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Abstract
A switchable metamaterial with bifunctionality of absorption and electromagnetically induced transparency is proposed based on the phase-transition characteristic of phase change material-vanadium dioxide. When vanadium dioxide is in the metallic state, an isotropic narrow absorber is obtained in the terahertz region, which consists of a top metallic cross, a middle dielectric layer, and a bottom vanadium dioxide film. By adjusting structure parameters, perfect absorption is realized at the frequency of 0.498 THz. This designed narrow absorber is insensitive to polarization and incident angle. Absorptance can still reach 75% for transverse electric polarization and transverse magnetic polarization at the incident angle of ${65^\circ }$. When vanadium dioxide is in the insulating state, the top metallic cross will interact with the bottom split ring resonator, and the interaction between them will lead to the appearance of electromagnetically induced transparency. The behavior of electromagnetically induced transparency works well for transverse electric polarization and transverse magnetic polarization at the small incident angle. The designed hybrid metamaterial opens possible avenues for achieving switchable functionalities in a single device.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, metamaterials have attracted considerable attention due to its unprecedented potential in manipulating electromagnetic waves. The unique reactions not found in natural materials are usually realized by designing and tailoring metal or dielectric elements with periodic patterns. The controllable abilities of artificially engineering metamaterials in amazing ways can provide more opportunities for new functions, such as negative refractive index [1–3], absorber [4–6], and electromagnetically induced transparency [7–9]. The properties of traditional metamaterials are mainly decided by the geometric arrangement of meta-atoms. One consequence of this is that their response to wave is usually fixed. In order to enrich the functionality, integration of active media (such as graphene [10–12], liquid crystal [13–15], and phase change material [16–18]) into traditional metamaterials is desirable to achieve dynamic control of components at different frequencies.
Phase change materials are one kind of promising functional materials, and it has been widely used in rewritable data storage and temperature sensor [19–21]. By combining with other structures, phase change material can offer a special opportunity for reversible devices. Vanadium dioxide (VO2) as a typical phase change material exhibits a transition from an insulating dielectric state to a conducting metal state at a critical temperature of around 340 K. It can be electrically triggered [22,23] or optically triggered [24,25] to achieve switchable performance. VO2 undergoes a physical structural change from monoclinic to tetragonal during phase transition within a very fast switching time, leading to a sudden change in conductivity. Large variation in conductivity can provide a good chance in the field of reconfigurable devices. So this unique feature makes VO2 a growing number of the improved modulation in many critical devices, especially in the terahertz frequency. In this work, we propose a hybrid metamaterial with bifunctionality of absorption and electromagnetically induced transparency for terahertz wave. When VO2 is in the metallic state, the design behaves as a narrow absorber. When VO2 is in the insulating state, the design behaves as an analog of electromagnetically induced transparency.
2. The designed scheme and discussion of the calculated result
As shown in Fig. 1, unit cell of the designed switchable metamaterial is composed of five parts. Every part from top to bottom is gold cross, silica (SiO2) spacer, VO2 film, gold split ring resonator (SRR), and the bottom SiO2 substrate. Within the scope of terahertz frequency, Drude model $\varepsilon (\omega ) = {\varepsilon _\infty } - \frac{{\omega _p^2(\sigma )}}{{{\omega ^2} + i\gamma \omega }}$ is taken to express dielectric permittivity of VO2, 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 [26–30]. In addition, $\omega _p^2(\sigma )$ and $\sigma$ are proportional to free carrier density. The plasma frequency ${\omega _p}$ dependent on $\sigma$ can be described 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 calculation process, different permittivities are adopted 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 state of insulator, the relative dielectric permittivity of VO2 is set to 12 with the conductivity of 0 S/m. These two assumptions are used to simulate phase-transition process of VO2. In the terahertz frequency, gold is modeled as a lossy metal, and its conductivity is $4.561 \times {10^7}$ S/m. SiO2 is considered to be lossless with relative permittivity of 3.8 [31,32]. Using these material parameters, the finite element method is employed for full-wave electromagnetic simulation. Unit cell boundary conditions are applied in the x and y directions, and open boundary is set in the z direction. In order to ensure the convergence of simulated results, simulation applies the adaptive fine mesh settings. The optimal geometrical parameters are obtained after careful calculations. Period, length of gold cross, thickness of SiO2, thickness of VO2, and width of gold rod are $P = 200\;\mu m$, $L = 170\;\mu m$, ${t_1} = 18\;\mu m$, ${t_2} = 1\;\mu m$, and $10\;\mu m$, respectively. The thickness of the used gold is $0.5\;\mu m$. Parameters of a and b are $53\;\mu m$ and $27\;\mu m$. In order to avoid Fabry-Perot resonance, the thickness of SiO2 substrate is infinite in simulation. Compared with the single functionality of the design in the [27], the present design can realize bifunctionality of absorption and electromagnetically induced transparency based on the phase-transition properties of VO2.
