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High-performance humidity sensor based on a micro-nano fiber Bragg grating coated with graphene oxide

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Abstract

A high-performance relative humidity (RH) sensor based on a micro-nano fiber Bragg grating (MFBG) coated with a graphene oxide (GO) film is fabricated with a chemical corrosion technique and optically driven deposition method. The diameter of MFBG is corroded to about 12 µm. GO film with the thickness of about 2.5 µm is uniformly coated on the MFBG surface. The change of RH results in the change of refractive index (RI) of GO film, that is, the change of effective RI of MFBG, which will at last result in the shift of reflected wavelength. The experimental results show that there is a good linear relationship between the wavelength shift of MFBG and RH changes in the RH range of 20% to 80% at constant temperature. The sensitivity is 17.361 pm/RH% and the linear correlation coefficient is 99.89%. In order to eliminate the impact of temperature cross sensitivity, the relative measurement is adopted and similar results are obtained. The average response and recovery times are measured to be about 3.2 s and 8.3 s, respectively. The sensor has the advantages of long stability, reversibility, quick response and simple structure. With such high performance, it can be used in widespread potential fields, such as biology, chemical processing and food processing.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Relative humidity (RH) measurement and control have very important applications in chemical processing, meteorological environment monitoring, biology, medicine, food and electrical appliances [13]. Nowadays, optical humidity sensors are widely concerned due to the advantages of high integration, high sensitivity and wide application range. Fiber optic and fiber Bragg grating (FBG) humidity sensors are more and more popular because they have strong anti-interference, small size and distributed measurement [47]. However, bare silica fibers are not sensitive to humidity and humidity-induced changes in the refractive index (RI) are usually ultra-small, which leads to significant difficulties in directly measuring RH. In order to improve sensitivity, fiber humidity sensors need to coat humidity sensitive materials in the sensing area. At present, there are many humidity sensors which combine humidity sensitive materials with optical fiber or grating, such as nonadiabatic tapered single mode fiber (SMF) coated with PDDA/Poly R-478 film [8], PVA-coated photonic crystal fiber (PCF) [9,10], agarose-infiltrated PCF interferometers [11], U-bend plastic-clad silica fiber coated with CoCl2-doped PVA film [12], U-shaped fiber coated by phenol red-doped PMMA [13], no-core fiber coated with HEC/PVDF hydrogel [14], a side-polished fiber (SPF) overlaid on a WS2 film [15], a tapered fiber coated with agarose gel [16], FBG coated with polymer [17,18] and optical fiber long-period grating humidity sensor coated with poly (ethylene oxide)/cobalt chloride [1921]. However, the poor permeability of the aboved materials will make water molecules difficult to enter the inside of them. So the RI will change little or no change and the RH sensitivity of the sensor is very low. Furthermore, the poor hydrophilicity of these materials results in very poor linearity, reversibility and humidity measurement range for these sensors.

Recently, Graphene Oxide (GO) has attracted significant attention and has become one of the most intriguing materials because of its many excellent electronic and photonic properties [22,23]. GO with the two-dimensional layered structure of graphene, has a large specific surface area and is modified with a variety of functional groups including hydroxyl, carboxyl and carbonyl [2426]. It is sensitive to humidity change in a wide range of humidity (6.4% - 93.5% RH), and its RI changes significantly with humidity [27,28]. Therefore, GO can be considered as an outstanding candidate for high sensitive RH sensing [29,30]. There is a humidity sensor based on the in-line Mach–Zehnder interferometer (MZI) fiber coated with GO, whose sensitivity is 0.349 dB/RH% with linear correlation coefficient of 98.9% [31]. Owing to the advantages of reversible, accurate, and stable over long time periods response, FBG is an attractive sensing element and can be used for absolute measurements and in-line multiplexed sensor chains. Many researchers combine FBG with GO to make humidity sensor. Jiang et al. proposed a tilted FBG humidity sensor coated with GO with a sensitivity of 0.02 dB/RH% in the range of 30% -80% [32]. Wang et al. also put forward a tilted FBG humidity sensor coated with GO. The sensitivity was 0.129 dB/RH% with a detection range of 10% - 80% [33]. However, the humidity sensor based on the detection of optical power has the shortcoming of vulnerable to power fluctuations [3436].

