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Abstract
The Brewster effect has been previously reported as an essential mechanism for terahertz (THz) wave sensing application. However, generally in a sensing application, a complex rotation apparatus is required for detecting the slight change in Brewster angle. Here, we propose a graphene-based Brewster angle device operating at a specific terahertz frequency capable of sensing the refractive index at a fixed incident angle. In other words, our sensing device could avoid the impact of Brewster angle shift and eliminate the need for high-precision rotating equipment, which is usually required in traditional sensing applications. The conversion from the refractive index to a Volt-level detectable voltage roots from the tunability of graphene’s Fermi level in the external electrical field. A linear correlation between the output voltage and the background refractive index is observed and theocratically analyzed. Furthermore, we present the improvement of our device in terms of sensing range and sensitivity by adjusting the permittivity of the dielectric substrate. As a demonstration of our proposed device, a detection range of 1.1-2.4 and a sensitivity of 20.06 V/RIU for refractive index is achieved on a high-resistance silicon substrate operating at 0.3 THz.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) radiation has been proven to be an excellent alternative for nondestructive detection due to its non-ionization property [1]. Furthermore, the outstanding sensitivity to inter-molecular interactions such as hydrogen bonding and Van der Waals force makes THz wave more attractive for identifying macromolecules such as amino acids, proteins, RNA, or DNA in biological and medical research [2]. Most reported detection applications based on terahertz waves are demonstrated by complex terahertz spectroscopy instruments, including picosecond-pulse terahertz time-domain spectroscopy (THz-TDS) or continuous-wave terahertz frequency-domain spectroscopy (THz-FDS). Beyond the fact that those spectroscopic investigations successfully proved the feasibility of THz radiation as an excellent sensing method, the instrument's bulky size and fragile structure hinder the THz waves from practical application.
Recent studies have revealed a trend that THz detection studies are transferring from spectroscopic investigations to functional sensors based on various physical mechanisms such as meta-material [3], surface plasmon [4], and the Brewster effect [5]. Spectroscopy instruments are still required for meta-material and surface plasmonic sensors since the permittivity of the target substance is generally characterized as resonance frequency shift [6,7] or phase-jump inversion [8,9] The Brewster effect has been previously reported for enhancing THz light-matter interaction [10] and ultra-broadband terahertz modulation [11] without spectroscopy instruments at a fixed frequency. More importantly, dielectric constant measurement employing the Brewster effect was proved feasible [12]. The variation in background dielectric behavior was measured as the change in the Brewster angles. However, due to its sensitive angle dependence, there is a relatively high requirement for the collimation of the THz beam [13]. Additionally, the goniometer and the rotation motor with high-precision are needed to measure and adjust the weak change in incident angle. Nonetheless, the conversion from spectral dielectric behavior to geometrical angle points to a possible way to realize THz sensing without complex spectroscopy instruments. Compared with the previous works [10–12], our BGS is capable of realizing the conversion from the refractive index of analyte to a Volt-level detectable voltage at a fixed incident angle. This means that through our BGS, the non-destructive detection of the different analytes’ refractive index could be achieved by reading the voltage value applied to graphene. What’s more, our BGS is designed on the basis that the electrically tuning graphene could compensate the Brewster angle shift caused by the change of analyte. Therefore, by applying voltage appropriately to control the Fermi level of graphene, our sensing device could avoid the impact of Brewster angle shift and eliminate the need for a high precision rotating equipment, which is usually required in traditional sensing application.
In this study, we present that the electrical-tunable graphene [14,15] can be applied to further simplify the THz sensing process based on the Brewster effect. Here, a Brewster angle incident graphene-based sensor (BGS) operating at a specific THz frequency is initially established. The electrically-tuning graphene is proved to be capable of compensating the Brewster angle shift caused by the change of analyte. As a result, the variation of background refractive index can be measured as the voltage applied on the graphene. With our proposed BGS, the narrow-band THz source and detector fixed at a specific angle without equipping any moving components could be applied to measure the THz refractive index of target substance.
This paper starts with the proof of feasibility on that appropriate Fermi level adjustment of the graphene could compensate for the Brewster angle shift, which is caused by the changes in refractive index. Then, the relationship between voltage and refractive index of analytes is established, followed by a series of mathematical derivations and theoretical fitting of the Finite element (FEM) simulation which aim at verifying this relationship. At the end, the influence and optimization of substrate’s refractive index for the sensitivity and detection range of the BGS is discussed. Due to the frequency dependence of the graphene’s conductivity, this result could be extended to other frequency bands and provide a new direction for sensing throughout the terahertz band.
