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Abstract
We proposed an ultrasensitive specific terahertz sensor consisting of two sets of graphene micro-ribbon with different widths. The interference between the plasmon resonances of the wide and narrow graphene micro-ribbons gives rise to the plasmon induced transparency (PIT) effect and enables ultrasensitive sensing in terahertz region. The performances of the PIT sensor have been analyzed in detail considering the thickness and refractive index sensing applications using full wave electromagnetic simulations. Taking advantage of the electrical tunability of graphene’s Fermi level, we demonstrated the specific sensing of benzoic acid with detection limit smaller than 6.35 µg/cm2. The combination of specific identification and enhanced sensitivity of the PIT sensor opens exciting prospects for bio/chemical molecules sensing in the terahertz region.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) radiation, with frequency lying between 0.1 to 10 THz, holds great promise in biological and security sensing applications. It has become a novel tool to identify bio/chem-molecules because the rotational and vibrational modes of them occur in the THz region [1–3]. However, the poor sensitivities of THz spectroscopy hinder its applications in detection of trace amount of bio/chem-molecules, which is essential for the diagnosing the prior stage of diseases and border security [4,5].
Previous work suggested that plasmon induced transparency (PIT) with highly confined electromagnetic field could provide a potential way to achieve ultrasensitive sensor in the THz region [5–12]. The PIT phenomena, analogue to the electromagnetic induced transparency (EIT) [13,14], is a quantum interference effect between two kinds of surface plasmon polaritons (SPPs). The interaction between the radiative (‘bright’) and non-radiative (‘dark’) SPPs modes gives rise to a narrow transmission window inside the absorption band. Generally, the quality factor (Q) of this transmission window is higher than those of the SPPs, which is favourable able to achieve larger figure of merit (FOM) for a sensor [15,16]. Various nano/micro-structures have been proposed to demonstrate the PIT effect, including photonic crystal structure [17], coupled resonator system and metamaterials structure [18,19].
Unfortunately, the geometrical parameters and electromagnetic properties of the most common metal-based PIT devices are difficult to tune after fabrication and can merely work at a fixed wavelength, which greatly hinder their practical applications. As an example, for the purpose of specifically identifying bio/chem-molecules, the wide-range THz ‘finger-print’ spectroscopy of these bio/chemical molecules need to be obtained. Thus, in order to take advantage of the PIT’s sensitivity as well as the ability of specifically identify bio/chem-molecules, the active control of the transparency window of PIT within a wide frequency range is highly demanded. A straight-forward approach to meet this goal is to embed active permittivity-dependent materials (such as superconductors, VO2) into metal-based PIT devices [20,21]. However, those methods inevitably result in poor sensitivity and limited achievable frequency range because they highly depend on the nonlinear properties of the active materials [22].
Graphene, a single layer atomic crystal of carbon, has attracted numerous attentions since its discovery due to its distinguished mechanical, electronic and optical properties [23–25]. Graphene plasmonic own extreme field confinement and low propagation losses [26], especially the Fermi level of graphene can be dynamically manipulated by using the external electrostatic gating, making it a perfect candidate for the specific detection of bio/chem-molecules. The protein sensing and fingerprint detection of external molecules have already been experimentally realized using graphene plasmonics in mid-infrared region [27–29]. There are also a few works focusing on developing graphene-based PIT/EIT devices in the THz region [30–33]. However, for those proposed structures, it’s quite difficult to practically tune the Fermi level of graphene because no electrodes are connecting to the graphene sheet.
