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Abstract
Potential applications of terahertz (THz) radiation are constantly being investigated for high-speed communication due to its large bandwidth. For example, frequency hopping communication technology would benefit from the large bandwidth. To attach the information to the carrier wave, THz modulators with deep and stable modulation at different frequencies are crucial, yet are still lacking. Here a THz modulator, designed by integrating a non-resonant field enhancement effect of periodic metal microslits to assist a Fabry-Perot resonance structure (MS-FP) is proposed and demonstrated. New equations are developed to describe the superior performance of the novel design. The >95% modulation depth is achieved by a SiO2/Si gated graphene device at 14 Fabry-Perot resonant frequencies across 1.4 THz bandwidth, outperforming the recently reported 75% modulation depth THz modulator with a similar Fabry-Perot structure.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The THz band (0.1 THz to 10 THz) is considered as the wireless communication future beyond “5G” for its significantly wide segments of unused bandwidth. The bandwidth resource is valuable for the wireless communication technology, especially for frequency hopping communication technology. In frequency hopping systems, the transmitter hops between available narrowband frequencies within a specified broad channel, which minimizes the possibility of failing communication at a particular frequency because of a fade or interference [1–3]. To impose information onto a carrier wave at different channels, a THz modulator operational at various frequencies is needed. THz modulators are not only crucial for THz communications [4,5] but also essential for compressive sensing-based THz imaging [6–9]. During the past two decades, THz sources and detectors have been well developed, but other THz components, such as external THz modulators, are still lagging behind. Various modulation approaches, such as thermal [10,11], electrical [12–14] and optical [15–17], have been explored to control THz radiation. For many applications, a voltage driving all-electronic modulator is highly desired. It removes the need for a high-power external laser source, allowing for integration into a more compact electronic system as well as more convenience in controlling the large-scale modulator array. Graphene is a good candidate for an all-electronic THz modulator, due to its Fermi level, as its carrier density and conductivity, can be changed by applying a gate voltage. THz modulators based on graphene have been widely reported [12,18,19]. However, a graphene-based THz modulator with deep modulation depth, low insertion loss, multiple operation channels is yet to be realized. Ion-gel gated graphene devices have high modulation depth (MD) and low driving voltage but low stability and slow modulation speed [20–22]. Metamaterial graphene modulators have shown advantages in many aspects, such as the MD (MD≈100%, at f=3.0 THz) [14] and the modulation speed (100 MHz) [23]. However, the above metamaterial-based THz modulators only operate at a single and high frequency. The Fabry-Perot (FP) microcavity structure has been proposed and used to enable modulation of multiple discrete frequency points [18,24,25]. In the FP structure, when the substrate optical thickness is an odd-multiple of a quarter-wavelength, the electric field is intensified at its interface. However, the improvement in the MD to 75% [24] is still not ideal for THz communications to provide the best signal quality and for THz imaging to offer a better image contrast. The FP structure has discrete operational frequencies, so is incapable of acquiring broadband THz data. Compared to the reported metamaterial-based THz modulators for compressive sensing-based THz imaging [6,26], our FP structure still offers more information in the frequency domain. The separated operational frequencies of the FP structure are suitable for modulation in different communication channels, and are needed in frequency hopping communication systems.
In this paper, we exploit the non-resonant electric field enhancement effect in periodic metal microslits working together with the FP resonator to further increase the electric field intensity and the THz absorption at the graphene interface. The bottom metal layer performs as a reflection layer to form a resonant cavity as well as an electric contact layer to apply a back-gate voltage. A series of equations to describe this model has been derived and verified experimentally by a SiO2/Si gated graphene resonant device, resulting in >95% MDs at multi-frequency channels.
