- Email: [email protected]
Figure of merit analysis of graphene based surface plasmon resonance biosensor for visible and near infrared
Optics Communications 435 (2019) 102–107
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Figure of merit analysis of graphene based surface plasmon resonance biosensor for visible and near infrared Shujing Chen a ,∗, Chengyou Lin b a
Beijing Key Laboratory of Materials Utilization of Nonmetallic Minerals and Solid Wastes, National Laboratory of Mineral Materials, School of Materials Science and Technology, China University of Geosciences, Beijing 100083, China b College of Science, Beijing University of Chemical Technology, Beijing 100029, China
ARTICLE
INFO
Keywords: Surface plasmon resonance Biosensor Figure of merit Graphene
ABSTRACT In this paper, the figure of merit (FOM) of a surface plasmon resonance (SPR) biosensor based on gold–graphene structure is studied in the visible and near infrared region. As the wavelength of incident light increases, the FOM of the proposed SPR biosensor with different number of graphene layers increases firstly and then decreases, indicating an optimal wavelength for realizing the largest FOM (called peak FOM). For the proposed SPR biosensor with monolayer graphene, the peak FOM that shows at 890 nm is up to 33.05 RIU−1 , which is 133% higher than the FOM (14.17 RIU−1 ) at 630 nm (near a common-used wavelength 633 nm). In addition, the effect of dispersion of graphene on the performance of the proposed biosensor is also analyzed. With the increase of the number of graphene layers, the peak FOM of the proposed biosensor decreases, but the optimal wavelength remains unchanged. Furthermore, the origin of FOM enhancement at optimal wavelength is determined by analyzing the electric field intensity inside the proposed SPR biosensor. Besides, the performances of SPR biosensors with different prism and metal are compared. It is believed that the FOM of a graphene based SPR biosensor can be enhanced by optimizing the wavelength of incident light and the number of graphene layers.
1. Introduction The surface plasmon resonance (SPR) technology has been used in the biochemical sensing for years due to its achievements of good performance and real-time analysis [1–5]. To excite the surface plasmon, many configurations can be used. One of them is Kretschmann configuration based on the angular interrogation. In this configuration, a thin metal film coats on the top of prism and the sensing medium touches the metal generally. When the propagation constant of a incidence light matches with that of the surface plasmon wave, a narrow dip (SPR dip) forms in the curve of reflectance as a function of incident angle [6]. The angle that realizes smallest reflectivity calls resonance angle, which is very sensitive to the variation in the refractive index (RI) of the sensing medium. Usually, the performance of a SPR sensor is evaluated by several parameters, such as resonance angle, the reflectance at the resonance angle, sensitivity and full width at half maximum (FWHM) of SPR dip [7–9]. To comprehensively evaluate the performance of an SPR sensor, the figure of merit (FOM), defined as the ratio between the sensitivity and the FWHM, has also been used [10]. Recently, several methods have been proposed to enhance the FOM of a SPR sensor. Adding a thin dielectric layer with high RI on top of the metallic layer was demonstrated for enhancing the FOM of
a SPR sensor with the spectral interrogation [10]. Using the liquid prism instead of the conventional solid prism was also verified for FOM enhancement [11]. In addition, the FOM can be improved by using a porous silica film with low-refractive-index [12] and adding an absentee layer on the top of the metallic layer [13]. The graphene possesses high surface-to-volume ratio and rich 𝜋 conjugation structure, and can be used in a SPR biosensor as the biomolecular recognition element (BRE) to functionalize the metal film for the enhancement of surface adsorption of the biomolecules [14–16]. Recently, various structures based on graphene have been proposed for enhancing the sensitivity of a SPR biosensor, such as gold–graphene [15], silver– graphene [17], gold–silicon–graphene [18], aluminum–graphene [19], TiO2 -SiO2 – gold–MoS2 – graphene [20], gold–MoS2 – graphene [21], and graphene–gold nanoparticles based [22,23] structures. In present, the spectral range of SPR biosensor application extends from visible to terahertz band [24,25]. It has been demonstrated that the performance of a SPR biosensor relies heavily on the dispersion (RI changing with wavelength) of the materials used in the biosensor. For example, Maharana et al. [26] achieved sensitivity enhancement in the near infrared region by using air mediated graphene multilayer in the SPR biosensor. Jha and Sharma [27] realized FOM enhancement of a SPR sensor in the near infrared region by using chalcogenide prism
∗ Corresponding author. E-mail address: [email protected] (S. Chen).
https://doi.org/10.1016/j.optcom.2018.11.031 Received 26 September 2018; Received in revised form 30 October 2018; Accepted 12 November 2018 Available online 16 November 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
S. Chen and C. Lin
Optics Communications 435 (2019) 102–107
√
0.75831𝜆2 0.08495𝜆2 + , (3) 𝜆2 − 0.01007 𝜆2 − 8.91377 where 𝜆 is the wavelength of incident light, taking μm as a unit. The refractive index (n) and the extinction coefficient (k) of gold, silver and mono layer graphene at considered wavelength range are taken from the measured data in Ref. [31] and Ref. [32] respectively, and shown in Fig. 2. The refractive index and the extinction coefficient of multilayer graphene is assumed to be the same with the ones of monolayer graphene in our considered wavelength range [33]. 𝑛H2 O (𝜆) =
1+
2.2. Reflectance coefficient Fig. 1. (Color online) Schematic diagram of the proposed SPR biosensor.
For simulation, the proposed SPR biosensor can be seen as an N-layer structure, therefore we employ the well-known transfer matrix method to calculate the expression of reflectivity [28]. [ ] 𝑁−1 [ ] ∏ 𝐴 𝐵 cos 𝛿𝑘 𝑖 sin 𝛿𝑘 ∕𝜂𝑘 M= = , (4) 𝐶 𝐷 𝑖𝜂𝑘 sin 𝛿𝑘 cos 𝛿𝑘 𝑘=2
and aluminum. However, the FOM of the common-used gold–graphene based SPR biosensor in the visible and near infrared region has not been investigated yet, and the dispersion of graphene on the FOM of the SPR biosensor is still unknown. In this paper, the thickness of gold film in the proposed biosensor is optimized at first for achieving minimal reflectivity. Then the sensitivity, FWHM and FOM of the proposed gold–graphene based SPR biosensor (Fig. 1) with optimized thickness of gold film is analyzed in the visible and near infrared region. In addition, the values of FOM of the proposed SPR biosensors with different graphene layers are compared in the considered wavelength range. Furthermore, the origin of FOM enhancement at the optimal wavelength is investigated by analyzing the electric field intensity in the proposed SPR biosensor.
𝑟p =
The proposed SPR biosensor is based on angular interrogation. The wavelength of incident light is assumed to be in the range of 580 to 1000 nm. We will discuss the dispersion properties of all used materials in the proposed SPR biosensor as a start.