In this paper, we reported a graphene-based ultrasensitive specific THz sensor utilizing the PIT resonance. The unit cell of our proposed graphene micro-ribbon array structure is consist of two kinds of graphene ribbons with different widths. The interference between the plasmonic resonances of the narrow graphene micro-ribbon (NGMR) and the wide graphene micro-ribbon (WGMR) gives rise to a narrow linewidth high-Q PIT resonance. As we mentioned before, this PIT resonance could be used to achieve ultrasensitive sensing. The geometric parameters of this PIT sensor is optimized by maximizing the FOM. Since the Fermi levels of the NGMR and WGMR of our proposed structure can be tuned individually, the PIT transmission window can maintain in a wide THz range enabling specific identification of bio/chem-molecules. As a demonstration, the specific sensing of trace amount benzoic acid using this PIT sensor is realized with detection limit smaller than 6.35 µg/cm2. Our proposed ultrasensitive specific PIT sensor has great potential applications in diagnosis of early stage disease and border security.
2. Configuration and theory
The schematic diagram of our designed graphene-based THz sensor structure is shown in Fig. 1. It consists of a graphene micro-ribbon array on a Si/dielectric layer substrate. In our work, the permittivity of the dielectric layer (εdie) and Si (εSi) are taken as 7.5 and 11.7 respectively [22,34]. The ribbon array is assumed to be periodic in the x-direction and ‘quasi’ infinitely extended in the y direction. The period of the graphene array is set to be P = 12.8 µm. Two sets of ribbons with different widths, W1 and W2 in a unit cell are separated from each other with distances Wd1 and Wd2. As illustrated in Fig. 1, the WGMR and NGMR are connected to different electrodes. Thus, the Fermi levels of them can be tuned individually by applying different corresponding bias voltages V1 and V2. The thicknesses of the dielectric layer and the silicon substrate are set to be tdie = 60 nm and tSi = 300 µm, respectively.
Fig. 1 Conceptual view of the PIT-sensor based on graphene micro-ribbon (GMR). The electromagnetic field is mainly concentrated at the edges of GMR, when excited by a THz wave, leading to the enhanced interaction between THz wave and the analyte. The tunability of the PIT sensor is achieved by changing the bias voltages (V1 and V2) applied on the two sets of GMR arrays.
The thickness of graphene layer is assumed to a typical value as tg = 1 nm [22] with a relative permittivity of εr (ω) = 1 + iσ(ω) / (ωε0tg), in which the conductivity σ(ω) at low frequencies can be described as [35]:
where, ε0 is the permittivity of vacuum, ω is the frequency of incident wave, EF is the Fermi energy, e is the charge of an electron, ћ is the reduced Planck constant. Γ is the scattering rate which are determined by (-eћνf 2) / (µEF), where νf = 106 m·s−1 is the Fermi velocity and µ = 10000 cm2 V−1 S−1 is the electron mobility of graphene [36].The resonant property of the graphene micro-ribbon structure is simulated using the commercial full-wave electromagnetic simulation software Comsol Multiphysics. In the simulation, the micro-ribbon array is illuminated by a normally incident transverse magnetic TM polarized plane wave (with the magnetic field component parallel to the y-direction). A periodic boundary condition is applied in the x-direction. While an open boundary condition is set along the z-direction.
Considering the fact that the PIT effect is a quantum interference phenomenon between two kinds of plasmons, the resonant frequencies of these two plasmons should be close to each other. By properly tuning the Femi levels of the WGMR and NGMR, the graphene plasmon resonant frequencies of the WGMR (W1 = 6 µm) and the NGMR (W2 = 2 µm) are adjusted to be around 4 THz as shown in Fig. 2(a). The corresponding Fermi levels of the WGMR and NGMR are about 1.96 eV and 0.5 eV, respectively. Detailed analysis of the Q-factors of the WGMR and NGMR plasmon resonances were performed by fitting the transmission spectra with Lorentzian lineshape [37]. The linewidth of plasmon resonance for the WGMR (NGMR) is 0.8 (0.24) THz, with corresponding quality factor Q = 2.5 (Q = 8.3). For the convenience to describe the PIT interference phenomena between the WGMR and NGMR, we term the strongly coupled WGMR array with broad plasmon resonance (lower Q-factor) as the ‘bright’ mode, while the weakly coupled NGMR array with sharp resonance (higher Q-factor) is termed as ‘quasi-dark’ mode.