In this paper, a micro-nano fiber Bragg grating (MFBG) humidity sensor based on GO film is presented for the first time as far as I am concerned. This humidity sensor based on optical wavelength drift detection overcomes the disadvantage of vulnerable to power fluctuations. The experiment results show there is a good linear relationship between the wavelength shift of MFBG and RH changes in the RH range of 20% to 80% at constant temperature or adopting temperature compensation method. The sensor has the advantages of long stability, reversible, quick response and simple structure.

2. Operating principle and fabrication of the humidity sensor

2.1 Operating principle

It is well known that the Bragg reflection condition of FBG is${\lambda _B}\textrm{ = 2}{n_{eff}}\Lambda $. Here ${\lambda _B}$ is the reflected peak wavelength of the FBG, ${n_{eff}}$ is the effective RI of the fiber, and $\Lambda $ is the periodic constant of the grating. Any change of ${n_{eff}}$ or $\Lambda $ will lead to the change of the reflected peak wavelength of the FBG. Ignoring the effect of thermal expansion or shrinkage on the FBG period and fiber size, that is to say, the FBG period Λ remains unchanged for the determined FBG. The effective RI ${n_{eff}}$ can be expressed as [37]:

$$n_{eff}^2 = n_1^2 - {\left\{ {\frac{{1 + \sqrt 2 }}{{1 + {{[{4 + k_0^4a_0^4{{({n_1^2 - n_2^2} )}^2}} ]}^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}} \right.}\!\lower0.7ex\hbox{$4$}}}}}}} \right\}^2}({n_1^2 - n_2^2} )$$

In the formula (1), the RI of the fiber core ${n_1}$ and wave number ${k_0}$ are constant, and the ${n_{eff}}$ change of the FBG is related to the radius of the optical fiber a and the RI of the cladding ${n_\textrm{2}}$. That is to say, the change of a or ${n_\textrm{2}}$ causes the change of ${\lambda _B}$. The FBG made by traditional SMF is not sensitive enough to detect evanescent wave because of the limitation of light wave by thick cladding, so it can not be directly used to measure environmental medium changes. If the cladding thickness of FBG is reduced to MFBG, the interaction between the light field and the environmental medium can be enhanced. By detecting the change of the reflected spectrum of MFBG, the change of the environmental medium can be detected. For a given MFBG, if the RI of the surrounding medium changes, the center wavelength of the reflected spectrum of the grating will change accordingly. The relationship can be derived as:

$$\Delta {\lambda _B} = 2\Lambda \frac{{\partial {n_{eff}}}}{{\partial {n_2}}}\Delta {n_2}$$

It can be concluded that the drift of reflected wavelength of MFBG $\Delta {\lambda _B}$ is the function of grating period $\Lambda $, sensitivity $\frac{{\partial {n_{eff}}}}{{\partial {n_2}}}$ obtained by ${n_{eff}}$ changing with ${n_\textrm{2}}$ and RI of ambient cladding $\Delta {n_\textrm{2}}$. $\frac{{\partial {n_{eff}}}}{{\partial {n_2}}}$ is related to the radius of MFBG and the RI of environmental cladding ${n_\textrm{2}}$, and they are non-linear. In order to increase sensitivity, MFBG needs to be coated with a moisture-sensitive material GO in the sensing area.