2.3. Performance parameters Sensitivity, FWHM and FOM can be calculated based on reflectance curve. In a typically reflectance curve, the minimum reflectivity 𝑅c is realized at the resonance angle 𝜃c , which changes with the varied RI of the sensing medium. The angular sensitivity S of a SPR sensor is defined as the ratio of resonance angle variation 𝛿𝜃c to the change in refractive index of sensing medium 𝛿n, expressed as
2.1. Dispersion properties The dispersion relations of BK7 prism [28], SF11 prism [29] and sensing medium (water) [30] are given as
1+
𝜆2
𝛿𝜃c ) (6) 𝛿𝑛 In our simulations, water containing ss-DNA biomolecules is assumed to be the sample, and placed in contact with the graphene. Graphene adsorbs the biomolecules on its surface and creates an additional layer of biomolecules (ss-DNA) of thickness around 100 nm, resulting in a local increase in the RI (𝛿𝑛 = 0.005) at the graphene surface. 𝑆=(
1.03961212𝜆2 0.231792344𝜆2 1.01046945𝜆2 + + , (1) 2 2 − 0.00600069867 𝜆 − 0.0200179144 𝜆 − 103.560653
𝑛SF11 = √ 1+
(5)
where M is the characteristic matrix of the 𝑁-layer structure for a ppolarized incident light. The matrix elements of M (A, B, C and D), can be used to calculate the amplitude reflection coefficient 𝑟p . 𝛿k and 𝜂k are the phase factor and the optical admittance for each layer in the SPR biosensor. 𝛿k = 2𝜋𝑁k 𝑑k cos 𝜃k ∕𝜆, in which 𝑁k and 𝑑k respectively denote the complex refractive index and the thickness of each layer. 𝜃k denotes the refractive angle in each layer. 𝜂k = 𝑛k /cos𝜃k is the optical admittance of each layer for p-polarized light. Finally, the reflectivity 𝑅p can be determined by 𝑅p = |𝑟p |2 . The reflectance curve of a SPR biosensor can be obtained by calculating the reflectivity as a function of incident angle.
2. Theory
𝑛BK7 = √
𝜂0 (𝐴 + 𝐵𝜂𝑁 ) − 𝐶 − 𝐷𝜂𝑁 , 𝜂0 (𝐴 + 𝐵𝜂𝑁 ) + 𝐶 + 𝐷𝜂𝑁
1.73759695𝜆2 0.313747346𝜆2 1.89878101𝜆2 + + , (2) 1.73759695 − 0.013188707 𝜆2 − 0.0623068142 𝜆2 − 155.23629
Fig. 2. (Color online) Refractive index n and extinction coefficient k of (a) metals and (b) graphene in the wavelength range of 580 to 1000 nm.
103
S. Chen and C. Lin
Optics Communications 435 (2019) 102–107
Fig. 3. (Color online) (a) Change of reflectivity at resonance angle versus the wavelength and the thickness of gold film. (b) Optimal thickness of gold film for different wavelength of incident light.
Fig. 4. (Color online) (a) FWHM and (b) Sensitivity of proposed SPR biosensor with monolayer graphene for different wavelength of incident light.
The FWHM can be determined by calculating full width at half maximum of the reflectance dip (𝛥𝜃0.5 ), expressed as FWHM = 𝛥𝜃0.5
(7)
Thus the value of FOM can be calculated by FOM =
𝑆 FWHM
(8)
3. Results and discussion 3.1. Thickness optimization of metal film Since a high-performance SPR biosensor should exhibit large depth of dip (i.e. small 𝑅c ), the thickness of gold film is optimized at first to achieve minimum reflectivity at resonance angle. Fig. 3(a) shows the reflectivity at resonance angle of a gold based SPR biosensor with different thickness of gold film in the wavelength range of 580 to 1000 nm. The near-zero 𝑅c can all be realized when the gold film takes the suitable thickness (optimal thickness) for different wavelength. In Fig. 3(b), the optimal thicknesses of gold film for the wavelengths 580 to 1000 nm are shown. It is seen the optimal thickness of the gold film increases as the wavelength increases from 580 to 710 nm at first, and then decreases as the wavelength increases from 710 to 1000 nm. The maximum value of optimal thickness of gold film is 52.6 nm, which shows at 710 nm. Those optimal thicknesses of gold film will be further used in the proposed SPR biosensor to large depth of dip.
Fig. 5. FOM of the proposed SPR biosensor with monolayer graphene for different wavelength of incident light.
light, as shown in Fig. 4. It can be seen that the FWHM and the sensitivity of the proposed biosensor both decrease when the wavelength increases from 580 to 1000 nm. The FOM of the propose SPR biosensor with monolayer graphene is also calculated, and shown in Fig. 5. It is interesting to note that when the wavelength increases from 580 to 890 nm, the FOM of the proposed SPR sensor with monolayer graphene increases from 9.16 RIU−1 to 33.05 RIU−1 at first, but decreases as the wavelength further increases from 890 to 1000 nm, as shown in Fig. 5.
3.2. Performance analysis of monolayer graphene based SPR biosensor
The changes of sensitivity, FWHM and FOM are originally due to the refractive index and extinction coefficient changes of gold and graphene under different wavelengths. Higher extinction coefficient and nearly unchanged refractive index of gold at larger wavelength (as
In order to analyze the performance of the proposed SPR biosensor, the FWHM and the sensitivity of the proposed SPR biosensor with monolayer graphene are investigated for different wavelength of incident 104
S. Chen and C. Lin
Optics Communications 435 (2019) 102–107
Table 1 Refractive index (n) and extinction coefficient (k) of materials at different wavelengths. Wavelength (nm)
Materials
Refractive index (n)
Extinction coefficient (k)
600
Gold Graphene
0.2487 2.7063
3.0740 1.3122
700
Gold Graphene
0.1310 2.7883
4.0624 1.4365
800
Gold Graphene
0.1535 2.8707
4.9076 1.5514
900
Gold Graphene
0.1743 2.9627
5.7227 1.6851
1000
Gold Graphene
0.2272 3.0842
6.4654 1.8240
proposed SPR biosensor with monolayer graphene shows at 890 nm, and is 133% higher than the FOM (14.17 RIU−1 ) at 630 nm, which is the wavelength near a common-used wavelength 633 nm. To further investigate the performance of the proposed SPR biosensor with monolayer graphene at the optimal wavelength, the reflectance curves (reflectance versus incident angle) of the biosensor at optimal wavelength (890 nm) and two other wavelengths (630 nm and 990 nm) are plotted in Fig. 6. The performance parameters of the SPR biosensor for three different wavelengths are also calculated, and listed in Table 2. The FOM exhibits maximum value at 890 nm, which is 133% and 24% higher than that one at 630 nm and 990 nm, respectively. The results indicate that the wavelength of incident light can be optimized to enhance the FOM of the gold–graphene based SPR biosensor. 3.3. Electric field analysis To study the origin of FOM enhancement achieved at the optimal wavelength, we calculate the electric field intensity enhancement factor (EFIEF) of the SPR biosensor for three wavelengths, as shown in Fig. 7. The EFIEF all exhibits largest value at the graphene-sample interface for three wavelengths, as shown in Fig. 7(a). The largest EFIEF increases from 13.477 to 51.811 when wavelength increases from 630 to 990 nm, which is considered to be the reason for decreasing FWHM with increasing wavelength, as demonstrated in Ref. [12]. Meanwhile, the curves of EFIEF at graphene-sample interface with respect to the incident angle for three wavelengths are plotted in Fig. 7(b). The integral of EFIEF for 630 nm exhibit the largest value (1237.90) compared with the ones at 890 and 990 nm (925.51 and 768.77). This result confirms the statement of correlation between the sensitivity enhancement and EFIEF integral as described by Benkabou et al. [36]. The similar behavior of electric field enhancement for the biosensor at 890 nm and 990 nm is originally due to the small differences of refractive index and extinction coefficient of gold and graphene at two wavelengths.
Fig. 6. (Color online) Reflectance curves of the proposed SPR biosensor with monolayer graphene at 630 nm, 890 nm and 990 nm.
