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Abstract
Active control of split ratios in terahertz (THz) beam splitters holds substantial potential for applications in imaging and spectroscopy. In this study, we introduce an approach for electrically controlling THz beam splitting with near non-dispersive characteristics, using the metasurface hybridized with single-layer graphene. Specifically, the resonant frequency of the metasurface is meticulously chosen to provide an enhanced effective conductivity that is almost frequency-independent. Furthermore, the split ratio can be manipulated by adjusting the gate voltage applied to graphene, thereby altering the effective conductivity of the hybrid metasurface without affecting its non-dispersive transmission and reflection characteristics. The feasibility of our approach is confirmed by the near non-dispersive split ratio across a wide operating frequency range, from 0.5 to 1.5 THz. The demonstration of this efficient, broadband, and tunable beam splitting ability validates the potential of gated graphene metasurfaces for advanced THz applications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The terahertz (THz) spectral region, typically spanning 0.1 to 10 THz, plays a pivotal role in various applications, including spectroscopy, sensing, imaging, and wireless data transfer and communications [1–5]. Precise beam splitting control within this frequency range is as crucial as in any other. Traditionally, high impedance silicon (Hi-Z Si) wafers have been employed for THz beam splitting. However, their applicability, particularly for broadband THz pulses, is limited due to temporal pulse replicas and spectral undulation caused by Fabry-Pérot effects [6,7]. Though the notion of passively controlling the splitting ratio through the application of a metallic coating on the substrate [8], leveraging its thickness-dependent conductivity, has been suggested, on-demand control of split ratios remains elusive. This demand necessitates the implementation of a THz beam splitter capable of non-dispersive, controllable beam splitting. The evolution of metamaterials and metasurfaces has recently motivated the use of phase gradient metasurfaces to steer normally incident THz beams along distinct paths [9–11]. Nevertheless, these gradient metasurfaces exhibit frequency-dependent responses as they are reliant on the resonant properties of their individual constituents.
At this juncture, it is crucial to underscore that the integration of graphene with metasurfaces has proven to be an effective approach for actively controlling THz beams. Graphene metasurfaces enable the active manipulation of wave characteristics, such as amplitude, phase, frequency, and polarization [12–18]. Within the THz frequency range, graphene interacts with THz waves through an intraband transition, leading to Drude-like conductivity. Ideally, the linear electronic band structure characteristic of graphene allows for gate-controlled, seamless conductivity variation, enabling its use as a tunable metal. When these unique properties of graphene are combined with meticulously designed metasurfaces, the efficient manipulation of THz waves is achievable. In this study, we introduce a graphene metasurface beam splitter (GMBS) that offers a nearly non-dispersive, electrically controllable splitting ratio at THz frequencies. The strong quasi-static response of the metasurface compensates for the comparatively low conductivity of graphene while maintaining minimal frequency dependence. Both numerical simulations and empirical measurements verify the efficacy of our methodology.
2. Numerical simulations
Figure 1 illustrates the primary design features and operational principles of the proposed GMBS. The constituent metallic meta-atom, shaped as a cross potent, is positioned adjacent to its four nearest neighbors with a minimal gap, leading to robust capacitive coupling between the meta-atoms [19,20]. The design parameters are as follows (refer to Fig. 1(a)): U = 20 µm, L = 18 µm, w = 2 µm, and a = 6 µm. Notably, the gap width (U − L) is set to 2 µm. The metasurface component, comprising metallic meta-atoms on a polyimide substrate (excluding attached graphene), is designed to resonate at a frequency of 4.79 THz (see the transmission amplitude plot in Fig. 1(a)). We intentionally set this resonance frequency higher than the targeted operational frequency of approximately 1 THz, the reasons for which will be elaborated later. By adjusting the Fermi level (EF) of graphene attached to the metasurface (Fig. 1(b)), the effective conductivity of GMBS can be modified, enabling an electrically controllable split ratio between transmitted and reflected THz beams (Fig. 1(c)). The polyimide substrate is patterned with two in-plane electrodes for side gating the graphene [21] and has a thickness of 1 µm to minimize the Fabry-Pérot effect within the desired frequency range. The use of an ion-gel as a gate-dielectric provides sufficient coverage of doping levels near the Dirac point at a few volts [22].
