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Sensing enhancement ammonia gas sensor based on a hybrid film fiber

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Abstract

A sensing enhancement sensor based on hybrid film fiber has been proposed to detect ammonia. The hybrid film coated on the MMF-SMF-MMF (Multimode Fiber–Single-mode Fiber–Multimode Fiber) structure is composed of single-walled carbon nanotubes with carboxylic acid groups (SWCNTs-COOH) self-assembled film and the silver film that was used to excite surface plasmon polariton (SPP) which contribute to enhancing the sensitive for refractive index (RI). The presence of free carboxylic acid functional groups and large surface area on the SWCNTs-COOH leads to high adsorption and selectivity toward amine compounds. The sensor works under a wavelength modulation scheme. And the resonance wavelength showed a red shift with an increase of the effective RI of the SWCNTs-COOH self-assembled film affected by ammonia concentration. The experimental results show that the sensor coated with hybrid film has high sensitivity and selectivity to ammonia gas. The proposed sensor is linearly responsive to ammonia concentration in the range 0 - 30 ppm, with a maximum sensitivity of 0.8 nm/ppm, the resolution 0.375 ppm, and the measured response 30 s, respectively. Finally, the sensor also has the advantages of simple structure and compact size, excellent stability, and low cost.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Ammonia (NH3) is a common colorless air pollutant, which is toxic and flammable [1]. When people are exposed to high levels of NH3, symptoms such as tearing, difficulty breathing and dizziness could be occurred [2,3]. To ensure occupational health, the limit concentrations of ammonia in farming areas and industrial workspaces need to be controlled at about 20 ppm because ammonia is also highly toxic at low concentrations [4,5]. Meanwhile, Ammonia is also widely used in our daily life. Large amounts of ammonia are used as agricultural fertilizer, synthetic fibers, plastics, and explosives [6]. Ammonia is also used as a biomarker for the detection of relevant reference indicators, such as human health and diseases, and the freshness of food [7,8]. Therefore, the research of NH3 sensors and test systems has a very urgent need and wide application [9].

Ammonia gas sensors based on different methods have been reported such as potentiometric electrodes [1012], semiconducting metal oxide [1315], surface acoustic wave [16], and optical fiber [17,18]. Compared with these technologies, optical fiber gas sensors have attracted much attention due to their small size, low-cost fabrication, long lifetime, immunity to electromagnetic interference, and capability for remote sensing [19,20]. To improve the performance of fiber gas sensors, several structures are proposed such as tapered fiber [21,22], etched fiber [23,24], side polished fiber [25], microspheres and micro-knots [3,26], and hetero-core structure fiber [27], which support a strong interaction between evanescent wave and sensing layer coated on the optical fiber. However, it is difficult to improve the performance with just varying fiber structural due to the limitation of the diffraction limit. Therefore, different functional materials are being explored to improve the sensing performance. Functional materials are the core of the ammonia gas sensor, which largely determines the sensitivity, response/recovery time, and gas selectivity of the sensor.

At present, several kinds of functional materials have been reported, such as semiconducting metal oxides [28], carbon nanomaterials [29,30], conductive polymer [31], and composite materials (containing more than two materials) [32,33]. Among these different materials, the low-dimensional carbon nanomaterials like carbon nanotubes and graphene have become the preferred material of the next generation of autonomous sensing technology for providing a higher specific surface area for gas adsorption because a large number of atoms are exposed to the gas environment, which helped to improve the response sensitivity of the sensor [3436]. Carbon nanotubes are hollow structures made of graphene sheets that are curled up at specific and separate angles [37]. Therefore, compared with graphene, the film formed by a large number of carbon nanotubes has more molecules interacting with gas molecules. In addition, the introduction of functional groups like -COOH on the surface can improve the absorption and selection of a particular gas [27]. Gas sensor based on carbon nanotube has large detection range and detection limit, even for a single gas molecule detection [38], the detecting performance of which is superior to the traditional gas sensors. In the past few years, the carbon nanotube is one of the most popular carbon nanomaterials in the development of a new type of gas sensor [39,40]. Thus, we selected single-walled carbon nanotubes with carboxylic acid groups (SWCNTs-COOH) as the functional materials for the proposed sensor due to the presence of free carboxylic acid functional groups and large surface area, which leads to high adsorption and selectivity toward amine compounds.