Fig. 2 (a) THz transmission spectra of graphene array for the wide ribbon array only (blue circles), the narrow graphene ribbon array only (red diamonds) and both the wide and narrow graphene ribbon arrays (black triangles) along with the analytic fitting (solid lines). The Fermi levels of the wide and narrow graphene ribbon array are fixed at 1.96 eV and 0.5 eV, respectively. (b) (c) Electric field distributions for graphene plasmon resonance dips with only the wide (W1 = 6 µm) and only the narrow (W2 = 2 µm) graphene ribbon array. Electric field distributions simulated at frequency points i, ii, and iii, corresponding to the frequencies, (d) 3.84 THz, (e) 4.04 THz, and (f) 4.21 THz, respectively.
When the WGMR and the NGMR arrays are lumped together, the PIT-like transmittance spectrum is observed as shown in Fig. 2(a). A sharp transmission window emerges between the two plasmon transmission dips around 4 THz, due to the destructive interference between the ’bright’ and ’quasi-dark’ modes. The transmittance spectrum of PIT effect is analysed with two coupled oscillators model [38]. According to this model, the linear susceptibility of coupled oscillators system is expressed as:
Here, Re[χ] represents the dispersion and Im[χ] gives the absorption (loss) within the medium. In this model, we use (1 - Im[χ]) to fit the transmission spectrum of the PIT. We found excellent agreement between the analytic fitting and simulation data shown in Fig. 2(a). The concerned fitting parameters ωb, ωd, γb and γd represent the resonance angular frequencies, the loss factors of the ’bright’ and the ’quasi-dark’ modes, respectively. In this case, the resonance frequencies of the ’bright’ and ’quasi-dark’ mode are ωb /2π = 3.96 THz and ωd /2π = 4.04 THz. The values of γb and γd are obtained from the linewidths of the curves for ‘bright’ mode and ‘quasi-dark’ mode, which are calculated to be around 0.81 THz and 0.23 THz, respectively. Q factors for PIT peaks were calculated by fitting the transmission spectrum with the Fano line shape given by [37,39]: TFano = |a1 + ia2 + b/(ω-ω0 + iγ)|2, where a1, a2 and b are constant real numbers, ω0 is the Fano resonance frequency, and γ is the overall damping rate of the resonance. The Q factor was then determined as Q = ω0 / 2γ. From the linewidths and resonance frequencies, we calculate the Q factors for the frequencies (i), (ii), and (iii) are 8.5, 19.2, and 18.7, respectively.
The electric field strength distributions of the WGMR and NGMR at resonance frequencies 4 THz are shown in Figs. 2(b) and 2(c). As demonstrated in these figures, strong field confinements take place at the ribbon edges in both cases. The maximum electric field intensity for the WGMR plasmon resonance is about 2 times smaller than that of NGMR. The electric field strength distributions for the three frequency positions of PIT resonance are presented in Figs. 2(d)-2(f). As can be seen from the figure, at the transmission dips (i) and (iii), strong field confinements occur at WGMR and NGMR edges and the enhanced ratio of electric field intensity is about 2.32 and 1.64, respectively. At peak (ii), the electric filed intensity in ’bright’ mode is transferred to the ’quasi-dark’ mode, thus the field confinement only takes place at the NGMR edges with a maximum enhanced ratio value of 3.1, which is due to destructive interference between the ‘bright’ and ‘quasi-dark’ modes.