Fig. 1. Operational principles of the proposed GMBS. (a) Metallic meta-atoms, configured as a cross potent, allow strong capacitive coupling. The metasurface, without graphene, resonates at 4.79 THz. (b) Adjusting the Fermi level of the attached graphene modifies the GMBS conductivity. The polyimide substrate, patterned with in-plane electrodes and a thickness of 1 µm, minimizes the Fabry-Pérot effect. Ion-gel used as a gate-dielectric enables sufficient doping near the Dirac point. (c) This provides an electrically controllable THz beam split ratio.
The fabricated GMBS is numerically simulated using a commercial finite element method (FEM) solver, CST Microwave Studio (refer to Section 3.1 for fabrication details). In these simulations, we model the optical conductivity of graphene using the Kubo formula [23], assuming an intraband scattering time of 60 fs. We assume the metallic component to be made of gold and model it using the Drude model with a collision frequency of 4.07 × 1013 rad/s and a plasma frequency of 1.37 × 1016 rad/s. We consider the complex permittivity of polyimide (PI) to be 3.284 − j0.144. We carry out all simulations under the assumption of oblique incidence at an angle of 45 degrees, from which we extract the transmission and reflection coefficients.
To highlight the benefits of employing GMBS in beam splitting applications, we first calculated the transmission and reflection amplitude of gated single-layer graphene (excluding the metasurface) as a function of both the Fermi level (from 0 to 1 eV) and the THz wave frequency (refer to Fig. 2(a-c)). At the charge neutral point (CNP, i.e., EF = 0 meV), where the graphene conductivity (real part) is at its lowest, the incident THz beam is transmitted with minimal reflection (see the transmission and reflection amplitudes represented by black lines in Fig. 2(c)). Expectedly, an increase in EF reduces the transmission amplitude and enhances the reflection amplitude. However, it is evident that a high Fermi level exceeding 1 eV is required to attain a nearly 1:1 split ratio (see the transmission and reflection amplitudes drawn with blue lines in Fig. 2(c)). A previous study revealed that as graphene becomes more conductive in graphene metasurfaces, the width of the resonance is broadened, and the on-resonance transmission increases due to the weakening of the capacitive coupling between adjacent meta-atoms. Consequently, at the off-resonance frequencies, the effective conductivity of gated graphene metasurfaces can be considerably enhanced without significantly deteriorating their non-dispersive properties by employing their quasi-static response [24]. Accordingly, the GMBS proposed in this study aims to implement this previous design strategy to significantly control the split ratio with minimal dispersion. This is most clearly demonstrated in Fig. 2(d-f), where the transmission and reflection amplitudes of the GMBS are plotted as a function of both the Fermi level and the THz wave frequency. The simulation results indicate two key observations: (1) At the CNP, the transmission (or reflection) amplitude of the GMBS is lower (or higher) than that of graphene at the same Fermi level, suggesting that the increase in effective conductivity is achieved through the use of meta-atoms. (2) With the GMBS, a 50:50 split ratio is controllable. All these advantages stem from the non-resonant contribution of the meta-atoms to increased conductivity.
Fig. 2. Demonstrating the advantage of metasurface structures for beam splitting applications. (a-c) Spectrally-resolved transmission and reflection amplitudes of gated single-layer graphene (without the metasurface) as a function of the Fermi level EF. (d-f) Spectrally-resolved transmission and reflection amplitudes for the GMBS as a function of EF, illustrating the increased effective conductivity and controllable 50:50 split ratio achieved through the use of meta-atoms.