2. Model and simulation of the Brewster angle device
Here, as a proof of concept, the schematic diagram of the Brewster angle device is shown in Fig. 1(a). The device includes a pair of continuous-wave THz emitter and detector, BGS, and display of voltage output for refractive index retrieving. Initially, the incident angle is registered at the Brewster angle of the device at its original state without substance and an external electric field. Single-frequency THz wave emitted by THz emitter is reflected to THz detector through the BGS. Then, the analyte is placed on an angle-sensitive BGS and the reflected THz signal is detected under the initial incidence angle. The specific parameters of graphene-based device have been reported in previous articles [16]. The Brewster angle will shift due to the change of refractive index caused by the introduced analyte, and the reflectivity would increase. Thus, the signal read out by detector will change from almost zero to relatively large. Next, the gate voltage is applied to graphene. When the readout signal of the detector returns to almost zero, the voltage applied is stopped and the value of the voltage is recorded. Finally, according to the corresponding relationship between voltage and refractive index proposed in this study, the refractive index of the analyte can be determined by the recorded voltage value. In sum, the device can control the Fermi level of graphene by applying voltage so that the angle shift caused by the change of refractive index can be compensated. Due to that, the variation of the refractive index caused by the introduced analyte is converted into the output of voltage applied, which would implement a high-precision refractive index sensing. It is noteworthy that our BGS is most suitable for the measurement of gaseous analyte’s refractive index. As for the potential implementation of the system for gaseous analytes, the device (including THz emitter and detector, BGS) could be simply placed in a gas chamber filled with target analytes. This implementation scheme could guarantee the surface integrity and stability of the graphene sheet, and eliminate the impact of the difference in refractive index between air surroundings and the analyte. Besides, the stability of graphene which is fabricated by Laser-Induced Graphene (LIG) method has been verified in our previous work [17]. In the fabrication of our BGS, we could also employ the LIG method to guarantee the stability of graphene sheet.
The simplified model of the BGS is shown in Fig. 1(b), which describes the reflection and refraction of incident terahertz waves at the interface. The reflection coefficient of the p-polarized terahertz wave can be described as:
It is widely known that when the p-polarized THz wave incident with an angle ${\theta _i}$, it will be totally refracted given on the condition that ${n_s}\cos {\theta _i} - {n_a}\cos \varphi + {Z_0}{\sigma _g}\cos {\theta _i}\cos \varphi = 0$ is satisfied. In this case, the incident angle ${\theta _i}$, which can minimize the reflection coefficient, is called Brewster angle ${\theta _B}$. As can be seen from Eq. (1), the minimum reflection coefficient ${r_{\min }}$ can be obtained only by changing the conductivity of graphene ${\sigma _g}$ or changing the refractive index of the analyte ${n_a}$ when the incident angle ${\theta _i}$ and substrate are invariant. In other words, given the condition that the Brewster angle effect persists with a fixed angle and an invariant substrate, the change of refractive index at a fixed incidence angle can be characterized by the conductivity of graphene. When it comes to Eq. (2), the corresponding relationship between the refractive index of the analyte and the conductivity of graphene can be transformed into the relationship between the refractive index and the Fermi level (applied voltage). Thus, the refractive index sensing can be realized without adjusting the angle of emitter and detector. The terahertz response of the BGS was calculated by using COMSOL Multiphysics software and FEM. The detailed steps used in the simulation are basically consistent with our previous work [16].
3. Results and discussion
3.1 Shift mechanism of the Brewster angle
According to Eq. (1) and Eq. (2), the Brewster angle would shift in case of the change of analyte(induced variation of ${n_a}$) and the enhancement of Fermi level(induced non-zero ${E_F}$).From another point of view, in order to eliminate the Brewster angle shift caused by the change of analyte(the refractive index of analyte ${n_a}$), we could adjust the applied voltage(the Fermi level ${E_F}$) properly to satisfy the equation while ignoring the imaginary part of ${\sigma _g}$. In this case, the incident angle which equal to the Brewster angle can be expressed by Eq. (4)
Thus, combined with Eq. (2), ${\theta _B}$ is negatively correlated with ${n_a}$ and positively correlated with ${\sigma _g}$(${E_F}$) supposing that the substrate material ${n_s}$ is determined.