2. Theory
The FP structure (as shown in Fig. 1(a) and 1(b)) provides multiple interactions between the THz light and graphene, thus the THz amplitude would have a higher sensitivity to changes in the graphene conductivity at the resonant frequencies. The sheet conductivity of the graphene layer (Fig. 1(a)) can be changed by applying a different voltage between the bottom gold layer and the top metal silts. The FP design also has the flexibility of tuning the resonant frequencies via incident angle, substrate material and thickness. The reported MD of a FP structure was around 75% at the resonant frequency points [24]. It is difficult to enhance the MD of the FP structure by increasing the conductivity of graphene in practice, as this would require a high quality solid-state insulation layer [27,28]. A new approach is required to improve the MD with the achievable conductivity of graphene. Metamaterials [29] are efficient at increasing the near-field intensity to improve the achieved modulation but normally at a single frequency, which would sacrifice the advantage of multiple operation frequencies in the FP design. Fortunately, a subwavelength metal microslit structure has a non-resonant field enhancement effect in the air gaps between the metal slits over a broadband range [30]. We integrate this non-resonant field enhancement effect with the FP resonance, greatly improving the THz absorption at the graphene whilst keeping the multiple resonant frequencies.
Fig. 1. (a) Schematic of a graphene-based subwavelength metal microslit assisted FP structure. The THz light is incident on the graphene surface with the E-field perpendicular to the stripes. (b) The cross-section view of Fig. 1(a) along the y-direction. The THz light has a 30° incident angle in this work and experienced multiple reflections inside the Si substrate (p→∞). A voltage was applied between the graphene and bottom gold layer. The influence of reflection from SiO2 layer can be ignored due to its subwavelength dimensions. (c) The cross-section view of Fig. 1(a) along the x-direction. The schematic shows the non-resonant E-field enhancement effect of metal wire grating. P is the period of the metal wire grating and g is the gap width of the grating.
The theory to calculate the metal microslits assisted FP cavity has not hitherto been developed. Tang et al. gave the modified Fresnel equation which could describe one-time reflection of the FP structure [24]. Here, we derive the equations from Fresnel’s law and boundary conditions to describe the metal microslits integrated FP structure when the number of reflected echoes turns to infinite (p→∞). As shown in Fig. 1(b), the THz light is incident on the graphene layer at an angle, and the refracted THz light will be totally reflected by the bottom metal layer. The multiple reflections will increase the absorption at the graphene layer. We start the derivation of the reflection coefficient without metal microslits. The polarization of the incident THz light is in s-polarization. The total reflection coefficient can be written as:
where, Er and Ei are the reflected and incident electric field amplitude, E1, E2, Ep is 1st, 2nd to the pth reflected electric field amplitude. If the first p reflected waves are superposed (as shown in Fig. 1(b)), the electric vector of the reflected light (Er) can be given by the expression:If the number of reflected waves is large; and in the limit as p → ∞, the expression reduces to
The total reflection coefficient becomes:
Fig. 2. The calculation (solid lines) and simulation (squares) results of the resonant structure (a) without and (b) with metal microslits, respectively, at different sheet conductivities of 0.2 mS (red color) and 0.9 mS (blue color). The metal microslits structure is 30 µm in period with a 50% fill ratio.
To verify the derived equation, the finite element method (FEM) was used to simulate the FP structure without and with the grating: the results are shown in Fig. 2(a) and (b) (see supplementary information for simulation details, Fig. S1). Two sheet conductivity values were simulated via simulation and calculated via Eq. (3). The resonant effect of the FP cavity in the frequency domain can be clearly observed in Fig. 2(a) and (b). Figure 2(a) shows the reflected intensity changing with the sheet conductivity in the absence of metal microslits. The lowest reflected intensity was around 0.2 at the sheet conductivity of 0.9 mS. In Fig. 2(b), the lowest reflected intensity was close to zero, which indicates the metal microslits (30 µm in period, 15 µm wide gap) assisted structure resulted in a deeper modulation with the same sheet conductivity. The calculation and simulation results match well with each other, which verifies the derivation of our theoretical equation.
The influence of the incident angle and substrate thickness on the resonant frequencies and MD are also investigated by our theoretical equations (as shown in Fig. 3(a) and (b)). The incident angle was set from normal reflection to 60° and the sheet conductivity of graphene was fixed at 0.2 mS. The results show the incident angle can only slightly tune the resonant frequencies, in contrast to the substrate thickness which can tune the resonant frequencies in a wider range. Figure 3(c) shows the E-field enhancement factor of the MS-FP structure compared with the FP structure. The enhancement ratio result shows the E-field amplitude increases by 3-fold at its maximum, which indicates the strongest E-field is at the edge of the metal microslits. The average enhancement ratio of the 30-15 µm metal microslits structure is around 2, which matches with our theoretical derivation.