Table 2 The performance parameters of the proposed SPR biosensor with monolayer graphene at three wavelengths. Wavelength Resonance angle Reflectivity (nm) (degree)
Sensitivity (degree/RIU)
FWHM (degree)
FOM (RIU−1 )
630 890 990
101.54 36.78 29.22
7.1664 1.1129 1.0065
14.1689 33.0486 29.0326
72.6041 64.9816 64.2017
0.00640 0.00006 0.00021
3.4. FOM comparison of graphene multilayer based SPR biosensors As mentioned above, the dispersion of graphene also plays an important role on the performance of the proposed SPR biosensor. In order to analyze the effect of dispersion of graphene on the FOM of proposed biosensor, the FOM of the proposed SPR biosensors with different number of graphene layers are calculated in the considered wavelength range, as shown in Fig. 8. The FOM of the proposed SPR biosensor with various graphene layers all increases when the wavelength of incident light increases from 580 to 890 nm firstly, and then decreases when the wavelength of incident light increases from 890 to 1000 nm. The optimal wavelength remains unchanged (890 nm) for the proposed SPR biosensors with varied graphene layers. The variation of peak FOM of the proposed SPR biosensor at 890 nm with respect to the wavelength of incident light is shown in Fig. 9. As
list in Table 1) leads to a smaller FWHM of SPR curve (Fig. 4(a)), as demonstrated by Lecaruyer et al. [34]. In addition, the increasing of extinction coefficient of graphene with wavelength (as list in Table 1) shallows the SPR curve [35], and weakens the SPR wave in the biosensor, which is considered to be the reason for the decreasing of sensitivity (Fig. 4(b)). The increase of FOM with the wavelength increasing from 580 to 890 nm originates from the decreasing speed of sensitivity is smaller than the one of FWHM. The largest FOM (peak FOM) of the
Fig. 7. (Color online) Electric field intensity enhancement factor (a) inside the SPR biosensors and (b) at graphene-sample interface with respect to the incident angle for 630 nm, 890 nm and 990 nm.
105
S. Chen and C. Lin
Optics Communications 435 (2019) 102–107
Fig. 8. (Color online) FOM of the proposed SPR biosensor with different number of graphene layers for different wavelength of incident light.
Fig. 11. (Color online) Reflectance curves of monolayer graphene SPR biosensors with optimized gold and silver film at 890 nm. Table 3 Performance parameters of monolayer graphene SPR biosensors with optimized gold and silver film at 890 nm. Prism
Metal
Resonance angle Reflectivity (degree)
Sensitivity (degree/RIU)
FWHM (degree)
FOM (RIU−1 )
BK7 BK7
Au Ag
64.9816 64.1610
36.78 31.90
1.1129 0.1917
33.0486 166.4318
0.00006 0.09300
3.5. Performance comparison of graphene based SPR biosensors with different prism and metal
results indicate that the optimized thickness of gold layer for SF11 based biosensor is higher than the one for BK7 based SPR biosensor when the wavelength changing from 580 nm to 650 nm, but lower from 650 nm to 1000 nm. In addition, the peak FOM for SF11 is 31.8967 RIU−1 , which is lower than the one of BK7 prism based biosensor, due to the lower refractive index of BK7. However, the optimized wavelength for SF11 prism based biosensor is the same with the BK7 prism based one, which is also 890 nm. The variation of peak FOM of the proposed SPR biosensor for SF11 prism with respect to the wavelength of incident light is shown in Fig. 10(b). As the increase of the number of graphene layers, the peak FOM decreases. The largest peak FOM (31.8967 RIU−1 ) shows when monolayer graphene is used for SF11 prism based SPR biosensor, which is the same to the case of BK7 prism based one. Compared with the results of BK7 prism based biosensors shown in Fig. 9, the peak FOM of the proposed SPR biosensor with BK7 prism is always higher than the one for SF11 when using different number of graphene layers.
To explore the effect of prism on the performance of a graphene based SPR biosensor, the SPR biosensor with SF11 prism is also studied. The optimization method of SF11 prism based SPR biosensor is the same as the BK7 prism based one. The optimized thickness of gold film and FOM in the wavelength of 580–1000 nm is calculated for SF11 prism based biosensor with monolayer graphene, as shown in Fig. 10(a). The
To investigate the metal effect on the performance of optimized SPR biosensors, a monolayer graphene based SPR biosensor with optimized silver film is compared with the one with optimized gold film at its optimized wavelength (890 nm). The reflectance curves (reflectance versus incident angle) of two biosensors at optimal wavelength are plotted in Fig. 11. Their performance parameters are also calculated, and listed in Table 3. It is found that the Ag based SPR biosensor exhibits
Fig. 9. (Color online) Variation of peak FOM with respect to the number of graphene layers.
the increases of the number of graphene layers, the peak FOM decreases. The peak FOM of the proposed SPR biosensor with monolayer graphene is highest among all biosensors (33.0486 RIU−1 ), indicating that the optimal number of graphene layer for largest FOM is one.
Fig. 10. (Color online) (a) Optimized thickness of gold and FOM of monolayer graphene based SPR biosensor with SF11 prism for different wavelength of incident light. (b) Variation of peak FOM with respect to the number of graphene layers for SPR biosensors with SF11 prism.
106
S. Chen and C. Lin
Optics Communications 435 (2019) 102–107
much higher FOM than Au based one (166.4318 RIU−1 Vs 33.0486 RIU−1 ), due to its much smaller FWHM (0.1917◦ Vs 1.1129◦ ). However, the sensitivity of Ag based biosensor is lower than the one of Au based biosensor (31.90◦ /RIU Vs 36.78◦ /RIU).
