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Abstract
We experimentally investigated the terahertz (THz) reflection modulation property of tungsten-(W-) doped vanadium dioxide (V1-xWxO2) thin film enabled by impedance matching at the interface, which behaves as a giant modulation within a broadband THz frequency range during insulator-to-metal transition. A systematical theoretical model for impedance matching is also established, which includes three factors: sheet conductivity of V1-xWxO2 thin film, incidence angle of THz wave, and refractive index of substrate. With the modeling, we demonstrated a method to continuously tune the impedance matching at the interface of substrate-V1-xWxO2 thin films-air. Four different conductivities of V1-xWxO2 thin films realized by tuning W-doping densities (x = 0, 0.35%, 0.51%, and 1.06%), three incident angles (35°, 45°, 60°), and three substrates (SiO2, Al2O3, and Si,) with refractive indices of 1.95, 2.7, 3.4 were used in our experiments to validate our proposed model. These results provide a promising route for continuously tuning broadband THz wave modulation with the impedance matching effect at the thin film interface.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High performance devices to manipulate and control terahertz (THz) waves, such as modulators and active filters, are in high demand to develop sophisticated communication and imaging systems [1–4]. Recently, high-efficiency tuning THz waves have been extensively studied and many materials including semiconductors [6,7], 2D materials [8–10], phase transition oxides [5,11,12] and metamaterials [13,14], have been used for THz modulating and switching. As a typical phase transition oxide, vanadium dioxide (VO2) is widely used to modulate THz waves with high modulation depth [20,21] based on insulator-metal transition (IMT) [15], which can be induced by temperature [16], electric fields [17], light [18] and pressure [19]. In transmission geometry, amplitude modulation depth of 85% is experimentally obtained by pristine VO2 thin films [11,20]. In our previous works [21], we proposed a more-effective THz amplitude modulation method based on impedance matching in reflection geometry, and experimentally achieved an amplitude modulation depth of 97.6% between the impedance matching state and metallic phase for 280 nm pristine VO2 thin films with THz incident angle of 35-degree. However, the temperature of impedance matching is too high for practical application. Moreover, previous works demonstrate that the modulation depth based on impedance matching was sensitive to the resistance switching characteristics of VO2 thin films. The impedance matching is also correlated with incident angle, the refractive index of the substrate and so on [22,23]. Therefore, by modifying the phase transition properties in the V1-xWxO2 thin films, the incident angle of THz wave and the refractive index of substrate, continuously tuning the impedance matching, is meaningful for the reflective THz wave modulation based on impedance matching.
In this work, we report on a systematic study of the effect of the incident angle, the refractive index of substrate and the phase transition properties of VO2 thin films on THz reflection modulation properties based on impedance matching. Our results show that a nearly room temperature of impedance matching can be achieved by continuously tuning the impedance matching based on varying the incident angle of THz wave, the refractive index of substrate, and the W doping of VO2 films. We believe that these results could offer insights into developing the high-performance THz wave modulators for practical applications.
2. Theoretical model
A schematic illustration of tiny reflections of THz wave at impedance matching state of VO2 thin films is shown in Fig. 1. Based on Fresnel equation, we can derive the relative amplitude reflection coefficient of the substrate/VO2 interface, rVO2-ref, as shown below [22]:
Fig. 1 Schematic illustration of tiny reflections of THz wave based on impedance matching in VO2 thin films. The influence factors of impedance matching are described (the refractive index of substrates n Sub, the incident angle θ Sub and the effective conductivity σ eff).
where θAir is the incident angle of THz from air medium to substrate medium, θSub is the incident angle of THz wave from substrate medium to VO2 thin film. The refractive indices of air and substrate were regarded as frequency independent constants with values of nAir = 1 and nSub, respectively. Z0 = 377Ω is the impedance of free space. σ represents the sheet conductivity of VO2 thin films, which equals d × σbulk. (d is the thickness of VO2 thin film and σbulk is the bulk conductivity).
When the relative amplitude reflection of THz wave rVO2-ref is zero, the impedance matching phenomena will emerge. The relationship of impedance matching on the incident angle, the refractive index of substrate and conductivity are described as [22]:
From the Eq. (2), the conductivity of impedance matching is determined by the refractive index of substrates and the incident angle of THz. The conductivity of impedance matching can be derived from Eq. (2) for fixed substrate and incident angle. We can achieve the impedance matching state when the effective sheet conductivity σ eff of VO2 films equal the conductivity of impedance matching σ match as the Eq. (3) show.
