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High performance all-fiber temperature sensor based on coreless side-polished fiber wrapped with polydimethylsiloxane

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Abstract

A novel fiber structure, coreless side-polished fiber (CSPF) that is wrapped by polydimethylsiloxane (PDMS), is demonstrated to be highly sensitive to temperature because of the high refractive index sensitivity of the CSPF and the large thermal optic coefficient of the PDMS. Our numerical and experimental results show that the several dips in the transmitted spectra of PDMSW-CSPF is originated from the multimode interference (MMI) in the CSPF and will blueshift with the increase of temperature. Furthermore, for such a PDMSW-CSPF, we investigate its temperature sensing characteristics and the influences of residual thickness (RT) and dip wavelength on the sensitivity both numerically and experimentally. In the temperature range of 30~85°C, the PDMSW-CSPF with RT = 43.26 μm exhibits a high temperature sensitivity of −0.4409 nm/°C, the high linearity of 0.9974, and the high stability with low standard deviation of 0.141 nm. Moreover, in the cycle experiments, where the environmental temperature was set to automatically increase and then decrease, the PDMSW-CSPF exhibits a low relative deviation of sensitivity (RSD) of down to ± 0.068%. Here, the RSD is defined as the ratio of sensitivity deviation to the average sensitivity measured in the heating/cooling cycle experiments. The lower RSD indicates that PDMSW-CSPF has better reversibility than other fiber structure. The investigations also show that the sensitivity of the PDMSW-CSPF could be enhanced further by reducing the residual thickness and choosing the dip at a longer wavelength.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Accurate temperature measurements and control play an important role in various applications such as chemical reaction, biomedical science, physics research, etc. Fiber optic temperature sensor has many advantages, including immunity to electromagnetic interference, chemical inertness, compact size and high sensitivity [1,2], which causes the fiber sensors attract to widespread interest in sensing applications. Multimode interference (MMI) is an important principle of optical fiber sensing. Usually, single-mode-multi-mode-single-mode fiber (SMSF) is employed to achieve MMI and temperature measurement [3–7]. However, the sensitivities of the above sensors are usually low. Therefore, many methods have been reported to enhance the sensitivity of the fiber sensor effectively, such as water-filled suspended-core fiber [8], photonic crystal fiber (PCF) [9–11], and LPFG-cascaded thin-core fiber [12]. However, these methods require two types of optical fibers spliced together. Therefore, it needs fabrication techniques such as splicing, precise alignment and other additional processes, which leads to high fabrication complexity and cost.

It has been reported that temperature fiber sensors can be achieved by using temperature sensitive material and fiber-optic refractive index sensor [13,14]. The sensitivity of this kind of temperature sensor is mainly determined by two aspects: 1) temperature sensitive material with high thermal optical coefficient and 2) high refractive index sensitivity of a fiber structure. There are many reports to realized temperature fiber sensors using high thermal optical coefficient materials [15–17], such as liquid and alcohols. Despite the high sensitivity for these temperature sensors [15,16], the liquid or alcohols may be leaked and evaporated away, which leads to poor reversibility of the sensors. Besides, the fiber structure for the sensors requires complex fabrication processes and increase the fabrication cost. Liquid crystal (LC) as a temperature sensitive material is exploited to realize fiber temperature sensor, for which an ultrahigh sensitivity of up to 4.72 nm/°C can achieved [17]. However, the temperature range of this sensor was limited to very narrow range (20~34.5°C) because of the narrow phase transition temperature range of the LC.