The simulations reveal a qualitative relationship among the resonance frequency, bandwidth, and the Fermi level required to attain a 50:50 split ratio. Figure 3 presents the transmission and reflection amplitudes of the GMBS for two distinct metasurface designs: one with a resonance frequency of 1.12 THz (Fig. 3(a-c)) and another at 1.67 THz (Fig. 3(d-f)). Note that the transmission amplitudes depicted in Fig. 3(c) and (f) employ different frequency ranges. The GMBS with the lower resonance frequency has a narrower bandwidth and requires a lower Fermi level to achieve the 50:50 split. This relationship provides insights into the interplay of the resonance frequency, bandwidth, and the Fermi level in GMBS designs.
Fig. 3. Transmission and reflection amplitudes of the GMBS for metasurface designs with resonance frequencies of 1.12 THz (a-c) and 1.67 THz (d-f) are shown. The insets show the resonance spectra for metasurfaces without graphene. Different frequency ranges are used for (c) and (f). Transmission and reflection maps show the relationship among resonance frequency, bandwidth, and Fermi level for a 50:50 split ratio. The lower resonance frequency design has a narrower bandwidth and lower Fermi level requirement for a 50:50 split.
3. Fabrication and measurement of GMBS
3.1 Fabrication of GMBS
The GMBS is fabricated using standard microelectromechanical systems (MEMS) technology, as depicted in Fig. 4(a). The initial step in the GMBS fabrication process involves preparing a polyimide film as a substrate. A polyimide solution (PI-2610, HD MicroSystems) is spin-coated onto a silicon substrate to produce a layer approximately 1 µm thick. This is then followed by a two-stage baking process for curing. Next, a negative photoresist solution (AZ nLOF 2035, MicroChem) is applied to the prepared polyimide layer using the same spin-coating technique. This photoresist layer is patterned using ultraviolet (UV) lithography, employing a chromium (Cr) mask with the desired pattern. A 10 nm thick chromium adhesion layer and a 200 nm thick gold layer are then sequentially deposited on top of the patterned photoresist. This deposited metal forms cross-potent meta-atom structures and in-plane electrodes via a lift-off process. Subsequently, CVD-grown graphene (provided by Graphene Square) is transferred onto the desired metasurface using a wet-transfer technique. During this transfer, a poly(methyl methacrylate) (C2 PMMA, MicroChem) support layer is utilized to ensure the integrity of the graphene, thus preventing any potential tears or wrinkles [25]. To control the Fermi level of graphene, we use an ion-gel gate dielectric with near-transparent characteristics at THz frequencies. Finally, the flexible polyimide film layer containing the entire device is separated from the silicon substrate and transferred to a Printed Circuit Board (PCB) for mechanical stability. Notably, the PCB contains a central aperture, which prevents the incident THz waves from interacting with the PCB.
Fig. 4. (a) Schematic illustration of the GMBS fabrication process. (b) Front view of the final GMBS device. (c) Schematic representation of the THz Time-Domain Spectroscopy setup utilized for measuring transmission and reflection amplitudes.
3.2 Measurement of transmission and reflection
A commercial THz time-domain spectroscopy system is used to characterize the fabricated GMBS (TOPTICA TeraFlash Pro, see Fig. 4(c)). THz pulses are generated by exciting a THz photoconductive antenna (PCA) with a femtosecond fiber laser. The GMBS sample plane is positioned at a 45° angle to the propagation direction of the incident THz beam. The receiving PCA is mounted on a mechanical rail so that its position can be rotated by an angle θ relative to the sample position. This specific configuration enables the quantification of the transmission (reflection) of THz beams through (from) the GMBS at a 0° (90°) angle. Two lenses with focal lengths of 50 mm and 100 mm were placed in series along the path of the beam to focus the THz beam generated by the PCA onto the GMBS. To mitigate the impact of water vapor absorption, a controlled humidity level of approximately 4.7% was maintained throughout the measurements [26,27].
