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Abstract
This letter presents a fabricated Dirac point modulator of a graphene-based terahertz electromagnetically induced transparency (EIT)-like metasurface (GrE & MS). Dynamic modulation is realized by applying three stimulus modes of optical pump, bias voltage, and optical pump–bias voltage combination. With increasing luminous flux or bias voltage, the transmission amplitude undergoes two stages: increasing and decreasing, because the graphene Fermi level shifts between the valence band, Dirac point, and conduction band. Thus, an approximate position of the Dirac point can be evaluated by the transmission spectrum fluctuation. The maximum modulation depth is measured to be 182% under 1 V. These findings provide a method for designing ultrasensitive terahertz modulation devices.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz metasurface is an artificially designed subwavelength two-dimensional metamaterial with a thickness from several to tens of micrometers. It can be used to regulate electromagnetic waves [1–6], for example, in modulators [7–10], absorbers [11,12], and polarizers [13], Terahertz encoder [14]. Metasurface has become a widespread research topic in the field of electromagnetic field. In particular, electromagnetically induced transparency (EIT) is a quantum interference phenomenon in a three-level atomic system, where an extremely narrow transparent window with low absorption and steep dispersion in an opaque medium is generated [15–20]. The EIT-like features of metasurfaces make them ideal for ultrasensitive THz modulator. Its transparent window is sensitive to changes in the microenvironment, which provides a well-defined frequency marker for precision measurements [15,21–24]. EIT metasurface can be used for effectively controlling electromagnetic waves, and has been widely used in optical manipulation.
In traditional metasurface devices, once the structure and dimension are determined, real-time dynamic regulation cannot be realized [7,25]. Therefore, materials with dynamically adjustable parameters should be used to obtain good electromagnetic wave modulation. Graphene is a honeycomb two-dimensional material composed of single-layer carbon atoms. It possesses unique electrical, mechanical, and thermal properties, and is sensitive to external photoelectric excitation. Therefore, it is considered to be the perfect material for dynamic modulation of terahertz waves [26–30]. Recently, devices modulated by dynamically adjustable materials have been rapidly developed. In 2013, Lee et al. fabricated a device consisting of graphene and a metasurface. When the voltage excitation was applied, the amplitude and phase of the transmission spectrum reached 47% and 32.2°, respectively [31]. In 2014, Zhang et al. realized more than 80% modulation depth between 0.28 THz and 0.36 THz by using the regulation characteristics of VO2 [32]. In 2020, Qiao et al. fabricated a terahertz device consisting of MoTe2 and Si. The maximum obtained modulation depth was 99% by tuning the pump light [33]. Recently, Yang et al. has used graphene for ultrasensitive modulation in terahertz frequencies and obtained the maximum modulation depth of 90% [7]. The Fermi level movement near the Dirac point in graphene was also detected. Currently. research on terahertz modulators is being actively conducted. In particular, the modulation depth of terahertz modulators in terahertz photoelectric devices is attempted to be increased.
In this study, a terahertz dynamically modulated device was fabricated by combining graphene with an EIT-like metasurface (GrE & MS). GrE & MS samples were dynamically modulated by three different methods: pump light application, bias voltage application, and combined bias voltage–optical pump modulation. The obtained transmission amplitude underwent an increasing stage and a decreasing stage. Somewhere in the middle region of the luminous flux (LF) or bias voltage, the transmission amplitude reached the highest position, when the graphene Fermi level was the closest to the Dirac point. In this work, the maximum modulation depth was measured to be 182%. The developed device has the potential application in new high-efficiency terahertz devices (Table 1).
Table 1. THz modulators type, materials, and Mda
2. Fabrication and method
Figure 1(a) shows a schematic diagram of the GrE & MS samples. The fabrication process is depicted in Fig. 1(b). First, a layer of polyimide (PI) film with a thickness of 5 µm was spin-coated on a 300-µm-thick quartz by using a glue homogenizer. Here, PI was used as the substrate for the structure, which enabled to retain the outstanding ambient stability of GrE & MS, including its excellent heat resistance and mechanical and dielectric properties. Next, two photoresists (LOR and AZ1500) were spin-coated on the polyimide film, exposed to ultraviolet light, and cleaned with a developer to obtain the required microstructure pattern. Subsequently, a 200-nm-thick aluminum layer was deposited on the exposed microstructure pattern by magnetron sputtering, and an EIT-like terahertz metasurface with the aluminum structure was obtained by acetone immersion and ultrasonic vibration. Next, a layer of the PI film with a thickness of 5 µm was spin-coated on the structure (for blocking the direct contact between the graphene and the aluminum structure). A layer of graphene with a thickness of 1 nm was grown by copper catalyzed chemical vapor deposition (CVD) and was transferred to the PI film by wet transfer.
