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Abstract
A multilayer metamaterial with switchable functionalities is presented based on the phase-transition property of vanadium dioxide. When vanadium dioxide is in the metallic state, a broadband absorber is formed. Calculated results show that the combination of two absorption peaks enables absorptance more than 90% in the wide spectral range from 0.393 THz to 0.897 THz. Absorption performance is insensitive to polarization at the small incident angle and work well even at the larger incident angle. When vanadium dioxide is in the insulating state, the designed system behaves as a narrowband absorber at the frequency of 0.677 THz. This narrowband absorber shows the advantages of wide angle and polarization insensitivity due to the localized magnetic resonance. Furthermore, the influences of geometrical parameters on the performance of absorptance are discussed. The proposed switchable absorber can be used in various applications, such as selective heat emitter and solar photovoltaic field.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials, artificially engineered materials, are able to realize some optical properties not found in nature materials. In recent years, metamaterial has aroused a great research interest due to its desirable characteristics [1,2]. Many fascinating optical behaviors have been created during the development of metamaterials, such as electromagnetically induced transparency [3,4], gradient metasurface [5,6], and invisible cloak [7,8]. It is well known that the biggest issue of the designed metamaterials is the existence of loss. Lots of methods are employed to reduce loss. By contrast, we can make good use of loss by carefully designing metamaterial structure. Selective absorption featured by exciting plasmonic resonance at a specific frequency has drawn extensive attention [9,10]. Reflection is minimized thanks to perfect match between impedance of metamaterial structure and that of free space. Utilizing metamaterial absorber, many useful applications are proposed and further improved, such as thermal imaging [11,12], solar cell [13–15], and scattering reduction [16–18]. Single-band absorption is not difficult to realize as the localized plasmonic resonance has inherent narrow bandwidth. Based on different principles, a variety of methods have been proposed to obtain broadband absorption, mainly including the combination of multiple resonances and interference in periodic metal-dielectric structures. Whether narrowband or broadband absorber, once the structure is well designed, functional properties will be difficult to change.
A critical challenge today is to develop new platforms where the change in optical characteristics can result in active adjustment and switching. Switchable devices can realize real-time control and operation of electromagnetic wave, and are becoming an interesting research topic. One potential approach in the field of switchable photonics is to integrate phase change materials with different optical devices [19–22]. Undoubtedly, vanadium dioxide (VO2) as one of phase change materials has been the focus of material research for reconfigurable components [23–26]. It undergoes a structural variation from an insulating monoclinic phase to a metallic tetragonal phase around 340 K. The phase transition occurring on some femtoseconds is accompanied by a large change in electrical and optical properties. Different approaches, including thermal approach [27], electrical approach [28], and optical approach [29], have been proposed to obtain VO2 reconfigurable devices in practice, such as optical memory [30], modulator [31], and filter [32]. In this work, utilizing the phase-transition property of VO2 [33–35], a multilayer hybrid metamaterial is proposed with a switchable behavior. When VO2 is in the metallic state, the design is a broadband absorber which consists of VO2 ring, dielectric spacer, and VO2 film. When VO2 is in the insulating state, the design is a narrowband absorber which mainly consists of metallic cross, thin dielectric spacer, and metallic film.
2. Design and method
As shown in Fig. 1, the system under consideration consists of six layers. Each layer from top to bottom is VO2 ring, silica (SiO2) film, VO2 film, metallic cross, SiO2 film, and a bottom continuous metallic film. The geometric parameters are optimized by numerical calculation, and they are selected as $P = 200\;\mu m$, ${r_1} = 23\;\mu m$, ${r_2} = 72\;\mu m$, ${t_1} = 55\;\mu m$, ${t_2} = 1\;\mu m$, ${t_3} = 10\;\mu m$, and $L = 95\;\mu m$. The thicknesses of VO2 ring, metallic cross, and metallic film are $0.09\;\mu m$, $0.4\;\mu m$, and $0.4\;\mu m$. The width of metallic cross is $4\;\mu m$. The whole structure is periodically arranged in X and Y directions. Drude model $\varepsilon (\omega ) = {\varepsilon _\infty } - \frac{{\omega _p^2(\sigma )}}{{{\omega ^2} + i\gamma \omega }}$ is taken to describe dielectric permittivity of VO2 in the terahertz range, where ${\varepsilon _\infty } = 12$ is dielectric permittivity at the infinite frequency, ${\omega _p}(\sigma )$ is the plasma frequency dependent on conductivity, and $\gamma$ is the collision frequency [36–39]. Besides, $\omega _p^2(\sigma )$ and $\sigma$ are proportional to free carrier density. According to [38], the plasma frequency ${\omega _p}$ as a function of $\sigma$ can be expressed as $\omega _p^2(\sigma ) = \frac{\sigma }{{{\sigma _0}}}\omega _p^2({\sigma _0})$ with ${\sigma _0} = 3 \times {10^5}\;S/m$, ${\omega _p}({\sigma _0}) = 1.4 \times {10^{15}}\;rad/s$, and $\gamma = 5.75 \times {10^{13}}\;rad/s$. In the process of calculation, different permittivities are used for different phase states of $V{O_2}$. The conductivity of VO2 is $2 \times {10^5}$ S/m (0 S/m) when it is in the metallic (insulating) state. In the insulating state, the relative dielectric permittivity of VO2 is 12 with conductivity of 0 S/m. These two conditions are employed to mimic the phase-transition process of VO2. The dielectric permittivity of SiO2 is 3.8 without loss [40,41]. Gold is modeled as the lossy metal with conductivity of $4.561 \times {10^7}$ S/m.