Compared with other thermal sensitive materials, PDMS is a better temperature sensitive material with higher negative thermal optical coefficient [18–21]. Recently, combined with the PDMS, various fiber structures with high refractive index sensitivity have been exploited to implement the high sensitive temperature sensor [19–21]. Although the sensitivity is one of important performance parameters for the fiber temperature sensor, the linearity and reversibility of the sensor is other important performance parameters in practical application. To quantitatively assess the reversibility of the temperature sensors, we here introduce relative sensitivity deviation (RSD), which is defined as the ratio of sensitivity deviation to the averaged sensitivity measured in the cycle experiments. A smaller RSD value indicates that the sensor has the better reversibility. Yang Rui [19] used the PDMS coated S shaped tapered multimode optical fiber refractive index sensor to detect temperature. Although the highest temperature sensitivity reached as −2.17 nm/°C in the range of 20~65°C, but experiment was not repeated and no discussions on the stability of the sensor has been mentioned. Martí [20] used PDMS to make a long period fiber grating (LPFG) cladding coated on a tapered fiber and demonstrated its temperature sensing characteristics. Although the highest sensitivity can reach to −1.328 nm/°C for the temperature increase process and reach to −1.1684 nm/°C for temperature decrease process in the range of 40~80°C, the poor RSD is calculated as ± 6.4%, which indicates a low reversibility for the sensor. Wang Qi [21] reports a PDMS-coated long period fiber grating (LPFG), whose sensitivity was 0.2556 nm/°C in the increase temperature experiment, and 0.2554 nm/°C in the decrease temperature experiment in the range of 40~80°C. A low RSD for the sensors was calculated as ± 0.04% for the PDMS-coated LPFG. It is shown that despite of the low sensitivity, the sensor has a very good reversibility with very low RSD. Usually, the high sensitivity and low RSD are difficult to achieve simultaneously. Therefore, it is of great significance for practical applications to make a high sensitivity temperature sensor with a good reversibility.

Here, we report a simple fiber structure referred to coreless side-polished fiber (CSPF) to implement MMI-based fiber temperature sensor. It has been reported that high refractive index sensitivity of 2647 nm/RIU for such CSPF can be achieved in surrounding refractive index (SRI) range of 1.40~1.42 [22]. On the other hand, the PDMS refractive index of 1.39~1.42 in the temperature range of 30~85°C matches the refractive index region where the CSPF exhibits high sensitivity. Therefore, the PDMS-wrapped CSPF (PDMSW-CSPF) has a potentially high temperature sensitivity. In the work, the temperature sensing characteristics of the novel fiber structure PDMSW-CSPF are investigated both numerically and experimentally. In the temperature range of 30~85°C, the temperature sensitivities of PDMSW-CSPF with RT = 43.26 μm are measured as −0.4412 nm/°C for temperature increase process, and as −0.4406 nm/°C for temperature decrease process. It is found that the average sensitivity is −0.4409 nm/°C and RSD=±0.068%. This shows the PDMSW-CSPF has a relatively high temperature sensitivity and good reversibility. The influences of the PDMSW-CSPF RT and dip wavelength on the temperature sensitivity are also investigated. The results show that reducing the residual thickness and choosing the dip at a longer wavelength could further enhance the sensitivity of the PDMSW-CSPF.

2. Principle

2.1 The Structure of PDMSW-CSPF

Figure 1(a) shows the schematics the three-dimensional structure of PDMSW-CSPF where the fiber core is shown in yellow. Unlike the typical side-polished fiber (TSPF) with an intact fiber core [23,24], the CSPF has no fiber core, and the residual thickness of CSPF (inset in Fig. 1(a)) is called RT. Figure 1(b) is the vertical section (yz-plane) of the PDMSW-CSPF, from which we can see that the entire polishing region of the CSPF is wrapped by PDMS and the CSPF structure consists of five sections: lead-in SMF, transitional section 1, coreless flat section, transitional section 2 and lead-out SMF.

 figure: Fig. 1

Fig. 1 Schematic diagrams of PDMS-wrapped CSPF: (a) three-dimensional view and (b) vertical section.

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2.2 Simulations

Beam propagation method (commercial BPM module from Rsoft Inc) is employed to simulate the transmission spectra and field evolution of the PDMSW-CSPF. In the simulation, the geometrical parameters of the PDMSW-CSPF are respectively set as follows: Length of the flat section Lf = 8 mm; lengths of the two transitional sections Lt1 = Lt2 = 4 mm; the core RI = 1.4681; the cladding RI = 1.4628 [25]; the core diameter is 8.2 μm and the cladding diameter is 125 μm. Here, the RT is respectively set to be 43.26 μm, 51.27 μm, 57.81 μm to simulate the three PDMSW-CSPFs with three different RTs, which are fabricated in the experiments (in Section 3.1). The curved polished surfaces of the transitional section 1 and 2 are modeled by a surface of an elliptic cylinder with a major axis of Lt1 and a minor axis of (125 - RT) μm. The refractive index of the material (PDMS) wrapped around CSPF is denoted by nPDMS.