The effective conductivity σ eff of VO2 can be continuously changed during IMT, and the effective conductivity σ eff of VO2 film can be described as follows [28,29]
𝜎metal and 𝜎insulator are the conductivity of the metallic phase and the insulating phase, fm and fi (fm + fi = 1) represent the volume fraction of the metallic and the insulating phase, respectively.
- (1). The properties of VO2 thin films
From the Eq. (3-5), the effective sheet conductivity σ eff of VO2 equals d × σeff bulk (σbulk is the effective bulk conductivity), which was determined by the properties of VO2 thin films, including the thickness of VO2 thin films, temperature of phase transition, the conductivity of the metallic phase and the insulating phase. The thickness of VO2 thin films were discussed in our previous work [21] and the thickness were 200 nm for all VO2 thin films in this work. The impedance matching temperature can be reduced due to lower phase transition temperature in V1-xWxO2 thin films.
- (2). The incident angle of THz wave
From the Eq. (2), when the refractive index of substrate nSub is constant, the conductivity of impedance matching σ match decreases with the increasing incident angle of THz wave (less than Brewster angle). Thus, the impedance matching temperature will reduce and the relative reflection of metallic phase of VO2 thin films will enhance at a large incident angle.
- (3). The refractive index of substrate
From the Eq. (2), when the incident angle of THz wave is constant, the conductivity of impedance matching σ match increases with the increasing refractive index of substrate. Thus, the impedance matching temperature will increase and the relative reflection of metallic phase of VO2 thin films will decrease on a high refractive index substrate.
In general, the phase transition properties of VO2 thin films, the incident angle of THz wave and the refractive index of substrates directly determine the impedance matching of VO2. To verify these theoretical conclusions, we experimentally studied the THz reflection modulation properties of VO2 thin films based on impedance matching by designing the different V1-xWxO2 films, different substrates and different incident angles.
3. Experimental setup, material fabrication and characteristic
In our experiment, we used our homemade terahertz time-domain spectroscopy (THz-TDS) system in refection mode [21] to investigate the impedance matching properties of VO2 films and the corresponding THz wave modulation properties by thermally inducing IMT. As shown in Fig. 1, the measured THz wave signal from the air/substrates interface was considered as reference signal, denoted Er1 and the changed THz wave signal from the substrates/VO2/air interface denoted Er2, was used to observe the impedance matching. The phase transition of all VO2 thin films were thermally triggered by steady heating on a thermostatic stage. The pristine VO2 thin films on different substrates (SiO2, Al2O3 and Si) and three kinds of different doped W content V1-xWxO2 thin films on SiO2 substrate were fabricated by using the inorganic sol-gel method [5]. By adjusting the coating time, the thickness of all VO2 thin films were controlled about 200 nm.
Figure 2(a-d) show the thermal hysteresis resistivity loops of the V1-xWxO2 thin films on SiO2 substrate with various doping concentration. The inset shows the derivative of the resistivity for the heating and cooling (red) transition curves (blue), which indicate the phase transition temperature of heating and cooling in the different V1-xWxO2 thin films. For the pristine VO2 and V1-xWxO2 thin films, they were all insulator phase at 25 °C and metallic phase at 90 °C and their phase temperature decreased with increasing W doped concentration. The figure shows that the resistivity decreases greatly when the V1-xWxO2 thin films transform into the metallic phase. It is observed that the V1-xWxO2 thin films with different doped concentration have different resistivity switching ratios. The resistivity of W-doping VO2 films declines than pristine VO2 films is observed at room temperature. The resistivity of W-doping VO2 films decreases with the increased doping contents, which is consistent with previous reports [24,26,27]. Figure 2(e) shows the phase transition temperature of V1-xWxO2 thin films with elevated W doped concentration. For the V1-xWxO2 thin films with the phase transition temperature are 61°C, 58°C, and 47°C, the corresponding W doped concentration are 0.35%,0.51%, and 1.06%, respectively. Figure 2(f) shows a typical XRD pattern of V1-xWxO2 thin films with different W doped concentration and it reveals to highly oriented (011) pristine VO2 and V1-xWxO2 thin films.
Fig. 2 (a-d) Thermal hysteresis resistivity loops of the V1-xWxO2 thin films with various doping concentration, the arrows indicate the heating and cooling process. The inset shows the derivative of the resistivity for the heating (red) and cooling (blue) transition curves. The phase transition temperature of heating and cooling in the different V1-xWxO2 thin films are indicated by red and blue words. (e) Phase transition temperature of V1-xWxO2 thin films with elevated W doped concentration. (f) XRD patterns of the different V1-xWxO2 thin films on SiO2 substrate.