Fig. 1. (a) 3D schematic of the designed switchable terahertz metamaterial. (b) The side view. (c) The top view of the narrowband absorber.
3. Results and discussions
Finite element method is used to simulate structure. Unit cell boundary conditions are applied in X and Y directions, and open boundaries are added to Z directions. Incident electromagnetic wave is propagating along negative Z direction through the system. Mesh size is carefully chosen until result converges sufficiently. So reflection coefficient (${S_{11}}$) and transmission coefficient (${S_{21}}$) of the proposed absorber are obtained in simulation. Electromagnetic absorptance (A) can be calculated directly from the following formula, $A = 1 - R - T = 1 - {|{{S_{11}}} |^2} - {|{{S_{21}}} |^2}$, where $R = {|{{S_{11}}} |^2}$ and $T = {|{{S_{21}}} |^2}$ are reflectance and transmittance obtained from frequency-dependent S-parameters. Because thickness of the bottom metal is $0.4\;\mu m$, transmission is completely suppressed for narrowband and broadband absorption. As shown in Fig. 2, the designed metamaterial absorber can achieve broadband absorption when VO2 is in the metallic state. Absorptance exceeds 90% in the frequency range of 0.393-0.897 THz. When VO2 changes from metal to insulator, the designed metamaterial absorber achieves narrowband absorption at the frequency of 0.677 THz. Thus the structure is switched from a broadband absorber to a narrowband absorber.
To reveal the working mechanism of the proposed metamaterial broadband absorber, effective optical parameters are retrieved using S-parameter extraction method [42]. These effective parameters can provide a perspective for understanding optical response of metamaterial absorber. As shown in Fig. 3, effective permittivity and permeability change slightly with frequency in the range of 0.4-0.9 THz, and real part of effective permittivity is close to that of effective permeability. Then real part of effective impedance is close to 1, and imaginary part of effective impedance is close to 0 around the maximum absorption band. It indicates that impedance matching condition is well satisfied between absorber and free space. In addition, at absorption peaks, imaginary part of effective refractive index is large. When electromagnetic wave passes through this effective medium, the corresponding absorption loss will be bigger. The effective optical path is ${\mathop{\rm Re}\nolimits} (n) \times {t_1} = 2.88 \times 55 = 158.4\;\mu m$ at 0.469 THz. It will give rise to a quarter-wavelength mode at the wavelength of $4{\mathop{\rm Re}\nolimits} (n) \times {t_1} = 633.6\;\mu m$. This value is almost equal to the first peak wavelength $639.66\;\mu m$ (0.469 THz). So the first absorption peak can be attributed to the lowest Fabry-Perot-type resonance. Similarly, at 0.859 THz, the absorption peak is a higher order Fabry-Perot-type resonance. At the same time, working mechanism of narrowband absorption is also investigated. From Fig. 4, it can be seen that electric current between metallic cross and bottom metallic film flows oppositely, and then enhanced magnetic field will be generated. This artificial magnetic resonance can ensure that there is a frequency where permittivity is almost equal to permeability. So near perfect absorption will happen at this frequency.
Fig. 3. The retrieved effective optical parameters (a) permittivity, (b) permeability, (c) refractive index, and (d) impedance when VO2 is in the metallic state.
Fig. 4. The distributions of electric currents in the surface of metallic cross (a) and metallic film (b) at the frequency of absorption peak. The directions of them are opposite. The enhanced magnetic field in dielectric spacer (c).