Moreover, for further enhance the interaction evanescent wave and sensing layer to improve sensitivity, surface plasmon polariton (SPP) has received extensive attention. SPP is a kind of electromagnetic wave propagating at the metal-dielectric interface, which is shown to be sensitive to environmental RI changes. In the optical fiber, when the wave vectors of the evanescent wave (EW) and the SPP are identical, the coupling resonance occurs, named surface plasmon resonance (SPR) which was manifested as a wave trough in the transmission spectrum and the wave trough shift after RI changes [41,42]. For gas sensors, the RI of the sensing layer changes after adsorption of the gas molecules, leading to wavelength shifts. The sensing performance will be enhanced by using the SPR technique. At present, to the best of our knowledge, most studies report impedance based investigation of NH3 detection [32,34,35]. The rare optical fiber sensors coated with SWCNTs are studied by measuring the change in output intensity from the optical fiber [30], which are not accurate enough to characterize the performance of sensors. During the last two decades, most of the research efforts on SPR-based sensors employed different kinds of sensing layers including reduced graphene with high sensitivity of 0.9 nm/ppm, more than ten times that of sensors not using SPR technology [43]. However, SWCNTs-based gas sensors relying on the wavelength modulation scheme using the surface plasmon resonance (SPR) technique have not been reported.

Here, we combine SWCNTs-COOH self-assembly film with the SPR technique based on the metal film coated on the MMF-SMF-MMF (Multimode Fiber–Single-mode Fiber–Multimode Fiber) structure to improve ammonia gas sensing performance. The sensor works under the principle of wavelength interrogation technique. And the resonance wavelength of SPR shifts with the effective RI of the SWCNTs-COOH self-assembled film affected by ammonia gas concentration. The experimental results show that the sensor responds better to NH3 other than N2, CO2, acetone, and alcohol. The maximum sensitivity of the sensor is 0.8 nm/ppm, while the resolution and measured response times are 0.375 ppm and 30 s, respectively. The sensor shows excellent character particularly in achieving good gas response at room temperature, high sensitivity, and selectivity to ammonia molecules.

2. Sensing principles

The sensor coated with metal film and the self-assembled film is based on the MMF-SMF-MMF structure shown in Fig. 1(a). The SMF with a core diameter of 9 µm is spliced in the middle of two MMF with a core diameter of 62.5 µm, which lead to most of the core mode leak into the cladding at an interface of the MMF and SMF as illustrated in Fig. 2(a). The Finite Element Method (FEM) is used to evaluate the transmission mode of the MMF-SMF-MMF structure. In the simulation, the structure is modeled by an equivalent planar waveguide model. The size of the structure and simulation result are shown in Fig. 2(b). We adjust the view ratio of X-axis and Y-axis to 1:60 due to the aspect ratio of the model being too large. We can see that most of the modes from the core of the MMF leak into the clad of the SMF. Such mode leakage generates an evanescent field in the course of cladding mode development when reflecting at the boundary surface between the cladding and the surrounding circumstances [44]. Meanwhile, if there is a metal film outside the cladding, SPP is excited and coupled with EW to form SPR, which is similar to Kretschmann-Raether's method. The schematic diagram is shown in Fig. 2(c)(In order to show the effect of the SPP and save computing resources, we have reduced the size of the optical fiber to obtain a schematic diagram). The propagation constant of the EW and SPP can be respectively expressed as [45]:

