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The sensitivity of surface plasmon resonance (SPR) sensors based on gratings using angular interrogation is improved by optimizing the 1st-order diffraction dip recently but still can not exceed the prism-based systems. To improve the sensitivity of grating-based systems in another way, we realize sharp dips of the higher diffraction orders and propose double-dips method (DDM), a new way using the separation of two sharp dips of different orders to improve the sensitivity of SPR sensors based on gratings with good linearity. By DDM, the grating-based systems’ sensitivity is improved into more than 237 deg/RIU, more sensitive than the prism-based systems in the same condition, and the quality parameter χ factor reaches more than 95. In different performance comparisons, DDM has roundly better performances than other methods. Moreover, when the grating profile errs from rectangle, DDM still works well.
©2008 Optical Society of America
1. Introduction
Surface plasmon optics is a very hot research field [1–4], and its applications are paid great attention to. Many devises based on surface plasmon have been proposed and applied widely. Among them, SPR sensor is one of the most important and successful application because of its high sensitivity, which is now widely used in biology, chemistry and environment monitor et al. Generally, the configuration of SPR sensors can be based on either attenuation total reflection (ATR) prism coupling or grating coupling because the propagation constant of surface plasmon wave is always higher than that of optical wave propagating in free space. Both configurations can use angular interrogation. At the moment, the prism-based systems are widely used in practice because their sensitivities are higher than the grating-based systems.
Recently, many researches on the sensitivity of SPR sensors using angular interrogation are reported. The angular sensitivity of the SPR sensor based on prism is reported increasing from 94.46 deg/RIU to 204.41 deg/RIU, but it goes with an increase of FWHM from 2.24 to 4.36 deg [5]. The angular sensitivities of the grating-based systems are reported recently as 103 deg/RIU in a short-range mode method, 97 deg/RIU in a typical single-mode method [6] and 70 deg/RIU in a metallic method [7]. All the grating-based methods above are improving the sensitivity through making the dips of the 1st diffraction order better but can not exceed the sensitivity of the prism-based systems. As discussed in Homola’s paper [8], in the 2nd diffraction order the grating-based system exhibits about the same sensitivity as that of the prism-based system. However, the dip of the 2nd order showed in Fig. 10(a) of [8] is too shallow to practical use to realize the high sensitivity.
We notice that if turn the attention from the 1st diffraction order to the higher orders, it may be another effective way of the sensitivity improvement in the grating-based system. In this work, a unique grating is designed to produce not only the 1st-order dip but also a deep enough high-order dip that can be located. Based on these two dips, we propose double-dips method (DDM) to improve the sensitivity of grating-based SPR sensors. The principle of DDM will be explained; the performances of DDM will be analyzed and compared to some other SPR sensing methods.
2. Principle of double-dips method (DDM)
To make use of the higher-order dips in the grating-based system, it is necessary to produce a deep and sharp reflectance minimum. Our rigorous coupled-wave calculation reveals the high-order reflection dips can be manipulated by changing the topography of the gratings [9]. Based on our analysis, a rectangle grating structure showed in Fig. 1(a) is designed, whose structure parameters are showed below. The period of the gold grating (Λ) is 1300nm. The widths of the upper region of the grating (u1 and u2) are 800nm and the depth of the grating (d) is 35nm. The gold lay is thick enough, thus the substrate is regardless. The wavelength (λ) of the incident plane wave light is 850nm (1.459ev). We use the angular interrogation type and consider the refractive index (na) of the analyte ranging from 1.32 to 1.37 RIU (refractive index unit). The optical constants for gold used are n=0.17, k=5.30 [10, 11]. Based on the structure introduced above, a very sharp -4th-order dip with FWHM (full width of half maximum) of 2.5 deg can be produced. Figure 1(b) gives the reflection spectrum of the structure shown in Fig. 1(a) calculated by rigorous coupled-wave analysis theory (RCWA) [12]. As the refractive index of the analyte varies from 1.32 to 1.37 RIU, the minimum position of the 1st-order dip shifts to the right and the -4th-order dip to the left. This results in the decrease of the separation between these two dips (w). Obviously, w changes more quickly than the 1st-order dip and the -4th-order dip with the change of refractive index of the analyte, hereby, a new method with higher sensitivity than the former ways can be designed based on this. This leads to double-dips method (DDM).