PDMS is a highly sensitive transparent material with a large negative thermal optic coefficient [13,14,26]. The PDMS refractive index (PDMSRI) n0=1.4204 at temperature 22 °C [13] and PDMS RI at other temperature are estimated by using nPDMS=n0+γΔT in our simulation, whereΔTis the temperature change and thermo-optic coefficient γ4.66×104/°C. Figure. 2 shows the simulated results of the PDMSW-CSPF with a RT of 43.26 μm. The transmitted spectra in Fig. 2(a) shows that a dip with an extinction ratio of ~15 dB blue-shifts from 1663 nm to 1640 nm when the temperature increases from 30°C to 80°C and the corresponding nPDMS dropped from 1.41621 to 1.39026. Here, transmission (T) is negative in value as shown in Fig. 2(a) because transmission definition of T=10×log(Pin/Pout) is used in the simulations, where Pin and Pout are respectively input and output power of the PDMSW-CSPF respectively.

 figure: Fig. 2

Fig. 2 Simulated results of the PDMSW-CSPF with a residual thickness (RT) of 43.26μm. (a) Transmission spectra with temperature (30~85°C); (b)~(g) field evolutions in vertical sections (yz-plane) along the PDMSW-CSPF with temperatures of 30°C (b), 40°C (c), 50°C (d), 60°C (e), 70°C (f) and 80°C (g).

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The appearance of peaks/dips in the transmitted spectrum of the PDMSW-CSPF, as shown in Fig. 2(a), can be explained by the multimode interference (MMI) in the CSPF [22]. Here, the flat section of CSPF works as a D-shape coreless multimode waveguide that enables multimode interference. Figures 2(b)-2(g) that show the optical field evolutions in the vertical sections (yz-plane) along a PDMSW-CSPF with RT = 43.26 μm, when the input wavelength is set at 1640 nm and temperatures are respectively set at 30°C, 40°C, 50°C, 60°C, 70°C, 80°C respectively with the corresponding nPDMS = 1.41621, 1.41150, 1.40678, 1.40207, 1.39735 and 1.39264. As shown in Figs. 2(b)-2(g), the incident light propagates in the fundamental mode along the lead-in SMF, and then is totally reflected by the polished surface. Consequently, the reflected light will be efficiently coupled into the coreless flat section, and thus the high-order modes are excited. Theses excited high-order modes, which contribute to the multimode interference in the CSPF, can be confirmed by the spatial frequency in the patterns of the field evolution [22]. Additionally, the high-order mode has strong evanescent field that strongly penetrates into the surrounding PDMS, which results in strong interaction between the optical fields guided by high-order mode and the surrounding PDMS, and thus high temperature sensitivity.

The blueshift of the dips in transmitted spectrum is contributed to change of PDMS refractive index caused by the change of the chamber temperature. Assuming two modes guided by flat section of the CSPF, such as j-th and k-th modes that contribute to the MMI and give rise to a dip, the dip blueshift could be understood qualitatively by the following equation [27]:

ϕ=2πLλ(njeffnkeff)=const,
where ϕ is the phase difference of the j-th and k-th modes when propagating along the L long CSPF, njeffand nkeffdenotes effective refractive indexes of j-th and k-th modes, λ is dip wavelength. According to the Eq. (1), when temperature increases and results in decrease in nPDMS and decrease in (njeffnkeff), the dip wavelength λ will blueshift so as to keep phase difference ϕ constant. Using partial derivative of Eq. (1) to the dip wavelength and nPDMS, we can obtain
Δϕ=ϕλΔλ+ϕnPDMSΔnPDMS=0.
Substituting nPDMS=γΔT into Eq. (2), we derive the sensitivity ST of PDMSW-CSPF to temperature,
ST=ΔλΔT=γλPDMS(njeffnkeff)(njeffnkeff)λλ(njeffnkeff),
where the operator x denotes partial derivative to x. Since the dispersion term λλ(njeffnkeff)is usually much smaller than ERI difference (njeffnkeff), we can neglect the dispersion term and simplify the sensitivity of Eq. (3) to,
ST=γλPDMS(njeffnkeff)njeffnkeff.
From Eq. (4), it can be seen that the temperature sensitivity is proportional to the three factors: (1) dip wavelength λ, (2) the thermo-optic coefficient γ of the material material and (3) relative change in the difference of njeff and nkeff that is caused by nPDMS change. The third factor is determined by the fiber structure. Therefore, we can enhance the temperature sensitivity by choosing a longer dip wavelength, a sensitive material with a larger thermo-optic coefficient, and a more sensitive fiber structure to the surrounding refractive index [28].