4. Experimental results
4.1. Impedance matching in different V1-xWxO2 films
Figure 3(a-d) show the measured time-domain electric fields of the reflective THz pulses for four different V1-xWxO2 (x = 0, 0.35, 0.51, and 1.06%) thin films during IMT at 45-degree incident angle. As shown in figures, for all the four V1-xWxO2 thin films, the amplitude of Er2 reaches a minimum because of impedance matching by the conductivity of VO2, and afterwards increases with reversal of the pulse’ phase (valley-peak to peak-valley). The temperature (Tc), at which the conductivity of V1-xWxO2 thin films equal to the conductivity of impedance matching, indicated by the green areas in figures and the value of Tc were in almost inverse proportion to the doped concentration of W content: 67°C, 58°C, 50°C, and 41°C for the doped concentration of 0%, 0.35%, 0.51%, and 1.06% respectively. It should be noted that Tc is closed to room temperature for V1-xWxO2 thin films with W-doped concentration of 1.06%.
Fig. 3 (a-d) Time domain signal of reflected THz pulses during phase transition from insulating state to the metallic state in different V1-xWxO2 thin films (x = 0%,0.35%,0.51%, and 1.06%).
The spectra of Er2 were obtained by using the fast Fourier transformation (FFT) with a rectangular time window function of 18 ps, as shown in Fig. 4(a-d). The blue solid symbols represent the state before impedance matching, the purple ball represents the impedance matching and the red open symbols represent the states after impedance matching. Coincided with time-domain THz pulses signal, the frequency-domain amplitude of Er2, ranging from 0 THz to 1.3 THz, first reaches a minimum and then increases during IMT of V1-xWxO2 thin films with different concentration of W-doped content. Shown in the figures, the results suggest that the amplitude modulation depth of Er2 is related to the resistivity of metallic phase and insulator phase for V1-xWxO2 thin films with different concentration of W-doped content.
Fig. 4 (a-d) Frequency-domain spectra of Er2 during phase transition from insulating state to the metallic state in different V1-xWxO2 thin films (x = 0%,0.35%,0.51%, and 1.06%) (the blue solid symbols represent the states before impedance matching, the purple ball represents the impedance matching states and the red open symbols represent the states after impedance matching)
To verify the relationship between the modulation depth and the resistivity of metallic phase and insulator phase for V1-xWxO2 thin films, the frequency-dependent THz relative reflections ranging from 0.3 THz to 0.9 THz, were calculated for all the four kinds of V1-xWxO2 thin films from their spectra during IMT, as shown in Fig. 5(a-d). We defined that the relative reflection is the ratio between the THz electric field at each temperature and the corresponding amplitude at 25°C. From the frequency-dependent THz relative refection, we obtained the temperature-dependent THz relative reflection at 0.5 THz.
Fig. 5 (a-d) THz relative reflection versus frequency in different V1-xWxO2 thin films (x = 0%,0.35%,0.51% and 1.06%). `
Base on transfer matrix method [21], we achieved the simulation results for the THz relative reflection values as a function of temperature. The fitting parameters in the simulation base on transfer matrix method were listed in Table 1, which include the bulk conductivity of metallic states and insulating states, the scattering time constant and the thickness of VO2 thin films [30]. In order to further analyze the THz relative refection of V1-xWxO2 thin films in Fig. 5, a full comparison of experimental and simulated results is provided as Fig. 6(a) shows. The variation of the THz relative refection with temperature and the value of Tc are well reproduced by simulation and the agreement is almost perfect for all the four types of V1-xWxO2 thin films. The THz relative reflection reduces to a minimum and then increases during IMT. It is clearly observed that Tc decrease greatly, due to the doped W element reducing the phase transition temperature of VO2.
Table 1. Fitting parameters in the simulation base on transfer matrix method
Fig. 6 (a) Comparison of the experimental (symbol) and simulated (solid line) THz relative reflection values versus temperature for the different the V1-xWxO2 thin film. (b) The impedance match temperature Tc of different V1-xWxO2 thin films. (c) The E-field amplitude modulation depths of the V1-xWxO2 thin films between the impedance matching state and the metallic phase.