Based on the above analysis, the reflection coefficient of the BGS with quartz substrate varying according to different refractive index of analyte and different Fermi level are explored and shown in Fig. 2(a) and Fig. 2(b). It could be found that the Brewster angle decreases with the increasing refractive index of analyte, but increases with the enhancing Fermi level, as shown in Fig. 2(c) and Fig. 2(d). The results we obtained by Fig. 2 is consisted with the relationship exhibited in Eq. (4), which provides the possibility for angle compensation in subsequent sensing applications. It should be noted that the reflection coefficient (Fig. 2(a)) and the Brewster angle (Fig. 2(c)) varying with different refractive indices are calculated while Fermi level is 0.2 eV. Besides, the reflection coefficient (Fig. 2(b)) and the Brewster angle (Fig. 2(d)) varying with different Fermi levels are calculated while the refractive index of analyte is 1.
Fig. 2. The reflection coefficient varies with (a) different refractive index and (b)different Fermi level; The Brewster angle varies with (c) different refractive index and (d)different Fermi leve@0.3THz.
3.2 Refractive index sensing realized by applied voltage
Equation (1) shows that the reflection coefficient r is simultaneously depended on the incident angle ${\theta _i}$, the refractive index of analyte ${n_a}$ and the conductivity of graphene ${\sigma _g}$ supposing that the substrate material is determined. To explore the effect of Fermi level on analytes with various refractive index, the reflection coefficient under a fixed incident angle is calculated as presented in Fig. 3(a). The Brewster angle of the BGS with a 0 V bias applied voltage (i.e., with a graphene conductivity of 0 S), is selected as the fixed incident angle. The minimum reflection coefficient ${r_{\min }}$ is marked by the bright yellow color. On this yellow curve, due to that the Brewster angle shift caused by the change of refractive index could be compensated by tuning Fermi level, the fixed incident angle is always equal to the Brewster angle of the BGS even if the refractive index of various analytes is different. The results we have obtained show that even in the case of analytes with different refractive indices, it is feasible for the BGS to achieve the same Brewster angle by adjusting the Fermi level of graphene. It is worth noting that the minimum reflection coefficient is not 0, but increases with the enhancement of Fermi level, which is caused by the imaginary part of the graphene’s conductivity.
Fig. 3. (a) The reflection coefficient varies with different Fermi levels and different refractive indices at a fixed incident angle(63°)@0.3THz; (b) Corresponding relationship between the Fermi level and the refractive index under quartz-based BGS; (c) Corresponding relationship between the applied voltage and the refractive index under quartz-based BGS.
The corresponding relationship between the Fermi level and the refractive index of analyte can be obtained and shown in Fig. 3(b) while the relationship between the refractive index and the applied voltage is shown in Fig. 3(c). Comparing the results presented in Fig. 3(b) and Fig. 3(c), it can be found that the curve of Fermi level tends to quadratic shape while the curve of applied voltage approaches to be linear. In order to explain this phenomenon, a series of mathematical derivations are carried out. For the conductivity of graphene ${\sigma _g}$, we can write it as follows:
When the imaginary part of ${\sigma _g}$ is ignored, it can be regarded as a function of ${E_F}^2$.Considering that the incident angle is fixed, according to Eq. (4), the following relationship is established.
where k is a constant coefficient.Thus, it can be found that ${n_a}$ can be regarded as a function of ${E_F}^2$ or regarded as a function of ${V_g}$ as shown in Eq. (7), which is consistent with the theoretical fitting results as shown in Fig. 3(b) and Fig. 3(c).
From Eq. (7), it can be seen that the linear relationship between applied voltage and refractive index is established. Based on this linear relationship, the process of refractive index sensing proposed in this research could be described as follow. First, the Brewster angle without applying voltage can be obtained based on Fresnel equation. Then, the transmitter and detector are fixed at this angle where there is no need for rotary motor with high precision. When the analyte is placed on graphene, the Brewster angle of the BGS shifts, and the reflected signal received by the detector at this angle will suddenly change from almost zero to relatively large. Next, the change of the reflected signal which caused by the Brewster angle shift can be compensated by tuning the gate voltage applied to graphene. Consequently, the reflected signal received by the detector becomes almost zero again. Based on Eq. (7), the refractive index of the analyte can be obtained in real time supposing that the applied voltage is determined. Ultimately, the refractive index sensing which operates at a specific terahertz frequency and a fixed incident angle will be achieved.