Fig. 1. (a). Schematic diagram of a grating based reflection type SPR sensor using angular interrogation. (b). Calculated reflectance spectra of rectangle-grating-based SPR sensors.
The reflectivity minimum in Fig. 1(b) can be understood from the surface plasmon resonance at the grating surface. Neglecting the perturbation on the dispersion properties of the surface plasmon wave by the grating relief, the resonant condition can be written out according to the momentum conservation for optical wave exciting surface plasmon wave via diffraction grating [8]:
where θR is the resonant angle (0 deg<θR<90 deg), m is an integer, εm is the dielectric constant of gold. Because the wave vector of surface plasmon is always greater than that of incident light, sign “+” on the right side of the equation corresponds to diffraction order m>0 and sign “-” corresponds to diffraction order m<0. From Eq. (1), the left sharp dip in Fig. 1(b), with FWHM of 1.07 deg, corresponds to the 1st diffraction order (m=1) and the right sharp dip, with FWHM of 2.5 deg, corresponds to the -4th order (m=-4).
Assuming εm≫n2 a, the resonant angle is calculated from Eq. (1) as following:
As refractive index of analyte (na) increases, resonant angle θR goes to bigger in the case of m>0 and becomes smaller in the case of m<0, which is identical with the rigorous coupled-wave calculation (Fig. 1(b)). When come to the sensitivity (S) using one dip, the following equation can be achieved from the derivation of Eq. (2):
It can be seen that the sensitivity is approximately proportional to diffraction order (|m|). The sensitivity using the higher order dip is larger than that using the lower order.
Double-dips method (DDM) is designed in such a way: based on the sharp dips of different diffraction orders produced by the system in Fig. 1(a), the change of w can be detected, which decreases with the increase of the refractive index of the analyte, and it can be turned to the parameter we want to measure such as refractive index of the analyte. Therefore, the sensitivity for DDM is defined as following:
In our designed grating structure (Fig. 1(a)), the 1st order and the -4th order dip are measured to sensing the refractive index of analyte, thus the sensitivity of our DDM grating SPR sensor is
Where θ-4 is the incident angle where the -4th-order dip appears and θ1 is the incident angle where the 1st-order dip appears. From Eq. (5), it can be seen unambiguously that DDM can improve the sensitivity of the grating-based SPR sensors by several times compared to the 1st-order dip sensors. But the price we have to pay for this sensitivity enhancement is the additional uncertainty of estimating two spectral shifts instead of one in the normal methods based on single resonant dip. Approximately, the uncertainty of the sensing variable in DDM is doubled because the width of the resonant dip of different diffraction orders changes not too much. Considering the great sensitivity enhancement, this payment of uncertainty is valuable.
3. Characteristics of double-dips method (DDM)
In the following, we discuss the quantitative comparisons through simulations. The sensitivity comparison among different methods is showed in Fig. 2(a) and the χ factors, which are defined as χ=S/FWHM in [8] and denote the overall performance of sensors, are compared in Fig. 2(b). Using the structure in Fig. 1(a), the results of DDM (including DDM14, which using the 1st-order and the -4th-order dip, and DDM24, which using the +2nd-order showed in Fig. 1(b) and the -4th-order dip), the conventional method just using the 1st-order dip (G 1st) and the method just using the -4th-order dip (G 4th) can be calculated. The results of BK7 glass prism-gold method at the wavelength of 850nm (Prism) in [8] are compared with. To show the recent results reported in this area, several concerned results of different grating structures and prism structures reported in literature recently are also presented in Fig. 2(a) and Fig. 2(b), separated by blank from the former 5 which using the same structure parameters. They are the results of grating-based systems of a short-range mode method (Sb-SR) and a typical single-mode method (typical) reported in [6], and a metallic method (metallic) reported in [7], and the results of prism-based systems with different prism refractive index of 1.597 (N1), 1.514 (N2) and 1.456 (N3) reported in [5].
