Ohm's law: J = σgE, where σg and E denote the conductivity of graphene and the electric field, respectively. The graphene conductivity σg can be expressed by the Kubo formula [42,43]:
In this system, the Fermi level of graphene is set as EF = 1.0 eV, the mobility is µ = 0.4 m2V-1s-1, and the relaxation time is expressed by τ = µEF/ (ev2F). Moreover, the Fermi level of graphene can be given by [44]:
In the THz band, the permittivity of the VO2 can be expressed by the Drude model, which can be written as [47]:
During the simulation calculation, we scan the S-parameter, and obtain the reflection coefficient S11 and the transmission coefficient S21. Here, T = |S21|2 and R = |S11|2. Therefore, the absorption of this system can be expressed as:
3. Results and analysis
Firstly, the absorption property of the proposed structure is analyzed without graphene. Figure 3(a) displays the schematic diagram of the structure and a terahertz light in the x-direction is incident vertically on the surface of the structure. Figure 3(b) displays the absorption spectra of the structure at different conductivities σvo2, where absorption gradually grows with the conductivity σvo2 being changed from 0 to 20 × 104 S/m. When the conductivity σvo2 reaches 20 × 104 S/m, the absorption is as high as 100% at f = 5.956 THz. In order to investigate the physical mechanism of this process change, we plot the surface electric field distribution at f = 5.956 THz when the temperature changes from 28 °C to 72 °C, as shown in Fig. 3(c). Figure 3(c) reveals that the electric field on the surface of the structure enhances with the increase of the temperature. Specifically, the electric field intensity exhibits no obvious change from 28 °C to 67 °C and from 69 °C to 72 °C, while jumps from 10 V/m to 50 V/m from 67 °C to 69 °C, which comes down to the transition from the insulating to the metallic state of VO2. At 28 °C-67 °C, the VO2 is the insulating state, and the conductivity σvo2 is relatively low, so only a small amount of electric field energy is bound inside and outside the ring-shaped VO2 in the x-direction. At this time, VO2 is equivalent to a layer of medium, the incident photons cannot resonate between the VO2 and gold layer, and they are all reflected so that the system represents low absorption, as shown in Fig. 3(b). At 67 °C-69 °C, the conductivity σvo2 grows rapidly and most parts of VO2 turn into metal, which strengthens the resonance with gold, which explains the climb of absorption. At 69 °C-72 °C, the phase transition of VO2 is completed and the VO2 becomes the metallic state, and the energy is mainly bound outside, indicating that the strong resonance of the incident photons between the ring-shaped VO2 and the VO2 film causes the absorption peak (see in Fig. 3(b)).
After discussing the situation without graphene, the effect of graphene that applied above the structure on the absorption performance is elaborated when x-direction polarized light is irradiated on the structure, as shown in Fig. 4(a). As mentioned before, the graphene is composed of two graphene strips (TGSs) and a graphene square block (GSB). Figure 4 (b) shows the change of absorption spectra with and without graphene when VO2 is a metal phase, where the red line stands for the results in the presence of graphene, while the blue line in the absence of graphene. The inset in Fig. 4(b) shows an enlarged view of the high broadband absorption from 5.1 THz to 7.3 THz. It’s observed that the absorption is obviously enhanced when graphene is added, and the absorption can reach almost 100% from a frequency point (f = 5.956 THz) to a wide frequency band, where the band width (A≈100%) can be up to 1.683 THz. In order to deepen the understanding of the role of graphene strips and blocks, we also display the absorption spectrum in the presence of TGSs and GSB alone in Fig. 4 (b), in which the pink and green dotted line denote the GSB and TGSs, respectively. Compared to the absence of graphene (the blue line), the absorption is enhanced from 94.2% to 99.7% at f1 = 5.340 THz when the TGSs exist alone, while the absorption is strengthened from 96.1% to 99.7% at f2 = 7.023 THz when the GSB exists alone. When GSB and TGSs contribute simultaneously to absorption enhancement, the absorption spectrum exhibits a broadband strong absorption (the red line), which indicates the common participation of GSB and TGSs in the resonate among the ring-shaped VO2 and the VO2 film further strengthens the resonate. Therefore, the GSB and TGSs play an important role in the absorption enhancement of this structure, respectively. In addition, we also depict the absorption curve (orange dotted line) in Fig. 4(b) when 2 µm-thickness VO2 film layer is not present. By comparing the presence (red solid line) and the absence of the VO2 film layer, it is observed from the inset that the absorption capability is improved significantly when the VO2 layer is present, bringing the broadband absorption closer to 100%. This is mainly due to fact that the VO2 layer is in the metal phase under temperature control and forms a resonant cavity with the patterned graphene and the ring-shaped VO2 layer, and the incident light resonates strongly between them, resulting in a significant increase of absorption.
