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Abstract
We describe a method for the active control of terahertz (THz) waves using hybrid vanadium dioxide (VO2) periodic corrugated waveguide. Unlike liquid crystals, graphene and semiconductors and other active materials, VO2 exhibits a unique insulator-metal transition characteristic by the electric fields, optical, and thermal pumps, resulting in five orders of magnitude changes in its conductivity. Our waveguide consists of two gold coated plates with the VO2-embedded periodic grooves, which are placed in parallel with the grooves face to face. Simulations show that this waveguide can realize mode switching by changing the conductivity of the embedded VO2 pads, whose mechanism is attributed to the local resonance induced by defect mode. Such a VO2-embedded hybrid THz waveguide is favorable in practical applications such as THz modulators, sensors and optical switches, and provides an innovative technique for manipulating THz waves.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As we all know, wireless communication transmits signals by electromagnetic waves. The frequency of electromagnetic waves determines the upper limit of communication transmission. The higher the frequency, the faster the communication speed. Terahertz (THz) band is the key of the next generation high-speed wireless communication (6 G) [1]. THz wave frequencies extending from 0.1–10 THz, which is located between microwaves and optical waves [2]. The THz spectral region provides a higher available bandwidth, and the extremely high frequency makes it possible to transmit data wirelessly at terabits per second [3,4]. However, due to signal distortion in free space, attenuation caused by atmospheric scattering and absorption of water vapor seriously limit the transmission of THz waves [5]. In the process of building 6 G network, multiple base stations need to be established to improve the transmission efficiency and transmission distance of THz wave, which greatly increases the construction and operation cost of the system. Therefore, the lack of THz transmission devices with low loss, long distance and low dispersion is the primary problem to be solved. In addition, conventional materials in nature are difficult to produce effective electromagnetic response in THz band, which creates many difficulties in developing THz functional devices and realizing effective manipulation of THz wave.
The appearance of metamaterials (MMs) with artificial periodic structure has greatly solved the problem of lack of natural materials [6,7]. Through the elaborate design of unit cell structure, artificial materials with arbitrary equivalent permittivity and permeability can be constructed. Although various MM-based THz devices can realize the effective control of THz wave, there are still some shortcomings, such as difficult material preparation, easy oxidation and corrosion of materials, difficult integration and so on. Compared with the THz wave transmission in free space, waveguide-type THz functional devices show great development potential in many applications, so various types of THz waveguides have been proposed and investigated one after another, such as hollow metallic waveguides [8,9], metal wire [10–12], dielectric waveguides [13,14], photonic crystal [15,16], plasmonic [17,18], THz fibers [19,20], and topological photonic waveguides [21,22]. However, for most practical applications, the functions of existing THz waveguide devices are far from meeting our requirements, because once the device is fabricated, the functions will be fixed, which greatly limits its application value. Therefore, it is urgently needed to employ high-performance tunable materials to make these waveguide devices more powerful.
At the THz level, the main active materials used are semiconductors [23], liquid crystals [24], phase-change materials such as superconductors [25], and 2D materials such as graphene [26] and MXene [27]. Their conductive or dielectric properties can be controlled or switched by thermal, optical, magnetic and electrical stimulation. However, the tunable range of constitutive parameters of materials is still limited, which leads to the low modulation depth of THz devices. Unlike other active materials, vanadium dioxide (VO2) shows great advantages in the development of active tunable THz functional devices because of its unique insulator-metal transition (IMT) characteristics [28]. The critical temperature of phase transition is only 68 °C, just a little higher than room temperature. The crystal structure of VO2 begins to change from insulating monoclinic phase to metal tetragonal phase, causing its conductivity to change by five orders of magnitude. In addition, light and electrical stimulation can also induce the phase transition. Unexpected, the response time of VO2 to light stimulation is only sub-picosecond [29]. These various excitation methods, low operating temperature and excellent photoelectric performance make VO2 a hot candidate for THz potential applications. Such excellent properties are rarely observed in other THz tuning materials.