Fig. 3. (a) and (b) The reflected intensity of the MG-FP structure at various frequencies with different incident angles and different substrate thickness. The sheet conductivity of graphene was as assumed to be 0.2 mS. The reflected intensity was normalized to unity. The colorbar represents the normalized reflected intensity (c) E-field enhancement ratio of the MG-FP structure along with the metal microslits length, which is compared to the FP structure. The inset above shows the simulation of a unit cell.
3. Experiment
A reflection THz time-domain spectroscopy system from Menlo Systems (TERA-K15) was used for the experiment with an incident angle of 30° (Fig. 4(a)). For more details of the experimental setup please refer to our previous work [33]. A 0.5×0.5 cm metal microslits was fabricated on a SiO2/Si substrate (square resistivity > 6K Ω·cm, double side polished) with standard photolithograph technique and metalized with 5 nm thick Ti and 200 nm thick gold. The metal microslits has a period of 30 µm and a 15 µm gap width. A piece of 1×0.5 cm graphene was transferred on the metal microslits. Half of the graphene was covered the metal microslits and the other half was on top of the SiO2 as a reference (the photo of the real device is shown in Fig. 4(b). The metal microslits also worked as a contact electrode to apply a voltage on the graphene and the GND electrode. The applied voltage was swept from –60 V to 60 V between the contact electrode and the GND electrode. The MD was calculated using the equation MD(V)=(1-I(V)/IBaseline)×100%, where IBaseline is the intensity of the least attenuated THz signal in the experiment. The time window in this experiment was set as 200 ps, which was limited by the THz-TDS (Terahertz time-domain spectroscopy) system. The THz signal after 100 ps was difficult to be distinguished from the noise (as shown in supplementary information Fig. S2). Therefore, we only show 100 ps optical delay signal in Fig. 4(c) and (d). The 200 ps time window is ample for calculating the MD accurately for this multi-reflection design.
Fig. 4. (a) Schematic diagram of the experimental setup with MG-FP modulator. (b) Photograph of the graphene area, clearly showing the bare graphene area (left) and graphene covered metal microslits area (right). (c) and (d) are reflected waveforms of the with/out metal microslits area by changing the gate voltages from −60 V (blue) to +60 V (orange).
Figure 4(c) and (d) show the reflected time domain signal from the graphene area with/without metal microslits. The signal is almost in the noise floor after the 6th echo. The relative changes of the signal amplitude are larger in the graphene area with a metal microslits (Fig. 4(d)) under the same voltage. Taking the 2nd echo as an example (the zoomed in figures and time-domain waveforms at more voltages are shown in the supplementary information, Fig. S3), the peak-to-peak value of the reflected time domain signal from the graphene area without metal microslits was modulated from 5.55 (at –60 V) to 5.13 (at 60 V), a relative change of 7.6%. Under the same voltage, the peak-to-peak value from the graphene area with metal microslits was from 4.89 (at –60 V) to 3.78 (at 60 V), a relative change of 22.7%.
4. Results and discussion
The signal in the frequency domain and its corresponding MD (as shown in Fig. 5) were calculated by fast Fourier transform. In Fig. 5(a) and (b), the amplitude of the frequency-domain signal from FP (Fig. 5(a)) and MS-FP (Fig. 5(b)) devices are shown. The minimum amplitude of the MS-FP device is much lower than that of the FP device, which indicates the MS-FP device is more efficient in modulating the THz signal. The overall MD from the graphene area without metal microslits is around 65% at FP frequencies (Fig. 5(c)), which is comparable with published results [18,24]. The graphene area with metal microslits significantly supersedes this with an overall modulation depth around 97% from 0.2 THz to 1.6 THz (Fig. 5(d)). At the frequency points of 0.22 THz, 0.31 THz and 0.84 THz, the MDs are over 99%. At high frequency points (such as 1.01 THz, 1.1 THz, 1.18 THz and 1.28 THz), the MDs are still above 95%. There are in total 14 frequency points across the 1.4 THz bandwidth with MD >95%. In general, the MD didn't monotonously decrease with frequency, instead it changed periodically in a small region. Three possible causes of this are: 1. the frequency resolution of our THz-TDs system may be not high enough to resolve the resonant peaks; 2. the high-order reflections may come out of focus on the detector (i.e. they experienced longer travel paths and lost focus); 3. the graphene is less conductive at higher frequencies [27]. When the frequency is above 1.36 THz, the MDs at 40 V are higher than those of 60 V, which could be explained by the aforementioned reasons. Overall, the MD of the MS-FP structure is more than 30% greater than the device with only a FP structure. The additional insertion loss from the microslits is around 2.6 dB at V= −60 V.
