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Abstract
Here we propose a hybrid dielectric waveguide grating with an ultrathin vanadium dioxide (VO2) thin film for achieving switchable dual-functional GMR filters. We show that, when the VO2 thin film undergoes the insulator-to-metal phase transition, the hybrid dielectric waveguide gratings enable the switch between the reflection and transmission filters. This work expands the research topic of GMR and provides valuable strategy for the design of novel reconfigurable devices for photonics.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Guided-mode resonance (GMR) refers to rapid variations in the intensity of propagating waves diffracted by a dielectric waveguide grating structure. Physically, resonant waveguide grating structures utilize a periodic modulation of the refractive index to couple the diffracted fields from an incident wave into a leaky guided mode supported by the structure [1–3]. Optical devices based on GMR effect have attracted considerable interest in recent decades due to their simple structures and versatile spectral characteristics. Examples such as narrowband filters [4–8], wideband reflectors [9,10], wideband polarizers [11,12], and polarization-independent elements [13] have resulted in revolutionary developments in applications from optical communications [14] to display [15] and sensing [16]. Usually, the functionality of conventional optical GMR devices is locked at the design stage, i.e., their spectral response is fixed by the grating profiles, geometrical parameters, and constituent material properties of the dielectric waveguide grating structure used. Compared to passive GMR devices, active GMR devices whose functionalities can be dynamically manipulated in both the space and time domains are very under-explored topic (although some interesting approaches have been made, for example by incorporating electro-optical material into structures [17–19]).
In this work, we address this important omission by developing novel hybrid dielectric waveguide grating structure, in which active control is achieved by incorporating an ultrathin vanadium dioxide (VO2) thin film into structure. VO2 is a phase-change material that has a reversible insulator-to-metal phase transition close to critical temperature of ∼340 K [20], by appropriate thermal [21], electrical [22], or optical stimuli [23]. Across the insulator-to-metal phase transition, the conductivity of VO2 can change by 4 ∼ 5 orders of magnitude, and its structural phase can be switched quickly (picosecond or faster) [24] and repeatedly (up to millions cycles) [25] between insulating and metal states. Therefore, VO2 is widely applied in many tunable and switchable applications [26–32]. To the best of our knowledge, the combining GMR effects with insulator-to-metal phase transition of VO2 thin films to achieve the functionality inversion of GMR filter, i.e., the spectral response of GMR filter is reversed, has never been reported.
2. Results and discussions
Figure 1(a) schematically shows the configuration we propose for dynamically tunable GMR filters; the top is an ultrathin VO2 grating, the second layer is a silicon grating, the third is a silica separation layer, the fourth is a silicon waveguide layer, and the bottom is a silica substrate. The physical parameters of device are denoted as follows: permittivity ɛ, grating period P, duty factor F, and thicknesses t, as shown in Fig. 1. The permittivity property of VO2 in the THz region was described by the Drude model ${\varepsilon _1}(\omega ) = {\varepsilon _\infty } - \omega _p^2/({\omega ^2} + i\omega \gamma )$[20], where ${\varepsilon _\infty } = 12$ is the permittivity at high frequency limit, $\gamma = 5.75 \times {10^{13}}$rad/s is the collision frequency, and ${\omega _\textrm{p}}$ is the plasma frequency dependent on the conductivity $\sigma$: $\omega _p^2 = (\sigma /{\sigma _0})\omega _p^2({\sigma _0})$ with ${\omega _p} = 1.4 \times {10^{15}}$rad/s for ${\sigma _0} = 3 \times {10^5}$S/m. In our simulation, the conductivity $\sigma$ of VO2 is assumed to be 10 S/m ($2 \times {10^5}$S/m) when it is in the insulating (metallic) state [20]. The phase-transition process of VO2 can be mimicked by the two assumptions. The permittivities of insulating and metallic VO2 thin films in the THz range are plotted in Figs. 1(c) and (d). In the insulating state, the VO2 can be considered as a nearly lossless dielectric. In the metallic state, the VO2 exhibits a huge negative real part of permittivity, which is crucial to achieve the functionality inversion of GMR filters.
Fig. 1. (a) Schematic configuration of the hybrid dielectric waveguide grating structure. (b) Front view of the unit cell of the hybrid dielectric waveguide grating structure. Spectral dispersion of the real and imaginary parts of the permittivity of insulating (c) and metallic (d) VO2 thin films in the THz range.