$${\beta _{ew}}\textrm{ = }\frac{{\textrm{2}\pi }}{\lambda }\sqrt {{\varepsilon _0}} \sin \theta ,$$
$${\beta _{SP}}\textrm{ = }\frac{{\textrm{2}\pi }}{\lambda }\sqrt {\frac{{{\varepsilon _\textrm{m}}{\varepsilon _d}}}{{{\varepsilon _\textrm{m}} + {\varepsilon _d}}}} .$$
where θ, ɛ0, ɛm, and ɛd are the incident angle, permittivities of the cladding, metal film, and medium, respectively at a given wavelength λ. In the optical fiber, there are many different angles for light with different wavelengths that satisfy total reflection. However, the only light that meets certain conditions can excite SPP. When βsp =βew, the SPR effect will be excited. And the value of the propagation constant corresponds to the λ is the resonance wavelength. From Eq. (2), we observed that the propagation constant of SPP only depends on the dielectric permittivity of the metal and the dielectric. Therefore, the small change of the RI of the medium adjacent to the metal film will produce a measurable shift of the resonance wavelength. When the gas molecules are attached to the surface of the fiber, the RI of the sensing layer changes, leading to wavelength shifts. At the interface between cladding of SMF and metal film, we build the model shown in Fig. 2(d) according to Kretschmann-Raether's method to generate the SPP. The materials are fiber cladding, metal film, and medium, respectively. Perfect Matched Layer (PML) boundary condition is used for the top boundaries. The left and right sides are the periodic boundary conditions, and the light is incident from the cladding obliquely. At the interface between the cladding and the metal, a part of the energy is lost, resulting in a reflection valley when the light reflects back to the cladding layer. Silver is well known as an SPR active metal, which gives better sensitivity with the wavelength interrogation techniques with shows a sharper resonance spectrum than other metals like gold [46]. Thus, we selected silver as the metal material for the SPR sensing. Figure 2(e) illustrates theoretically SPR spectra for different RI (1.333, 1.343, 1.353, 1.363, 1.372, and 1.38). We took the wavelength at the reflection valley as the resonance wavelength corresponding to the measurement of the refractive index. Additionally, the increase of the RI to be detected causes the resonance wavelength to shift toward a longer wavelength. The calculated result illustrated the sensitivity of the structure for RI could reach 3800 nm/RIU. SPR provides the possibility of the high sensitivity of the sensor for self-assembled carbon nanotube film which has higher adsorption and selectivity for ammonia molecules.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the proposed sensor.

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 figure: Fig. 2.

Fig. 2. (a) Schematic diagram of the side view in MMF-SMF-MMF structure; (b) Simulation of mode in MMF-SMF-MMF structure without Ag film. The core of the SMF and MMF are 9 µm and 62.5 µm respectively, and the cladding of the SMF and MMF are 125 µm. The length of the SMF is 10 mm. The refractive index of core and cladding are 1.45 and 1.44 respectively. The view ratio of X-axis and Y-axis is 1:60, and the view ratio of X-axis and Y-axis of the insert is 1:1 ; (c) Schematic diagram of the mode in MMF-SMF-MMF structure with Ag film; (d) SPP mode, the thickness of Ag film is 40 nm; (e) SPR wavelength as a function of refractive index.

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3. Experiment and discussion

3.1 Fabrication of the metal film on the MMF-SMF-MMF

The hybrid film on the surface of the fiber gas sensor is made in two steps: metal film and self-assembled film. And Ag film for SPR sensing is coated on the surface of the cladding of the SMF. The plating method is ion beam sputtering, and the thickness of the silver film is 45 nm. Finally, the device coated with Ag film is put into a vacuum oven to anneal for two hours at 200°C to ensure that the film much smoother. The sensing section is fixed in a custom plexiglass measuring box (volume: 140 L). This method not only guarantees good results but also has the advantages of simple operation and low cost.

According to the sensing principle of optical fiber SPR, we first conducted experiments to verify the refractive index sensing performance of the sensor. We used a halogen lamp (Thorlabs, SLS201L,) as the light source that provides a wide spectrum from 360 nm to 2600 nm to connect the sensing part. Then the spectral data will be transmitted to the computer with the spectrometer (Ocean Optics USB4000, 200–1100 nm) as shown in Fig. 3. In order to avoid unfavorable fluctuation, the sensor region was firmly fixed on a glass slide. Before the experiment, we prepared NaCl solutions with mass concentrations of 0%, 5%, 10%, 15%, 20%, and 25% respectively. The corresponding RIs are 1.333, 1.343, 1.353, 1.363 1.373, and 1.38 respectively [47] at a room temperature of 25°C. We first measured and recorded the transmission spectrum of the sensor as the reference spectrum before immersing it in the solution. Then the transmission spectrums after the sensor immersed in NaCl solutions corresponding to different RIs are also measured and recorded. To ensure the spectrums recovered as before, the sensor was rinsed for 1 min by deionized water after each measurement. Finally, the measured spectrum was divided by the reference spectrum to get the normalized spectrum. The characteristics of the normalized spectrum are shown in Fig. 4. We take the wavelength at the lowest point of the normalized spectrum as the resonance wavelength.

 figure: Fig. 3.