[10] A. Shalabney, I. Abdulhalim, Figure-of-merit enhancement of surface plasmon resonance sensors in the spectral interrogation, Opt. Lett. 37 (2012) 1175–1177. [11] G. Lan, S. Liu, Y. Ma, X. Zhang, Y. Wang, Y. Song, Sensitivity and figure-ofmerit enhancements of liquid-prism spr sensor in the angular interrogation, Opt. Commun. 352 (2015) 49–54. [12] Q. Meng, X. Zhao, C. Lin, S. Chen, Y. Ding, Z. Chen, Figure of merit enhancement of a surface plasmon resonance sensor using a low-refractive-index porous silica film, Sensors 17 (2017) 1846. [13] Z. Chen, X. Zhao, C. Lin, S. Chen, L. Yin, Y. Ding, Figure of merit enhancement of surface plasmon resonance sensors using absentee layer, Appl. Opt. 55 (2016) 6832–6835. [14] X. Luo, T. Qiu, W. Lu, Z. Ni, Plasmons in graphene: Recent progress and applications, Mater. Sci. Eng. R 74 (2013) 351–376. [15] L. Wu, H. Chu, W. Koh, E. Li, Highly sensitive graphene biosensors based on surface plasmon resonance, Opt. Express 18 (2010) 14395–14400. [16] G.X. Ni, A.S. McLeod, Z. Sun, L. Wang, L. Xiong, K.W. Post, S.S. Sunku, B.Y. Jiang, J. Hone, C.R. Dean, M.M. Fogler, D.N. Basov, Fundamental limits to graphene plasmonics, Nature 557 (2018) 530–533. [17] S.H. Choi, Y.L. Kim, K.M. Byun, Graphene-on-silver substrates for sensitive surface plasmon resonance imaging biosensors, Opt. Express 19 (2011) 458–466. [18] R. Verma, B.D. Gupta, R. Jha, Sensitivity enhancement of a surface plasmon resonance based biomolecules sensor using graphene and silicon layers, Sensors Actuators B 160 (2011) 623–631. [19] P.K. Maharana, T. Srivastava, R. Jha, On the performance of highly sensitive and accurate graphene-on-aluminum and silicon-based spr biosensor for visible and near infrared, Plasmonics 9 (2014) 1113–1120. [20] J.B. Maurya, Y.K. Prajapati, V. Singh, J.P. Saini, Sensitivity enhancement of surface plasmon resonance sensor based on graphene-MoS2 hybrid structure with TiO2 SiO2 composite layer, Appl. Phys. A 121 (2015) 525–533. [21] S. Zeng, S. Hu, J. Xia, T. Anderson, X.Q. Dinh, X.M. Meng, P. Coquet, K.T. Yong, Graphene-MoS2 hybrid nanostructures enhanced surface plasmon resonance biosensors, Sensors Actuators B 207 (2015) 801–810. [22] S. Zeng, K.V. Sreekanth, J. Shang, T. Yu, C.K. Chen, F. Yin, D. Baillargeat, P. Coquet, H.P. Ho, A.V. Kabashin, K.T. Yong, Graphene-gold metasurface architectures for ultrasensitive plasmonic biosensing, Adv. Mater. 27 (2015) 6163–6169. [23] S. Zeng, D. Baillargeat, H.P. Ho, K.T. Yong, Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications, Chem. Soc. Rev. 43 (2014) 3426–3452. [24] L. Chen, N. Xu, L. Singh, T. Cui, R. Singh, Y. Zhu, W. Zhang, Defect-induced fano resonances in corrugated plasmonic metamaterials, Adv. Opti. Mater. 5 (2017) 1600960. [25] B. Ruan, Q. You, J. Zhu, L. Wu, J. Guo, X. Dai, Y. Xiang, Terahertz biochemical sensor based on strong coupling between waveguide mode and surface plasmons of double-layer graphene, IEEE Sens. J. 18 (2018) 7436–7441. [26] P.K. Maharana, R. Jha, S. Palei, Sensitivity enhancement by air mediated graphene multilayer based surface plasmon resonance biosensor for near infrared, Sensors Actuators B 190 (2014) 494–501. [27] R. Jha, A.K. Sharma, High-performance sensor based on surface plasmon resonance with chalcogenide prism and aluminum for detection in infrared, Opt. Lett. 34 (2009) 749–751. [28] J.B. Maurya, Y.K. Prajapati, V. Singh, J.P. Saini, R. Tripathi, Improved performance of the surface plasmon resonance biosensor based on graphene or MoS2 using silicon, Opt. Commun. 359 (2016) 426–434. [29] S.K. Srivastava, R. Verma, B.D. Gupta, Theoretical modeling of a self-referenced dual mode spr sensor utilizing indium tin oxide film, Opt. Commun. 369 (2016) 131–137. [30] S. Kedenburg, M. Vieweg, T. Gissibl, H. Giessen, Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and nearinfrared spectral region, Opt. Mater. Express 2 (2012) 1588–1611. [31] P.B. Johnson, R.W. Christy, Optical constants of the noble metals, Phys. Rev. B 6 (1972) 4370. [32] J. Weber, V. Calado, M. Van de Sanden, Optical constants of graphene measured by spectroscopic ellipsometry, Appl. Phys. Lett. 97 (9) (2010) 2010. [33] W. Li, G. Cheng, Y. Liang, B. Tian, X. Liang, L. Peng, A.R.H. Walker, D.J. Gundlach, N.V. Nguyen, Broadband optical properties of graphene by spectroscopic ellipsometry, Carbon 99 (2016) 348–353. [34] P. Lecaruyer, M. Canva, J. Rolland, Metallic film optimization in a surface plasmon resonance biosensor by the extended Rouard method, Appl. Optics 46 (2007) 2361– 2369. [35] F. Benkabou, M. Chikhi, Surface plasma oscillations at silver surfaces with thin transparent and absorbing coatings, Surf. Sci. 72 (1978) 577–588. [36] F. Benkabou, M. Chikhi, Theoretical investigation of sensitivity enhancement in dielectric multilayer surface plasmon sensor, Phys. Status Solidi A 211 (2014) 700– 704.
4. Conclusion In this paper, the figure of merit of the gold–graphene based SPR biosensor has been theoretically investigated in visible and near infrared region. The thickness of gold film is optimized at first to achieve minimum reflectivity at resonance angle for different wavelength. Then, the sensitivity, FWHM and FOM of the proposed SPR biosensor with optimal thickness of gold film and monolayer graphene is investigated in the wavelength region of 580 to 1000 nm. When the wavelength increases from 580 nm to 890 nm, the FOM of the proposed SPR sensor with monolayer graphene increases from 9.16 RIU−1 to 33.05 RIU−1 at first, but decreases as the wavelength further increases from 890 to 1000 nm. The largest FOM (peak FOM) of the proposed SPR biosensor with monolayer graphene shows at 890 nm, and is 133% higher than the FOM (14.17 RIU−1 ) at 630 nm, which is the wavelength near a common-used wavelength 633 nm. In addition, the effect of dispersion of graphene on the FOM of proposed SPR biosensor is analyzed. The results indicate that with the increase of the number of graphene layers, the peak FOM of the proposed biosensor decreases, but the optimal wavelength remains unchanged. Furthermore, the performances of graphene based SPR biosensors with different prism and metal are compared. In summary, the FOM of a graphene based SPR biosensor can be improved by optimizing the wavelength of incident light and the layer number of graphene. This research provides a way for improving the FOM of a graphene based SPR biosensor, and may be useful for high-performance SPR sensors development. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 11547241) and the Fundamental Research Funds for the Central Universities, China (Grant No. 2652017340). References [1] C. Nylander, B. Liedberg, T. Lind, Gas detection by means of surface plasmon resonance, Sensors Actuators 3 (1983) 79–88. [2] S. Pal, A. Verma, S. Raikwar, Y.K. Prajapati, J.P. Saini, Detection of DNA hybridization using graphene-coated black phosphorus surface plasmon resonance sensor, Appl. Phys. A 124 (2018) 394. [3] L. Pang, G.M. Hwang, B. Slutsky, Y. Fainman, Spectral sensitivity of twodimensional nanohole array surface plasmon polariton resonance sensor, Appl. Phys. Lett. 91 (2007) 123112. [4] M.R. Rakhshani, M.A. Mansouri-Birjandi, High sensitivity plasmonic refractive index sensing and its application for human blood group identification, Sensors Actuators B 249 (2017) 168–176. [5] K. Tiwari, S.C. Sharma, N. Hozhabri, Hafnium dioxide as a dielectric for highlysensitive waveguide-coupled surface plasmon resonance sensors, AIP Adv. 6 (2016) 045217. [6] A. Shalabney, I. Abdulhalim, Sensitivity-enhancement methods for surface plasmon sensors, AIP Adv. 5 (2011) 571–606. [7] P.K. Maharana, P. Padhy, R. Jha, On the field enhancement and performance of an ultra-stable spr biosensor based on graphene, IEEE Photonics Technol. Lett. 25 (2013) 2156–2159. [8] K. Tiwari, S.C. Sharma, N. Hozhabri, High performance surface plasmon sensors: Simulations and measurements, J. Appl. Phys. 118 (2015) 093105. [9] P.K. Maharana, R. Jha, P. Padhy, On the electric field enhancement and performance of SPR gas sensor based on graphene for visible and near infrared, Sensors Actuators B 207 (2015) 117–122.