In order to further explore the effect of graphene on the absorption, the electric field distributions of the ring-shaped VO2 layer and graphene layer are plotted in Figs. 4(c) and (d). According to the previous discussion without graphene (see Fig. .3(c) when σvo2 = 20 × 104 S/m), the electric field energy is mainly distributed outside the ring in the x-direction. When the TGSs and GSB are added above the structure, the energy is concentrated outside and inside the ring at the ring-shaped VO2 layer. At f1 = 5.340 THz, the field energy is increased outside the ring in the y-direction, indicating that the role of TGSs on the resonance to enhance the absorption from 94.2% to 99.7%. At f2 = 7.023 THz, the GSB contributes to the resonance between GSB and VO2 film, so that the most energy is obviously confined inside the ring to strengthen the absorption from 96.1% to 99.7%. The graphene layer in Fig. 4(c) and Fig. 4(d) reveals that the energy is distributed around the TGSs and GSB, respectively, proving that their respective roles in the absorption enhancement at f1 = 5.340 THz and f2 = 7.023 THz. All these confirm the prominent role of TGSs and GSB in absorption enhancement at f1 = 5.340 THz and f2 = 7.023 THz, respectively.
Figure 5(a) demonstrates the absorption spectra when the VO2 is the insulating state. Without graphene (the blue curve), the resonance is invalid so that there is no absorption. When the TGSs and GSB are simultaneously added, two absorption resonate peaks appear at f3 = 5.545 THz and f4 = 7.684 THz, respectively, where the absorption can reach as high as 100% and 90.7%, respectively. Here, the VO2 is equal to a layer of medium, and the graphene forms a new resonant cavity with the gold. In addition, when TGSs and GSB respectively exist alone, resonance between the TGSs and gold generates the first absorption peak (the green dotted line), while the GSB produces the second peak (the pink dotted line), as shown in Fig. 5(a). The mutual coupling between TGSs and GSB incurs the dual-channel absorption. Therefore, when VO2 is the insulating phase, the TGSs and GSB contribute to these two absorption peaks to realize the dual-channel absorption, respectively. Figure 5(b) shows the electric field distribution of the ring-shaped VO2 layer at f3 = 5.545 THz and f4 = 7.684 THz. At the VO2 insulating state, there is no energy outside the ring-shaped VO2 in the x-direction, while the most energy is distributed outside the ring in the y-direction at f3 = 5.545 THz and inside at f4 = 7.684 THz, which is caused by the TGSs and GSB, respectively. Figure .5(c) reveals the marked effect of the TGSs and GSB at f3 = 5.545 THz and f4 = 7.684 THz, respectively, which supports that the two absorption peaks are derived from the TGSs and GSB, respectively. The above verifies the vital role of graphene in this system to enhance resonance, and achieve broadband high absorption and dual-channel absorption.