Fig. 3. Schematic diagram of the experimental setup.

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 figure: Fig. 4.

Fig. 4. (a) SPR spectra of the MMF-SMF-MMF structure coated with Ag film, (b) Variation of SPR resonance wavelength with different values of RI

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Figure 4(a) illustrates that the resonance wavelength shifts toward the longer wavelength with the increasing RI, which is in agreement with the theoretical calculation illustrated in Fig. 2(b). From Fig. 4(b), the quantity of resonance wavelength shift was observed to be 136 nm for the RI change span of 0.047, from 1.333 to 1.38 RI, which can be a basis to determine the measurement resolution of the RI. The maximum spectral sensitivities derived from the wavelength shift curve were calculated to be 4250 nm/RIU for an RI of 1.38. Another important parameter to quantify the sensing performance of a device is the resolution. The resolution is defined as the smallest measurable physical parameter change, which can be expressed as R / S, where R is the resolution of the spectrometer and S is the sensitivity of the sensor. The obtained detectable resolution for RI of 1.38 is 7.05× 10−5 RIU, with a wavelength resolution of the spectrometer of 0.3 nm. SPR provides the possibility of high sensitivity for the subsequent ammonia detection. Then we would fabricate the SWCNTs-COOH self-assembly films on the surface of the MMF-SMF-MMF structure coated with Ag film.

3.2 Fabrication of the SWCNTs-COOH self-assembly films

The principle of the SWCNTs-COOH self-assembly films is electrostatic interaction. And the surface of the sensor was deposited with poly (acrylic acid) (PAA), poly (allylamine hydrochloride) (PAH), and SWCNTs-COOH sensing film for the detection of ammonia gas. Briefly, we obtained SWCNTs-COOH self-assembly films by layer by layer (LBL) assembling technique using a procedure published by Xinyue Huang [27]. PAH (98% average Mw = 15000, powder) and PAA (Mw=450,000, powder) were dissolved in deionized water to obtain a solution of 2 mg/ml respectively. SWCNTs-COOH with an outer diameter of 1–2 nm and a length of 5–30 um and PAA (1:1 wt/wt) were dispersed in deionized water to give a total concentration of 2 mg/ml.

The self-assembly process is shown in Fig. 5. It is known that PAH and PAA are the typical positively charged and negatively charged polyelectrolytes, respectively. In this study, the assembling was initiated by the positively charged PAH solution. The MMF-SMF-MMF structure was immersed into the PAH solution for 10 min to obtain the positively charged membranes. After 1 min rinsing by water to remove the superfluous PAH, the fiber structure with a positively charged membrane was immersed into the negatively charged PAA solution for 10 min to obtain the negatively charged membrane. Then the sensor was immersed into the PAH and PAA+ SWCNTs-COOH blended solution alternatively to form the function film. Then the fiber structure was rinsed for 1 min by deionized water to remove the superfluous molecules and dried with nitrogen. After repeating this step 6 times, we can obtain the (PAH/PAA) + [PAH/ (PAA + SWCNTs-COOH)]6 multilayer film. Finally, the fiber structure was placed into the oven to dry under 60 °C for 10 h. After drying, the (PAH/PAA) + [PAH/ (PAA + SWCNTs-COOH)]6 multilayer film was characterized by a scanning electron microscope (SEM) as shown in Fig. 6. We can observe in Fig. 6(a) (It’s not easy to focus, so we obtained SEM image at a certain angle) that the thickness of the prepared multilayer film is about 250 nm. Figure 6(b) shows the surface of the multilayer film that a large number of carbon nanotubes gathered on the surface of the film, forming many gaps in the filamentous structure. Therefore, the existence of SWCNTs-COOH increases the specific surface area of the film and makes the ammonia gas fully in contact with the film, which provides necessary conditions for the detection of ammonia.

 figure: Fig. 5.

Fig. 5. The schematic illustration of the self-assembly process.

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 figure: Fig. 6.

Fig. 6. The SEM images of self-assembled films (a) thickness, (b) surface.