For sensing applications, the tighter field confinement usually means higher sensitivity of the sensor [38]. The computed percentage of near-field intensity confined within a given distance d from graphene surface for five concerned modes are presented in Fig. 3. For all of the five modes, the electric fields are all confined within 4 µm from the graphene surface. Especially for the PIT peak (ii), the electric field is strongly confined within a distance about 2 µm. To provide a more quantitative way to describe the confinement of the electric field, the distance that 90% of the electromagnetic energy is confined within are listed in Table 1 For the WGMR, NGMR resonant frequencies and the positions (i), (ii), (iii) of the PIT spectrum, 90% of electromagnetic energy are confined within distances of 1.7 µm, 0.8 µm, 0.9 µm, 0.75 µm, and 1.4 µm, respectively. The Q factors of these modes are also listed in Table 1 From the table we found that the Q factors for the five concerned modes are 2.5, 8.3, 8.5, 19.2, 18.7, respectively. Considering the fact that the PIT peak (ii) has the strongest field confinement as well as the highest Q factor, we utilize this peak for the sensing applications in the following sections.
Fig. 3 Percentage of space-integrated near-field intensity confined within a volume extending a distance d from the surface of graphene. Inset shows a zoom-in for d between 0 and 1.5 µm.
Table 1. Calculated 90% field confinement distance, and Q-factor values for the simulated transmission curves shown in Fig. 2(a).
3. Performance of the PIT sensor
For the sensing applications, the Q factor of the resonance peak is an important parameter. However, the increase of the Q factor usually leads to the decrease of the transmission intensity (ΔI) of the resonance peak [40], thus resulting in poorer sensing performance. To quantitatively estimate the potential sensing performance of a resonance peak, we use the product of Q factor and the transmission intensity of the resonance peak as the FOM of a sensor [40]. In order to achieve better sensing performance of the PIT sensor, we investigated the influences of the geometric parameters of the sensor structure by optimizing the value of FOM. The geometric parameters we mentioned above have already been optimized.
Here we investigate the sensing mechanism of our optimized PIT sensor. Different thicknesses of analyte with different refractive indexes are deposited on the surface of the device. The thickness and the refractive index of the analyte are denoted as da and na, respectively. First, the influence of the analyte thickness on the response of the PIT resonance was investigated. Figure. 4(a) depicts the amplitude transmission spectra of the PIT resonator computed for different values of the thicknesses da with refractive index of 1.6, where we observe gradual red shifting of the PIT resonance when the thickness of the analyte increases. The frequency shift of PIT peak is compared with that without any analyte on the PIT sensor. The frequency shifts of the PIT peaks with different analyte thicknesses are illustrated in Fig. 4(b). The red shifts of PIT peak for analyte thicknesses 0.1, 0.4, 0.7, 1.0 and 1.3 µm are 0.06, 0.12, 0.14, 0.165, and 0.175 THz, respectively. A saturation phenomena are emerging when the analyte thickness approaches 1.3 µm. This results are consistent with that confinement distance of the electromagnetic field for PIT peak is about 1 µm. Next, we investigated the transmission spectrum of the PIT sensor with different refractive indexes of the analyte. The simulated results are shown in Fig. 4(c) for the analyte thickness da = 1.3 µm. The resonance frequency of PIT peak shifts to a low value when the refractive index of the analyte increases from 1.0 to 1.8 in steps of 0.4. Here, the total frequency shift of the resonance frequency is about 0.28 THz. Since the transmission spectra of PIT resonances are different for different thicknesses of the analytes, we investigate the sensitivity of the PIT resonance by varying the refractive index for the different analyte thicknesses. The sensitivity is defined as frequency shift of the peak induced by the variation for the refraction index per unit. Figure. 4(d) shows the shifts of PIT resonance frequency versus refractive index for different thicknesses of analyte. For all analyte thicknesses, the frequency shifts increase linearly as the refractive index of the analyte increases. We calculate the frequency sensitivities for different analyte thicknesses by linear fitting the frequency shifts of PIT transmission peaks. The calculated frequency sensitivities for different thicknesses are shown in Fig. 4(e). We find that the sensitivities increase with the increasing analyte thickness which can be represented by exponentially fitting curves revealing it nearly saturate with analyte thickness approaches 1.3 µm. The asymptotic frequency sensitivity is about 0.36 THz/RIU. We converted these numbers into Δλ/RIU by using |dλ / dn| = c/f02 × (df /dn), where c is the speed of light, f0 is the resonance frequency, and n represents the refractive index of the analyte. In terms of Δλ/RIU, the corresponding sensitivities for the 1.3 um thick analyte depositing are 6.75 × 103 nm/RIU, which is are much higher than reported traditional metamaterial sensors [11,16,31,41–43]. Table 2 compares the refractive index sensitivity for different sensors previously reported.
