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MnO2-based dual channel surface plasmon resonance fiber sensor for trace glutathione and refractive index detection

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Abstract

Glutathione (GSH) plays vital role in human biological systems, so its rapid and sensitive detection is necessary for health condition monitoring. In this work, a simple structure for dual channel GSH and refractive index (RI) detection is proposed. By introducing Au-MnO2 thin film coating on the fiber surface for the first time, GSH solution would lead to the dissolution of MnO2, the change in GSH levels could be monitored over a short period in channel 2. For channel 1, ITO-Ag thin film is applied for RI change detection. After optimization, the GSH detection sensitivity reached about -2.361 nm/mM in the range of 0.005-50 mM, and the RI sensitivity reached 1704.252 nm/RIU in the range of 1.331-1.3895 RIU. Channel 1 could also put into GSH detection in the high concentration scale to enlarge the sensor’s range and 0.095 nm/mM of sensitivity is acquired within the range of 50-600 mM. With the presence of MnO2 film, the detection sensitivity increased 25.663 times. Neither channel interferes with the operation of the other. Proposed sensor provides stability, high selectivity and elevation in GSH detection sensitivity, which shows great potential for environmental and biological detection field and their applications.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Glutathione (GSH) is a vital material in human and animal cells, and it serves many functions in biological systems [1]. GSH is one of the most abundant in vivo antioxidant low-molecular-mass thiols, and occurs predominantly intracellularly in levels of 0.5 mM to about 10 mM [2]. Abnormal GSH level in cells may cause multiple diseases, so an easy and efficient way to detect GSH is quite important for medical development and diagnostic applications [3,4].

In recent years, many approaches for GSH detection have been proposed, such as high-performance liquid chromatography, electrochemistry, colorimetric assay, photoelectrochemistry, surface-enhanced raman scattering, and enzyme-linked immunosorbent assay [5]. Most of previous methods shows a low efficiency, long detection time and small detection ranges, which expand the cost and time for medical researchers. Yan et al. designed a fluorescence “turn off-on” nano-sensor based on a graphene quantum dots (GQDs)-manganese dioxide (MnO2) nanosheet, but the sensor had a detection range of only 0.5-10 µmol/L [5]. Another design of a carbon dots (CDs)-based sensor for the magnetic/fluorometric bimodal detection of GSH had a linear range of 1-200 µM in fluorescence mode and 5-200 µM in the magnetic resonance (MR) mode, but its fabrication process was complicated and time-consuming [6].

Surface plasmon resonance (SPR) is one of the most popularly used sensing mechanism, and a lot of work had been proposed to meet multiple sensing demands, including refractive index (RI), temperature, and magnetic field etc. Liu et al. proposed a highly sensitive temperature D-shape sensor based on SPR, which achieved a temperature sensitivity of -0.978 nm/°C between 25 °C and 100 °C [7]. Cheng et al. proposed a UV and temperature SPR sensor, which achieved the detection for high temperature sensitivity and UV radiation [8]. Iván et al. proposed a Fabry-Perot interference (FPI) sensor fabricated using a thin titanium dioxide (TiO2) film, which achieved high repeatability and response speed [9]. Mach-Zehnder Interferometer (MZI) sensor is commonly used for small-range detection for RI or temperature, which brings high detection limit, but it did not possess high sensitivity or range [10]. Although other sensing mechanisms possess many merits, but SPR has high detection sensitivity and easy fabrication, which makes it more suitable for present study.

Inspired by the researches above, MnO2 is found to be the key starting substance of GSH detection, and corresponding experimental protocol comes up based on the experience of our previous work [11]. In this paper, an MnO2-based SPR sensor exhibiting substantially improved detection performance through the utilization of MnO2 dissolution by GSH is proposed and realized. Specifically, a sensitivity of -2.361 nm/mM in the range of 0.005-50 mM was achieved, which is higher and over a wider range compared to existing approached. The RI detection capability is also integrated to realize a dual-channel SPR sensor with a sensitivity of 1704.252 nm/RIU in the range of 1.331-1.3895 RIU. The proposed sensor enables novel GSH sensing applications and medical researching, and also achieves the detection for GSH by SPR sensor in a relatively low level.