The impedance matching theory [48] is a classical theory to explain the absorber. At 4.0-9.0 THz, we obtain S-parameters to invert the relative impedance Z of the absorber, where the relative impedance Z can be expressed by:
In practical applications, the external conditions are generally controlled to modulate the absorber. Given the favorable dynamic tunability of graphene, the Fermi level EF can be controlled by an applied gate voltage Vg according to Eq. (5). Figures 7(a) and (b) illustrate the influences of the different EF on the absorption at different VO2 phase. Here, The black dotted curve marks 90% absorption. In Fig. 7(a), the absorption spectrum has a blue-shift feature, but the absorption width greater than 90% does not increase significantly, which mainly comes down to the dominant role of the metal phase VO2 in the absorption resonance, as well as the limited enhancement role of graphene. In Fig. 7(b), the insulating phase VO2 does not participate in the resonance, the graphene exhibits strong resonance with gold, and is accompanied by a significant blue-shift, where an asynchronous optical switch can be realized at fK1 = 5.782 THz and fK2 = 6.898 THz. At fK1 = 5.782 THz, the optical switch is set as “OFF” state at EF = 0.8 eV, while as “ON” state at EF = 1.1 eV. Conversely at fK2 = 6.898 THz, the optical switch is set as “ON” state at EF = 0.8 eV, while as “OFF” state at EF = 1.1 eV. Therefore, the Fermi level EF can be adjusted to achieve the optical switch. In addition, the study of the polarization characteristics is vital for the application of the absorber, which can reduce the limitations in practical applications. Figures 7(c) and (d) show the absorption spectra with the increase of polarization angle θ at different VO2 phase. In Fig. 7 (c), at θ < 45°, it can be observed that the absorption width (A > 90%) has no obvious change, while the width has obviously widened at θ > 45°, which is mainly caused by the rotational asymmetry of the graphene. Thereby, when VO2 is a metal phase, the broadband absorption shows polarization sensitivity due to the rotational asymmetry of graphene. In addition, Fig. 7(d) reveals that the first absorption peak exhibits polarization sensitivity at f3 = 5.545 THz, while the second absorption peak shows polarization insensitivity at f4 = 7.684 THz, which is caused by the rotational symmetry and asymmetry of the GSB and TGSs, respectively. Interestingly, at θ = 45°, while the first absorption peak fades away, a new absorption peak gradually appears near f = 8.896 THz. Here, the new peak is masked by the red dotted line. Therefore, the proposed structure can be applied to multifunctional modulators, such as optical polarizers, switches, and absorbers.
The above discussion validates that the proposed structure further improves the absorption performance of the absorber, and exhibits excellent modulation means. On the one hand, the band width of the almost 100% absorption can reach as high as 1.631 THz; on the other hand, the interconversion between broadband absorption and two-channel absorption can be controlled by the temperature. Some recent literatures on broadband absorption are shown in Table 1.
4. Conclusions
This paper proposes an absorber based on patterned graphene and VO2 hybrid metamaterials, which realizes the conversion between broadband high absorption and dual-channel absorption. The physical property of VO2 can be adjusted by temperature, so that VO2 can be regulated between the metal phase and the insulating phase. The introduction of patterned graphene can greatly enhance the resonance reaction of incident photons in the system, achieving a broadband ≈100% absorption and a two-channel absorption. The vital effect of GSB and TGSs on absorption at different VO2 phases is also proved, not only to enhance resonance and achieve broadband high absorption, but also to achieve a dual-channel absorption. In addition, the absorber can be controlled by changing external conditions, which enables multifunctional applications such as optical switches, polarizers, and broadband absorption. So, the proposed absorber provides guidance for absorber regulation and multifunctional modulator
Funding
National Natural Science Foundation of China (11804093, 11847026, 12164018, 61764005); Natural Science Foundation of Jiangxi Province (20192BAB212003, 20202ACBL212005, 20202BABL201019, 20224ACB201008); Science and technology project of Jiangxi Provincial Department of Education (GJJ210603).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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