In general, the geometry of device has some influences on its resonant frequency and absorption level. Therefore, in order to better design absorber, lots of numerical simulations are needed before actual production. When investigating influence of a parameter in the following discussions, other parameters remain unchanged as initial settings. As shown in Fig. 5(a), inner radius (${r_1}$) of VO2 ring increases from $10\;\mu m$ to $60\;\mu m$, absorption band becomes narrower and the corresponding intensity has an obvious decrease. Figure 5(b) shows simulated results of absorptance with different outer radii (${r_2}$). It can be observed that working bandwidth and intensity of absorption becomes better as outer radius of VO2 ring changes from $30\;\mu m$ to $72\;\mu m$. When outer radius further increases, absorptance becomes a little lower. The influence of thickness (${t_1}$) of SiO2 on absorptance is also investigated. Figure 5(c) shows simulated absorptances as a function of frequency and thickness of SiO2 while other geometrical parameters are fixed. When thickness increases from $20\;\mu m$ to $55\;\mu m$, increase of thickness firstly causes increase of absorption peak, and then absorption becomes to deteriorate after the optimized thickness value. The influences of length (L) of metallic cross and thickness (${t_3}$) of SiO2 are investigated in Figs. 6(a)–6(b). As shown in Fig. 6(a), the position of perfect absorption has a red shift with increase of length of metallic cross. This is mainly due to increase in current loop. With increase of thickness of SiO2, intensity of absorption peak in Fig. 6(b) firstly increases and then decreases. So there is an optimal value for absorption. The position of absorption peak has a little red shift. The above discussions confirm the role of geometrical parameters in improving the performance of absorption, and point out the trajectory of optimization process.
Fig. 5. (a) The dependence of inner radius (${r_1}$) of VO2 ring on absorptance under normal incidence with structure parameters ${r_2} = 72\;\mu m$ and ${t_1} = 55\;\mu m$. (b) The dependence of outer radius (${r_2}$) of VO2 ring on absorptance under normal incidence with structure parameters ${r_1} = 23\;\mu m$ and ${t_1} = 55\;\mu m$. (c) The thickness (${t_1}$) of SiO2 on absorptance under normal incidence with structure parameters ${r_1} = 23\;\mu m$ and ${r_2} = 72\;\mu m$.
Fig. 6. The dependence of length (L) of metallic cross (a) and thickness (${t_3}$) of SiO2 (b) on absorptance under normal incidence with other structure parameters unchanged.
In practice, it would be better if a metamaterial absorber shows strong tolerance to the variation of incident angle. The influence of oblique incidence on the performance of the designed absorber is studied. Absorptance spectra at different incident angles are plotted in Figs. 7(a) and 7(c) for transverse electric (TE) polarization and Figs. 7(b) and 7(d) for transverse magnetic (TM) polarization. As can be seen from Figs. 7(a) and 7(c), absorptance does not change for TE-polarized wave within the incident angle $45^{\circ}$. When incident angle is larger than $60^{\circ}$, absorptance decreases significantly with the increase of incidence angle. For TM-polarized wave, main absorption peak in Fig. 7(b) becomes slightly narrower as incident angle increases. Although there are some diffraction modes in Figs. 7(b) and 7(d), absorption coefficient can still reach a high value when incident angle becomes larger. The results of TE and TM polarizations show that the designed absorber exhibits excellent performance at wide incident angles. Although period ($200\;\mu m$) and thickness of broadband absorber ($56.09\;\mu m$) are large, the ratios are 0.43 ($200/461.54$) and 0.12 ($56.09/461.54$) between them and the center working wavelength ($461.54\;\mu m$, 0.65 THz). Absorption in narrowband absorber is caused by the localized magnetic resonance, and it is not dependent on period. The ratio is only 0.02 between ${t_3}$ ($10\;\mu m$) and the center working wavelength ($461.54\;\mu m$, 0.65 THz). So the performance of the proposed device is less sensitive to incident angle.
Fig. 7. Angle dependence of broadband absorber for TE (a) and TM (b) polarizations when VO2 is in the metallic state. Angle dependence of narrowband absorber for TE (c) and TM (d) polarizations when VO2 is in the insulating state.
4. Summary
The design of a switchable absorber is introduced with properties of narrow and broad bands. When vanadium dioxide is in the metallic (insulating) state, it is a broadband (narrowband) absorber. In order to study the mechanism of broadband absorption, a retrieval process is adopted to extract effective electromagnetic parameters. Narrowband absorption is mainly caused by the localized magnetic resonance. Angular tolerance of metamaterial absorber is also studied. The results show that when incident angle is less than $45^{\circ}$, the performances of narrowband and broadband absorbers are very good for TE polarization. Absorptances of narrowband and broadband absorbers become to deteriorate for TM polarization due to the appearance of higher-order diffractions. According to recent works about VO2 deposited on SiO2 in experiment [43–46], our design can be realized based on currently experimental conditions. Metamaterial absorber proposed in this work has the characteristics of the simple configuration and switchable function, and can be used for terahertz modulation, thermal emitter, and electromagnetic energy harvesting.
Funding
National Natural Science Foundation of China (11974294, 11504305).
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