107
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Figure of merit analysis of graphene based surface plasmon resonance biosensor for visible and near infrared Shujing Chen a ,∗, Chengyou Lin b a
Beijing Key Laboratory of Materials Utilization of Nonmetallic Minerals and Solid Wastes, National Laboratory of Mineral Materials, School of Materials Science and Technology, China University of Geosciences, Beijing 100083, China b College of Science, Beijing University of Chemical Technology, Beijing 100029, China
ARTICLE
INFO
Keywords: Surface plasmon resonance Biosensor Figure of merit Graphene
ABSTRACT In this paper, the figure of merit (FOM) of a surface plasmon resonance (SPR) biosensor based on gold–graphene structure is studied in the visible and near infrared region. As the wavelength of incident light increases, the FOM of the proposed SPR biosensor with different number of graphene layers increases firstly and then decreases, indicating an optimal wavelength for realizing the largest FOM (called peak FOM). For the proposed SPR biosensor with monolayer graphene, the peak FOM that shows at 890 nm is up to 33.05 RIU−1 , which is 133% higher than the FOM (14.17 RIU−1 ) at 630 nm (near a common-used wavelength 633 nm). In addition, the effect of dispersion of graphene on the performance of the proposed biosensor is also analyzed. With the increase of the number of graphene layers, the peak FOM of the proposed biosensor decreases, but the optimal wavelength remains unchanged. Furthermore, the origin of FOM enhancement at optimal wavelength is determined by analyzing the electric field intensity inside the proposed SPR biosensor. Besides, the performances of SPR biosensors with different prism and metal are compared. It is believed that the FOM of a graphene based SPR biosensor can be enhanced by optimizing the wavelength of incident light and the number of graphene layers.
1. Introduction The surface plasmon resonance (SPR) technology has been used in the biochemical sensing for years due to its achievements of good performance and real-time analysis [1–5]. To excite the surface plasmon, many configurations can be used. One of them is Kretschmann configuration based on the angular interrogation. In this configuration, a thin metal film coats on the top of prism and the sensing medium touches the metal generally. When the propagation constant of a incidence light matches with that of the surface plasmon wave, a narrow dip (SPR dip) forms in the curve of reflectance as a function of incident angle [6]. The angle that realizes smallest reflectivity calls resonance angle, which is very sensitive to the variation in the refractive index (RI) of the sensing medium. Usually, the performance of a SPR sensor is evaluated by several parameters, such as resonance angle, the reflectance at the resonance angle, sensitivity and full width at half maximum (FWHM) of SPR dip [7–9]. To comprehensively evaluate the performance of an SPR sensor, the figure of merit (FOM), defined as the ratio between the sensitivity and the FWHM, has also been used [10]. Recently, several methods have been proposed to enhance the FOM of a SPR sensor. Adding a thin dielectric layer with high RI on top of the metallic layer was demonstrated for enhancing the FOM of
a SPR sensor with the spectral interrogation [10]. Using the liquid prism instead of the conventional solid prism was also verified for FOM enhancement [11]. In addition, the FOM can be improved by using a porous silica film with low-refractive-index [12] and adding an absentee layer on the top of the metallic layer [13]. The graphene possesses high surface-to-volume ratio and rich 𝜋 conjugation structure, and can be used in a SPR biosensor as the biomolecular recognition element (BRE) to functionalize the metal film for the enhancement of surface adsorption of the biomolecules [14–16]. Recently, various structures based on graphene have been proposed for enhancing the sensitivity of a SPR biosensor, such as gold–graphene [15], silver– graphene [17], gold–silicon–graphene [18], aluminum–graphene [19], TiO2 -SiO2 – gold–MoS2 – graphene [20], gold–MoS2 – graphene [21], and graphene–gold nanoparticles based [22,23] structures. In present, the spectral range of SPR biosensor application extends from visible to terahertz band [24,25]. It has been demonstrated that the performance of a SPR biosensor relies heavily on the dispersion (RI changing with wavelength) of the materials used in the biosensor. For example, Maharana et al. [26] achieved sensitivity enhancement in the near infrared region by using air mediated graphene multilayer in the SPR biosensor. Jha and Sharma [27] realized FOM enhancement of a SPR sensor in the near infrared region by using chalcogenide prism
∗ Corresponding author. E-mail address: [email protected] (S. Chen).
https://doi.org/10.1016/j.optcom.2018.11.031 Received 26 September 2018; Received in revised form 30 October 2018; Accepted 12 November 2018 Available online 16 November 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
S. Chen and C. Lin
Optics Communications 435 (2019) 102–107
√
0.75831𝜆2 0.08495𝜆2 + , (3) 𝜆2 − 0.01007 𝜆2 − 8.91377 where 𝜆 is the wavelength of incident light, taking μm as a unit. The refractive index (n) and the extinction coefficient (k) of gold, silver and mono layer graphene at considered wavelength range are taken from the measured data in Ref. [31] and Ref. [32] respectively, and shown in Fig. 2. The refractive index and the extinction coefficient of multilayer graphene is assumed to be the same with the ones of monolayer graphene in our considered wavelength range [33]. 𝑛H2 O (𝜆) =
1+
2.2. Reflectance coefficient Fig. 1. (Color online) Schematic diagram of the proposed SPR biosensor.
For simulation, the proposed SPR biosensor can be seen as an N-layer structure, therefore we employ the well-known transfer matrix method to calculate the expression of reflectivity [28]. [ ] 𝑁−1 [ ] ∏ 𝐴 𝐵 cos 𝛿𝑘 𝑖 sin 𝛿𝑘 ∕𝜂𝑘 M= = , (4) 𝐶 𝐷 𝑖𝜂𝑘 sin 𝛿𝑘 cos 𝛿𝑘 𝑘=2
and aluminum. However, the FOM of the common-used gold–graphene based SPR biosensor in the visible and near infrared region has not been investigated yet, and the dispersion of graphene on the FOM of the SPR biosensor is still unknown. In this paper, the thickness of gold film in the proposed biosensor is optimized at first for achieving minimal reflectivity. Then the sensitivity, FWHM and FOM of the proposed gold–graphene based SPR biosensor (Fig. 1) with optimized thickness of gold film is analyzed in the visible and near infrared region. In addition, the values of FOM of the proposed SPR biosensors with different graphene layers are compared in the considered wavelength range. Furthermore, the origin of FOM enhancement at the optimal wavelength is investigated by analyzing the electric field intensity in the proposed SPR biosensor.
𝑟p =
The proposed SPR biosensor is based on angular interrogation. The wavelength of incident light is assumed to be in the range of 580 to 1000 nm. We will discuss the dispersion properties of all used materials in the proposed SPR biosensor as a start.