Fig. 1. (a) Sample of GrE & MS; (b) Fabrication process of the sample, I. Spin-coating 5 µm polyimide on SiO2; II. Fabricating an aluminum structure on a polyimide film; III. Spin-coating 5 µm polyimide on the aluminum structure; IV. Coating the polyimide film with graphene; (c) Raman spectra of the graphene monolayer on a quartz substrate measured by a laser with a wavelength of 514 nm; (d) Top view of the sample, specific structural parameters: Px = 100 µm, Py = 100 µm, R1 = 34 µm, R2 = 10 µm, R3 = 10 µm, R4 = 15 µm, and ω = 5 µm. (e) Electron micrograph of GrE & MS.
Finally, the graphene was covered with ionic gum, and two probes were connected to the ionic gum and the graphene, respectively, for bias voltage application. The structure and its dimensions are shown in Fig. 1(d). A photomicrograph of the periodic cell structure is shown in Fig. 1(e).
The Raman spectra of the graphene were measured by a laser with a wavelength of 514 nm, as shown in Fig. 1(c). The Raman spectrum mainly includes the G peak, D peak, and 2D (G’) peak. Among them, the D peak (∼1350 cm-1) is the disordered vibration peak of graphene. The full width of the half peak of 2D is 56 cm-1. The results above show the high quality of the graphene [35].
The dielectric constant of graphene can be expressed using the following expression [36,37]:
where $\omega $ is the frequency of an incident terahertz wave and ε0 is the dielectric constant of the vacuum (8.85 × 10−12 F/m).The surface conductivity of graphene $\mathrm{\sigma }(\mathrm{\omega } )$ can be estimated by the following equation:
By using the Kubo formula, the conductivity of graphene includes two parts: inter band conductivity and intra band conductivity, which can be expressed as [11,37–39]:
From the previous analysis, the electrical conductivity of graphene can be dynamically regulated by changing the chemical potential, and its Fermi level can be tuned by adjusting external bias voltage or LF [11].
Description of optical properties of Al by Drude model [37]:
Figure 2 shows an 8f confocal terahertz time-domain spectroscopy system (THz-TDS) used in our measurement. For the THz-TDS setup, a LED optically pumped all-fiber femtosecond laser was used to realize terahertz wave time-domain spectroscopy. The terahertz time scan of 40 ps was used to obtain a spectral resolution of 40 GHz with a bandwidth of 0.2–1.5 THz. We introduced dry air into the THz-TDS setup to maintain a constant environment. The room temperature was about 24°C; the room humidity was about 2.7%. During the measurements, the normally incident terahertz wave was along + z. The laser was centered at a 1560 nm wavelength with a 100 fs pulse duration and a 100 MHz repetition rate. Here, a laser emitter with a wavelength of 532 nm (green light) was utilized as the source of pump light, as shown in Fig. 1(a), and its spot diameter was ∼3 mm. A probe system with two probes was used for applying bias voltage to the graphene, as shown in Fig. 2(c).
Fig. 2. Schematic diagram of THz-TDS; (a) Schematic view of the THz-TDS measurement setup; (b) Experimental photoelectric equipment: THz-TDS system; (c) Source of bias voltage and laser controller.
3. Results and discussion
First, the EIT metasurface without graphene was simulated, as shown in Fig. 3. In the simulation, the incident electromagnetic light was applied at a position normal to the plane of the metasurface (i.e, the z-axis) with its polarization along the y-direction. The metal adopted was lossy aluminum with the conductivity of ${\sigma _{Al}} = 3.56 \times {10^7}S/{m^{ - 1}}$. PI (dielectric constant ε: 3.1 and tangent loss µ: 0.05) was adopted as a flexible substrate.
Fig. 3. Transmission spectrum and electric field of GrE & MS; (a) Transmission spectrum; (b) Simulated group time delay; Electric field distributions (c) at 0.70 THz, (d) at 0.87 THz, and (e) at 1.19 THz.