Recently, researchers have designed a variety of THz tunable devices using VO2 films as thermal- or electrical-sensitive elements and realized the active control of THz waves amplitude, phase and polarization [30–39]. For example, in 2017, Wang et al. designed four types of hybrid resonators and highly tunable THz MMs using integration of VO2 structures and conventional metallic resonating [30]. In 2019, Zhang et al. experimentally implemented a THz wave mode switch based on VO2-embedded hybrid MMs, using not only a thermal stimulus, but also electrical and optical stimuli [31]. In 2020, tunable bifunctional THz metamaterial based on Dirac semimetals and VO2 is proposed one after another [35,36]. In 2021, Li et al. experimentally demonstrated a THz bandstop-to-bandpass converter based on VO2 hybrid metasurface [37]. In 2022, Imam et al. demonstrated a one-dimensional unidirectional THz absorber with thermal switching from broadband to narrowband and tunable multiple narrowband absorption with VO2-graphene-based defective photonic crystal [38]. In the same year, Wu et al. introduce a defect layer into a 1D photonic crystals containing hyperbolic metamaterials to achieve an anomalous defect mode with polarization-sensitive characteristics [39]. However, most of these devices are based on MM structures, and hybrid VO2 waveguide devices with potential advantages in THz transmission are rarely reported.
Here, we propose a VO2-embedded hybrid THz waveguide with periodic groove structure and realize the transmission control of THz wave and tuning. Based on the IMT of the embedded VO2 pads, we manipulate THz waves to achieve mode switching by changing the temperature of waveguide. The periodic grooves produce a frequency stop band in THz frequency range at low temperature (50 °C) due to the insulation phase of VO2, whereas the VO2 in metal phase at high temperature (70 °C) destroys the periodicity of the structure, resulting in an extraordinary transmission in the stop band. The continuous tunability of THz wave transmittance can be achieved by changing the thermal stimulation. Besides, compared with the heating process, the cooling process is more difficult to tune the transmission of THz wave due to the different conductivity characteristics of VO2 materials. The simulated dispersion curves and electric fields at different temperatures confirm that the thermal control mechanism is attributed to the local resonances induced by metal phase VO2 defects. Our proposed hybrid VO2 THz waveguide could be applied for manipulating the THz waves in practical applications. In the following section, we show the schematic diagram of the designed THz waveguide. Active control of THz waves is demonstrated in Sec. 3. In Sec. 4, the thermal control mechanism is confirmed. Sec. 5 concludes the main results we have obtained and looks forward to the application prospects.
2. Hybrid VO2 THz corrugated waveguides
Here, we propose a novel VO2-embedded periodic corrugated waveguide and realize the transmission control of THz wave. The structure diagram is shown in Fig. 1. Figure 1(a) presents the three-dimensional view of the waveguide, which is consists of two parallel silicon plates with periodic grooves, and its inner surface is coated with gold film to ensure the transmission of THz wave in the waveguide, as shown by the gray and yellow area. The groove in the middle of the waveguide is filled with polyimide (PI), as shown by the green area. A layer VO2 film with a thickness of 10 µm is coated on PI surface to tune the THz wave, as shown by the purple strip. The front view in Fig. 1(b) clearly shows the details of the structure surrounded by black dotted lines. The geometric parameters of the designed waveguide structure are as follows: the period length Λ=200 µm, the gap between upper and lower plates d = 200 µm, and the width and depth of the groove are w = 100 µm and h = 40 µm respectively.
Fig. 1. Schematic diagram of the proposed hybrid VO2 periodic corrugated waveguide: (a) three-dimensional view; (b) front view; (c) and (d) equivalent waveguide structure when VO2 is in insulating phase at low temperature and in the metal phase at high temperature.
It can be boldly predicted that the transmission of THz waves in such waveguide will change significantly when the embedded VO2 pads undergoes IMT. Specifically, at room temperature, VO2 is an insulating phase and transparent to THz waves, the designed waveguide will show perfect periodicity and the equivalent waveguide structure is shown in Fig. 1(c). At this time, the Bragg resonance and the induced frequency stop band will occur, which will suppress the effective transmission of THz wave in the waveguide. However, VO2 will change from insulation to metal phase by thermal excitation, the periodicity of the waveguide will be destroyed, as shown in Fig. 1(d). The strong THz local resonance will occur due to the created defect structure, which will greatly enhance the transmission efficiency of THz wave.