2. Material and equipment

The main part of proposed sensor is fiber, and the fibers used in this paper are thin core fiber (TCF) and the multi-mode fiber (MMF). The MMF used in the proposed structure has a core diameter of 105.0 µm, and an outer diameter of 125.0 µm. The TCF has a core and outer diameter of 3.8 and 125.0 µm, respectively. The two sensing regions are consisted of TCF, and each section of TCF is chosen in a proper length of 12 mm, and so as the length of MMF in the middle. When light transmit from MMF and enter the splicing surface of MMF-TCF, the light inside the MMF’s core would flow into the cladding of TCF and excite cladding modes due to the large core size difference. The cladding modes which were excited at the MMF-TCF surface would be captured by the Au film coated on the TCF to excite SPR effect [12]. The TCF and MMF were acquired from Yangtze Optical Fibre and Cable Joint Stock Limited Company, in order to ensure the uniformity of the proposed fiber structure. Other types of fibers, such as hollow core fiber(HCF) and photonic crystal fiber(PCF) also possess excellent performance, but they are relatively expensive to acquire, which would increase the cost for large-scale preparation. All the fibers were spliced by fusion splicer (Japan, Fitel, S179), and all the thin film structure are fabricated using magnetron sputtering machine (HF Kejing, VTC-16-SM). The choice in fiber type and the splicing length came from our previous works, and the setup of experimental instruments remained the same.

An iridium-tin-oxide (ITO)/Ag film (with thicknesses of 15 nm ITO and 50 nm Ag) was fabricated for RI sensing. The relative discuss on the film thickness is shown in many previous works, so the optimized parameter is chosen properly [13]. NaCl solutions of different levels were prepared to validate the device’s RI detection capability, and the RI of the solution were calculated by using an Abbe refractometer. The Au/MnO2 film was used to detect GSH, with thickness of Au was set to 50 nm, which is chosen in many previous study [14,15]. GSH solution is used to dissolve MnO2 film, and it is purchased from Aladdin China. The light source and the spectrometer are used in this paper, and they were a halogen light source (Ocean Insight, HP-2000LL, 400-2500 nm) and a spectrum analyzer (Ocean Insight,SB2000 + VIS-NIR, 350-1000 nm).

3. Methods and principle

In the SPR sensor proposed in this paper, the transmitted energy spills into the cladding of the TCF from the MMF, which would generate huge evanescent field [16]. When the phase matching condition is met between it and the surface plasmon wave, then the SPR phenomenon is excited. The phase matching condition is shown as follows [17]:

$$\frac{{2\pi }}{\lambda }\sqrt {{\varepsilon _0}} \textrm{sin}\theta = \frac{{2\pi }}{\lambda }\sqrt {\frac{{{\varepsilon _1}{\varepsilon _2}}}{{{\varepsilon _1} + {\varepsilon _2}}}} $$
where λ indicates the light wavelength, and $\theta $. is the angle of incident light. ε0 indicates the dielectric constant of the fiber medium, which ε2 shows the dielectric constant of the surrounding environment. ε1 is the real part of dielectric constant of the metal film [18]. Moreover, while the ε1 and ε2 are different in two channels, so the resonance wavelength would be separated, allowing the dual channel operation of the sensor.

The Ag thin film is popular as a metal material to excite the SPR, as its resonance wavelength is generally smaller than that of the Au, so it can be used in smaller wavelength to detect RI or humidity in different design scenarios. The permittivity of the silver εAg(ω) is described by the following Drude model [19]:

$${\varepsilon _{A\textrm{g}}}(\omega ) = {\varepsilon _\infty } - \frac{{\omega _p^2}}{{\omega (\omega + i{\omega _\tau })}}$$
where ε∞ = 9.84, ωp = 1.36 × 1016, and ωτ = 1.018 × 1014, ω represents the angular frequency. As for the ITO, which has many merits in the SPR sensing field, it elevates the sensitivity of Ag film with ITO coated inside. And the relative permittivity of ITO is given by [20]:
$$\varepsilon = {\varepsilon _\infty } - \frac{{\omega _p^2}}{{{\omega ^2} + i\omega \Gamma }}$$

In Eq. (3), ε means the dielectric constant of ITO, ε is the high frequency dielectric constant, ωp is the plasma frequency, and Γ is the electron scattering rate, ω represents the angular frequency. And the complex dielectric function of the gold layer εAu(ω) can be represented by the Drude-Lorentz formula [21]:

$${\varepsilon _{A\textrm{u}}}(\omega ) = 1 - \frac{{\omega _p^2}}{{\omega (\omega + i{\omega _c})}}$$
where ωp = 1.36 × 1016 rad/s and ωc = 1.45 × 1014 rad/s, and ω represents the angular frequency.