2.2 Fabrication and characterization of MFBG

MFBG is fabricated by chemical etching method. The home-made FBG is fabricated by a programmable double exposure system based on dynamic optical shielding plate [38]. A KrF excimer laser (COMPex Pro110F) with 248 nm is used as ultraviolet light source. The SMF is placed in pure hydrogen at 12 MPa and 20 °C for 7 days to make hydrogen loaded fiber. The uniform grating is fabricated by using the phase mask of zero order fused silica with a period of 1059.39 nm. When the reflectivity is above 99%, the writing time is 55 s in this condition. The length of FBG is 1 cm. The reflected spectrum is shown in Fig. 1(a). It can be seen the reflected wavelength is 1552.826 nm, 3 dB bandwidth is 0.43 nm, and the extinction ratio is 23 dB. The fabrication of MFBG is used the hydrofluoric acid (HF). The colorless and transparent HF liquid has a strong irritant odor. It mainly corrodes glass, metal and silicon containing substances, and has a strong corrosive effect. But it has no corrosive effect on plastic. Firstly, the prepared FBG is fixed on the plexiglass plate, and 40% HF liquid is dropped on the grid area to be corroded in a fume hood. It should be noted not to move the plexiglass plate to avoid the uneven corrosion caused by the shaking of HF liquid. The size of the fiber grating depends on the concentration of HF and the corrosion time. Because the HF concentration is well configured in this experiment, the grid area diameter is controlled by changing the corrosion time. The results show that when the corrosion time is 10 minutes, the cladding layer will not be corroded and the diameter of the grid area is 125 µm. When the corrosion time is increased to 15 minutes, 20 minutes, 25 minutes and 30 minutes, the diameter of the grid area is 105 µm, 69 µm, 35 µm and 12 µm respectively. If the corrosion time is increased continuously, the FBG fractures. The smaller the grid area diameter is, the higher the sensitivity of the humidity sensor is. In this experiment, MFBG with grid area diameter of 12 µm is used. Then the MFBG is washed repeatedly with clear water and deionized water for 5 minutes, so as to dilute the HF liquid remaining in the MFBG groove and reduce the corrosion rate. Finally, the MFBG with the plexiglass plate is placed carefully in an ultrasonic cleaner for 2 minutes so as to completely remove the HF remaining in the MFBG corrosion tank and prevent the fiber from further corrosion. Otherwise, it will have a serious impact on the subsequent experimental results. The reflected spectrum of MFBG is shown in Fig. 1(b). It is found that the reflected center wavelength is blue-shift when FBG changes to MFBG. This phenomenon is due to the decrease of $\frac{{\partial {n_{eff}}}}{{\partial {n_2}}}$ after the grating is corroded. Scanning electron microscope (SEM: Quanta FEG250) is used to observe the images of FBG and MFBG shown in Figs. 2(a) and (b). It can be seen that the FBG diameter is about 125 µm and the MFBG diameter is about 12 µm. The cladding of FBG is reduced greatly to MFBG. Thus a strong evanescent field could penetrate into the outside of the MFBG, enhancing the interaction with the surrounding media.

 figure: Fig. 1.

Fig. 1. Reflected spectra of (a) FBG, (b) MFBG, (c) MFBG coated with GO.

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 figure: Fig. 2.

Fig. 2. Scanning electron micrographs of (a) FBG, (b) MFBG.

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2.3 Coating and characterization of GO film

The GO used in this experiment is the GO aqueous solution with particle diameter greater than 500 nm and concentration of 20% from Suzhou Graphene Technology Co., Ltd. The coating method of optically driven deposition is selected [39,40]. The MFBG is immersed into droplets of the GO solution, at the same time a laser with a center wavelength of 1060 nm and a power of 75 mW is passed through the MFBG for 20 minutes. The output power from the other side of the sensor is monitored by a power meter. Due to the light pressure effect and heat effect, GO could be deposited on the surface of MFBG. Then the MFBG coated with GO is put in the half-opened chamber to dry for 36 h. For comparison, the reflected spectrum of MFBG coated with GO is shown in Fig. 1(c). It can be seen that the power is about 1 dB higher than that in Fig. 1(b). This is because the GO film acts as the cladding and binds the optical signal in the core. The distribution of GO film on the surface of MFBG can be observed by SEM shown in Fig. 3(a). As can be seen that there are many folds and wrinkles in the deposited GO film, which are caused by the roughness of the corroded surface of the MFBG. These folds and wrinkles will help to expand the effective area of water molecules absorbed, thus improving the sensitivity of environmental humidity. And it can be seen that the size of GO flakes are about 2 µm and the thickness is about 2.5 µm. The larger sizes of GO flakes can enhance the absorption ability of the water molecules. Different concentration of GO solution will affect the thickness of GO film coated on the MFBG. But as mentioned in the Ref. [31], if the GO film is too thin (such as 5 layers, about 6 nm) or too thick (such as 20 µm), its ability to absorb water molecules will be reduced. Too thin GO film with absorbing little water molecules will narrow the detection range of RH. On the contrary, when the thickness of GO is too large, the RI of GO film in the outer layer (near the air) changes with the change of absorbing water molecules, while the RI of GO film in the inner layer (near the MFBG surface) hardly changes because of the limited permeability of absorbing water molecules. Therefore, too thin or too thick GO film does not help the proposed RH sensor. In order to confirm the atomic structure of the GO film, the Raman spectrum is measured for the GO film on the MFBG at room temperature with a Raman instrument of model Lamda 250. The Raman spectrum of GO film is seen as Fig. 3(b), where the characteristic peaks are located at 1340 cm-1 and 1600 cm-1, corresponding to the D band and G band, respectively [33]. The G-band corresponds to the mutual stretching mode of SP2 atom pair, and its intensity indicates the number of SP2 structure in the material. The D-band corresponds to the respiratory vibration mode of benzene ring atom, also is known as the disorder induced Raman spectrum peak. Its intensity characterizes the disorder degree of the material. The intensity ratio of D peak to G peak (ID/IG) is used to characterize the ordered degree of GO structure. The larger the ID/IG is, the more structural defects are, that is, the lower the ordered degree is, the more oxygen-containing functional groups are, and the better the hydrophilicity is [41]. The value of ID/IG is greater than 1 in this paper, which shows that the GO film has good hydrophilicity and makes a great contribution to improving the sensitivity of humidity sensor.

