1. Introduction

Electromagnetically induced transparency (EIT) is a quantum destructive interference effect firstly observed in a three-level atomic system, characterizing by narrow and sharp transparency windows within a broad absorption spectrum [1]. This effect is accompanied with strong dispersion property and usually applied to achieve slow light phenomenon and enhanced nonlinear effect, etc. In the early stage of the EIT research, harsh experimental conditions such as stable laser source and ultra-low temperature are not accessible, which greatly hinder the potential applications. Thereafter, analogue EIT effect is observed in optical resonant systems such as photonic crystals [2] and plasmonic metamaterials [3], where strict experimental conditions are no longer needed. Then, practical applications based on EIT effect are proposed, like slow light devices [4,5], sensors [6,7] and optical memories [8], etc. In 2008, Zhang et al. firstly observed the EIT effect in a metal strip-based metamaterial under accessible experimental conditions [9]. Then, metal split-ring resonators are proposed to improve the performance by breaking structure symmetry and its Q-factor can reach up to 68 [10]. However, due to the inevitable ohmic loss and radiative loss of metallic materials, high Q-factor is hardly achieved in the near-infrared region [11]. Then dielectric metamaterials based on Mie resonance are proposed with low non-radiative loss and the pattern sizes are miniaturized down to nanoscale [12–16].

In order to meet the development of device multi-functionality, active metamaterials with tunable properties are highly needed since the functions are fixed once the structure is designed in passive ones. Therefore, active elements like graphene [17–20], phase change materials [21–23] and semiconductors [24,25] are widely used for tunable electromagnetic effects. Among all the active materials, vanadium dioxide (VO₂) is one of the most attractive candidates due to its reversible insulator-to-metal transition [26] at an accessible threshold of 340 K [27]. That is, VO₂ is in its insulate state with a monoclinic structure at room temperature and can easily change to metallic state with a rutile structure when the temperature is above the phase change threshold. Moreover, the phase transition of VO₂ can be attained not only by thermal effect but also by electric effect [28] and light excitation [29], which will greatly enrich the design options and expand its application scenarios.

Recent years, anisotropic metasurfaces are proposed to achieve polarization multiplexed EIT effects [30,31]. Due to the different electromagnetic coupling mechanism, two polarization-dependent EIT windows form with different properties. This enables applications at two independent polarization states and is greatly beneficial to the device miniaturization and integration. However, the latest researches in this area mainly focus on THz region and do not involve the attractive application of refractive index sensors. Extending the work to a shorter wavelength like near-infrared region with sensing application is of great importance for practical use, which has seldom been reported. Moreover, dielectric metasurfaces based on silicon is compatible with current integrated circuit technique in fabrication, which is advantageous for future optoelectronic device integration.

In this paper, we propose a simple anisotropic VO₂-Si based metasurface to achieve tunable EIT effect in the near-infrared region. Two sharp EIT peaks emerge at different wavelengths in the spectra under the excitation of x- and y-polarized light. The mechanism is further analyzed and electric and magnetic dipole resonances are responsible for the EIT effect. By changing the conductivity of VO₂, the EIT peak intensity can be actively manipulated without frequency shifting, which leads to a tunable slow light effect. The maximum group delay and group index can reach 3.25 ps and 5265 for x-polarized incidence and 6.48 ps and 10514 for y-polarized incidence, respectively. Moreover, it shows good performance as a refractive index sensor at room temperature, which the sensitivity (${S_x} = 717{\,}nm{\,}RI{U^{ - 1}}$, ${S_y} = 446{\,}nm{\,}RI{U^{ - 1}}$) and figure of merits ($FO{M_x} = 7{\rm{97}}$, $FO{M_y} = {\rm{1312}}$) are competitive with previous reports in near-infrared region. Therefore, the proposed metasurface presents polarization multiplexed EIT effect and has great application potential in optical modulations, slow light devices and sensors, etc.

2. Result and discussion

The proposed VO₂-Si based metasurface is schematically depicted in Fig. 1(a) and Fig. 1(b) is the metasurface unit cell with geometric parameters. Here, Si nanocube (SNC) and VO₂ nanocube (VNC) are arranged at intervals on quartz substrate. Optimized geometric parameters are selected and the thicknesses of SNC, VNC and substrate layer are all 185 nm. The side lengths of SNC and VNC are $a = 400{\,}nm$ and $b = 290{\,}nm$, respectively. The space between the two elements is $d = 245{\,}nm$ . Here, the software CST Microwave Studio is applied by using a finite element frequency domain solver. In the simulation, periodic boundary conditions are set at x and y directions, and the period ${p_x} = {p_y} = p = {\,}1500{\,}nm$ . The proposed metasurface is excited by normally incident x- and y-polarized light along the z direction.