The basic theory of dissolution on the MnO2 film is shown in Fig. 1. As we can see, the GSH would react with MnO2 at acidic condition, and MnO2 would generate GSSG and Mn2+, which proves that MnO2 thin film would dissolve when the GSH is added above its surface. With the presence of GSH, the MnO2 film would be gradually dissolved by the increasing concentration of GSH. To illustrate this effect more clearly, the MnO2 film is coated on a blank glass slide in Fig. 2(a). After 5 minutes waiting, the brown MnO2 film would dissolve into a relatively light color, which indicates the fade of MnO2 in Fig. 2(b).

 figure: Fig. 1.

Fig. 1. The basic reaction equation and demonstration.

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 figure: Fig. 2.

Fig. 2. (a) Using glass slide to demonstrate the dissolution and add GSH solution, (b) with the concentration increasing, surface of slide gradually changes into transparent.

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To determine the dissolution condition, a smart phone software was introduced to identify the RGB status of the color shown on the glass slide indicators. By placing the beacon dot on the middle of each solution section, software would identify the RGB value in Fig. 3 (a). Moreover, the R/G values are better indicators of lightness, so the linear fit of the R/G curve in Fig. 3 (b) would indicate that the MnO2 thin film would dissolve at first, and the color lightness would remain nearly unchanging after 50 mM. In conclusion, this color recognition picker app could identify the dissolution process during the increasing of GSH solution, and help the researchers to determine the detection range. The identifier app could only roughly tell the tendency of the dissolution in MnO2 film, and there may be other interference to affect the results in this method. The precise result requires better detection techniques to complete the sensing of GSH solution.

 figure: Fig. 3.

Fig. 3. (a) Using smart phone software to identify the RGB level of the color on glass slide, (b) the relationship between R/G and GSH concentration.

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After introducing the chemical reaction on which the proposed sensor is based, the sensor structure is shown in Fig. 4(a). First is the TCF, which is coated with an Au-MnO2 film; it is designated as channel 2 and is used for the detection of GSH. By utilizing the light energy propagating inside the cladding of TCF from the MMF, great SPR response can be achieved through an MMF-TCF-MMF structure [22,23]. For the other sections of the proposed sensor, the ITO thin film is coated inside the Ag film to excite the SPR in a more sensitive way, this section designated as channel 1 to detect RI [24]. Moreover, the sensor deployment is shown in Fig. 4(b), where the sensing structure is connected to the light source and the spectrometer, where the final spectrum would be displayed on computer. By introducing two separated liquid chamber and placing the sensing region inside them, the spectrum on computer would change with the adding of target sensing matter.

 figure: Fig. 4.

Fig. 4. (a) Dual channel SPR sensor structure and film layout, (b) experimental design and setup for detection.

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4. Experiments and results

In this part, the degree to which GSH affects the heavy metal film is first investigated, and especially if the Ag or Au film is sensitive to GSH itself. Before that, the RI value of different GSH concentration should be identified by Abbe refractometer, as shown in Fig. 5. After that, GSH solution was tested by ITO/Ag film to see the response in Fig. 6 (a). Compared to the RI test in Fig. 6 (b), the detection for GSH is less sensitive than that of NaCl, as illustrated by the corresponding curves of Fig. 7 (c). Sensitivity of the detection for GSH dropped from 1704.252 nm/RIU to 1624.40 nm/RIU, which proves that this thin film structure has no specific selectivity for GSH. The decrease in sensitivity is most likely caused by the macromolecular properties of GSH, which affect the dispersion in solution. About the repeatability of channel 1, it was tested in Fig. 6 (c), which proves its good repeatability. When the RI is increased or decreased, its RI sensitivity does not change substantially, and the corresponding resonance wavelengths remain relatively stable. In Fig. 6. (d), the temporal stability is discussed, and it is evident that its resonance wavelength remained stable for at least 40 minutes.

 figure: Fig. 5.