Fig. 4 (a) Simulated amplitude transmission spectra with different thicknesses of analyte. (b) Frequency shift versus the thicknesses of the analyte located on the surface of device for a fixed refractive index of 1.6. (c) Simulated amplitude transmission spectra with different refractive index. (d) Frequency shift versus the refractive index of the analyte located on the surface of device for thickness changed from 0.1 µm to 1.3 µm. (e) Sensitivity of frequency versus the thickness of the analyte.
Table 2. Comparison of refractive index sensitivity reported in various PIT/EIT sensor.
4. Specific sensing application
In addition to sensitivity, another important requirement of a THz sensor is the ability to identify the analyte. For most of the sensors, higher Q factor with tighter confined electromagnetic field usually means higher sensitivity. However, the narrow linewidth of resonance accompanying with high-Q sensor makes it difficult to realize the specific sensing of analyte with broad absorption band [44]. Fortunately, the introducing of tunable property can make a THz senor maintain the high-Q feature in a wide THz range. Thus, the tunability of a THz sensor can make it possess both the sensitivity and selectivity at the same time. We simulate the transmission response of the PIT sensor for various Fermi levels of graphene to analyse the tunability properties. In order to maintain the PIT feature, we tune the Fermi levels of the WGMR and NGMR simultaneously according to Fig. 5(a) to make the plasmon resonant frequencies of the WGMR and NGMR equal to each other. From Fig. 5(b), we notice that the PIT peaks shifts to higher frequency when increasing the Fermi level. The frequency of PIT transmission peak drifts from 1.5 THz to 4.5 THz, when the Fermi level of the WGMR are adjusted from 0.24 eV to 2.53 eV. The frequency range of specific sensing is dependent on highest achievable Fermi level. For higher Fermi level, the frequency range is wider.
Fig. 5 (a) Graphene SPP resonance frequency versus different Fermi energy (EF) for the NGMR and WGMR. (b) Simulated amplitude transmission spectra of the structure with same parameters as used in Fig. 2 with Fermi level of the wider graphene array changes from 0.24 eV to 2.53 eV.
To demonstrate the specific sensing performance of our PIT sensor, we use the benzoic acid as the analyte. Benzoic acid, C6H5COOH, is generally used as preservative in food-stuffs to increase its shelf life, because it is effective to control mold and inhibit yeast growth, and can prevent a wide range of bacterial attack as well. Considering its potential risk to human health, the use of benzoic acid is strictly controlled. The specific sensing of small amount benzoic acid is not only important for the quality assurance purposes but also for consumer interest and protection [45].
For the benzoic acid, there are four absorption peaks locating at 2.13, 2.36, 2.86, and 3.06 THz with corresponding linewidths 0.20, 0.18, 0.22 and 0.14 THz and absorption amplitude 119.5, 36.3, 101.9 and 56 cm−1 [46]. The real and imaginary parts of refractive index of benzoic acid using the multi-Lorentzian lineshape are presented in Fig. 6(a). Figure. 6(b) depicts the amplitudes of transmission spectrum for the PIT sensor with and without benzoic acid deposited on it. By tuning the PIT peak away from the absorption peaks of benzoic acid, the frequency shift of PIT peak is about 0.2 THz when deposited on 1 µm benzoic acid. According to the frequency sensitivity of the PIT sensor [Fig. 4(e)], the real part of refractive derived from the frequency shift is around 1.58, which is nearly equal to the actual value of it. Then we electrically tune the Fermi levels of the WGMR and NGMR to adjust the PIT peak to the frequency 2.13 THz, and obtain the amplitude of transmission for benzoic acid with (orange solid line) and without absorption (black dash line) in Fig. 6(b). An attenuation of PIT peak is observed when taking consideration of the absorption, but we did not observe any obvious dip at the PIT peak. The reason for that is due to the fact that the linewidth of PIT peak is smaller than the linewidth of the absorption peak of benzoic acid.