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3.3 Detection performance of hybrid film for ammonia gas

The measurements were carried out in an environment with a constant temperature and humidity. The proposed sensor coated with the hybrid film was tested with different concentrations of ammonia gas. Ammonia gas detection is carried out in a gas chamber with a volume of 140 L as shown in Fig. 3. In the experiment, gas concentration is controlled by ammonia evaporating (NH4OH, 25%, analytical purity) into the gas chamber for sensing. The NH3 concentration can calculate by using Eq. (3) [48].

$${C_{ppm}} = \frac{{{V_{\mu L}} \times {D_{gm{L^{ - 1}}}}}}{{{M_{gmo{l^{ - 1}}}} \times {V_{mL}}}} \times 22.4 \times {10^6},$$
where Cppm, VµL, DgmL−1, VmL, and Mgmol−1 are the required gas concentration, the volume of the liquid analyte, density of the liquid analyte, volume of the gas chamber, and molecular weight of the liquid analyte, respectively. Then we begin the experiment for the detection of NH3 concentration. In particular, it is worthing to note that the reference spectrum is the transmission spectrums without the SWCNTs-COOH self-assembly films. Then we measured and recorded the transmission spectrums corresponding to different concentrations of NH3 ranging from 0 ppm to 1000 ppm calculated by using the Eq. (3). To ensure the spectrums recovered as before, the sensor was treated with pure N2 after each measurement for different concentrations. Finally, we obtained the normalized transmission spectrum by dividing the measurement spectrum from the reference spectrum. Figure 7(a) shows the normalized transmission spectrum corresponding to the NH3 concentration range from 0 to 1000 ppm and the inset shows the zoomed section of the NH3 concentration from 0 to 30 ppm. It may be noted that with the increase of NH3 concentration, the resonance wavelength shows a monotonic red-shift. When the NH3 diffuse into the gas chamber, the chemisorption will undergo between ammonia molecules and the SWCNTs-COOH, which thus causes an increase in the RI of the SWCNTs-COOH self-assembly films coating on the surface of the sensor. The sensing mechanism of the SWCNTs-COOH self-assembly films at room temperature can be explained based on charge transfer between NH3 and SWCNTs-COOH. When NH3 is adsorbed by SWCNTs-COOH, it donates an electron, which would affect hole concentration in the SWCNTs-COOH, thereby changing its RI accordingly [49]. Figure 7(b) shows the shift of the resonance wavelength determined from the SPR spectrum with the NH3 concentration. The shift in the resonance wavelength for the range of 0 - 30 ppm is around 12.5 nm and indicating a good linear response to the NH3 concentrations. For the concentration at the range of 90 to 200 ppm, the shift of the resonance wavelength is less, not more stable. From 90 to 120 ppm, the wavelength shifts 2 nm. And from 120 to 200 ppm, the wavelength shifts 1.5 nm. Then the resonance wavelength hardly shift at all. Therefore, for higher concentrations over 200 ppm, it appears to saturate. For NH3 gas sensing, the obtained maximum sensitivity of the sensor is estimated to be 0.8 nm/ppm at the concentration of 5 ppm, and the average sensitivity is estimated to be 0.417 nm/ppm at the range of 0 - 30 ppm. These values correspond to the detectable resolution of the concentration of ammonia gas is 0.375 ppm, assuming that the wavelength resolution of a spectrometer is 0.3 nm.

 figure: Fig. 7.

Fig. 7. (a) The transmission spectra shift of the sensor with different NH3 concentrations (b) The wavelength shift upon the concentration of NH3

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We are more concerned about the time response characteristics of the sensor with high sensitivity at low concentrations, so we tested the repeatability of the sensor at the NH3 concentrations of 10 ppm, as shown in Fig. 8(a). When injecting ammonia gas into the gas chamber, the transmission spectrums were recorded every 5 s until the spectrum is stable, and the time used is the response time of the sensor when the ammonia concentration is 10 ppm. After opening the chamber and injecting into dry N2, the transmission spectrums returned to their original position, and the time taken is the recovery time. The response and recovery times are found to be about 30 s and 120 s, respectively. It indicated that the sensor absorbs ammonia molecules rapidly but desorbs them slowly. This is because the strong adsorption force between SWCNTs-COOH and gas ammonia molecules makes the gas more difficult to desorb, resulting in a longer recovery time [49]. After testing twice, the resonance wavelength shifts decreased significantly with the increase of the tests. The change in sensor performance may be caused by the slight degradation of the surface coating after we rinsed the sensor with N2. Therefore, the self-assembled film can be further optimized, such as enhancing the molecular bond strength by lengthening the drying time of the film.

 figure: Fig. 8.