4. Performance characterizations
4.1 Demonstration of gate-controlled beam splitting
Figure 5(a-d) depicts the measured transmission and reflection amplitude maps for gated graphene and GMBS, specifically illustrating how these amplitudes vary with the frequency of THz waves and the applied gate voltage to graphene. As confirmed by the maps, the CNP is located nearly at the same gate voltage ${V_{\textrm{CNP}}}$ = 1.7 V for samples both with and without metasurface structures (indicated by the black dashed lines in Fig. 5(a-d)). The incremental gate voltage is defined, for reference, as the magnitude of the voltage difference between the applied gate voltage and the voltage at the CNP, i.e., $\Delta V = |{{V_\textrm{g}} - {V_{\textrm{CNP}}}} |$. As the incremental gate voltage $\Delta V$ increases, the measured transmission (reflection) amplitude of gated graphene decreases (increases) across a broad frequency range. Note that a positive correlation exists between the Fermi level and the incremental gate voltage, i.e., $|{{E_\textrm{F}}} |\propto \Delta {V^{1/4}}$ if the residual carrier concentration is ignored. This relationship allows for a direct comparison between the measured amplitudes and those calculated with a change in the Fermi level (refer to Sec. 2). However, a saturation behavior in conductivity is observed experimentally at larger incremental gate voltages (see, for instance, the bottom portion of the maps in Fig. 5(a, b)). At this high Fermi level, where short-range scattering becomes dominant [28], the conductivity of graphene no longer increases appreciably, which was not accounted for in the simulations. This limited conductivity control precluded the observation of a balanced split ratio in our measurements with gated graphene.
Fig. 5. (a-d) Transmission and reflection amplitude maps for gated graphene and GMBS, demonstrating amplitude variations with THz wave frequency and gate voltage. The CNP is located at nearly the same gate voltage for both samples. (e, f) Comparisons of spectrally-resolved amplitudes for two representative gate voltage levels. (g, h) Plots of transmission and reflection amplitudes at 0.5 THz as functions of gate voltage, corresponding to white dashed lines on the maps. Increased tunability offered by GMBS is evident in the relative change in transmission.
The advantages of introducing a non-resonant metasurface are evident in the gate-controlled transmission and reflection amplitudes (see Fig. 5(c, d)). First, the balanced split ratio (approximately 50:50) can be achieved at a relatively low gate voltage level of ${V_\textrm{g}} = $ 0.4 V (or $\Delta V = $ 1.3 V, as shown by the blue dashed lines in Fig. 5(c, d)). To show this more clearly, in Fig. 5(e, f), we compare the spectrally-resolved transmission and reflection amplitudes of gated graphene and GMBS for two representative gate voltage levels. Although there is a small reduction in non-dispersiveness, the aforementioned advantage is clearly apparent, thereby confirming the viability of the GMBS as a practical broadband beam splitter. Secondly, the incorporation of a non-resonant metasurface enhances the extent to which transmission and reflection can be adjusted. To illustrate this point more clearly, the transmission and reflection amplitudes of gated graphene and GMBS, measured at 0.5 THz, are plotted as a function of gate voltage in Fig. 5(g, h). These plots correspond to the white dashed lines shown on the maps (Fig. 5(a-d)). The degree of tunability is quantified by the relative change in transmission, denoted as $\Delta t/{t_{\textrm{CNP}}}$, where $\Delta t$ is the difference between t and ${t_{\textrm{CNP}}}$. The relative change in transmission for gated graphene is estimated to be 11%, while for GMBS it is 49% (when the upper limit of gate voltage variation, $\Delta {V_{\textrm{max}}}$, is set to 3.7 V). This suggests that a wider range of split ratios can be accommodated for a given range of gate voltage levels. When the upper limit of gate voltage variation, $\Delta {V_{\textrm{max}}}$, is set to 3.7 V, a continuously variable ratio from 77:23 to 40:60 is observed experimentally for GMBS, but only from 96:4 to 87:13 for gated graphene.