3. Fabrication and experimental setup

3.1 Samples and fabrications

The CSPF used in the experiment can be fabricated by polishing a SMF [22] (Corning SMF-28e) with a core diameter of 8.2 μm and a cladding diameter of 125 μm. Figure. 3(a) shows the zoom-in microscopic image of vertical section of the coreless flat section, from which the RT of 51.27 μm is measured. The flat polished surface of CSPF is shown in Fig. 3(b). Three CSPFs with three different RTs are fabricated by controlling the polishing time. The variations of residual thickness along the CSPF are measured by the microscopy (Zeiss Axio Scope A1) for the three CSPFs, as shown in Fig. 3(c). From Fig. 3(c), the three CSPFs are all measured to be ~4 mm in transitional section length and ~8 mm in length of the flat sections. The RTs of the three CSPF are measured as 43.26 μm, 51.27 μm and 57.81 μm, respectively.

 figure: Fig. 3

Fig. 3 (a) Microscopic image of the flat section of the CSPF with a RT of 51.27 μm; (b) Microscopic image of polished surface of the CSPF; (c) Variations of residual thicknesses for the three fabricated CSPFs.

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The PDMS solution is made by mixing two precursors of elastic material (Sylgard 184-A) and hardener (Sylgard 184-B) with a 10:1 ratio. After stirring for 15 min at the speed of 500 rad/min, PDMS solution containing bubbles is obtained. Then, the bubbles are removed by centrifugal for 20 min at the speed of 10000 rmp/min. When the PDMS solution without a bubble is prepared, the solution is mold into a 30 mm × 3 mm × 3 mm cube embedded with the CSPF passing through inside and then is heat at 70 °C for 10 hours. When the PDMS is cured and solidified, the CSPF wrapped by a PDMS cube is fabricated successfully.

3.2 Experimental setup

Figure 4 schematically illustrates the experimental setup to investigate the temperature sensing characteristics of the three PDMSW-CSPFs. In the experiment, the PDMSW-CSPF is fixed on the glass substrate by using ultra-violet glue (UV glue, Norland Optical Adhesive 65). The fixed PDMSW-CSPF is placed in a temperature chamber, and a commercial thermocouple monitors the temperature of the chamber. A computer is used to record the temperature of chamber in real time. The temperature of the chamber is set to be increased by a 5 °C step from 30°C to 85°C and the transmitted spectrum of the PDMSW-CSPF is correspondingly measured by an optical spectrum analyzer (OSA, YOKOGAWA AQ6370D). In the measurement, light from a broadband source (BBS, ANDO AQ4305) with a broad wavelength range of 1000~1700 nm is launched into the PDMSW-CSPF.

 figure: Fig. 4

Fig. 4 Schematic of experimental setup to investigate the temperature sensing characteristics of the PDMSW-CSPF.

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4. Results and discussions

4.1 Spectrum shift with temperature

Figure 5 shows the blueshift in the transmitted spectra of the PDMSW-CSPF with RT = 57.81 μm when temperature increases from 30 °C to 85 °C. The experimental and simulated spectra are respectively shown in Fig. 5(a) and 5(b). As shown in Fig. 5(a) and 5(b), the shape and dips of the measured transmitted spectrum of the PDMSW-CSPF are very similar to that of the simulated spectrum. This verifies that the dips in the measured spectrum are originated from the MMI in the CSPF. However, the position and extinction ratio (ER) of the dip in the experiment is slightly different from that in the simulation. The ER difference of dips between experiment and simulation is due to the neglecting roughness of the polished surface in our simulation model, since the roughness will cause high loss in a guided mode that contributes to the MMI and thus leads to a shallow dip. The slight difference between the experiment and simulation in the core and cladding RI of the CSPF leads to the different dip positions in the transmitted spectrum. Nevertheless, both experiment and simulation shows that the dips in transmitted spectrum of PDMSW-CSPF will blueshift when the chamber temperature increases, which confirms that PDMS has a negative thermo-optical coefficient since the only decrease in PDMS RI can lead to the spectral blueshift.

 figure: Fig. 5

Fig. 5 The shift of transmitted spectra of the PDMSW-CSPF with RT = 57.81 μm with temperature increase from 30 °C to 85 °C for (a) experiment and (b) simulation.