Fig. 8. The repeatability and selectivity of the sensor. (a) The repeatability of the sensor response to the ammonia at a concentration of 10 ppm, (b) Selectivity of the response of the sensor to ammonia and other analytes.

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In the experiment, it is very important to detect the selectivity of the sensor. Figure 8(b) shows the response of the sensor with SWCNTs-COOH self-assembly film for different types of gases at a concentration of 1000 ppm. The relative wavelength shifts of less than 10% were observed when the sensor was placed in the N2, CO2, acetone, and alcohol. This is due to the larger absorption and stronger charge transfer capability of NH3, attributed to the carboxy groups on the basal plane of SWCNTs that promotes adsorption of NH3. Furthermore, the adsorption nature of carbon nanomaterials is highly selective to polar molecules such as NH3 and has much lower sensitivity towards nonpolar molecules such as N2 and CO2 [50]. Therefore, the sensor has obvious selectivity to NH3.

4. Conclusion

In this paper, we used SWCNTs-COOH self-assembly film as the sensing layer, combining with the SPR technique for ammonia gas sensing enhancement. The sensor based on the hybrid film exhibited a maximum sensitivity of 0.8 nm/ppm, with the resolution 0.375 ppm, and the measured response ∼30 s, respectively. In addition, the sensor exhibited excellent selectivity and stability. Meanwhile, numerous materials such as organic compound films, semiconductor metal oxides, carbon nanomaterials, and composites of these materials have been used in the literature for the sensing of ammonia gas. The sensing performance with other reported NH3 gas sensors has provided in Table 1. Comparison with carbon nanomaterials based NH3 gas sensors, Our sensors have better performance. Due to its high sensitivity, low cost, and simple structure, this structure demonstrates the immense potential for the development of other gas sensors based on an optical fiber coated with sensing material layers.

Tables Icon

Table 1. Comparison of Ammonia Sensors Based on Various Optical Techniques

Funding

National Natural Science Foundation of China (61705147, 61705148, 61905169).

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.

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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 (8)

Fig. 1.
Fig. 1. Schematic diagram of the proposed sensor.
Fig. 2.
Fig. 2. (a) Schematic diagram of the side view in MMF-SMF-MMF structure; (b) Simulation of mode in MMF-SMF-MMF structure without Ag film. The core of the SMF and MMF are 9 µm and 62.5 µm respectively, and the cladding of the SMF and MMF are 125 µm. The length of the SMF is 10 mm. The refractive index of core and cladding are 1.45 and 1.44 respectively. The view ratio of X-axis and Y-axis is 1:60, and the view ratio of X-axis and Y-axis of the insert is 1:1 ; (c) Schematic diagram of the mode in MMF-SMF-MMF structure with Ag film; (d) SPP mode, the thickness of Ag film is 40 nm; (e) SPR wavelength as a function of refractive index.
Fig. 3.
Fig. 3. Schematic diagram of the experimental setup.
Fig. 4.
Fig. 4. (a) SPR spectra of the MMF-SMF-MMF structure coated with Ag film, (b) Variation of SPR resonance wavelength with different values of RI
Fig. 5.
Fig. 5. The schematic illustration of the self-assembly process.
Fig. 6.
Fig. 6. The SEM images of self-assembled films (a) thickness, (b) surface.
Fig. 7.
Fig. 7. (a) The transmission spectra shift of the sensor with different NH3 concentrations (b) The wavelength shift upon the concentration of NH3
Fig. 8.
Fig. 8. The repeatability and selectivity of the sensor. (a) The repeatability of the sensor response to the ammonia at a concentration of 10 ppm, (b) Selectivity of the response of the sensor to ammonia and other analytes.

Tables (1)

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Table 1. Comparison of Ammonia Sensors Based on Various Optical Techniques

Equations (3)

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βew = 2πλε0sinθ,
βSP = 2πλεmεdεm+εd.
Cppm=VμL×DgmL1Mgmol1×VmL×22.4×106,
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