Fig. 6 (a) Real part (red dash line) and imaginary part (blue solid line) of benzoic acid refractive. (b) Simulated amplitude transmission spectra of the structure with (red dash dot line), without (blue solid line) benzoic acid applied on it, and with the PIT peak at the frequency of absorption peak I for the absorption is taken into consideration (orange solid line) and not (black dash line), here the thickness of analyte is 0.7 µm. (c) Extinction spectra of benzoic acid film with different thicknesses.
From the above analysis, frequency sweeping technique can be adopted to realize the specific detection. The extinction spectra of the sensor are presented in Fig. 6(c) with various surface densities (thicknesses as 0.05, 0.1, 0.25, 0.4, 0.7 µm) of the benzoic acid. In Fig. 6(c) T0 and T are the amplitudes of transmission for the PIT peak versus frequency without and with absorption, respectively. Four spectral peaks are observed in the extinction spectra, the frequencies of the peaks locating at 2.13, 2.37, 2.86, 3.07 THz agree well with the four absorption peaks of benzoic acid, respectively. As considering the signal to noise ratio for a practical THz system is usually higher than 1000, a detection limit smaller than 6.35 µg/cm2 was achieved. Thus we demonstrated the specific ultrasensitive sensing of the benzoic acid.
5. Conclusions
In summary, we demonstrated a high-Q tunable ultrasensitive THz sensor with PIT resonance via the interference between the ’bright’ and ’quasi-dark’ modes. The influence of the thickness and refractive index of an analyte on the frequency sensitivity is studied in detail. The frequency sensitivity of 0.36 THz/RIU and FOM of 3.64 for peak (ii) have been achieved. Moreover, taking advantage of the electrical tunability of graphene, the specific ultrasensitive sensing of benzoic acid with detection limit smaller than 6.35 µg/cm2 had been demonstrated. The ability of specific identification and enhanced sensitivity of the graphene PIT sensor opens a novel way for bio/chem-molecules sensing in the terahertz region.
Appendix
Influence of the scattering rate of graphene
The scattering rate Γ determined by the formula (-eћνf 2) / (µEF), where νf =106 m·s−1 is the Fermi velocity. For a certain Fermi level, the scattering rate Γ is determined by the electron mobility µ of graphene with a typical value from 3000 to 20,000 cm2 V−1 S−1 [36]. The amplitudes of transmission with different electron mobility for Fermi level at 0.8 eV are shown in Fig. 7(a). The PIT effect holds with negligible frequency shift under different values of electron mobility, while the amplitude peak changed significantly. However, the absolute change of amplitude peak is not important for our specific sensing purpose, since we care more about the relative change of the peak. Considering the performance of our sensor is based on the ability of electric field confinement at the PIT resonance peak. The percentage of space-integrated near-field intensity confined within a volume extending a distance d from the surface of graphene with different µ for Fermi level at 0.8 eV are show in Fig. 7(b). The 90% field confinement distances for electron mobility rate at 3000 and 20,000 cm2 V−1 S−1 is almost the same. Thus, in our simulation, we set the mobility to 10,000 cm2 V−1 S−1 as a moderate value.
Funding
National Key Basic Research Program of China (2015CB755405); National Natural Science Foundation of China (NSFC) (61427814, 11704358); Foundation of President of China Academy of Engineering Physics (201501033).
Disclosures
There are no conflicts to declare.
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