Moreover, we also found that the difference between Tc (67°C, 58°C, 50°C, and 41°C) and the phase transition temperature (68°C, 61°C,58°C and 47°C) is almost proportion to W-doped concentration, as shown in Fig. 6(b). This result can be attributed to the resistivity of VO2 at insulator phase became lower with increasing W-doped concentration, leading to less conductivity required to achieve impedance matching. As shown in the figures, there is two amplitude modulation behavior: one is from insulator phase of VO2 thin film to impedance matching state, the other is from impedance matching state to metallic phase. The modulation property between the metallic phase and impedance matching state is more efficiency than the modulation property between the insulator phase and impedance matching state, as the Fig. 6(a) shows. E-field amplitude modulation depths of V1-xWxO2 thin films were calculated by from the impedance matching state to the metallic phase, as shown in Fig. 6(c). Coincided well with our previous works [21], the modulation of V1-xWxO2 thin films based on impedance matching is broadband modulation behavior as well, and the maximum amplitude modulation depths is 72%, 53%,73% and 76% for V1-xWxO2 thin films with W-doped concentration of 0%, 0.35%, 0.51% and 1.06%, respectively. It should be noted that the highest modulation depth was achieved by the V1-xWxO2 thin films with the W-doped concentration of 1.06%, and that the value of Tc is lowest as well.
To sum up, by investigating the pristine VO2 thin film and V1-xWxO2 thin films with different W-doped concentration (x = 0.35,0.51,1.06%), our results indicate that high reflection amplitude modulation depth of THz E-field with low impedance matching temperature can be achieve by highly-doping W content of V1-xWxO2 thin films.
4.2. Impedance matching of VO2 at a different incident angle
To verify the effect of the incident angle of THz wave on modulation properties of VO2 thin films based on impedance matching, as the above theoretical model shows, we experimentally investigated the impedance matching properties of VO2 thin films by modifying the incident angle of THz waves. Figure 7(a-c) shows the measured reflective THz time-domain signals of VO2 during IMT at three different incident angles (35-degree, 45-degree and 60-degree). For different incident angle, Er2 in insulator phase is suppressed with increasing incident angle. On the contrary, Er2 in metallic phase increases with increasing incident angle. The reflective THz pulse signal at Tc is indicated by a green area. The value for incident angles of 35-degree, 45-degree and 60-degree are 68°C, 67°C and 62°C, respectively. This was attributed to the lower matching conductivity required for the larger incident angle, as the Eq. (1-2) show.
Fig. 7 Variation of reflected THz pulses during VO2 phase transition from insulating state to the metallic state at (a) 35-degree, (b) 45-degree and (c) 60-degree incident angle, respectively.
Figure 8(a–c) show the obtained spectra of Er2 at different incident angle (35-degree, 45-degree and 60-degree). From the spectra of Er2, we calculated the frequency-dependent THz relative reflection of pristine VO2 thin films for different incident angles, Fig. 8(d–e) shows. As the figures show, the largest relative reflection of metallic VO2 thin films was achieved by incident angle of 60-degree, among the three incident angles.
Fig. 8 Frequency-domain spectra of Er2 during VO2 phase transition from insulating state to the metallic state at 35-degree (a), 45-degree (b) and 60-degree (c), respectively. THz relative reflection versus frequency for VO2 films at 35-degree (d), 45-degree (e) and 60-degree (f), respectively. Blue lines with solid symbols represent spectra before pulse polarity reversal, purple ball represents the spectra of impedance matching and red lines with open symbols represent the spectra after pulse polarity reversal.
To further clarify the effect of incident angle of THz wave on modulation properties of VO2 thin films, we simulated the THz relative reflection of VO2 thin film versus temperature for different incident angle by transfer matrix method as above shows. A well-matched comparison of experiment results from Fig. 8 and simulation results for THz relative reflection at 0.5 THz, is shown in Fig. 9(a). As the figure shows, the THz relative reflection values of metallic VO2 thin films is monotonously increase with incident angle. This is attributed that the large incident angle of THz pulse lead to the low reflective amplitude of Er2 when VO2 film at insulator phase, as the Fig. 8(a) shows. Moreover, the magnitude of Tc decreases with increasing the incident angle of THz pulses as shown in Fig. 9(b), which mean that low impedance matching conductivity is required for large incident angle. It is well consistent with the analysis of our theoretical model. Additionally, we calculate the frequency-dependent modulation depth of VO2 thin films from the impedance matching state to the metallic phase, as Fig. 9(c) shows. It is observed that the modulation behavior for the three incident angle is a broadband modulation, and the maximum E-field amplitude modulation depths for incident of 35-degree, 45-degree and 60-degree is 90%, 72% and 87%, respectively. These results suggest that increasing suitably the incidence angle can improve the modulation depth and decrease the impedance matching temperature as well.