 

Fig. 1. (a) The schematic of the proposed polarization multiplexed EIT metasurface. (b) Top and side views of the metasurface unit cell.

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In the simulation, the permittivity of Si and quartz substrate are set as 11.9 and 2.19, respectively. As a typical phase-change material, the property of VO₂ in the near-infrared region can be obtained from experiment. At room temperature, VO₂ is in its insulate state and the permittivity of VO₂ is approximately 9 [27,32]. When the temperature is above the phase transition threshold, VO₂ changes into metallic state which can be described by the Drude model:

Here, the permittivity at the infinite frequency is ${\varepsilon _\infty } = 3.95$, plasma frequency is ${\omega _p} = 3.33{\,}eV$ and scattering rate is $\gamma = 0.66{\,}eV$ [33]. Moreover, in simulation the conductivity of VO₂ is chosen to be 20 S/m for the insulate state and 10⁵ S/m for the metallic state [34].

To explore the optical performance of the VO₂-Si based metasurface in the near-infrared region, the transmission spectra for x- and y-polarized light incidence are simulated at room temperature, as shown in Fig. 2(a). Two sharp EIT windows emerge at 1436.1 nm and 1417.2 nm respectively and the peak intensities can reach up to 97% for both polarization states. Full width at half maximum (FWHM) and quality factor (Q-factor) are introduced to describe the property of the EIT effect by $Q = {\lambda _0}/FWHM$, where ${\lambda _0}$ is the central wavelength of the EIT peak. In this way, the FWHM and Q-factor of the two EIT peaks are calculated to be 0.8 nm and 1795 for x-polarization condition and 0.3 nm and 4724 for y-polarization condition. Here, the resonance wavelength, transmit intensity, FWHM and Q-factor of the two modes are different, which are considerable in the metasurface designing. The polarization dependent effect indicates that the metasurface is a good candidate for polarization multiplexed EIT device, which can flexibly switch the EIT phenomenon on demand by alter the incident polarization state.

 

Fig. 2. (a) Simulated transmission spectra for x- and y-polarized light incidence. (b) Simulated transmission spectra of the sole VNC and SNC.

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The transmission properties of the sole SNC and VNC are shown in Fig. 2(b). Due to the structure symmetry in x and y axis, the same spectra are observed for both x- and y-polarized light incidence. A transmission dip shows up at 1411.9 nm in the sole SNC, while a constant transmission amplitude is detected for the sole VNC. The electric and magnetic field distributions of SNC (y-polarization, 1411.9 nm) are further analyzed in Fig. 3(a) and 3(b), and the results are obtained from the middle cross section of the SNC. Clearly, the electric field concentrates around the SNC and rotates clockwise while the magnetic field passes through it from right to left, which indicates the SNC serves as a dipole antenna and couples strongly to the free-space excitation. Therefore, the bright mode resonance is formed in the SNC. For the sole VNC, no transmission dip is observed in the spectrum and the electric and magnetic fields are quite weak compared with the SNC ones, which indicates the VNC cannot be directly excited by the incident light and works as the dark mode. Moreover, the coupling between the bright and dark modes results in the collective oscillation in SNC. To be more specific, the interference between the two modes forms a typical 3-level resonant system, as shown in Fig. 3(e). $|0\rangle$ is the ground state, $|1\rangle$ is the metastable state and $|2\rangle$ is the excited state. In our case, the bright mode is excited along the direct path ($|0\rangle\rightarrow|2\rangle$) and the dark mode is excited along the indirect path ($|0\rangle\rightarrow|2\rangle\rightarrow|1\rangle\rightarrow|2\rangle$. Destructive interference occurs in the two excitation pathways between the bright and dark modes, which generates the EIT effect as a result.

 

Fig. 3. (a, b) Simulated electric and magnetic field vector diagrams of the sole SNC for y-polarized incidence at the dip position of 1411.9 nm. (c, d) Simulated electric and magnetic field vector diagrams of the sole VNC for y-polarized incidence at 1411.9 nm. (e) Schematic diagram of the interference between the bright and dark modes.

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To explore the underlying mechanism of the polarization dependent EIT phenomenon, the electromagnetic field distribution and the vector diagrams at EIT peak wavelength are analyzed and shown in Fig. 4. All the results are obtained from the middle cross section of the nanocubes. When the proposed metasurface is excited by x-polarized light, the electric field mainly concentrates near the upper and lower surface of the SNC and passes through it from top to bottom, while the magnetic field rotates clockwise in the SNC. According to the Mie-type resonance theory, this is the typical electromagnetic field distribution of electric dipole (ED) resonance and suggests it occurs at the EIT peak position of 1436.1 nm [35,36]. For the y-polarization incident condition, the electric field concentrates inside the SNC and rotates clockwise, and the magnetic field passes through from bottom to top. That is, magnetic dipole (MD) resonance occurs at the EIT peak position of 1417.2 nm [37,38]. It is worth to mention that the magnetic field are mainly restricted in the SNC due to the strong MD resonance, resulting in a small energy loss. Therefore, the Q-factor of the y-polarized condition is higher than that of the x-polarized condition.