Fig. 5. The linear fit of the RI value for different concentration of the GSH.

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 figure: Fig. 6.

Fig. 6. (a) The reaction of ITO-Ag film for the GSH solution, (b) the reaction of ITO-Ag film for the RI detection, (c) the repeat test about channel 1, (d) the time stability for channel 1.

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 figure: Fig. 7.

Fig. 7. (a) The reaction of Au film for the GSH solution, (b) the reaction of Au film for the RI detection, (c) the sensitivity comparison for the data above.

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After investigating the sensing properties of ITO/Ag film for the GSH, it’s more necessary to see how Au film response to the GSH solution. Then 50 nm of Au film is coated on the fiber surface to form the sensor structure, and the investigation results are shown in Fig. 7 (a). Moreover, the Au film is also used to detect RI in Fig. 7 (b), and the sensitivity comparison are shown in Fig. 7 (c). The sensitivity did not change substantially during GSH and RI detection, and these two comparisons in Fig. 6 and Fig. 7 show that there is no apparent selectivity for GSH on both ITO/Ag and Au film. Therefore, it is vital to investigate improved methods for GSH level detection with sufficiently high sensitivity and the capability to detect trace levels. As it was mentioned previously, MnO2 thin film is a perfect material for GSH sensing, so it was introduced inside the SPR sensor system. Before the experimental trial, proper simulation on how the MnO2 film would affect the SPR should be done. COMSOL Multiphysics 5.2 had been used to create a 2D cross section of the fiber in sensing region, and the corresponding electric field distribution is shown in Fig. 8. (a). Moreover, the confinement loss of the fundamental mode is discussed by altering the thickness of the MnO2 film. As evident from Fig. 8. (b), the resonance wavelength of curve has a red shift while increasing the thickness of MnO2 film. To meet the demand of wavelength modulation, 5 nm of MnO2 film was chosen. The confinement loss was also elevated by the increasing thickness of MnO2, and the peak width widen with it.

 figure: Fig. 8.

Fig. 8. (a) The electric field distribution of fiber 2D cross section. (b) simulation of different MnO2 film thickness.

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As shown in Fig. 9, with the MnO2 film deposited on the Au surface, the resonance wavelengths first showed a sign of blue shift as the level of GSH gradually increased, but after the 50 mM level, this trend changed into slight red shift, as shown in Fig. 9(b). Observing this phenomenon, and combining the dissolution status that was discussed in Fig. 3, it can be concluded that dissolution occurred before 50 mM and beyond that point the increase of the RI or GSH level causes the wavelength to shift back, but at a slower rate. An additional issue is that the initial resonance wavelength is small, and it is likely to interfere with the other channel. Thus, wavelength modulation is necessary for channel 2, and the film thickness of MnO2 is an obvious choice to achieve this. To bring the resonance wavelength to a bigger scale, the thickness of MnO2 is successively increased from 4 nm to 5 nm at 0.5 nm intervals. From Fig. 9 (c)-(f), we can conclude that the initial resonance wavelength shows a red shift with the increasing of film thickness, and the detection range still remain the same. Moreover, the detection sensitivity also increased from -1.68 nm/mM to -2.67 nm/mM. Such an increase of the sensing wavelength and sensitivity enables the fulfillment of the design purpose of the dual channel sensor. The comparison on how the thickness of MnO2 affect the GSH sensitivity and the starting wavelength point is shown in Fig. 9 (g). The starting point would show a red shift once the thickness increased, which fit the pattern of the simulation in Fig. 8 (b).

 figure: Fig. 9.

Fig. 9. (a) Au-MnO2 film (Au-50 nm, MnO2-4 nm) at the response for GSH solution, (b) linear fit for resonance wavelength, (c) Au-MnO2 film (Au-50 nm, MnO2-4.5 nm) at the response for GSH solution, (d) linear fit for resonance wavelength, (e) Au-MnO2 film (Au-50 nm, MnO2-5 nm) at the response for GSH solution, (f) linear fit for resonance wavelength, (g) the starting point and the sensitivity vary with the thickness of MnO2 film.