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4.2 Influence of the RT on the sensitivity

The temperature sensing characteristics of the three fabricated PDMSW-CSPFs with RTs of 43.26 μm, 51.27 μm and 57.81 μm are, respectively, investigated both numerically and experimentally. The measured transmitted spectra with the increase of temperature in the range of 30~85°C are shown in Fig. 6(a), 6(c) and 6(e), while the simulated spectra with the temperature are shown in Fig. 6(b), 6(d), and 6(f). Wherein, the circles indicate the dips that are traced to sense the temperature increment. Tracing the shift of the dip, we obtain the dependencies of the dip wavelength on the temperature experimentally in Fig. 6(g) and numerically in Fig. 6(h). Although the simulated spectra are different from experimental ones as shown in Fig. 6(a)-6(f), the both simulated and experimental results show the linear relationship between the dip wavelength shift and the temperature, as shown in Figs. 6 (g) and 6(h).

 figure: Fig. 6

Fig. 6 The measured transmitted spectra of the PDMSW-CSPFs with RTs of (a) 43.26 μm, (c) 51.27 μm and (e) 57.81 μm; Simulated transmission spectra of the PDMSW-CSPFs with RTs of (b) 43.26 μm, (d)51.27 μm and (f) 57.81 μm; Measured (g) and simulated (h) dependencies of dip wavelength on temperature of PDMSW-CSPFs; Measured (i) and simulated (j) dependencies of dip wavelength on temperature sensitivity.

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To investigate the influence of the RT of the PDMSW-CSPF on the sensitivity more rigorously, we choose the dips near a same wavelength for different RTs. As a result, we can reduce the impact of dip wavelength as low as possible because the sensitivity depends on the dip wavelength as seen from Eq. (4). From Fig. 6 (g) and 6(h), the temperature sensitivities of the PDMSW-CSPF with different RTs can be measured experimentally and calculated numerically. The sensitivities for RT = 43.26 μm, 51.27 μm, 57.81 μm were experimentally measured as 0.3084 nm/°C, 0.2734 nm/°C, 0.2544 nm/°C, respectively. The linear correlations of the three PDMSW-CSPFs were, respectively, fitted as 0.9943, 0.9905, 0.9840, which indicate that our fabricated PDMSW-CSPFs could have high linearity and can be used in practical application. Correspondingly, the three PDMSW-CSPFs with the same RTs were numerically investigated and the simulated sensitivities were, respectively, calculated as 0.3213 nm/°C, 0.3119 nm/°C and 0.2892 nm/°C with linear correlations of 0.9896, 0.9861 and 0.9874. Using the above results, the relationship between RT and temperature sensitivity can be obtained, which is shown in Fig. 6(i) for the experimental and in Fig. 6(j) for the simulation. Both experiment and simulation results show that the sensitivity increase with the thinner RT of the PDMS-CSPF. This is because the reduced RT leads to stronger evanescent field outside the CSPF for the MMI modes and thus results in a more sensitive fiber structure with a larger coefficient (njeffnkeff)/nPDMS. Additionally, it is shown in Figs. 6(i) and 6(j) that the sensitivity calculated from the simulation is slightly higher than that measured from the experiment. This is because the dip wavelength chosen in the simulation is longer than that in the experiment.