In the previous work, we have presented the resonance theory of THz wave in such a periodic waveguide and provided a complete description of wave propagation and accurately predicted the spectral band structure and properties of the waveguide [40]. The relationship between these resonances and waveguide geometries could be clearly described by the reference lines in the first Brillouin zone:
Fig. 2. References for the dispersion curves in the first Brillouin zone. The blue and red lines represent the first and second transverse modes with different spatial harmonics, respectively.
Active control of THz waves based on hybrid VO2 periodic corrugated waveguides was demonstrated by using the COMSOL Multiphysics based on the finite-element method, in which a two-dimensional model was considered. The refractive index of air inside waveguide is set to 1. The refractive index of the filled PI in groove is 1.9 and the absorption coefficient is 10 cm−1 [41]. The filled PI is transparent to THz waves and used to support VO2 thin films. The refractive index of Si substrate with negligible loss is set to 1.96 at THz frequencies [42]. The relative permittivity of gold is described by a Drude model ɛu = 1–ωp2/ω(ω+iΓ) with plasma frequency ωp = 1.37 × 106 rad/s and collision frequency Γ=1.2 × 1014 rad/s [43]. The incident and transmitted THz waves are selected as a first TE mode radiation. The THz wave powers at inlet and outlet can be computed using the boundary integration tool to calculate transmission coefficients. In addition, the ultra-fine grids are adopted to ensure the accuracy of the calculation results, the frequency step is set to be 0.001 THz. Meanwhile, we also simulated the electric fields Ez along the z direction in the waveguide. The dispersion characteristics of the waveguide at different temperatures are obtained by spatial Fourier transform of the electric fields on the central axis of the waveguide.
We describe the IMT characteristic of VO2 in THz band based on the Bruggeman effective medium theory (EMT). The dielectric function εC can be expressed as [44]
3. Thermally controlled THz mode switching
We investigate the THz response of the hybrid VO2 periodic corrugated waveguides under a thermal stimulus. The simulated transmission spectra at different temperatures for heating process are shown in Fig. 3(a). Clearly, the periodic groove structure produces a wide stop band in the frequency range of 0.96 to 1.06 THz at 50 °C, which greatly prevents the transmission of THz wave in the waveguide. Unexpectedly, as the temperature increases, an extraordinary transmission near 0.996 THz in this stop band is excited and gradually enhanced. The transmission reaches the maximum at 70 °C. The amplitude modulation depth of the THz wave is 98.86%. In addition, the transmission peak shows a slight blueshift of the resonance frequency. This is because the refractive index and dielectric constant of VO2 changes during the IMT, which is equivalent to the change of geometric size of the waveguide structure composed of VO2, resulting in the frequency shift. What's more exciting is that we can also remove the transmission peak by lowering the temperature of the waveguide. However, obviously different from the heating process, the cooling process is more difficult to control THz wave transmission. The simulation results are presented in Fig. 3(b).
Fig. 3. Simulated one- and two-dimensional THz transmission spectra of the proposed hybrid VO2 THz waveguide device at different temperatures: (a) and (c) heating processes; (b) and (d) cooling processes.
Although we have just simulated the THz transmission spectra at several temperatures, we can still roughly infer the tunable performance of the waveguide by observing the change trend of the curves. In order to show the continuous tuning behavior more intuitively and clearly, a two-dimensional graphic of the temperature-dependent THz transmission spectra in the same frequency range is depicted in Figs. 3(c) and (d). The calculated steps of the frequency and temperature are 0.001 THz and 1 °C, respectively. The red areas on the left and right represent the edges of the stop band. For heating process shown in Fig. 3(c), it can be clearly seen that the transmission of THz wave around 0.996 THz in the waveguide can be controlled continuously by thermal stimulation, but the applied temperature is required to be above 60 °C, thermal stimulation below this temperature cannot enhance the transmission. In addition, although cooling can also effectively manipulate the transmission peak, but the temperature should be below 55 °C, as shown in Fig. 3(d). The sensitive temperature in the cooling process is lower. The frequency shift of the transmission peak is also observed more clearly.