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After the separate sensing experiments are introduced, the trial for dual channel sensing should be carried out. In Fig. 10, sensing for channel 1 and channel 2 are shown and the linear fits of wavelengths are also demonstrated in Fig. 10 (b) and (d). In Fig. 10 (a), GSH is detected within the range of 0.005-50 mM, and the second channel shows a sign of blue shift trend, and in Fig. 10 (b), the calculation of the corresponding sensitivity for both channels are calculated, the GSH-detection sensitivity reached -2.361 nm/mM with the other unoccupied channel staying relatively stable, and its limit of detection (LOD) was calculated as 4.43 mM. In Fig. 10 (c), the RI was also detected in the same range of 1.331-1.3895 RIU, and the sensitivity for channel 1 reached 1704.252 nm/RIU, with an LOD of 0.0028 RIU. Both channels remained stable while unoccupied and the two sensitivity ranges differed by a factor of at least 13, so the proposed dual channel sensor could be considered stable. As for the elevation on sensitivity, comparison on Au and Au-MnO2 film on the detection for GSH is shown in Fig. 11, where it is shown that the introduction of the MnO2 film causes an average sensitivity increase of 25.663 times. This means that the sensor achieves very good sensing performance with a simple design and easy fabrication process.

 figure: Fig. 10.

Fig. 10. (a) Two channels working together with channel 2 detecting GSH, (b) the linear fit of the resonance wavelength of two channels, (c) two channels working together with channel 1 detecting RI, (d) the linear fit of the resonance wavelength of two channels.

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 figure: Fig. 11.

Fig. 11. The sensitivity elevation after introducing the MnO2 film.

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The channel 2 is used for GSH detection in the range of 0.005-50 mM, and channel 1 is designed for general RI detection. As for the usage scenario of the proposed sensor, channel 1 could also be used to detect GSH, but only in a wide range and high concentration solution. According performance is shown in Fig. 12, and it was tested in 0-600 mM, where it has a sensitivity of 0.095 nm/mM. Good linearity is acquired in such a big test range, and although the sensitivity is lower than channel 2, but it possesses wide detection range, which could meet various demand in GSH detection.

 figure: Fig. 12.

Fig. 12. (a) The GSH detection performance for channel 1, (b) linear fit of the wide range of GSH solution.

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Tables Icon

Table 1. Comparison About Different Works For GSH Sensing

In the channel 1’s operation detection range of GSH (0.005-50 mM), its refractive index (RI) is low as water and it’s undetectable for the RI channel, which is why the channel 2(GSH sensing) is brought up. For higher range of GSH solution, the RI of it is higher to put it into channel 1(RI sensing) for detection. In brief, range of 0.005-50 mM is just for channel 2, but not for entire sensor. The proposed sensor could detect the GSH solution denser than 50 mM by channel 1. Even though channel 1’s response was tested during the above experiments using NaCl solutions, to prove it has the capability to detect higher levels of GSH, there is no reason to limit its operation to NaCl or GSH solution analysis. Besides, the comparison of this work with other previous work on GSH detection had been illustrated in Table 1, where the proposed sensor in this paper exhibits wider range and high sensitivity.

The selectivity of proposed sensor was analyzed through a comparison of GSH with other possible interference factors. And the specific response for each material was recorded, which is shown in Fig. 13. Several common metal ions and the macromolecular substance like glucose and L-Cysteine has been introduced. All of them were made into same solution level of 3 mM, and each test was guaranteed to be separated and isolated from all the interference. As the result shown in Fig. 13, it is evident that the proposed sensor shows good selectivity performance, which can support it to work in complicated environment.

 figure: Fig. 13.

Fig. 13. The selectivity test for each interference solution at the concentration of 3 mM.

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The application of the proposed sensor could be extended into the health detection and environmental monitoring, so different kinds of base solutions were tested for interference, and the results are shown in Fig. 14. Tap water is acquired from the toilet nearest to the lab, and the lake water is collected from the lake in Nanhu Park, Shenyang. As for the river water, it’s collected from Hun River, Shenyang. The lake water and river water had been handled with a simple filtration to avoid the large size impurities. The human blood serum is provided by the volunteers, and it’s fabricated by the steps as [27].

 figure: Fig. 14.

Fig. 14. The anti-interference test for other base solutions with 3 mM of GSH.