Fig. 9 (a) Comparison of the experimental (symbol) and simulated (solid line) THz relative reflection values versus temperature for VO2 thin films at 35-degree, 45-degree and 60-degree. (b) The impedance match temperature Tc of pristine VO2 thin films at different incident angle. (c) The Modulation depth of VO2 thin films between the impedance matching state and the metallic phase at the different incident angle.
4.3. Impedance matching of VO2 on the different substrates
Besides the W doped VO2 and the different incident angle, the refractive index of substrates also is vital to achieving impedance matching of VO2 during phase transition, as our theoretical model shows. For studying the effect of refractive index of substrates on the impedance matching of VO2, the pristine VO2 thin films on three substrates which of the incremental refractive index (SiO2:1.95 [22], Al2O3:2.7 [25] and Si:3.4 [22]) were deposited. Figure 10(a-c) shows the measured reflective THz time-domain signals of VO2 at different substrates with the incident angle of 45-degree, during IMT. The green area in the figure denoted the Tc for VO2 film on different substrate, and the magnitude of Tc for SiO2, Al2O3 and Si is 67°C,69°C and 73°C, as Fig. 10 shows. Moreover, with increasing the refractive index of substrate, the amplitude of Er2 decreases in metallic VO2 thin film. The spectra of Er2 for (a) SiO2, (b) Al2O3 and (c) Si substrate at incident angle of 45-degree were attained by FFT, shown in Fig. 11(a-c) and the corresponding frequency-dependent THz relative reflection calculated from spectra of Er2, are shown in Fig. 11(d-f). As the figures show, the THz relative reflection is inverse proportion to the refractive index of substrate. For VO2 films on Si substrates, the lowest THz relative reflection was experimentally achieved.
Fig. 10 Variation of reflected THz pulses during VO2 phase transition from insulating state to the metallic state at 45-degree on (a) SiO2, (b) Al2O3 and (c) Si substrate, respectively.
Fig. 11 Frequency-domain spectra of Er2 during VO2 phase transition from insulating state to the metallic state on (a) SiO2, (b) Al2O3 and (c) Si substrate, respectively. (d-f) Corresponding THz relative reflection versus frequency for VO2 films on different substrates.
Based on transfer matrix method, the THz relative reflection values versus temperature for different substrates were simulated. Figure 12(a) shows the comparison of experiment results from Fig. 11 and simulation results THz relative reflection at 0.5 THz as a function of temperature for SiO2, Al2O3 and Si substrate. The experiment results are well reproduced by simulation. As the Fig. 12(b) show, the magnitude of Tc is proportion to the refractive index of substrate, which is attributed that substrate with the higher refractive index require larger conductivity of VO2 film to meet impedance matching. On the contrary, THz relative reflection of VO2 at metallic phase decrease with increasing the refractive index of substrate. Consequently, the modulation depth decreases. These results are consistent with our theoretical model. Moreover, we calculate the frequency-dependent modulation depth of VO2 thin films from impedance matching state and the metallic phase at different substrates, shown in Fig. 12(c). The maximum E-field amplitude modulation depths of pristine VO2 thin films on SiO2, Al2O3 and Si substrates is 72%, 53% and 42% over the range from 0.3 THz to 0.9 THz, respectively. It is clearly indicated that the higher modulation depth can be obtain by depositing VO2 film on substrate with low refractive index.
Fig. 12 (a) Comparison of the experimental (symbol) and simulated (solid line) THz relative reflection values versus temperature for VO2 thin films on SiO2, Al2O3 and Si substrate. (b) The impedance match temperature Tc of pristine VO2 thin films on different substrates. (c) The modulation depth of VO2 thin films between the impedance matching state and the metallic phase on different substrates.
5. Discussion
In order to broaden the application of modulation based on impedance matching, achieve larger continuous, broadband, wide-angle and near room temperature modulation properties, we simulated the impedance matching of V1-xWxO2 thin films at a different incident angle and refractive index, as shown in Fig. 13. The curves and the symbols represent the simulation results and the experiment data, and the experiment data were well consistent with the simulation results.