Figure 3(a) shows the transmission spectra of a single three-shaped resonator (includes three C-shaped structures connected together, called as bright model 1), a C-shaped resonator (bright model 2), and an EIT-like metasurface (bright models 1 and 2 combined together). Two valleys and one peak are in the transmission spectrum at 0.70, 1.19, and 0.87 THz, respectively. The valleys of bright models 1 and 2 almost coincide with the valleys of the EIT model. The two bright modes interfere with each other and form a transparent window at 0.87 THz.
The electric field distributions of the EIT-like metasurface at the two valleys and one peak were also calculated. At 0.70 THz, bright model 1 was excited by a terahertz wave, whereas bright model 2 could not be excited, as shown in Fig. 3(c). In contrast, At 1.19 THz, bright model 2 was excited, whereas bright model 1 could not be excited, as shown in Fig. 3(d). At 0.87 THz, the two bright models interfered with each other resulting in a transparent window, as shown in Fig. 3(e). An important characteristic of the EIT-like metasurface is the group delay. A slow-light effect can be realized by using a strong dispersion effect of materials at the transparent window. The slow-light effect can be described by the group time delay (tg), and its calculation formula is [41]
where φ(ω) is the phase of the system under different frequencies.At the transparent window, the EIT-like device has an obvious group delay, as shown in Fig. 3(b), and the maximum group time delay is up to 5.5 ps. Therefore, the EIT-like characteristic of the metasurface is verified. At the transparent window, the structure is sensitive to changes in the microenvironment, which provides an efficient way for optical manipulation.
To scrutinize the modulation effects of GrE & MS, three control modes of dynamically modulation were carried out using THz-TDs: pump light application, bias voltage application, and joint modulation by bias voltage and optical pump. Under the application of pump light, the LF increased from 0 mW/cm2 to 154.8 mW/cm2, and the transmission amplitude underwent an increasing stage and a decreasing stage, with a turning point near 63.5 mW/cm2, as shown in Fig. 4(a). Under the applied bias voltage, the measurement results showed similar characteristics. However, the upward trend of the transmission amplitude was not that significant, as shown in Fig. 4(c). That is, the transmission amplitude reached the highest position when the bias voltage was 1 V. Under the joint modulation by bias voltage and pump light (tuning the LF under a bias voltage of 1 V), the transmission amplitude also underwent two different stages, similar to the LF application. The transmission amplitude reached the highest position when the LF was 2.7 mW/cm2, as shown in Fig. 4(e). With an increase in the LF or bias voltage, the transmission amplitude also did not exhibit a single increasing or decreasing trend, as shown in Fig. 4.
Fig. 4. Transmission spectrum of GrE & MS and shift of the Fermi level; (a-b) Under different LFs; (c-d) Under different bias voltages; (e-f) Under different LFs with a bias voltage fixed at 1 V.
These characteristics of the transmission amplitude are explained by shifting of the graphene Fermi level between the valence band, Dirac point, and conduction band [7,34,42,43]. In ideal graphene, the internal carrier concentration is in equilibrium at the Dirac point. However, owing to the doping concentration and the disorder of particle motion, the graphene in GrE & MS is different from the ideal one. When p-doped graphene is used in GrE & MS, its initial Fermi level EF0 is in the valence band. In the experiment, ionic gum was used as the end of the electrode, and the weak voltage of ionic gum caused the electron accumulation inside the graphene. Herein, the graphene used for GrE & MS was p-doped graphene, and its initial Fermi level (EF0) was in the valence band, as shown in Fig. 4(b).
In Fig. 4(a), the transmission amplitude increases with the applied LF from 0 mW/cm2 to 63.5 mW/cm2. Next, the transmission amplitude shows a downward trend with increasing the LF to 154.8 mW/cm2. Here, as the LF is increased from 124.4 mW/cm2 to 154.8 mW/cm2, the decreasing trend is insignificant. When the graphene is modulated by the pump laser, the internal photogenerated carrier concentration increases, which leads to the movement of the Fermi levels EF1 and EF2 upward close to the Dirac point [7,34,42,43], and the graphene conductivity decreases. Further, with increasing number of terahertz waves passing through the graphene film, the transmission amplitude increases continuously when the pump laser power increases in the range of 0 mW/cm2–63.5 mW/cm2.