Fig. 1. (a) Three dimensional schematic of the unit cell of the designed switchable terahertz metamaterial. (b) The top view of the unit cell. (c) The side view of the unit cell.
2.1 The designed switchable metamaterial behaves as a narrow absorber when VO2 is in the metallic state
In recent years, metamaterial absorber has attracted great attention due to their high absorption, low density, and small thickness. The first metamaterial absorber using electric ring resonator is proposed by Landy. From that moment on, this kind of absorber based on electric and/or magnetic resonance has been extensively studied. Usually, a metamaterial absorber is a metallic pattern-insulator-metallic film configuration. Localized plasmonic resonance exhibits the characteristics of wide angle and polarization insensitivity through proper device design. The theoretical unit absorption at a certain frequency can be obtained by matching the impedance of metamaterial absorber with that of free space.
In our design, the top gold cross, the middle SiO2 spacer, and the bottom VO2 film will form a typical metallic pattern-insulator-metallic film configuration when VO2 is in the metallic state. Since there is a bottom VO2 film with the thickness of $1\;\mu m$ to suppress wave propagation (transmittance (T), $T \approx 0$), absorptance (A) can be calculated by $A = 1 - R - T = 1 - {|{{S_{11}}} |^2} - {|{{S_{21}}} |^2} = 1 - R$, where ${|{{S_{11}}} |^2}$ and ${|{{S_{21}}} |^2}$ are reflectance (R) and transmittance (T), respectively. Absorptance can be maximized by minimizing reflectance of the proposed system. After careful optimization for normally incident waves, some structure parameters are obtained as mentioned earlier. As shown in Fig. 2, it is found that the designed system possesses a low reflectance, and there is a perfect absorption peak with an efficiency of 100% at the frequency of 0.498 THz. This design of narrow absorber may have some possible applications in energy harvesting, sensor, and photo-switch.
Fig. 2. Simulated reflectance and absorptance of the designed system at normal incidence when VO2 is in the metallic state.
In order to understand the physical origin of this absorption, the amplitude and phase of S-parameter (${S_{11}}$ and ${S_{21}}$) are calculated at normal incidence. Because the ratio between the working wavelength ($602.4\;\mu m$) and period ($200\;\mu m$) is ∼3, it is reasonable to retrieve the real and imaginary parts of the effective optical parameters (permittivity, permeability, refractive index, and impedance). As shown in Fig. 3, there is an electric resonance at the frequency of 0.5475 THz. the top gold cross is responsible for this electric dipole resonance. At the same time, a magnetic resonance is found at the frequency of 0.5 THz. As shown in Fig. 4, it is caused by the anti-parallel current between the top gold cross and the bottom VO2 film. This current loop gives rise to an artificial magnetic dipole moment, which will interact strongly with incident magnetic field. Thus, our design realizes the simultaneous excitation of electric and magnetic resonances. The effective impedance of the designed absorber can be calculated by the formula ${Z_{eff}} = \sqrt {\frac{{{\mu _{eff}}}}{{{\varepsilon _{eff}}}}} = \sqrt {\frac{{{{(1 + {S_{11}})}^2} - S_{21}^2}}{{{{(1 - {S_{11}})}^2} - S_{21}^2}}}$ [33], where ${\varepsilon _{eff}}$ and ${\mu _{eff}}$ are the effective permittivity and permeability, respectively. The effective impedance varies with permittivity and permeability. When permittivity is equal to permeability, the impedance of absorber equals that of free space. The real and imaginary parts of the impedance are plotted in Fig. 3(d). The result shows that when the frequency is 0.497 THz, the real part of absorption peak is 0.9 and the imaginary part is -0.12. So the designed system has low reflectance and high absorptance by almost matching their impedance with that of free space. These characteristics show typical absorption phenomena. So near-unity absorption is achieved at the designed spectral band.