 

Fig. 4. Simulated electric and magnetic field distribution and vector diagrams at the two EIT peak positions. (a-d) Top and cross section views indicate the electric dipole resonance occurs for the x-polarized condition at 1436.1 nm. (e-h) Top and cross section views indicate the magnetic dipole resonance occurs for the y-polarized condition at 1417.2 nm.

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The far-field scattered power in the Cartesian coordinate system is further calculated to evaluate the ED and MD resonance contribution in the EIT effect, which the multipole intensity formulas [19,39] are used in the calculation. Here, only five dominant scattering powers of multipoles are considered, which are electric dipole, magnetic dipole, electric quadrupole, magnetic quadrupole, and toroidal dipole, respectively. They are abbreviated as ED, MD, EQ, MQ and TD. The normalized results near the EIT peaks are shown in Fig. 5. Obviously, the power of EQ, MQ and TD are so weak and their contributions can be ignored. The intensity of ED (MD) reaches a maximum at the resonant wavelength for x-pol (y-pol) incidence, which is several times greater than that of MD (ED). In other words, ED (MD) dominates the EIT generation in x-pol (y-pol) condition, which strongly supports our previous viewpoints.

 

Fig. 5. Normalized scattered power of multipoles of the proposed metasurface. (a) x-polarized condition. (b) y-polarized condition.

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On the other hand, the EIT-like effect can be dynamically modulated by adjusting the conductivity of VO₂ upon thermal effect. Figure 6(a) and 6(c) depict the transmission spectra at the near-infrared region when the conductivity of VO₂ changes from 20 S/m to 10⁵ S/m for x- and y-polarized light incidence. To characterize the EIT effect intuitively, we plot the point-line diagram of the transmission intensities at the two EIT peak wavelengths with different conductivity of VO₂, as shown in Fig. 6(b) and 6(d). As the conductivity of VO₂ increases, the peak transmission for both the two polarization states decrease rapidly in Fig. 6(a) and 6(c), the minimum values of peak transmission are 28% and 6% for x- and y-polarized conditions, respectively. When the transmission at peak wavelength is lower than that at two dips, we consider the EIT phenomenon disappears. Therefore, the effect disappears at 2×10⁴ S/m (x-pol) and 3×10⁴ S/m (y-pol). After that, the transmission intensity increases slowly with the increasing conductivity and finally reaches 61% and 19% at 10⁵ S/m. Figure 6(b) and 6(d) intuitively show the evolution of the EIT phenomenon. The blue curve represents the change of the EIT peak transmission intensity and the red curve shows the transmission intensity without EIT effect. Furthermore, the conductivity modulation only changes the peak intensity and its wavelength is stabilized. This is also one of the advantages of VO₂ as the active element.

 

Fig. 6. (a, c) Simulated transmission spectra for x- and y-polarized light incidence when the conductivity of VO₂ is setting as 20 S/m, 2×10² S/m, 2×10³ S/m, 2×10⁴ S/m, 4×10⁴ S/m, 10⁵ S/m. (b, d) The transmission intensities at the EIT peak position for x- and y-polarized incidences.

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The electromagnetic field distribution at different conductivity of VO₂ is also plotted in Fig. 7. The strongest electromagnetic field emerges at 20 S/m and it weakens as the conductivity of VO₂ increases. Then, the electric dipole and magnetic dipole completely disappear when VO₂ turns into metallic state, resulting in the disappearing of the EIT peak. The modulation depth of the transmission is defined as $({T_{(peak,max)}} - {T_{(peak,min)}}) \times \mathit{100}\%$, which is up to 70% and 91% for x- and y-polarized conditions, respectively. From another aspect, the modulation depth can also be defined as $({T_{(peak,insulator)}} - {T_{(peak,metalic)}}) \times \mathit{100}\%$, and the values are 37% and 78%. In a word, the tunable EIT effect is achieved by adjusting the conductivity of VO₂, and the on/off states of the EIT effect can be easily realized in the phase transition process.

 

Fig. 7. The changes of the electric and magnetic field distributions at different conductivity of VO₂.