4.2 Comparison between GMBS and conventional BS
The broadband characteristics of the proposed GMBS can be further confirmed by analyzing transmitted and reflected THz waveforms in the time domain. To provide a clear experimental characterization, we conducted measurements on the transmitted (reflected) THz waveforms through (from) both the GMBS and a commercially available BS (referred to as CBS, acquired from TYDEX). The CBS is made of a high resistivity floating zone (HRFZ) silicon wafer with a thickness of 1 mm and has a nominal split ratio of 54:46 (from the specification sheet provided by the manufacturer). The broadband THz pulse that passes through the input facet of CBS undergoes multiple internal reflections. As a result of this Fabry-Pérot etalon effect, the transmitted and reflected THz waveforms contain a series of pulse replicas with a diminishing peak field (note also the phase reversal in the reflected pulse replica). For the case of CBS, such delayed replicas are clearly seen in the transmitted and reflected THz waveforms (Fig. 6(a, b)). In contrast, due to the negligible thickness of GMBS compared to the central wavelength of the incident THz pulse, such delayed pulse replicas cannot be resolved in the transmitted and reflected THz waveforms for GMBS (Fig. 6(a, b)). In these measurements, the gate voltage is adjusted ($\Delta V = $ 1.3 V) so that the GMBS provides a 50:50 split ratio.
Fig. 6. Experimental and spectral characterization of the GMBS and a commercially available BS (CBS). (a, b) Transmitted and reflected THz waveforms through the GMBS and CBS. Note the absence of delayed pulse replicas in the GMBS, compared to the clear presence in the CBS due to the Fabry-Pérot etalon effect. (c) Spectrally resolved transmission and reflection amplitudes for CBS showing Fabry-Pérot resonances. The free spectral range (FSR) at approximately 1 THz corresponds well with theoretical predictions. (d) Spectrally resolved transmission and reflection amplitudes for GMBS. Measurements for GMBS were adjusted to provide a 50:50 split ratio ($\Delta V = $ 1.3 V).
The presence of pulse replicas in transmission and reflection is manifested in the spectral domain by typical Fabry-Pérot resonances for the case of CBS. Figure 6(c) illustrates the spectrally resolved transmission and reflection amplitudes obtained by performing a Fourier transform on the waveforms with a time window of approximately 100 ps (corresponding to that shown in Fig. 6(a, b)). At around 1 THz, the free spectral range (FSR) is measured to be 0.0391 THz, which corresponds approximately with the theoretically calculated value of 0.0312 THz (obtained assuming a refractive index of 3.4 for silicon). In the case of GMBS, however, the spectrally-resolved transmission and reflection amplitudes show negligible spectral undulation (Fig. 6(d)). This feature may be especially useful for high spectral resolution experiments, such as explosive and molecule vibration detection with extremely sharp spectral features [29,30].
5. Conclusion
In conclusion, we have carried out a comprehensive design, simulation, fabrication, and experimental investigation of a GMBS with potential applications in THz beam splitting. The GMBS effectively utilizes the interaction between THz waves and engineered metallic meta-atoms, in addition to the electrically adjustable conductivity of graphene, thereby offering a tunable broadband split ratio between transmitted and reflected THz beams. Our experimental results confirm that the GMBS when compared to gated graphene, can achieve a balanced 50:50 split ratio at a relatively lower gate voltage. From a broader perspective, the design of the GMBS, with its adjustable split ratio feature, could pave the way for new opportunities in THz wave manipulation, enriching the toolsets in THz system designs.
Funding
Institute of Information & Communications Technology Planning & Evaluation (2022-0-00624); National Research Foundation of Korea (2021R1C1C100631612, 2022R1A2C301335312).
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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