Fig. 3. Retrieved effective physical parameters (a) permittivity, (b) permeability, (c) refractive index, and (d) impedance in the case of perfect absorption.
Fig. 4. The distributions of electric currents in the top surface of the metallic cross (a) and the VO2 film (b) for the magnetic resonance. The directions of them are opposite. The enhanced magnetic field in the spacer layer (c).
In practical applications, the direction of incident wave is random. It would be better if the performance of absorber is still well for different polarization and incident angle. Figure 5(a) shows absorptance as a function of polarization angle and frequency at normal incidence. The polarization angle varies from X direction (${0^\circ }$) to Y direction (${90^\circ }$). Because of the rotational symmetry of the system, one advantage of this absorber is independent on polarization angle. The calculated results also reveal that the proposed absorber is insensitive to polarization angle, indicating that its possible application is great. All of the above results are calculated at normal incidence. Actually, the performance of absorption is very important at oblique incidence because there is no ideal plane wave in practice. As shown in Figs. 5(b-c), absorptance spectra of transverse electric (TE) and transverse magnetic (TM) polarized waves are numerically obtained. Absorptance of TE polarization (${k_x},\;{k_z},\;{E_y},\;{H_x},\;{H_z}$) becomes to deteriorate when incident angle is larger than ${45^\circ }$. In this case, parallel component of magnetic field is getting weaker with the increasing of incident angle, and it will result in a weaker magnetic dipole resonance. So the coupling between electromagnetic field and the system becomes weaker. Absorptance of TM polarization (${k_x},\;{k_z},\;{E_x},\;{E_z},{H_y}$) does not change much even at incident angle of ${75^\circ }$. This is because magnetic field at large incident angles are still confined efficiently in the middle dielectric layer. So the designed absorber is polarization-independent of TE and TM waves over a wide range of incident angles.
Fig. 5. Polarization dependence at normal incidence (a) and angle dependence of absorber for TE (b) and TM (c) polarizations when VO2 is in the metallic state.
2.2 The designed switchable metamaterial behaves as an analog of electromagnetically induced transparency when VO2 is in the insulating state
Electromagnetically induced transparency is produced by destructive interference between two different quantum paths in a three-level atomic system. It can make the initially opaque medium transparent. But, due to the low temperature environment and the necessity of high intensity laser, potential applications of electromagnetically induced transparency are strongly limited in the atomic system. Because of the emergence of metamaterial and the promotion of new application prospects, various metamaterials using different structures with room temperature operation have been proposed to mimic the original quantum phenomenon of electromagnetically induced transparency. Recently, classical analogs of electromagnetically induced transparency mimicking quantum interference effect have attracted great interest due to its fascinating applications in plasmonic sensing and slow light device.
In classical plasmonic configurations, the coupling of a bright mode often induced in metallic rod and a dark mode often induced in SRR can result in destructive interference between the adjacent resonators, thus leading to a narrow transparency window within an opaque band. Here, when VO2 is in the insulating state, the top gold cross interacts with the bottom SRR giving rise to the production of an analog of electromagnetically induced transparency. Figure 6 shows the calculated results of transmission (${S_{21}}$) for the designed electromagnetically induced transparency at normal incidence, presenting three transmission curves of single gold cross, single gold SRR, and the whole system. The gold cross is excited with electric resonance at 0.538 THz, where the generated electric dipole parallel to incident electric field. SRR is excited with the magnetic resonance appearing at 0.54 THz. Electromagnetically induced transparency-like phenomenon occurs due to destructive interference between electric and magnetic resonances.