3.3 Optimization of the BGS
The detection range and sensitivity of the BGS is explored for further evaluating the sensing performance of the BGS. When the change in Fermi level $\mathrm{\Delta }{E_F}$, which is caused by the refractive index change of 0.1, is less than 0.01 eV, we believe that the applicable detection range of the BGS has been exceeded. After determining the detection range, the sensitivity of the BGS is defined by the slope of the curve of refractive index varying with voltage.
In order to optimize the detection range and sensitivity of the device, we further analyzed the possible influence factors. As we all know, Brewster angle occurs when light is incident from the optically thinner medium to the optically denser medium. Therefore, the refractive index of the substrate is highly likely to affect the detection range of the BGS. With that in mind, the substrate material is replaced with high-resistance silicon, which possesses higher refractive index, to further explore the influence of ${n_s}$ on detection range. The reflection coefficient varies with refractive index of analyte and Fermi level of graphene with a high-resistance silicon substrate are shown in Fig. 4(a). The minimum reflection coefficient ${r_{\min }}$ is marked by the bright yellow color. Besides, the correspondence relationship of Fermi level with refractive index is shown in Fig. 4(b) while the corresponding relationship of applied voltage with refractive index is shown in Fig. 4(c). The shape of the theoretical fitting curve presented in Fig. 4(b) and Fig. 4(c) is consistent with the results shown in Fig. 3, which verifies the reliability of the calculation results expressed in Eq. (7).
Fig. 4. (a) The reflection coefficient varies with different Fermi levels and different refractive indices at a fixed incident angle(74°)@0.3THz; (b) Corresponding relationship between the Fermi level and the refractive index under high-resistance silicon-based BGS; (c) Corresponding relationship between the applied voltage and the refractive index under high-resistance silicon-based BGS.
As a consequence, the detection range and sensitivity with both quartz substrate and high-resistance silicon substrate are calculated as shown in Table 1. The detection range of the BGS with quartz substrate is between 1.1-1.4 while the sensitivity is 9.58 V/RIU. In contrast, the detection range of the BGS with high-resistance silicon substrate is between 1.1-2.4 while the sensitivity is 20.06 V/RIU. Therefore, the substrate with a higher refractive in the BGS index can indeed realize a much wider detection range and a much higher sensitivity for the refractive index of analyte. It should be noted that the functional mechanism of BGS determines that the incident angle would remain constant for the same substrate even if the different analytes are introduced, and the Fermi level should be logically and strictly adjusted according to the Eq. (7) for different analytes. As a result, the sensing performance of BGS does not actually depend on Fermi level and incident angle. It should be mentioned that for gaseous analytes which our BGS is originally and mainly designed for, by placing the THz emitter, THz detector as well as the BGS in a gas chamber filled with target analytes, applying 74° as the fixed incident angle would not require the emitter in air environment to produce waves with a larger incident angle. Our BGS could really be feasible to keep a detection range of 1.1 to 2.4. However, for solid analytes, our BGS currently cannot realize the detection range of 1.1-2.4 when applying 74° as the fixed incident angle. More potential implementation plans need to be provided for solid analyte to eliminate the impact of the size of incident angle.
Table 1. Detection range and sensitivity of the BGS on different substrates
4. Conclusion
In this work, the voltage controlled BGS operating at a specific terahertz frequency, which is capable of sensing the refractive index at a fixed incident angle, is proposed. The BGS is designed on the basis that the electrically-tuning graphene could compensate the Brewster angle shift caused by the change of analyte. The relationship between the voltage (Fermi level) and the refractive index of analytes is established by a series of mathematical derivations and theoretical fitting of the FEM simulations, which help achieve the conversion from the refractive index of analyte to a Volt-level detectable voltage and realize the refractive index sensing. Furthermore, the detection range and sensitivity of the BGS with different substrate materials are analyzed. It is found that by employing the substrate with higher refractive index, the detection range and sensitivity of the BGS could be enhanced. As a result, the BGS with high-resistance silicon substrate can achieve a detection range of 1.1-2.4, and a sensitivity of 20.06 V/RIU for refractive index at 0.3THz. Due to the frequency dependence of graphene’s conductivity, this result could be extended to other frequency bands and provide a new direction for sensing throughout the terahertz band.
Funding
National Key Research and Development Program of China (2021YFA0718901); National Natural Science Foundation of China (62005014); National Natural Science Foundation of China (62205348); Fundamental Research Funds for the Central Universities (FRF-IDRY-21-014).
Disclosures
The authors have no conflicts to disclose.
Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
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