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Slow light characteristics is one of the most charming applications of EIT effect. For the proposed metasurface, a tunable slow light effect is achieved with polarization multiplexed ability. The group delay and group index of the EIT effect are calculated as [40]:

Here, ${\tau _g}$ is the group delay, ${n_g}$ is the group index, $\varphi $ is the phase, $\omega $ is the angular frequency, c is the light speed in vacuum, ${v_g}$ is the group velocity and h is the thickness of the proposed metasurface. Figure 8 shows the group delay and group index of the EIT metasurface with different conductivity of VO₂. For both polarization states, the maximum value of group delay and group index is obtained when VO₂ is in its insulate state. As for the x-polarized condition, the group delay decreases from 3.25 ps to 0 ps and the group index decreases from 5265 to 0 when the conductivity of VO₂ changes from 20 S/m to 2×10⁴ S/m. As the conductivity of VO₂ continues to increase, the values of group delay and group index remain 0. It is because when the conductivity is higher than 2×10⁴ S/m, the EIT effect completely disappears as well as the slow light effect. Similarly, for the y-polarized condition the group delay and group index can be manipulated from 6.48 ps to 0 ps and 10514 to 0, respectively. In other words, the group velocity can be flexibly manipulated from c/5265 to c (x-pol) and c/10514 to c (y-pol) by changing the conductivity of VO₂ from 20 S/m to 10⁵ S/m. Therefore, a tunable slow light phenomenon is achieved in the polarization dependent EIT metasurface, which promises potential applications in integrated slow light device.

 

Fig. 8. Group delay and group index for the proposed metasurface. (a) x-polarization condition. (b) y-polarization condition.

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On the other hand, the narrow-band transparency window is extremely sensitive to the minor changing of the surrounding refractive index, and enables the proposed metasurface as a high-performance polarization multiplexed sensor. In order to evaluate its refractive index sensing performance, a factor of figure of merit (FOM) is introduced, which is defined as [41]:

Here, S is the wavelength shift per refractive-index-unit change and $\varDelta \lambda$ is the linewidth of the transmission peak. Firstly, the transmission spectra at different refractive index are shown in Fig. 9. Sharp EIT windows are clearly observed and show a red-shift with the increasing refractive index. By plotting the peak wavelength in Fig. 9(b) and 9(d), the curves are fitted and the slopes are calculated as the sensitivity of the refractive index sensor, which are as high as (${S_x} = 717{\rm{\;\;}}nm{\rm{\;\;}}RI{U^{ - 1}}$, ${S_y} = 446{\rm{\;\;}}nm{\rm{\;\;}}RI{U^{ - 1}}$), respectively. Here the subscripts x and y represent the polarization states of the incident light. Combined with average linewidth of $\varDelta {\lambda _x} = 0.90{\rm{\;\;}}nm$ and $\varDelta {\lambda _y} = 0.34{\rm{\;\;}}nm$, the FOM is calculated as ($FO{M_x} = 7{\rm{97}}$, $FO{M_y} = {\rm{1312}}$). Compared with previously reported results, the sensor presents comparable sensitivity and higher FOM values in the near-infrared region [12,19] for both incidence conditions. It is worth mentioning that the conductivity of VO<INF>2</INF> is stable at room temperature, therefore the sensor prototype has not only better performance but also high reliability.

 

Fig. 9. (a, c) Simulated transmission spectra shift with the change of environment refractive index for x- and y-polarized incidences. (b, d) Fitted curve of peak shift for x- and y-polarized incidences.

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3. Conclusion

In conclusion, a VO₂-Si based dielectric metasurface is proposed to achieve polarization multiplexed EIT effects with tunability in the near-infrared region. Distinct and sharp EIT windows appear at the incidence of x- and y- polarized light, which is ascribed to the strong electric and magnetic dipole resonance. The Q-factors of the EIT windows can reach up to 1795 (x-pol) and 4724 (y-pol) with insulating VO₂, and lead to strong dispersion and large group delays. Accompanied with the phase transition process, the conductivity of VO₂ experiences a great change and results in tunable EIT phenomenon. The total modulation depth of the transmittance can reach up to 70% (x-pol) and 91% (y-pol), respectively. Tunable slow light effect and large group delay is also observed. The group velocities can be continually manipulated between c/5265∼c (x-pol) and c/10514∼c (y-pol) for the two incident conditions. Moreover, the proposed metasurface can work as a polarization multiplexed refractive index sensor in the near-infrared region with high sensitivity (${S_x} = 717{\rm{\;\;}}nm{\rm{\;\;}}RI{U^{ - 1}}$, ${S_y} = 446{\rm{\;\;}}nm{\rm{\;\;}}RI{U^{ - 1}}$) and figure of merit ($FO{M_x} = 7{\rm{97}}$, $FO{M_y} = {\rm{1312}}$). Therefore, this work provides a new prototype for the design of tunable metasurface, which will be beneficial to the development and application of optical modulations, tunable slow light devices and high-performance refractive index sensors.