In this work, we focus on the dynamically tunable polarization-dependent filter functionality. To explore the resonant response of the hybrid dielectric waveguide grating structure, we need solve the eigenmode equation describing guided modes for this structure. Since the waveguide layer is separated from the grating by a low-index separation layer, the guided mode localized at the waveguide layer is weakly perturbed by the grating. In the case, we can ignore the influence of grating period on the dispersion relationship of guided modes. Therefore, the eigenmode equation describing guided modes for this hybrid dielectric waveguide grating structure is similar to that of the uniform dielectric slabs, which is given by [33]
Fig. 2. (a) Calculated dispersion curve of the guided-mode for the TM-polarized lights in uniform dielectric slabs. (b) Transmission response of the hybrid dielectric waveguide grating structure for the normal-incidence TM-polarized lights when the VO2 is in the insulating (blue solid line) and metallic (red dashed line) states. Transmission as a function of the frequency and the VO2 grating thickness when VO2 is in the insulating (c) and metallic (d) states. Field distributions (|Hy|) at the resonant frequency of 1.22715 THz when VO2 is in the insulating (d) and metallic (e) states.
To identify the theoretical analysis, we calculated the transmission spectral response of hybrid dielectric waveguide grating structure for the normal incident TM-polarized lights using rigorous coupled wave analysis (RCWA) [34], as shown in Fig. 2(b). To ensure excellent numerical convergence of the results, 10 Fourier harmonics are retained in our calculations. Here the thickness of VO2 grating is ${t_1} = 0.8$μm. The duty factor is selected as F = 0.91 for achieving narrow linewidth and symmetrical line shape. In Fig. 2(b), the results show that the resonance occurs at the frequency of f = 1.22715 THz, which agrees well with the theoretical analysis in Fig. 2(a). When the VO2 is in the insulating state, a transmission dip with near zero transmission is obtained at the resonant frequency of f = 1.22715 THz with the spectral full width at half maximum (FWHM) of 0.0022 THz, and the sideband transmission is larger than 94% in the frequency range of 1.15–1.3 THz. In this case, the device in the insulating state can be served as a high-efficiency and narrowband reflection filter. In contrast, when the VO2 is in the metallic state, a transmission peak with a transmission of 87% is formed at the same resonant frequency with the spectral FWHM of 0.0092 THz, while the sideband transmittance is less than 3% in the frequency of 1.15–1.3 THz. As a consequence, the device in the metallic state can be served as a high-efficiency and narrowband transmission filter. The switchable filter functionality is a significant improvement compared with active GMR devices previously reported, where the filter functionality was only switched between on and off, but not reversed [17–19].
It should be emphasized that the VO2 grating plays a critical role in achieving switchable filter functionality. Therefore, we evaluate the influence of the VO2 grating thickness on the device performance in the insulating and metallic states. The transmission contours of device are calculated as a function of frequency and the VO2 grating thickness for the normal incident TM-polarized lights, as shown in Figs. 2(c) and 2(d). In the insulating state, the resonant frequency almost does not change when the VO2 grating thickness changes from 0 to 2.5 μm. The switchable filter functionality can be observed when the VO2 grating thickness is larger than 0.25 μm. And in both states, keeping all the other geometrical parameters the same, the resonant frequency almost does not change when the VO2 grating thickness changes from 0.25 to 2.5 μm. Therefore, the switchable GMR filter has the good fabrication tolerances for the VO2 grating thickness.
To illustrate the physical mechanism of the TM-polarized reflection and transmission filters, we calculate the field distributions at the resonant frequency of f = 1.22715 THz in the x-z plane, as shown in Figs. 2(c) and 2(d). In both states, the fields are strongly localized in the waveguide layer and show a predominant TM0 shape but with different amplitudes. These features indicate that the GMR are excited simultaneously in the both states. In principle, the transmission filter functionality is achieved due to the destructive interference between the broad background reflection provided by the metallic VO2 grating and the narrow GMR reflection of the dielectric waveguide grating. As a consequence, the destructive interference leads to a transmission enhancement at the resonance. In Fig. 2(b), we note that the peak efficiency of transmission filter in the metallic state does not reach 100% and the FWHM of filter increases compared to the insulating state; this is because that the loss of VO2 in metallic state leads to the absorption of part of the incident lights. On the other hand, the metallic VO2 gratings enhance the intensity of evanescent diffraction waves. A stronger evanescent diffraction wave indicates a stronger coupling between the guided mode and the incident lights, which, in turn, yields increased FWHM.