2.3. Performance parameters Sensitivity, FWHM and FOM can be calculated based on reflectance curve. In a typically reflectance curve, the minimum reflectivity 𝑅c is realized at the resonance angle 𝜃c , which changes with the varied RI of the sensing medium. The angular sensitivity S of a SPR sensor is defined as the ratio of resonance angle variation 𝛿𝜃c to the change in refractive index of sensing medium 𝛿n, expressed as
2.1. Dispersion properties The dispersion relations of BK7 prism [28], SF11 prism [29] and sensing medium (water) [30] are given as
1+
𝜆2
𝛿𝜃c ) (6) 𝛿𝑛 In our simulations, water containing ss-DNA biomolecules is assumed to be the sample, and placed in contact with the graphene. Graphene adsorbs the biomolecules on its surface and creates an additional layer of biomolecules (ss-DNA) of thickness around 100 nm, resulting in a local increase in the RI (𝛿𝑛 = 0.005) at the graphene surface. 𝑆=(
1.03961212𝜆2 0.231792344𝜆2 1.01046945𝜆2 + + , (1) 2 2 − 0.00600069867 𝜆 − 0.0200179144 𝜆 − 103.560653
𝑛SF11 = √ 1+
(5)
where M is the characteristic matrix of the 𝑁-layer structure for a ppolarized incident light. The matrix elements of M (A, B, C and D), can be used to calculate the amplitude reflection coefficient 𝑟p . 𝛿k and 𝜂k are the phase factor and the optical admittance for each layer in the SPR biosensor. 𝛿k = 2𝜋𝑁k 𝑑k cos 𝜃k ∕𝜆, in which 𝑁k and 𝑑k respectively denote the complex refractive index and the thickness of each layer. 𝜃k denotes the refractive angle in each layer. 𝜂k = 𝑛k /cos𝜃k is the optical admittance of each layer for p-polarized light. Finally, the reflectivity 𝑅p can be determined by 𝑅p = |𝑟p |2 . The reflectance curve of a SPR biosensor can be obtained by calculating the reflectivity as a function of incident angle.
2. Theory
𝑛BK7 = √
𝜂0 (𝐴 + 𝐵𝜂𝑁 ) − 𝐶 − 𝐷𝜂𝑁 , 𝜂0 (𝐴 + 𝐵𝜂𝑁 ) + 𝐶 + 𝐷𝜂𝑁
1.73759695𝜆2 0.313747346𝜆2 1.89878101𝜆2 + + , (2) 1.73759695 − 0.013188707 𝜆2 − 0.0623068142 𝜆2 − 155.23629
Fig. 2. (Color online) Refractive index n and extinction coefficient k of (a) metals and (b) graphene in the wavelength range of 580 to 1000 nm.
103
S. Chen and C. Lin
Optics Communications 435 (2019) 102–107
Fig. 3. (Color online) (a) Change of reflectivity at resonance angle versus the wavelength and the thickness of gold film. (b) Optimal thickness of gold film for different wavelength of incident light.
Fig. 4. (Color online) (a) FWHM and (b) Sensitivity of proposed SPR biosensor with monolayer graphene for different wavelength of incident light.
The FWHM can be determined by calculating full width at half maximum of the reflectance dip (𝛥𝜃0.5 ), expressed as FWHM = 𝛥𝜃0.5
(7)
Thus the value of FOM can be calculated by FOM =
𝑆 FWHM
(8)
3. Results and discussion 3.1. Thickness optimization of metal film Since a high-performance SPR biosensor should exhibit large depth of dip (i.e. small 𝑅c ), the thickness of gold film is optimized at first to achieve minimum reflectivity at resonance angle. Fig. 3(a) shows the reflectivity at resonance angle of a gold based SPR biosensor with different thickness of gold film in the wavelength range of 580 to 1000 nm. The near-zero 𝑅c can all be realized when the gold film takes the suitable thickness (optimal thickness) for different wavelength. In Fig. 3(b), the optimal thicknesses of gold film for the wavelengths 580 to 1000 nm are shown. It is seen the optimal thickness of the gold film increases as the wavelength increases from 580 to 710 nm at first, and then decreases as the wavelength increases from 710 to 1000 nm. The maximum value of optimal thickness of gold film is 52.6 nm, which shows at 710 nm. Those optimal thicknesses of gold film will be further used in the proposed SPR biosensor to large depth of dip.
Fig. 5. FOM of the proposed SPR biosensor with monolayer graphene for different wavelength of incident light.
light, as shown in Fig. 4. It can be seen that the FWHM and the sensitivity of the proposed biosensor both decrease when the wavelength increases from 580 to 1000 nm. The FOM of the propose SPR biosensor with monolayer graphene is also calculated, and shown in Fig. 5. It is interesting to note that when the wavelength increases from 580 to 890 nm, the FOM of the proposed SPR sensor with monolayer graphene increases from 9.16 RIU−1 to 33.05 RIU−1 at first, but decreases as the wavelength further increases from 890 to 1000 nm, as shown in Fig. 5.
3.2. Performance analysis of monolayer graphene based SPR biosensor
The changes of sensitivity, FWHM and FOM are originally due to the refractive index and extinction coefficient changes of gold and graphene under different wavelengths. Higher extinction coefficient and nearly unchanged refractive index of gold at larger wavelength (as
In order to analyze the performance of the proposed SPR biosensor, the FWHM and the sensitivity of the proposed SPR biosensor with monolayer graphene are investigated for different wavelength of incident 104
S. Chen and C. Lin
Optics Communications 435 (2019) 102–107
Table 1 Refractive index (n) and extinction coefficient (k) of materials at different wavelengths. Wavelength (nm)
Materials
Refractive index (n)
Extinction coefficient (k)
600
Gold Graphene
0.2487 2.7063
3.0740 1.3122
700
Gold Graphene
0.1310 2.7883
4.0624 1.4365
800
Gold Graphene
0.1535 2.8707
4.9076 1.5514
900
Gold Graphene
0.1743 2.9627
5.7227 1.6851
1000
Gold Graphene
0.2272 3.0842
6.4654 1.8240
proposed SPR biosensor with monolayer graphene shows at 890 nm, and is 133% higher than the FOM (14.17 RIU−1 ) at 630 nm, which is the wavelength near a common-used wavelength 633 nm. To further investigate the performance of the proposed SPR biosensor with monolayer graphene at the optimal wavelength, the reflectance curves (reflectance versus incident angle) of the biosensor at optimal wavelength (890 nm) and two other wavelengths (630 nm and 990 nm) are plotted in Fig. 6. The performance parameters of the SPR biosensor for three different wavelengths are also calculated, and listed in Table 2. The FOM exhibits maximum value at 890 nm, which is 133% and 24% higher than that one at 630 nm and 990 nm, respectively. The results indicate that the wavelength of incident light can be optimized to enhance the FOM of the gold–graphene based SPR biosensor. 3.3. Electric field analysis To study the origin of FOM enhancement achieved at the optimal wavelength, we calculate the electric field intensity enhancement factor (EFIEF) of the SPR biosensor for three wavelengths, as shown in Fig. 7. The EFIEF all exhibits largest value at the graphene-sample interface for three wavelengths, as shown in Fig. 7(a). The largest EFIEF increases from 13.477 to 51.811 when wavelength increases from 630 to 990 nm, which is considered to be the reason for decreasing FWHM with increasing wavelength, as demonstrated in Ref. [12]. Meanwhile, the curves of EFIEF at graphene-sample interface with respect to the incident angle for three wavelengths are plotted in Fig. 7(b). The integral of EFIEF for 630 nm exhibit the largest value (1237.90) compared with the ones at 890 and 990 nm (925.51 and 768.77). This result confirms the statement of correlation between the sensitivity enhancement and EFIEF integral as described by Benkabou et al. [36]. The similar behavior of electric field enhancement for the biosensor at 890 nm and 990 nm is originally due to the small differences of refractive index and extinction coefficient of gold and graphene at two wavelengths.
Fig. 6. (Color online) Reflectance curves of the proposed SPR biosensor with monolayer graphene at 630 nm, 890 nm and 990 nm.