Fig. 2. (a). Sensitivity comparison among different methods. (b) χ factor comparison among different methods.
In Fig. 2(a), it can be seen that DDM14 is 7.4 times as the G 1st, and 2.4 times as the Prism. Compared to G 4th, DDM14 still has better performance by 16%. If use the +2nd-order dip, which appears in the reflectance spectra in Fig. 1(b), the sensitivity of DDM can be improved further. Comparing the bar of DDM24 with other bars, DDM24 is 7.9 times as G 1st and higher than G 4th by 24%. The sensitivity improvement brought in by DDM predicted in the academic analysis above can be proved during these comparisons. The sensitivities of the recent methods showed aside, including grating methods and prism methods, are not as good as the results of DDM. Besides, it can be paid attention to in Fig. 2(a) that the sensitivity of DDM is the summation of the sensitivities of the two dips used, which is predicted in Eq. (5).
Figure 2(b) shows the comparison of the χ factor among different methods. To consider the worst condition, the wider FWHM of the two dips in DDM (FWHM of the -4th-order dip) is used in the calculation of the χ factor of DDM. However, this does not break the good performance of DDM. Obviously, the two highest bars are the two results of DDM. The prism-based method N3 with good sensitivity has a bad χ factor because of its wide FWHM. Considering both factors in Fig. 2, DDM has roundly better performance than others.
Figure 3 shows the linearity comparison among different methods based on the same structure in Fig. 1(a). It can be seen that all four grating-based method have good linearity with good values of correlation coefficient (R).
Fig. 3. Linearity comparison among different methods. The lines of G 1st and G 4th are the incident angles where the dips appear as functions of the refractive index of analyte, and the lines of DDM14 and DDM24 are w as functions of the refractive index of analyte.
At last, the grating profile is changed into trapezia by setting u1 into 760nm while other parameters remain the same as Fig. 1(a), and the reflectance spectra of this trapezia-grating-based SPR sensor is showed in Fig. 4. In Fig. 4, there are sharp dips of different orders nearly the same as the rectangle-grating-based system (Fig. 1(b)). From Fig. 5(a), it can be seen that after changing the grating profile into trapezia, the sensitivities are equal to the rectangle grating system. After using the 1st-order and -4th-order dip to realize DDM in this trapezia grating system, the sensitivity (DDM14) is improved into 240 deg/RIU, 7.6 times as the sensitivity gotten by just using the 1st-order dip in this system, and the linearity (R=0.9983) is good. If use the +2nd-order and -4th-order dip in this trapezia system, the DDM sensitivity (DDM24) is 255 deg/RIU, 8 times as the 1st-order way and the R value is 0.9985. Figure 5(b) shows the χ factor comparison. The trapezia grating system has a better performance in this aspect because of its narrower FWHM (the FWHM of the -4th order dip is 1.85 deg and the 1st order’s is 0.84 deg). When the grating profile errs from rectangle, DDM still works well and the analysis about its characters above remains.
Fig. 5. (a). Sensitivity comparison between rectangle grating and trapezia grating based SPR sensors among different methods. (b). χ factor comparison between rectangle grating and trapezia grating based SPR sensors among different methods.
4. Conclusion
In this work, sharp dips of higher diffraction orders are realized at first in the grating-based SPR sensor with angular interrogation. Moreover, we propose double-dips method (DDM) to further improve the sensitivity of the grating-based system greatly into more than 237 deg/RIU with good linearity and good χ factors of more than 95, better than the prism-based system in the same condition, and prove the roundly better performance of DDM than other methods through several character comparisons. At last, DDM remains its good performance in the gratings with profiles erring from rectangle. In the future work, we will do more research on the higher diffraction orders and try to make more use of them.
Acknowledgments
This research was supported by the National Key Basic Research Program of China 2006CB302905, the Key Program of National Natural Science Foundation of China 60736037, the National Natural Science Foundation of China No.10704070 and the Science and Technological Fund of Anhui Province for Outstanding Youth.
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