 figure: Fig. 3.

Fig. 3. Characterization of GO film (a) SEM image, (b) Raman spectrum

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3. Experimental setup

The configuration of the proposed RH sensing system is shown schematically in Fig. 4. The amplified spontaneous emission (ASE) light from erbium-doped fiber amplifier (EDFA) as a broadband light source is connected to the “1” port of the circulator, and output from the “2” port to the MFBG through the SMF. The MFBG coated with GO is installed and fixed on the temperature controller in home-made enclose humidity chamber made in acrylic board. The temperature is adjusted and the humidity around the MFBG is controlled by a humidifier. A commercial humidometer (RITERS HTC-2) with a resolution of 1 RH% is also placed in the humidity chamber to monitor the RH variation. The humidity change in the chamber is adjusted by inputting dry or humid air from the inlet. Increasing the ratio of humid air will increase the RH value and vice versa. The reflected light from MFBG is displayed on the Yokogawa AQ6370C optical spectrum analyzer (OSA) with 0.02 nm resolution from the “3” port of the circulator. The change of the MFBG reflected spectrum is monitored in real time while changing the humidity.

 figure: Fig. 4.

Fig. 4. Schematic diagram of the humidity sensor

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4. Experimental results and discussions

4.1 Drift-wavelength-based humidity sensing

The RH in the chamber is changed very slowly by the humidifier and monitored in real time by the hygrometer. When the RH in the chamber is increased with 10% steps in the RH range of 10%∼90% at 20°C room temperature, the reflected spectra of the MFBG coated with 2.0 mg/ml GO solution are measured shown in Fig. 5(a). The lines of different colors and shapes represent the reflected spectrum of MFBG at different humidity. In order to show the variation of the central wavelength of the reflected spectrum with RH more clearly, part of the spectra are amplified from 1549 nm to 1552 nm, shown in Fig. 5(b). It can be seen that with the increase of humidity, the reflected center wavelength moves to the longer wavelength. Because there are plenty of functional hydrophilic groups such as -COOH, -OH in the GO film, it has a strong hygroscopicity [4244]. When the RH increases, GO film will absorb more water molecules. The water molecules will adhere to the surface of GO or swell the GO film, thus increase the thickness of the GO film. And the effective RI of MFBG increases. Therefore the reflected center wavelength becomes larger.

 figure: Fig. 5.

Fig. 5. Reflected spectra of MFBG coated with GO at 2.0 mg/ml (a) Wavelength ranges from 1535 to 1565 nm, (b) Wavelength ranges from 1549 to 1552 nm.

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In order to prove the reversibility of the humidity sensor, the reflected central wavelengths are measured when the RH in the chamber is increased and then decreased with 10% steps in the RH range of 10% ∼ 90% shown in Fig. 6(a). It can be seen there is little changes between the central wavelengths of the RH increased and decreased processes, which proves that the sensor based MFBG coated with GO film has a very good reversibility under the RH variation. To investigate the sensitivity of the sensor, the relationship between the reflected central wavelength and RH is fitted as Fig. 6(b). It can be seen there is a linear relationship between the wavelength shift and the RH in the RH range of 20% ∼ 80%. When the RH is lower than 20%, the change in the central wavelength of the reflected spectrum is very small. Because the water molecules are not enough to penetrate the GO film, the effective RI changes little. When the RH exceeds 80%, the center wavelength tends to be stable, because the absorption of water molecules by the GO film tends to be saturated. Although the RH continues to increase, the effective RI does not change. The sensitivity of 17.361 pm/RH% with a linear correlation coefficient of 99.89% in the range of 20% ∼ 80% is obtained.

 figure: Fig. 6.