Table 2 The performance parameters of the proposed SPR biosensor with monolayer graphene at three wavelengths. Wavelength Resonance angle Reflectivity (nm) (degree)
Sensitivity (degree/RIU)
FWHM (degree)
FOM (RIU−1 )
630 890 990
101.54 36.78 29.22
7.1664 1.1129 1.0065
14.1689 33.0486 29.0326
72.6041 64.9816 64.2017
0.00640 0.00006 0.00021
3.4. FOM comparison of graphene multilayer based SPR biosensors As mentioned above, the dispersion of graphene also plays an important role on the performance of the proposed SPR biosensor. In order to analyze the effect of dispersion of graphene on the FOM of proposed biosensor, the FOM of the proposed SPR biosensors with different number of graphene layers are calculated in the considered wavelength range, as shown in Fig. 8. The FOM of the proposed SPR biosensor with various graphene layers all increases when the wavelength of incident light increases from 580 to 890 nm firstly, and then decreases when the wavelength of incident light increases from 890 to 1000 nm. The optimal wavelength remains unchanged (890 nm) for the proposed SPR biosensors with varied graphene layers. The variation of peak FOM of the proposed SPR biosensor at 890 nm with respect to the wavelength of incident light is shown in Fig. 9. As
list in Table 1) leads to a smaller FWHM of SPR curve (Fig. 4(a)), as demonstrated by Lecaruyer et al. [34]. In addition, the increasing of extinction coefficient of graphene with wavelength (as list in Table 1) shallows the SPR curve [35], and weakens the SPR wave in the biosensor, which is considered to be the reason for the decreasing of sensitivity (Fig. 4(b)). The increase of FOM with the wavelength increasing from 580 to 890 nm originates from the decreasing speed of sensitivity is smaller than the one of FWHM. The largest FOM (peak FOM) of the
Fig. 7. (Color online) Electric field intensity enhancement factor (a) inside the SPR biosensors and (b) at graphene-sample interface with respect to the incident angle for 630 nm, 890 nm and 990 nm.
105
S. Chen and C. Lin
Optics Communications 435 (2019) 102–107
Fig. 8. (Color online) FOM of the proposed SPR biosensor with different number of graphene layers for different wavelength of incident light.
Fig. 11. (Color online) Reflectance curves of monolayer graphene SPR biosensors with optimized gold and silver film at 890 nm. Table 3 Performance parameters of monolayer graphene SPR biosensors with optimized gold and silver film at 890 nm. Prism
Metal
Resonance angle Reflectivity (degree)
Sensitivity (degree/RIU)
FWHM (degree)
FOM (RIU−1 )
BK7 BK7
Au Ag
64.9816 64.1610
36.78 31.90
1.1129 0.1917
33.0486 166.4318
0.00006 0.09300
3.5. Performance comparison of graphene based SPR biosensors with different prism and metal
results indicate that the optimized thickness of gold layer for SF11 based biosensor is higher than the one for BK7 based SPR biosensor when the wavelength changing from 580 nm to 650 nm, but lower from 650 nm to 1000 nm. In addition, the peak FOM for SF11 is 31.8967 RIU−1 , which is lower than the one of BK7 prism based biosensor, due to the lower refractive index of BK7. However, the optimized wavelength for SF11 prism based biosensor is the same with the BK7 prism based one, which is also 890 nm. The variation of peak FOM of the proposed SPR biosensor for SF11 prism with respect to the wavelength of incident light is shown in Fig. 10(b). As the increase of the number of graphene layers, the peak FOM decreases. The largest peak FOM (31.8967 RIU−1 ) shows when monolayer graphene is used for SF11 prism based SPR biosensor, which is the same to the case of BK7 prism based one. Compared with the results of BK7 prism based biosensors shown in Fig. 9, the peak FOM of the proposed SPR biosensor with BK7 prism is always higher than the one for SF11 when using different number of graphene layers.
To explore the effect of prism on the performance of a graphene based SPR biosensor, the SPR biosensor with SF11 prism is also studied. The optimization method of SF11 prism based SPR biosensor is the same as the BK7 prism based one. The optimized thickness of gold film and FOM in the wavelength of 580–1000 nm is calculated for SF11 prism based biosensor with monolayer graphene, as shown in Fig. 10(a). The
To investigate the metal effect on the performance of optimized SPR biosensors, a monolayer graphene based SPR biosensor with optimized silver film is compared with the one with optimized gold film at its optimized wavelength (890 nm). The reflectance curves (reflectance versus incident angle) of two biosensors at optimal wavelength are plotted in Fig. 11. Their performance parameters are also calculated, and listed in Table 3. It is found that the Ag based SPR biosensor exhibits
Fig. 9. (Color online) Variation of peak FOM with respect to the number of graphene layers.
the increases of the number of graphene layers, the peak FOM decreases. The peak FOM of the proposed SPR biosensor with monolayer graphene is highest among all biosensors (33.0486 RIU−1 ), indicating that the optimal number of graphene layer for largest FOM is one.
Fig. 10. (Color online) (a) Optimized thickness of gold and FOM of monolayer graphene based SPR biosensor with SF11 prism for different wavelength of incident light. (b) Variation of peak FOM with respect to the number of graphene layers for SPR biosensors with SF11 prism.
106
S. Chen and C. Lin
Optics Communications 435 (2019) 102–107
much higher FOM than Au based one (166.4318 RIU−1 Vs 33.0486 RIU−1 ), due to its much smaller FWHM (0.1917◦ Vs 1.1129◦ ). However, the sensitivity of Ag based biosensor is lower than the one of Au based biosensor (31.90◦ /RIU Vs 36.78◦ /RIU).