With increasing LF to 93.9 mW/cm2, the Fermi level EF3 may skip the Dirac point and enter the guide band, increasing the graphene conductivity. Therefore, the transmission amplitude exhibits a downward trend. The turning point is near 63.5 mW/cm2, which shows that when the LF is 63.5 mW/cm2, the graphene Fermi level is the closest to the Dirac point. At the same time, the Fermi levels EF4 and EF5 move away from the Dirac point in the conduction band. As a result, the transmission amplitude exhibits a downward trend with increasing LF from 124.4 mW/cm2 to 154.8 mW/cm2, but the trend is not obvious. This is because the photogenerated carrier concentration becomes increasingly saturated in this process. The shift of the Fermi level to the position near the Dirac point can be inferred from the change trend of the transmission spectrum.
The transmission spectrum of GrE & MS under different bias voltages is shown in Fig. 4(c). The transmission amplitude also undergoes an increasing stage and a decreasing stage. The turning point is at the position of a 1 V bias voltage, where the Fermi level EF1 is the closest to the Dirac point, which leads to a decrease in the graphene conductivity and an increase in the transmission amplitude. In Fig. 4(d), the Fermi levels EF2, EF3, and EF4 are shifted away from the Dirac points, which indicates that with increasing bias voltage, the graphene conductivity gradually increases, and the transmission amplitude decreases.
The third modulation method is tuning the LF under a bias voltage of 1 V. With increasing LF to 2.7 mW/cm2, the transmission amplitude shows a downward trend. We believe that the reason is the movement of the Fermi level EF1 away from the Dirac point in the conduction band. For the Fermi levels EF2–EF5, with increasing LF from 33.1 mW/cm2 to 154.8 mW/cm2, the amplitude of the transmission spectrum decreases, but the trend is not obvious. This indicates that the graphene has reached the saturation state, as shown in Fig. 4(e).
Here, we summarize the results of the three modes of modulation. Terahertz waves can be modulated by pump light, but the modulation of photogenerated electrons on the terahertz waves is not sufficient for achieving high modulation depth. In contrast, under the bias voltage application, the measurement results show that the modulation effect is particularly prominent. Further, when the bias voltage modulation is combined with pump light, higher Fermi level and ultrasensitive modulation sensitivity can be achieved. Such a modulator has the potential application in new high-efficiency terahertz photonic devices.
In order to illustrate the modulation effect of GrE & MS, the following formula is introduced to characterize the modulation depth of the transmission amplitude [7,34,41]:
where ${T_i}$ is the transmission amplitude under different incident LF, bias voltage or LF and bias voltage excitations and ${T_{MIN}}$ is the lowest transmission amplitude under different excitations. In particular, under LF, bias voltage, and combined LF and bias voltage modulations, ${T_{MIN}}$ is the transmission amplitude when LF = 0 mW/cm2, bias voltage is 7 V, and LF = 93.9mW/cm2 and bias voltage is 1 V, respectively.Figure 5(a) shows the modulation depth of GrE & MS under different LFs .The maximum modulation depth is 45% when the LF is 63.5 mW/cm2. Here, the Fermi level EF2 is the closest to the graphene Dirac point. This shows that the graphene is ultrasensitive to external stimuli when its Fermi level is near the Dirac point. Figure 5(b) shows the modulation depth for different LFs at a bias voltage of 1 V. When the LF is 2.7 mW/cm2, GrE & MS reaches the maximum modulation depth of 109%. Here, the Fermi level is also the closest to the Dirac point. Figure 7(c) shows the modulation depth of GrE & MS under different bias voltages. The measured maximum modulation depth is up to 182% under a bias voltage of 1 V, which is 4.44 times higher than that of the pump light modulation alone.
Fig. 5. Modulation depth; (a) Under different LFs without a bias voltage; (b) Under different LFs at a bias voltage of 1 V; (c) Under different bias voltages without an LF.
GrE & MS has an excellent modulation effect, especially when the bias voltage is applied separately. The reason is that the EIT metasurface is sensitive to changes in the microenvironment, which provides an efficient way for optical manipulation. Furthermore, graphene is ultrasensitive to external stimuli when its Fermi level is near the Dirac point. Thus, combining graphene with the EIT metamaterial results in an excellent modulation effect. Overall, GrE & MS enables efficient terahertz modulation.