Fig. 6. The characteristics of the sensor (a)Variation of peak wavelength of MFBG with RH, (b)Variation of peak wavelength shift of MFBG with RH.

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To investigate the dynamic performance of the sensor, the RH in the chamber is set to switch between the fixed RH levels of 40% and 80%. Three cycles of the RH switching over a period of 60 min are measured and shown in Fig. 7. It can be seen that the changes and fluctuations of the wavelengths are almost the same as that of the humidity changes. In the first cycle, it can be seen that the reflected peak wavelength shift from 1550.458 nm to 1551.133 nm as the RH increased from 40% to 80%. When the RH decreased from 80% to 40%, the peak wavelength decreased from 1551.133 nm to 1550.410 nm. It is shown that the sensor has good repeatability and reversibility without any hysteresis. At the same time, the average response time and recovery time are measured to be about 10.8 s and 19.6 s.

 figure: Fig. 7.

Fig. 7. The changes and fluctuations of wavelengths with humidity

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4.2 Influence of temperature on humidity sensor and its compensation method

When the temperature acts on the fiber grating, due to the thermal expansion and the thermo-optical effect of the fiber, the effective RI and the grating period are changed, which cause the reflected wavelength to drift. To investigate the effect of temperature on the MFBG coated with GO film, the temperature controller in the enclose humidity chamber shown in Fig. 4. is turned off. In this case, when the humidity changes, the temperature will change accordingly. Thus the reflected wavelength drifts are caused by both temperature and humidity acting on MFBG and are linearly superimposed. It is found that the reflected peak wavelength of MFBG is red-shifted with the increase of humidity. But the temperature decreased caused by the increased humidity causes the peak wavelength blue-shift. Thus the measurement of the humidity is not accurate. Because the bare FBG is not sensitive to RH and only responds to temperature, the relative measurement of bare FBG and MFBG cascaded is adopted to eliminate the influence of temperature.

In the experiment, in order to investigate whether the responses of FBG and MFBG coated with GO to temperature is the same, the changes of reflection wavelength of the two are measured at 20% RH, and plotted the graph shown in Fig. 8.

 figure: Fig. 8.

Fig. 8. Temperature responses of FBG and MFBG coated with GO

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It can be seen from Fig. 8 that the temperature responses of FBG and MFBG coated with GO are 9.04 pm/°C and 9.72 pm/°C, respectively. The difference between the two is very small. So in order to improve the accuracy of measurement results, the cascaded FBG and MFBG coated with GO can be used to compensate for temperature responses under different humidity.

Therefore, in the experiment, the bare FBG with the reflected center wavelength of 1534.872 nm is cascaded with MFBG coated with GO film. When the humidity is 20%, the spectra are shown in Fig. 9(a). The difference between the two peak wavelengths is the wavelength change $\Delta \lambda$ caused by the humidity change. When the RH is 20%, it can be seen $\Delta \lambda$ is 41 pm. When the humidity is 30%, $\Delta \lambda$ is 234 pm shown in Fig. 9(b). When the humidity are 40%, 50%, 60%, 70%, 80%, $\Delta \lambda$ are 440 pm, 571 pm, 753 pm, 951 pm, 1104 pm, respectively.

 figure: Fig. 9.

Fig. 9. Reflection spectra of cascaded bare FBG and GO-coated MFBG (a) RH = 20%, $\Delta \lambda$=42.4 pm, (b) RH = 30%, $\Delta \lambda$=235.2 pm.

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It can be seen from Fig. 9 that with the increase of the humidity, the peak wavelength difference between FBG and MFBG increases gradually, which is consistent with the relationship between the wavelength drift and humidity under constant temperature. The relationship between the wavelength drift and humidity obtained by the temperature compensation method is shown in Fig. 10. The sensitivity is 17.629 pm/RH%, the coefficient with a linear correlation is 99.80% at the range 20%∼80%. This result is similar to the conclusion under the constant temperature condition.

 figure: Fig. 10.

