† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11547183 and 11547241), the Higher Education and High-quality and World-class Universities, China (Grant No. PY201612), the National Key Research and Development Program of China (Grant No. 2016YFB0302003), and the Natural Science Foundation of Beijing (Grant No. 2162033).
A surface plasmon resonance (SPR) sensor with a high-order absentee layer on the top of metallic film is proposed. The performance of the SPR sensor with NaCl, MgO, TiO2 or AlAs high-order absentee layer is analyzed theoretically. The results indicate that the sensitivity and the full width at half maximum of those SPR sensors decrease with the increasing of the order of absentee layer, but the variation of the figure of merit (FOM) depends on the refractive index of absentee layer. By improving the order of absentee layer with high-refractive-index, the FOM of the SPR sensor can be enhanced. The maximum value of FOM for the SPR sensor with high-order TiO2 (or AlAs) absentee layer is 1.059% (or 2.587%) higher than the one with one-order absentee layer. It is believed the proposed SPR sensor with high-order absentee layer will be helpful for developing the high-performance SPR sensors.
As a valuable and standard analytical tool, surface plasmon resonance (SPR) sensors are widely used in gas molecule detection, drug diagnostics and biosensing,[1–3] and the spectral range of its application extends from visible and infrared bands to terahertz band now.[4–6] The Kretschmann prism coupling configuration is a simple and useful configuration of the SPR sensor. In this configuration, a high refractive index prism is coated with a thin metal layer touching the analyte (sensing medium).[7,8] When a p-polarized incident light illuminates on the SPR sensor, the surface plasmon wave (SPW) will occur at the interface between metal layer and analyte if the phase matching condition is satisfied.[9] The resonant condition is generally controlled by the incident angle or wavelength of the excitation light, which is usually referred to as the angular or wavelength interrogation. Under the phase matching condition, the electromagnetic field of the SPW becomes strongest when the energy of the light is completely absorbed, causing a sharp dip to appear on the reflectivity curve.[10,11]
To evaluate the performance of an SPR sensor, several performance parameters are generally used, such as the sensitivity (S), the full width at half maximum (FWHM), and the figure-of-merit (FOM).[2,11,12] The sensitivity is defined as the ratio between the shift of the resonance angle or wavelength and the change of the refractive index of analyte.[13] Many methods of improving the sensitivity were proposed recently, such as adding graphene and air gap,[14] dielectric layer[13,15] or semiconductor layer[16] in an SPR sensor. The FWHM of reflectance curve is another important parameter, which determines the detection accuracy of SPR sensor.[17] Exciting long-range surface plasmons by adding dielectric layer between the prism and metal layer was proven to be an efficient method to reduce the FWHM (or increase the detection accuracy).[18] The FOM is defined as the ratio between the sensitivity and the FWHM. It was demonstrated that the FOM can be enhanced by adding a thin dielectric layer with high refractive index on the top of the metallic layer in SPR sensor in the spectral interrogation.[19] In addition, using the liquid prism instead of the conventional solid prism was also verified for FOM enhancement.[11]
The absentee layer is an optical layer whose optical thickness satisfies the integer multiple of half-wavelength. Generally, the absentee layer has no effect on the reflectance or transmittance of the film system at the considered angle or wavelength, which is often used to adjust the spectral curve without changing the basic profile.[20,21] In our previous study,[22] a half-wavelength absentee layer was used in an SPR sensor for FOM enhancement. In this paper, we further investigate the performance of the SPR sensor with a high-order absentee layer.[23] By analyzing the sensitivity, FWHM and FOM of the SPR sensor with different-order absentee layer, we find that the FOM of the SPR sensor can be enhanced by improving the order of high-refractive-index absentee layer.
The SPR sensor with a high-order absentee layer is shown in Fig.
Based on the thin film theory, the tangential fields at the first (prism-metal layer) interface are related to those at the third (absentee layer-analyte) interface by
Because H3/E3 = η3 and H1/E1 = Y, equation (
Using Eq. (
For an absentee layer, its optical thickness generally fulfills
In this paper, the absentee layer with m = 1 is called one-order absentee layer, and its thickness fulfills da = λ/2n2 cosθ2. The absentee layer with m < 1 is named high-order absentee layer, and its thickness fulfills d2 = mda. The phase factor of an absentee layer δ2 = mπ, and its characteristic matrix becomes a unity matrix at the target angle, which is
Therefore, at the target angle, such as the resonance angle of a traditional SPR sensor, the extra reflections cancel out at the interfaces because no additional phase shifts are introduced. But at other incident angles, equations (
The performance of an SPR sensor can be described by several parameters, such as the resonance angle θres, depth of dip Rres (the reflectance at the resonance angle), sensitivity, FWHM, and FOM. In the angular interrogation mode, the resonance angle θres changes with the refractive index of the analyte
The FWHM can be determined by calculating FWHM value of the reflectance dip(Δθ0.5), and expressed as
Thus the FOM can be calculated from
Using the theoretical method described above, the performance of the SPR sensor with high-order absentee layer can be analyzed. The wavelength of the incident light is assumed to be 653.2 nm. A 45-degree SF-11L glass (n0 = 1.776) is used as the prism material in SPR sensors. Gold (Au) (n1 = 0.166 + 3.15i) film with an optimized thickness of 50 nm(d1 = 50 nm) is employed as the metal film. The water (n3 = 1.33) is assumed to be the analyte.