According to wavevector match condition of Eq. (3), the operating frequency of GMR filters is highly sensitive to the incident angles. Figures 3(a) and 3(c) illustrate the spectra as a function of the incident angle θ for the hybrid dielectric waveguide gratings. At nonnormal incidence (θ≠0), the resonance is split into two branches due to the coupling of the +1 and −1 evanescent diffracted wave to the guided mode of the waveguide occurring at different frequencies. The sensitivity of the resonance location to the incident angle can be used effectively to tune the operating frequency of the filter to the desired value. Here it should be noted that the peak value of filter is also highly sensitive to the incident angles when the VO2 is in the metallic state. For the branch of high frequency, the peak value of filter is declined gradually as the incident angle increases; this is because that the reflection phase of metallic VO2 grating is changed when the incident angle is nonnormal. As a consequence, the destructive interference between the broad background reflection provided by the metallic VO2 grating and the narrow GMR reflection of the dielectric waveguide grating is destroyed. For the branch of low frequency, the peak value of filter is increased gradually as the incident angle increases; this is because the reflection phases of GMR at the two branches are opposites. As a consequence, the peak value of filter at the low frequency has opposite evolution compared with high one.
Fig. 3. Transmission as a function of the frequency and the incident angle when VO2 is in the insulating (a) and metallic (b) state. The geometric parameters are the same as in Fig. 2(b).
On the other hand, the frequency-adjustable filters can also be obtained by changing the geometric parameters of devices. The dielectric grating (the second layer) acts as a coupler, which enables a wavevector match between the incident light and guided mode in the waveguide layer. When the grating period is varied, the wavevector match condition will change. From Eqs. (1) and (3), we can obtain the desired resonant frequency by suitably tuning the grating period. Figures 4(a) and 4(c) show the transmission responses of the devices with various grating periods. The relationship between the resonant frequency and the grating period is shown in Fig. 4(e). The resonant frequency decreases with the increase in the grating period. The resonant frequencies obtained by RCWA (orange stars) agree well with the theoretical analysis (blue line) [see Fig. 4(e)]. On the other hand, the waveguide layer, served as an optical cavity, plays an important role in controlling the confinement and interference of lights. The geometrical variations of waveguide layer will modify the cavity dimension, and hence change the resonant frequency. Figures 4(b) and 4(d) show the transmission responses of the devices with various thickness of waveguide layer. The relationship between the resonant frequency and the thickness of waveguide layer is shown in Fig. 4(f). The resonant frequency decreases with the increase in the thickness of waveguide layer. And we note that the spectral lineshape and sideband level are altered when the thickness of waveguide layer changes. The symmetrical lineshape and low sideband level can be obtained by virtue of antireflection design of thin-film structure by suitably tuning the thickness of silica separation layer.
Fig. 4. Transmission responses of the hybrid dielectric waveguide grating structure with various periods of the grating (a, c) and thicknesses of waveguide layer (b, d) for a normal-incidence TM-polarized lights when the VO2 is in the insulating (a, b) and metallic (c, d) state. The remaining parameters are the same as in Fig. 2(b). The resonant frequency as a function of the grating period (e) and the thickness of waveguide layer (f).
The switchable filter functionality demonstrated above only works at the single frequency at the normal incidence. In practice, however, the multi-channel device is highly desired. From Eq. (1), the order of the guided mode will increase with the increase in the thickness of waveguide layer. Figures 5(a) and 5(c) show the transmission responses of the hybrid dielectric waveguide grating structure with the increased thickness of waveguide layer for the normal-incidence TM-polarized lights. The double- and three-channel switchable filters are obtained when the thicknesses of waveguide layer increase to t4 = 123 μm [see Fig. 5(a)] and t4 = 190 μm [see Fig. 5(c)], respectively. By contrast, for incident TE-polarized light (electric field parallel to the y direction), the switchable filter functionality can not be achieved [see Figs. 5(b) and 5(d)]; this is because that the background reflection provided by the metallic VO2 grating is nearly 100% for incident TE-polarized lights, resulting in the incident lights can not be coupled into the waveguide layer. As a consequence, the GMR effects in TE polarization can not be excited when the VO2 is in the metallic state.
Fig. 5. Transmission spectra of the hybrid dielectric waveguide grating structure with the thickness of waveguide layer t4 = 123 m (a, b) and t4 = 190 m (c, d) for the normal-incidence TM- (left) and TE-polarized (right) lights when the VO2 is in the insulating and metallic states.
3. Conclusion
In conclusion, a novel hybrid dielectric waveguide grating structure with an ultrathin phase-change material VO2 is proposed to realize the switchable optical GMR filter functionalities in the THz region. The switchable functionality is achieved by combining GMR effects in dielectric waveguide gratings with metal-insulator phase transition of VO2 thin films. Although this is a theoretical work, our scheme is feasible experimentally [26]. Benefitting from the strong switching effect, the hybrid dielectric waveguide grating structure may find many potential applications in terahertz technologies, such as dynamically tunable terahertz filters, linearly polarizers, polarization modulators, and other reconfigurable devices for terahertz radiations.
Funding
Major Discipline Academic and Technical Leaders Training Program of Jiangxi Province (20204BCJ22012); National Natural Science Foundation of China (12064025, 11604136).
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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