Fig. 6. Simulated transmission spectra for a single gold cross, a single gold SRR, and the whole structure at normal incidence when VO2 is in the insulating state.
To get a deeper understanding of the physics of this EIT behavior, surface current distributions are calculated in Fig. 7 at the frequencies of two transmission dips and a transmission peak. The direction of electric field is along Y axis. At the frequency of 0.477 THz, electric current in gold cross is strong, and electric current of SRR is very weak in the second and fourth quadrants. At the frequency of 0.505 THz, electric current is very strong in the second and fourth quadrants of SRR, which cannot be directly excited by external electric field. It should be noted that for external incident polarization, only the cut wire parallel to the incident electric field is excited, while for the SRR whose gap is perpendicular to the direction of incident polarization, it will not be excited. At the frequency of 0.6175 THz, electric current is strong in gold cross and the first and third quadrants of SRR, which can be directly excited by external electric field. The observed characteristics of electric current validate the existence of electromagnetically induced transparency. Therefore, destructive interference between gold cross and gold SRR leads to this phenomenon.
Fig. 7. Surface current distributions at the frequencies of 0.477 THz (a), 0.505 THz (b), and 0.6175 THz (c).
Transmission spectra are calculated for different polarization angles at normal incidence. As shown in Fig. 8(a), it can be found from the results that this analog of electromagnetically induced transparency can keep the same behavior when polarization angle varies. It is entirely determined by the symmetry of the designed structure, which contributes to desirable polarization-insensitive applications. Meanwhile, in order to verify the performance of this design under different incident angles, oblique incidence is also investigated. As shown in Figs. 8(b-c), with the increasing of incident angle for TE polarization and TM polarization, transmission behavior varies differently. The performance of the first dip at 0.477 THz is very stable for TE and TM polarizations when incident angle is smaller than ${45^\circ }$. For TE polarization, transmission peak will have a splitting when incident angle is larger than ${15^\circ }$, which is mainly caused by the change of vertical component of magnetic field. Transmission dip will be destroyed by the diffraction at 0.6175 THz. This behavior is also found for TM wave when incident angle is larger than ${20^\circ }$, because the wavelength in SiO2 will be effectively shorten.
Fig. 8. Simulated transmission of the designed metamaterial with different polarization angles at normal incidence (a) and incident angles of TE polarization (b) and TM polarization (c) when VO2 is in the insulating state.
3. Summary
A switchable metamaterial is presented with the dual-function design of absorber and analog of electromagnetically induced transparency. This design is based on the insulator-metal phase transition of VO2. When VO2 is in the metallic state, the designed switchable metamaterial behaves as a narrow absorber. Calculated results show that this narrow absorber is insensitive to polarization and works well even at larger incident angle [34,35]. When VO2 is in the insulating state, the interaction between the top gold cross and the bottom gold SRR leads to the formation of a classical analog of electromagnetically induced transparency. The performance of electromagnetically induced transparency is good at the small incident angle. Using the phase transition of VO2 between insulator and metal, the designed hybrid metamaterial without any geometrical changes can be switched from an absorber to an analog of electromagnetically induced transparency. Therefore, VO2 can pave a new way to achieve multiple functionalities in a single device for the development of optical switchable components [36–40]. This design of the switchable metamaterial may find some potential applications in the fields of thermal emitter, optical filter, and slow-wave device.
Funding
National Natural Science Foundation of China (11974294 11504305); Foundation of Fujian Educational Committee (JAT170002); Fundamental Research Funds for the Central Universities (20720180010); Natural Science Foundation of Fujian Province (2019J01005).
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