In addition, NaCl, MgO, TiO2, and AlAs absentee layers are considered in our study, and their refractive indices are nNaCl = 1.541, nMgO = 1.741, nTiO2 = 2.2789, and nAlAs = 3.112, respectively. According to Eq. (
![]() | Table 1. Refractive indices of materials at 653.2-nm wavelength of light. . |
Firstly, the performance of the SPR sensor with different-order NaCl absentee layer is studied. Figure
![]() | Fig. 2. (color online) Reflectivity curves of the SPR sensors with different-order NaCl absentee layer (m = 1, 2, 3, 4). |
In Fig.
![]() | Table 2. Performance parameters of the SPR sensors with different-order NaCl absentee layer (m = 1, 2, 3, 4). . |
When m increases from 1 to 4, the sensitivity decreases from 5.4°/RIU to 1.4°/RIU, and the FWHM also decreases from 0.313° to 0.083°. Consequently, the FOM decreases from 17.246 RIU−1 to 17.178 RIU−1. The decreasing of the FOM should be due to larger decrease rate of the sensitivity than that of the FWHM as m increases. Compared with the SPR sensor with one-order absentee layer, the SPR sensor with high-order NaCl absentee layer can obtain small FWHM, but low sensitivity and FOM.
Secondly, the performance of the SPR sensor with different-order MgO absentee layer is investigated. Figure
![]() | Fig. 3. (color online) Reflectivity curves of the SPR sensors with different-order MgO absentee layer (m = 1, 2, 3, 4). |
As m increases from 1 to 4, the sensitivity decreases from 19.7°/RIU to 6.1°/RIU, and the FWHM also decreases from 1.155° to 0.361°. Thus, the FOM decreases from 17.053 RIU−1 to 17.038 RIU−1. The decreasing of the FOM comes from larger decrease rate of the sensitivity than that of the FWHM as m increases. Although the SPR sensor with high-order MgO absentee layer can achieve smaller FWHM than that with one-order absentee layer, it cannot obtain the larger FOM.
![]() | Table 3. Performance parameters of the SPR sensors with different-order MgO absentee layer (m = 1, 2, 3, 4). . |
Next, the performance of the SPR sensor with different-order TiO2 absentee layer is studied. Figure
In Fig.
![]() | Fig. 4. (color online) Reflectivity curves of SPR sensors with different-order TiO2 absentee layer (m = 1, 2, 3, 4). |
![]() | Table 4. Performance parameters of the SPR sensors with different-order TiO2 absentee layer (m = 1, 2, 3, 4). . |
Finally, the performance of the SPR sensors with different-order AlAs absentee layer is investigated. Fig.
![]() | Fig. 5. (color online) Reflectivity curves of SPR sensors with different-order AlAs absentee layer (m = 1, 2, 3, 4). |
![]() | Table 5. Performance parameters of SPR sensors with different-order AlAs absentee layer (m = 1, 2, 3, 4). . |
The sensitivity decreases from 56.0 to 32.2°/RIU, and the FWHM decreases from 3.372° to 1.897° as m increases from 1 to 4. Like the case of AlAs absentee layer, the FOM also increases, in this case, from 16.619 RIU−1 to 16.953 RIU−1. The reason for the increasing of the FOM should be attributed to the smaller decrease rate of the sensitivity than that of the FWHM as m increases. Compared with the SPR sensor with one-order absentee layer, the SPR sensor with high-order AlAs absentee layer can also realize small FWHM and large FOM simultaneously.
![]() | Fig. 6. (color online) Distributions of |Ex|2 of SPR sensors with different-order (m = 1, 2, 3, 4) (a) NaCl, (b) MgO, (c) TiO2, and (d) AlAs absentee layer. |
To investigate the origin of performance difference of SPR sensors with different-order absentee layer, the distributions of normalized tangential electric field intensity (|Ex|2) of SPR sensors with different-order absentee layer are plotted in Fig.
The origin of the sensitivity decreasing with increasing m is also studied by analyzing the electric field intensity. In Fig.
Figure
Figure
Figure
To further investigate the FOM enhancement of the SPR sensor with high-order absentee layer, we study the FOMs of the SPR sensors with different-order TiO2 and AlAs absentee layer as shown in Fig.
In this paper, the performance of the surface plasmon resonance sensor with high-order absentee layer is theoretically investigated. By analyzing the performance paramaters (sensitivity, FWHM and FOM) of SPR sensors with high-order absentee layer, we find that with the increasing of the order of absentee layer, the sensitivities and FWHMs of those SPR sensors both decrease, but the variation of FOM depends on the refractive index of absentee layer. To achieve FOM enhancement, only high-refractive-index absentee layer (such as TiO2 or AlAs absentee layer) can be used. By investigating the FOM enhancement of the SPR sensor with high-order absentee layer, we also find the FOM cannot increase indefinitely with the increasing of the order of absentee layer, but tends asymptotically towards a maximum value. The maximum value of FOM for the SPR sensor with high-order TiO2 (or AlAs) absentee layer is 1.059% (or 2.587%) higher than the one with one-order absentee layer.
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