To further investigate the differences in controlling THz waves using heating and cooling, we present the shift of transmission spectra vs temperature within cooling and heating process at 0.996 THz, as shown in Fig. 4. It is clear that the change curves of the transmission spectra during the heating and cooling processes do not completely coincide, but similar to hysteresis loops. It can be explained that the change of VO2 conductivity is not completely reversible during heating and cooling process [45], which may lead to different tunable behaviors. Based on the IMT characteristics of VO2, we have successfully controlled the effective transmission of THz wave in the periodic waveguide. More importantly, the response time can reach the order of sub-picosecond, which is difficult to achieve in other THz structure and materials. In addition to thermal control, optical and electrical stimulus can also be used as manipulative means, which has been experimentally confirmed in Ref. [31]. The diversity of the stimuli is favorable in practical applications such as THz modulators, phase-array antennas, and wireless communications, and represent an innovative technique for manipulating THz waves.
Fig. 4. The shift of transmission spectra vs temperature within cooling and heating processes at 0.996 THz.
4. Thermal control mechanism
We have demonstrated that the proposed THz waveguide can continuously manipulate transmission of THz waves with the assistance of the VO2 IMT. To further investigate the physical mechanism of the thermal control, it is necessary to clarify the electric field distribution of THz waves in the waveguide at different temperatures. Figure 5(a) shows the simulated electric fields at 0.996 THz during heating. We can see that when the thermal control temperature is below 56 °C, the electric field energy of the incident THz waves is completely isolated near the inlet of the waveguide, the energy detected at the outlet is almost zero. This is because VO2 shows an insulating phase at low temperature and is transparent to THz waves. So, the waveguide can be equivalent to a perfectly periodic structure, resulting in the strong Bragg resonance. Such resonance causes a great attenuation on the incident THz waves. As the temperature continues to rise, VO2 gradually changes from insulation to metal phase, the electric fields near the outlet are significantly enhanced, reaching the maximum at 70 °C. THz wave transmission in the waveguide is manipulated by thermal excitation.
Fig. 5. Simulated electric fields corresponding to the transmission peak at 0.996 THz of the proposed hybrid VO2 THz periodic waveguide structure at different temperatures (50–70 °C): (a) heating processes; (b) cooling processes.
The main reason for this fascinating phenomenon can be explained that metal phase VO2 covers the groove, which is equivalent to introducing a wide convex defect into the waveguide. The formed defects destroy the perfect periodicity of the structure, and then stimulate strong local resonance. Such resonance gradually localizes the incident THz electric field energy in the middle of the waveguide, as indicated by the black dotted line. The continuous accumulation of wave energy leads to the enhancement of transmissions in stop band. Furthermore, the electric fields coupled at defect location are symmetrical along the x-axis direction, indicating the local resonance mode with Bragg nature. The local resonance induced by the defect structure in such a periodic waveguide has been confirmed in Ref. [47]. By observing the electric field distribution shown in Fig. 5(b), we can see that the transmission of THz wave can also be suppressed by cooling the waveguide, but it is relatively difficult. A similar phenomenon has been observed in Figs. 3(b) and (d).
The dispersion diagram during heating is also depicted in Fig. 6 to reveal the thermal control mechanism of the waveguide. The dispersion curves break off at 50 °C, the corresponding band gap in the frequency range of 0.96 to 1.06 THz is created, which means that THz wave cannot propagate through the waveguide in those frequency ranges. Since the breakpoint is just located at the boundary of the first Brillouin region (β=±k/2), it is caused by Bragg resonance in a periodic structure, and the VO2 in insulating phase does not play a role. As expected, when the temperature rises to 60 °C, an obvious transmission appears in the band gap. And with the continuous increase of temperature, the transmission is gradually enhanced, illustrating the localized resonance modes induced by metal phase VO2 defect, as indicated by yellow arrow. The dispersion curves during the cooling process also exhibits completely different variation rule at the frequency position of transmission peak within the bandgap, as shown in Fig. 7.