Fig. 5. (a) and (b) show the FP resonant effect of the device in frequency domain without and with metal microslits. The frequency domain is modulated by changing the applied voltages from −60 V (blue) to 60 V (orange). (c) and (d) are the corresponding MDs of the MG-FP device (without and with metal microslits). The black dashed lines outline the improvement due to the metal microslits structure.
In order to show the difference of the modulation depth between the microslits with graphene and the bare graphene area, the THz images of the graphene device at the voltages of −60V and 60 V were taken by raster scan with the Menlo K15 time-domain system (Fig. 6(a)-(e)). The FP resonant frequency (f = 0.836 THz) was selected to show the absorption of the graphene with/out the metal microslits (Fig. 6(c) and (e)). At f = 0.836 THz, the amplitude of the reflected THz signal has a larger difference from the microslits area than that from the bare graphene area (as highlighted with the white dashed rectangular). For comparison, the amplitude difference of the THz signal at f=0.891 THz is difficult to be observed (Fig. 6(d) and (f)). The amplitude of the reflected signal at f=0.891 THz (Fig. 6(d) and (f)) is higher than that at f = 0.836 THz (Fig. (c) and (e)), which follows the same trend in Fig. 6(b). The resonant frequency of the graphene with microslits area and the bare graphene area is slightly different (∼20 GHz), which is due to the limited frequency resolution in the experiment (∼40 GHz). Even at the resonant frequency (f = 0.8438 GHz) of the bare graphene area, the amplitude change is still smaller than that of the graphene with microslits area. The experimental results indicate the MS-FP device has a high modulation effect, which matches with our theory. The visual imaging results show the potential of the MS-FP device to be extended to a modulator array for THz spatial modulation. Based on this, a THz imaging system could be built by randomly coding the individual modulators in the array based on compressive-sensing theory [34].
Fig. 6. Photo and THz images of the MG-FP device under different gate voltages at two frequency points. The white dashed lines highlight the graphene with microslits and bare graphene areas, which are labelled by red and green arrows. (a) Front view of the graphene modulator. (b) The amplitude of the reflected THz signal in the frequency domain at f=0.836 THz (black line) and 0.891 THz (red line). The blue and orange solid lines represent the signal from the area without microslits; the blue and orange dashed lines represent the signal from the area with microslits. (c) and (d) are the images of the device under V= −60 V at f = 0.836 THz and 0.891 THz, respectively. (e) and (f) are the images of the device under V = 60 V at f = 0.836 THz and 0.891 THz, respectively.
The modulation speed of this design is limited by the device size and architecture rather than by any intrinsic physical properties of the material. The current device is large due to it being a proof-of-concept hence it is slow, thus future work will look into optimizing the speed of the device as well as having smaller and more desirable sized graphene areas.
5. Conclusion
In conclusion, we proposed and tested a graphene-based metal microslits assisted FP structure, which showed deep modulation of the THz signal from 0.2 THz to 1.5 THz. The metal microslit assisted structure performed >95% MDs at 14 frequencies. The MS-FP device has the potential to be employed in THz frequency hopping communication systems. The proposed modulator can also be extended for large-scale matrix manipulation, which is suitable for spatial THz light modulation.
Funding
National Natural Science Foundation of China (61805148, 61975135); International Cooperation and Exchange Programme (61911530218); Shenzhen International Cooperation Research Project (GJHZ20190822095407131); Natural Science Foundation of Guangdong Province (2019A1515010869); Guangdong Medical Research Foundation (A2020401); Shenzhen University New Researcher Startup Funding (2019134); Foundation for Distinguished Young Talents in Higher Education of Guangdong (YQ2015141); Guangdong Special Support Program of Top-notch Young Professionals (2015TQ01R453); Research Grants of Hong Kong (14201415, 14206717).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Supplemental document
See Supplement 1 for supporting content.
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