The coupled resonator model can also characterize the modulation effect of the graphene EIT-like metasurface. The interference and the coupling in GRE & MS can be analyzed by coupled differential equations [7,37,44].
As the energy losses are related to the imaginary part of χ;, the transmission amplitude can be written as
where ℊ signifies the coupling strength for the incident terahertz wave related to the geometric parameter of the designed structure.A theoretical fitting curve is obtained by using Eqs. (9) and is compared with the experimental results. The fitting parameters are shown in Fig. 6 as functions of the LF or bias voltage. The theoretical fitting curves are in close agreement with the experimental results. It can be seen that δ changes insignificantly with stimuli, whereas γ1, γ2, and κ change significantly.
Fig. 6. Fitting curves for the coupled harmonic resonators model are compared with the experimental results; (a)-(f) Comparison diagram for different LFs; (g)-(h) Comparison diagram for different bias voltages.
Diagrams of the obtained fitting parameters with the coupled resonator model are shown in Fig. 7. Figure 7(a) shows the fitting parameters γ1, γ2, δ, and κ as functions of LF. The loss factors of γ1 and γ2 also undergo a decreasing stage and an increasing stage. With increasing LF from 0 mW/cm2 to 63.5 mW/cm2, the loss of GrE & MS gradually decreases. When the LF is increased from 63.5 mW/cm2 to 154.8 mW/cm2, the Fermi level of the graphene is in the conduction band and gradually moves away from the Dirac point, which leads to a gradual increase in the GrE & MS loss. At the same time, the detuning coefficient δ does not change with LF. The fitting results are consistent with the transmission spectrum of Fig. 4, which is consistent with the previous analysis of the shift of the Fermi level near the Dirac point.
Fig. 7. Fitting parameters γ1, γ2, δ, and κ as functions of the LF and bias voltage; (a) Under different LFs; (b) Under different bias voltages.
Figure 7(b) shows the fitting parameters γ1, γ2, δ, and κ as functions of bias voltage. The loss factors of t γ1 and γ2 also show a decreasing stage and an increasing stage because graphene is sensitive to the voltage stimuli. When the bias voltage is 1 V, the Fermi level EF1 of the p-doped graphene directly skips the Dirac point. When the voltage is continued to increase, the Fermi level gradually moves away from the Dirac point in the conduction band, resulting in an increase in the loss of the resonators. It can be seen that the detuning coefficient δ does not change. The coupling coefficient decreases first, then increases, which is also roughly consistent with the change trend of the graphene Fermi level.
4. Conclusions
In summary, a Dirac point modulator of graphene-based terahertz EIT-like metamaterials is proposed. The fluctuation of the Fermi level of graphene at the Dirac point was detected by three modes of modulation: pump light modulation, bias voltage modulation, and joint modulation by optical pump and bias voltage. The study analyzed the fluctuation of the graphene Fermi level near the Dirac point and its affect on the transmission amplitude. Based on the obtained results, the modulator exhibits an excellent modulation effect, and the maximum modulation depth is up to 182% under the bias voltage modulation. To analyze the influence of the graphene on terahertz modulation, the coupled resonator model was used, and its influence on the coupling parameters was determined. The graphene-based terahertz EIT-like metamaterials provide an efficient way for terahertz modulation.
Funding
Anhui Provincial Department of Housing and Urban-Rural Development (2021-YF61); Anhui University of Science and Technology (2021CX2067); Natural Science Foundation of Shandong Province (ZR2020FK008, ZR202102180769, ZR2021MF014); National Natural Science Foundation of China (61675147, 61701434, 61735010); National Key Research and Development Program of China (2017YFA0700202, 2017YFB1401203); the Qingchuang Science and Technology Plan of Shandong Universities (2019KJN001); Taishan Scholar Project of Shandong Province (tsqn201909150).
Acknowledgments
This work was supported by Science and Technology Foundation of Housing and Urban Rural Construction of Anhui Province, the National Natural Science Foundation of China (NSFC), Special Funding of the Taishan Scholar Project, the Natural Science Foundation of Shandong Province, the National Key Research and Development Program of China, funding from the Qingchuang Science and Technology Plan of Shandong Universities and Graduate Innovation Fund of Anhui University of Science and Technology. We thank languageediting.osa.org for editing the English text of a draft of this manuscript.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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