Fig. 13 (a) Simulated impedance matching temperature Tc of different W-doping VO2 films on SiO2 substrate as a function of various incident angle from 10 to 65 degree, the experimental results are indicated by different marks. Black symbols denote the measured Tc of pristine VO2 at 35-degree, 45-degree and 60-degree incident angle and color balls denote the measured Tc of different V1-xWxO2 thin films at 45-degree incident angle. (b) Simulated impedance matching temperature of different W-doping VO2 films at 45-degree incident angle as a function of substrate refractive index, the experimental values are plotted by different colors and marks. Black symbols denote the measured Tc of pristine VO2 on SiO2, Al2O3 and Si substrate and color balls denote the measured Tc of different V1-xWxO2 thin films on SiO2 substrate.
Figure 13(a) shows the relationship of impedance matching temperature on the incident angle from 10-degree to 65-degree. The impedance matching temperature decreases slightly with the increasing incident angle between 10-degree to 55-degree. When the increasing incident angle is close to the Brewster angle (63-degree) [22], the impedance matching temperature decreases abruptly. Due to the lower phase transition temperature of V1-xWxO2 thin films, the impedance matching temperature move down to lower. Moreover, the low resistant in V1-xWxO2 thin films with highly W-doped will enable insulator phase V1-xWxO2 thin films to impedance match at a small certain incident angle. These results suggested that the V1-xWxO2 thin films were able to reach impedance matching at large incident angle range and reduced the condition of impedance matching by adjusting the incident angle. Figure 13(b) shows the simulated impedance matching temperature of different V1-xWxO2 thin films at 45-degree incident angle as a function of substrate refractive index. In these cases, with the increasing refractive index of the substrate, the impedance matching temperature became higher. From Fig. 13(b), it was observed that the V1-xWxO2 thin films with highly W doped content were able to impedance matching on insulator phase when the substrate refractive index reduced. It was attributed to the low conductivity of impedance matching at low refractive index meet the high conductivity of the insulator phase V1-xWxO2 thin films than pristine VO2. Similarly, the impedance matching condition needs large conductivity for highly refractive index substrate, but low conductivity of metallic phase of V1-xWxO2 thin films (x = 0.35%) doesn’t satisfy the conductivity of impedance matching, as shown in Fig. 13(b).
Figure 13 demonstrate the continuous THz wave modulation of impedance matching in V1-xWxO2 thin films by varying incident angle and refractive index. These simulated results also provide a promising route for THz modulation applications of VO2 thin films which achieved room temperature, broadband and large continuous modulation based on impedance matching. A new analytical model for describing electromagnetic hysteresis in phase change is very helpful in building the impedance matching analytical model of VO2 thin films [31].
6. Conclusions
In conclusion, we described a theoretical model for THz wave modulation of VO2 thin films based on impedance matching, which suggested V1-xWxO2 thin films by doping, incident angle and the refractive index of substrates were able to optimize and broaden the application of modulation. Based on the theoretical model, we deposited different V1-xWxO2 thin films (x = 0.35%,0.51%, and 1.06%) on SiO2 substrate and pristine VO2 thin films on different refractive index substrates (on SiO2, Al2O3 and Si substrate). The impedance matching of VO2 thin films under different condition (V1-xWxO2 thin films by doping, incident angle and the refractive index of substrates) were performed and discussed. By W doping, the impedance matching temperature of V1-xWxO2 thin films reduced (67°C, 58°C 50°C, and 41°C, respectively) and reach large E-field amplitude modulation depths between the impedance matching state and the metallic phase (72%, 53%,73% and 76%, respectively) at the same time. Furthermore, the impedance matching temperature of pristine VO2 thin films was reduced with increasing the THz wave incident angle. The impedance matching of VO2 thin films on different substrates also suggested that chose a suitable substrate can further improve the modulation properties based on impedance matching. Finally, the impedance matching temperature of different V1-xWxO2 thin films as a function of the THz wave incident angle and the refractive index of substrates were simulated which are consistent with measured results. These results provide a promising route for THz modulation applications of VO2 thin films which achieved room temperature, broadband and large continuous modulation based on impedance matching.
Funding
National Key Basic Research Program of China (No. 2015CB755405); the National Natural Science Foundation of China (Nos. 61427814, 11404226, 11704358, and 61771327); NSAF (No. U1730138); the Foundation of President of CAEP (No. 201501033); and the National Science and Technology Ministry of Science and Technology Support Program (No. 2015BAI01B01).
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