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For the tap water-based solution test, the response decreased a little and it would possibly because of the bleaching powder inside tap water and the interference ions such like Mg2+. To avoid large shift affected by the RI difference, the serum concentration was chosen as 100:1 to acquire proper GSH response. Above all, the proposed sensor possesses high stability which shows potentials for both blood test and environmental monitoring.

5. Conclusions

GSH level detection has great potential in human immune system study, and the development of simple and rapid detection methods is a current trend. In this work, a simple structure for dual-channel GSH and refractive index (RI) detection is proposed. By introducing Au-MnO2 thin film coating on the fiber surface for the first time, GSH solution causes the dissolution of MnO2, allowing the determination of the GSH level as a function of the resonance wavelength. After optimization, the GSH detection sensitivity reached about -2.361 nm/mM in the range of 0.005-50 mM, and the RI sensitivity reached 1704.252 nm/RIU in the range of 1.331-1.3895 RIU. By utilizing two channels, 0-600 mM of GSH solution could be detected. A stable sensor performance was achieved and the two channels remained isolated. The proposed sensor is robust and offers increased GSH detection sensitivity, and its wide detection range enables an increased number of research applications.

Funding

111 Project (B1009); Fundamental Research Funds for the Central Universities (N160404009, N170405007); National Natural Science Foundation of China (11604042, 61775032).

Acknowledgments

Thanks everyone who had contributed to this article.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (14)

Fig. 1.
Fig. 1. The basic reaction equation and demonstration.
Fig. 2.
Fig. 2. (a) Using glass slide to demonstrate the dissolution and add GSH solution, (b) with the concentration increasing, surface of slide gradually changes into transparent.
Fig. 3.
Fig. 3. (a) Using smart phone software to identify the RGB level of the color on glass slide, (b) the relationship between R/G and GSH concentration.
Fig. 4.
Fig. 4. (a) Dual channel SPR sensor structure and film layout, (b) experimental design and setup for detection.
Fig. 5.
Fig. 5. The linear fit of the RI value for different concentration of the GSH.
Fig. 6.
Fig. 6. (a) The reaction of ITO-Ag film for the GSH solution, (b) the reaction of ITO-Ag film for the RI detection, (c) the repeat test about channel 1, (d) the time stability for channel 1.
Fig. 7.
Fig. 7. (a) The reaction of Au film for the GSH solution, (b) the reaction of Au film for the RI detection, (c) the sensitivity comparison for the data above.
Fig. 8.
Fig. 8. (a) The electric field distribution of fiber 2D cross section. (b) simulation of different MnO2 film thickness.
Fig. 9.
Fig. 9. (a) Au-MnO2 film (Au-50 nm, MnO2-4 nm) at the response for GSH solution, (b) linear fit for resonance wavelength, (c) Au-MnO2 film (Au-50 nm, MnO2-4.5 nm) at the response for GSH solution, (d) linear fit for resonance wavelength, (e) Au-MnO2 film (Au-50 nm, MnO2-5 nm) at the response for GSH solution, (f) linear fit for resonance wavelength, (g) the starting point and the sensitivity vary with the thickness of MnO2 film.
Fig. 10.
Fig. 10. (a) Two channels working together with channel 2 detecting GSH, (b) the linear fit of the resonance wavelength of two channels, (c) two channels working together with channel 1 detecting RI, (d) the linear fit of the resonance wavelength of two channels.
Fig. 11.
Fig. 11. The sensitivity elevation after introducing the MnO2 film.
Fig. 12.
Fig. 12. (a) The GSH detection performance for channel 1, (b) linear fit of the wide range of GSH solution.
Fig. 13.
Fig. 13. The selectivity test for each interference solution at the concentration of 3 mM.
Fig. 14.
Fig. 14. The anti-interference test for other base solutions with 3 mM of GSH.

Tables (1)

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Table 1. Comparison About Different Works For GSH Sensing

Equations (4)

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2 π λ ε 0 sin θ = 2 π λ ε 1 ε 2 ε 1 + ε 2
ε A g ( ω ) = ε ω p 2 ω ( ω + i ω τ )
ε = ε ω p 2 ω 2 + i ω Γ
ε A u ( ω ) = 1 ω p 2 ω ( ω + i ω c )
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