Fig. 10. The changes of peak wavelength difference $\Delta \lambda$ with RH

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4.3 Application in monitoring human breath

It is interesting to apply the humidity sensor based MFBG coated with GO film in monitoring human breath. The experimental setup is shown in Fig. 11(a). The ASE light from EDFA is connected to the “1” port of the circulator, and output from the “2” port to the MFBG through the SMF. The OSA is used to monitor the RH variation and record the reflected light from MFBG when a person blows into the sensor. The reflected peak wavelengths for ten human breathing cycles are shown in Fig. 11(b). A zoom-in of two breathing cycles are seen as Fig. 11(c). It can be seen that the peak reflection wavelength changes about 720 pm for breathing out and comes back to the original peak wavelength for breathing in. The response time is about 3.0 s and 3.8 s, and recovery time is about 7.6 s and 8.1 s in these two cycles. The average response time of ten cycles is calculated as 3.2 s, and the average recovery time is 8.3 s. The response time and recovery time of this sensor are comparable to other types of sensors [15,45].

 figure: Fig. 11.

Fig. 11. (a) The experimental setup of monitoring human breath, (b) The peak wavelength variation for ten human breathing cycles, (c) The zoom-in of two breathing cycles.

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5. Conclusion

A high-performance RH sensor based on MFBG coated with GO is fabricated successfully with the chemical corrosion technique and optically driven deposition method. GO can be used to improve the sensitivity of optical fiber humidity sensor because the RI varies greatly with humidity owing to its good hydrophilicity. Firstly, MFBG is prepared by corrosion of FBG, and then GO film with the thickness of 2.5 µm is uniformly coated on the surface of MFBG by optically driven deposition. The reflected wavelength drift of MFBG is measured with the changes of the external humidity under the constant temperature. It is found that there is a good linear relationship in the RH range of 20% to 80%. The sensitivity is 17.361 pm/RH% and the linear correlation coefficient is 99.89%. In addition, in order to eliminate the impact of temperature cross sensitivity, the relative measurement of bare FBG that is not sensitive to RH and MFBG cascaded is adopted. In the RH range of 20% to 80%, a high sensitivity of 17.629 pm/RH% with a high linear correlation coefficient of 99.80% is achieved. The average response and recovery times are measured to be 3.2 s and 8.3 s for the sensor, respectively. The experimental results show that the sensor has the advantages of wide detection range, high sensitivity, reversible, quick response and simple structure. It will be an outstanding RH sensor for research in the fields of chemistry, medicine and biology.

Funding

National Key Scientific Instrument and Equipment Development Projects of China (61627814); Undergraduate Innovative Test Program of China (URTP2019110008, BEIJ2019110001); State Key Laboratory of Advanced Optical Communication Systems and Networks.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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Figures (11)

Fig. 1.
Fig. 1. Reflected spectra of (a) FBG, (b) MFBG, (c) MFBG coated with GO.
Fig. 2.
Fig. 2. Scanning electron micrographs of (a) FBG, (b) MFBG.
Fig. 3.
Fig. 3. Characterization of GO film (a) SEM image, (b) Raman spectrum
Fig. 4.
Fig. 4. Schematic diagram of the humidity sensor
Fig. 5.
Fig. 5. Reflected spectra of MFBG coated with GO at 2.0 mg/ml (a) Wavelength ranges from 1535 to 1565 nm, (b) Wavelength ranges from 1549 to 1552 nm.
Fig. 6.
Fig. 6. The characteristics of the sensor (a)Variation of peak wavelength of MFBG with RH, (b)Variation of peak wavelength shift of MFBG with RH.
Fig. 7.
Fig. 7. The changes and fluctuations of wavelengths with humidity
Fig. 8.
Fig. 8. Temperature responses of FBG and MFBG coated with GO
Fig. 9.
Fig. 9. Reflection spectra of cascaded bare FBG and GO-coated MFBG (a) RH = 20%, $\Delta \lambda$=42.4 pm, (b) RH = 30%, $\Delta \lambda$=235.2 pm.
Fig. 10.
Fig. 10. The changes of peak wavelength difference $\Delta \lambda$ with RH
Fig. 11.
Fig. 11. (a) The experimental setup of monitoring human breath, (b) The peak wavelength variation for ten human breathing cycles, (c) The zoom-in of two breathing cycles.

Equations (2)

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n e f f 2 = n 1 2 { 1 + 2 1 + [ 4 + k 0 4 a 0 4 ( n 1 2 n 2 2 ) 2 ] 1 / 1 4 4 } 2 ( n 1 2 n 2 2 )
Δ λ B = 2 Λ n e f f n 2 Δ n 2
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