Fig. 6. Dispersion curves of the proposed hybrid VO2 THz periodic waveguide structure at different temperatures for heating process.
Fig. 7. Dispersion curves of the proposed hybrid VO2 THz periodic waveguide structure at different temperatures for cooling process.
By plotting the corresponding field distribution and dispersion characteristics, the thermal control mechanism of the proposed hybrid VO2 THz waveguide has been clarified. To further investigate the transmission performance of THz wave in the waveguide, we simulate the dependence of the transmission spectra on the width of embedded VO2 pad at 70 °C, as shown in Fig. 8. We find that with the increasing width w from 40 to 160 µm, the transmission peak is obviously moves to lower frequency range, illustrating that the width has a great impact on the local resonances. As another important geometry parameter, the influence of number of periods on wave transmission is also investigated.
Fig. 8. Effects of the widths of metal VO2 defect on THz wave transmission performance at 70 °C for heating processes.
Figure 9(a) show the variation of the transmission spectra when the number of periods N changes from 9 to 21. The increased N has little effect on the frequency position of transmission peak, but it greatly affects the bandwidth. To clarify its physical mechanism, we simulate electric fields in Fig. 9(b) and further confirm the localized resonance caused by metal phase VO2 defect at high temperature. We can see that as the number of periods N increases, the localization effect is greatly enhanced, thereby narrowing the bandwidth of the transmission peak. We also simulate THz transmission spectra with different number of periods for the lossless perfect electrical conductor boundary. It is confirmed that the attenuation of amplitude is mainly caused by the losses of VO2, PI, and gold materials, so it is independent of the number of periods. Referring to Fig. 8, the frequency position of the transmission peak is only related to the geometric size of the defect, so the change of the number of periods cannot affect its resonance frequency.
Fig. 9. Effects of number of periods on THz wave transmission performance at 70 °C for heating processes: (a) Transmission spectra; (b) Electric field distribution.
We may use laser ablation and metal coating technology to prepare the hybrid VO2 periodic corrugated waveguides. Firstly, a periodic groove structure is machined on the surface of a silicon substrate using a laser lithography technology. Then, a layer of gold film is sputtered on the surface of the structure using a magnetic co sputtering coating technology. Note that the thickness of the gold film should be greater than the skin depth of gold in the THz band [48,49] to ensure effective transmission of THz waves. After obtaining a corrugated waveguide structure coated with gold, we use liquid PI to fill one of the grooves, wait for it to solidify, cover the waveguide surface with a mask, and then proceed with VO2 coating.
5. Conclusions
Based on the IMT characteristic of VO2, we have designed a thermally controlled THz wave transmission waveguide. The proposed waveguide consists of VO2-embedded two parallel plates with periodic grooves. When we heated the waveguide, the transmission of THz wave around 0.996 THz was significantly enhanced. Conversely, cooling can also effectively suppress the wave transmission. The amplitude modulation depth of the THz wave was 98.86%. The simulated electric fields and dispersion curves at different temperatures confirmed the thermal control mechanism. At 50 °C, the waveguide behaved as a perfect periodic structure due to the insulation phase VO2 and produced a wide Bragg stop band, which effectively suppressed THz wave transmission. Metal phase VO2 at 70 °C created a defect in the waveguide, which excited a strong local resonance, an unexpected transmission was observed. The design method and tuning mechanism of the proposed hybrid VO2 THz waveguide paves the way for creating active tunable THz functional devices, such as THz modulators, sensors and optical switches.
Funding
National Natural Science Foundation of China (62001132, 12064005); Natural Science Foundation of Guangxi Province (2020GXNSFBA159047, 2021GXNSFAA220073, 2021GXNSFAA220086, 2021GXNSFDA075006); Innovation Project of GUET Graduate Education (2022YCXS032, 2022YCXS033, 2022YCXS041).
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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