[10] A. Shalabney, I. Abdulhalim, Figure-of-merit enhancement of surface plasmon resonance sensors in the spectral interrogation, Opt. Lett. 37 (2012) 1175–1177. [11] G. Lan, S. Liu, Y. Ma, X. Zhang, Y. Wang, Y. Song, Sensitivity and figure-ofmerit enhancements of liquid-prism spr sensor in the angular interrogation, Opt. Commun. 352 (2015) 49–54. [12] Q. Meng, X. Zhao, C. Lin, S. Chen, Y. Ding, Z. Chen, Figure of merit enhancement of a surface plasmon resonance sensor using a low-refractive-index porous silica film, Sensors 17 (2017) 1846. [13] Z. Chen, X. Zhao, C. Lin, S. Chen, L. Yin, Y. Ding, Figure of merit enhancement of surface plasmon resonance sensors using absentee layer, Appl. Opt. 55 (2016) 6832–6835. [14] X. Luo, T. Qiu, W. Lu, Z. Ni, Plasmons in graphene: Recent progress and applications, Mater. Sci. Eng. R 74 (2013) 351–376. [15] L. Wu, H. Chu, W. Koh, E. Li, Highly sensitive graphene biosensors based on surface plasmon resonance, Opt. Express 18 (2010) 14395–14400. [16] G.X. Ni, A.S. McLeod, Z. Sun, L. Wang, L. Xiong, K.W. Post, S.S. Sunku, B.Y. Jiang, J. Hone, C.R. Dean, M.M. Fogler, D.N. Basov, Fundamental limits to graphene plasmonics, Nature 557 (2018) 530–533. [17] S.H. Choi, Y.L. Kim, K.M. Byun, Graphene-on-silver substrates for sensitive surface plasmon resonance imaging biosensors, Opt. Express 19 (2011) 458–466. [18] R. Verma, B.D. Gupta, R. Jha, Sensitivity enhancement of a surface plasmon resonance based biomolecules sensor using graphene and silicon layers, Sensors Actuators B 160 (2011) 623–631. [19] P.K. Maharana, T. Srivastava, R. Jha, On the performance of highly sensitive and accurate graphene-on-aluminum and silicon-based spr biosensor for visible and near infrared, Plasmonics 9 (2014) 1113–1120. [20] J.B. Maurya, Y.K. Prajapati, V. Singh, J.P. Saini, Sensitivity enhancement of surface plasmon resonance sensor based on graphene-MoS2 hybrid structure with TiO2 SiO2 composite layer, Appl. Phys. A 121 (2015) 525–533. [21] S. Zeng, S. Hu, J. Xia, T. Anderson, X.Q. Dinh, X.M. Meng, P. Coquet, K.T. Yong, Graphene-MoS2 hybrid nanostructures enhanced surface plasmon resonance biosensors, Sensors Actuators B 207 (2015) 801–810. [22] S. Zeng, K.V. Sreekanth, J. Shang, T. Yu, C.K. Chen, F. Yin, D. Baillargeat, P. Coquet, H.P. Ho, A.V. Kabashin, K.T. Yong, Graphene-gold metasurface architectures for ultrasensitive plasmonic biosensing, Adv. Mater. 27 (2015) 6163–6169. [23] S. Zeng, D. Baillargeat, H.P. Ho, K.T. Yong, Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications, Chem. Soc. Rev. 43 (2014) 3426–3452. [24] L. Chen, N. Xu, L. Singh, T. Cui, R. Singh, Y. Zhu, W. Zhang, Defect-induced fano resonances in corrugated plasmonic metamaterials, Adv. Opti. Mater. 5 (2017) 1600960. [25] B. Ruan, Q. You, J. Zhu, L. Wu, J. Guo, X. Dai, Y. Xiang, Terahertz biochemical sensor based on strong coupling between waveguide mode and surface plasmons of double-layer graphene, IEEE Sens. J. 18 (2018) 7436–7441. [26] P.K. Maharana, R. Jha, S. Palei, Sensitivity enhancement by air mediated graphene multilayer based surface plasmon resonance biosensor for near infrared, Sensors Actuators B 190 (2014) 494–501. [27] R. Jha, A.K. Sharma, High-performance sensor based on surface plasmon resonance with chalcogenide prism and aluminum for detection in infrared, Opt. Lett. 34 (2009) 749–751. [28] J.B. Maurya, Y.K. Prajapati, V. Singh, J.P. Saini, R. Tripathi, Improved performance of the surface plasmon resonance biosensor based on graphene or MoS2 using silicon, Opt. Commun. 359 (2016) 426–434. [29] S.K. Srivastava, R. Verma, B.D. Gupta, Theoretical modeling of a self-referenced dual mode spr sensor utilizing indium tin oxide film, Opt. Commun. 369 (2016) 131–137. [30] S. Kedenburg, M. Vieweg, T. Gissibl, H. Giessen, Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and nearinfrared spectral region, Opt. Mater. Express 2 (2012) 1588–1611. [31] P.B. Johnson, R.W. Christy, Optical constants of the noble metals, Phys. Rev. B 6 (1972) 4370. [32] J. Weber, V. Calado, M. Van de Sanden, Optical constants of graphene measured by spectroscopic ellipsometry, Appl. Phys. Lett. 97 (9) (2010) 2010. [33] W. Li, G. Cheng, Y. Liang, B. Tian, X. Liang, L. Peng, A.R.H. Walker, D.J. Gundlach, N.V. Nguyen, Broadband optical properties of graphene by spectroscopic ellipsometry, Carbon 99 (2016) 348–353. [34] P. Lecaruyer, M. Canva, J. Rolland, Metallic film optimization in a surface plasmon resonance biosensor by the extended Rouard method, Appl. Optics 46 (2007) 2361– 2369. [35] F. Benkabou, M. Chikhi, Surface plasma oscillations at silver surfaces with thin transparent and absorbing coatings, Surf. Sci. 72 (1978) 577–588. [36] F. Benkabou, M. Chikhi, Theoretical investigation of sensitivity enhancement in dielectric multilayer surface plasmon sensor, Phys. Status Solidi A 211 (2014) 700– 704.
4. Conclusion In this paper, the figure of merit of the gold–graphene based SPR biosensor has been theoretically investigated in visible and near infrared region. The thickness of gold film is optimized at first to achieve minimum reflectivity at resonance angle for different wavelength. Then, the sensitivity, FWHM and FOM of the proposed SPR biosensor with optimal thickness of gold film and monolayer graphene is investigated in the wavelength region of 580 to 1000 nm. When the wavelength increases from 580 nm to 890 nm, the FOM of the proposed SPR sensor with monolayer graphene increases from 9.16 RIU−1 to 33.05 RIU−1 at first, but decreases as the wavelength further increases from 890 to 1000 nm. The largest FOM (peak FOM) of the proposed SPR biosensor with monolayer graphene shows at 890 nm, and is 133% higher than the FOM (14.17 RIU−1 ) at 630 nm, which is the wavelength near a common-used wavelength 633 nm. In addition, the effect of dispersion of graphene on the FOM of proposed SPR biosensor is analyzed. The results indicate that with the increase of the number of graphene layers, the peak FOM of the proposed biosensor decreases, but the optimal wavelength remains unchanged. Furthermore, the performances of graphene based SPR biosensors with different prism and metal are compared. In summary, the FOM of a graphene based SPR biosensor can be improved by optimizing the wavelength of incident light and the layer number of graphene. This research provides a way for improving the FOM of a graphene based SPR biosensor, and may be useful for high-performance SPR sensors development. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 11547241) and the Fundamental Research Funds for the Central Universities, China (Grant No. 2652017340). References [1] C. Nylander, B. Liedberg, T. Lind, Gas detection by means of surface plasmon resonance, Sensors Actuators 3 (1983) 79–88. [2] S. Pal, A. Verma, S. Raikwar, Y.K. Prajapati, J.P. Saini, Detection of DNA hybridization using graphene-coated black phosphorus surface plasmon resonance sensor, Appl. Phys. A 124 (2018) 394. [3] L. Pang, G.M. Hwang, B. Slutsky, Y. Fainman, Spectral sensitivity of twodimensional nanohole array surface plasmon polariton resonance sensor, Appl. Phys. Lett. 91 (2007) 123112. [4] M.R. Rakhshani, M.A. Mansouri-Birjandi, High sensitivity plasmonic refractive index sensing and its application for human blood group identification, Sensors Actuators B 249 (2017) 168–176. [5] K. Tiwari, S.C. Sharma, N. Hozhabri, Hafnium dioxide as a dielectric for highlysensitive waveguide-coupled surface plasmon resonance sensors, AIP Adv. 6 (2016) 045217. [6] A. Shalabney, I. Abdulhalim, Sensitivity-enhancement methods for surface plasmon sensors, AIP Adv. 5 (2011) 571–606. [7] P.K. Maharana, P. Padhy, R. Jha, On the field enhancement and performance of an ultra-stable spr biosensor based on graphene, IEEE Photonics Technol. Lett. 25 (2013) 2156–2159. [8] K. Tiwari, S.C. Sharma, N. Hozhabri, High performance surface plasmon sensors: Simulations and measurements, J. Appl. Phys. 118 (2015) 093105. [9] P.K. Maharana, R. Jha, P. Padhy, On the electric field enhancement and performance of SPR gas sensor based on graphene for visible and near infrared, Sensors Actuators B 207 (2015) 117–122.
107