4.3 Influence of the dip wavelength on the sensitivity

Due to the MMI in the flat section of the CSPF, several dips will appear in the transmitted spectrum, which can be confirmed by the simulated and measured spectra in Figs. 7(a) and 7(b). Here, RT = 43.26 μm of the PDMSW-CSPF is chosen to investigate the influence of the dip wavelength on the temperature sensitivity both experimentally and numerically. The measured and simulated transmitted spectra are shown in Fig. 7(a) and Fig. 7(b), respectively. The wavelength of the dip at 30°C is defined as“reference wavelengths”(RW). Difference between the dip wavelength at T>30°C and the RW is defined as the “wavelength shift”(WS). The WS is negative because the negative thermo-optic effect of the PDMS. To investigate the influence of the RW on temperature sensitivity, the dip wavelength shift with temperature are, respectively, obtained by tracing the dips 1~3 in the experiment as shown in Fig. 7(c), and by tracing the dips 1~7 in the simulation as shown in Fig. 7(d). Here, the RWs are chosen at 1319 nm, 1519.1 nm and 1560.9 nm, respectively, for the dips 1~3 in the experiment, while at 1294 nm, 1330.6 nm, 1382 nm, 1439 nm, 1500 nm, 1564.5 nm and 1663 nm for the dips 1~7 in the simulation. The influence of RW on sensitivity is analyzed experimentally in Fig. 7(e) and numerically in Fig. 7(f). From Fig. 7(c), the temperature sensitivities in the range of 30~85°C for the dips 1~3 are, respectively, fitted as 0.3221 nm/°C, 0.4250 nm/°C and 0.4412 nm/°C with corresponding linearity of 0.9914, 0.9937 and 0.9974. The influence of RW on the sensitivity is also analyzed by the simulations. From Fig. 7(f), the temperature sensitivities for the dips 1~7 are, respectively, simulated to be 0.2494 nm/°C, 0.2893 nm/°C, 0.3084 nm/°C, 0.3420 nm/°C, 0.3441 nm/°C,0.4101 nm/°C and 0.4525 nm/°C with corresponding linearity of 0.9890,0.9833,0.9874,0.9889,0.9897,0.9849 and 0.9863. Therefore, the relationship between the sensitivity and the RW is obtained and shown in Fig. 7(d). Both the simulations and the experiments indicate that the wavelength shift has a high linear correlation with the temperature change as shown in Fig. 7(c) and 7(d), and that the sensitivity increases with RW becoming longer as shown in Figs. 7(e) and 7(f). It is interestingly noticed that the sensitivity of such PDMSW-CSPF linearly increases with RT, which is in good agreement with the prediction of Eq. (4). Moreover, it is also found that the sensitivities measured at the same RW in the experiment are in agreement with the simulations, which confirms again that the wavelength shift caused by the temperature is originated from the MMI mechanism of the CSPF. As shown in Fig. 7(e), the relatively high sensitivity of 0.4412 nm/°C can be achieved by the fabricated PDMSW-CSPF with RT = 43.26 μm when choosing the RW at 1560.0 nm. The sensitivity should be enhanced by choosing a longer RW, as proved by Eq. (4) and the simulations shown in Fig. 7(f).

 figure: Fig. 7

Fig. 7 Influence of the RW on the sensitivity of the PDMSW-CSPF results for the CSPF with a RT of 43.26μm. Transmission spectrum: (a) the measured spectra, (b) the simulated spectra. Shift of the dip with temperature at different RWs: (c) measured, (d) simulated. The corresponding sensitivities in the temperature ranges: (e) measured, (f) simulated.

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4.4 Reversibility of the PDMSW-CSPF sensor

Since the reversibility of a high sensitive fiber sensor is usually poor [20], we choose the high sensitive PDMSW-CSPF with RT = 43.26 μm to investigate the reversibility of the sensor. As shown in Figs. 8(a)-(c), the linear dependences of the dip wavelength on the temperature are, respectively, measured by tracing dip1, dip2 and dip3 in a heating/cooling cycle experiments. In Fig. 8(a)-(c), it is shown that the black squares for the heating experiment overlapped with the red squares very well, which indicates the PDMSW-CSPF has a good reversibility. Form the linear dependence, the sensitivities of the dip1, dip2 and dip3 are, respectively, fitted as 0.3221 nm/°C, 0.4250 nm/°C and 0.4406 nm/°C for the heating experiment, and fitted as 0.3212 nm/°C, 0.4205 nm/°C and 0.4412 nm/°C for the cooling experiment, as shown in Fig. 8(d). The corresponding linearity of the dip1~3 are also obtained as high as 0.9914, 0.9937 and 0.9974 for the heating, and as 0.9943, 0.9922 and 0.9965 for the cooling. The heating/cooling experimental results show that such PDMSW-CSPF can have very high linearity that will be much desirable and useful in practical application. Here, we introduce the “relative sensitivity deviation” (RSD) as a criterion to assess the reversibility of the temperature sensor. The RSD is defined as the ratio of sensitivity deviation to the average sensitivity in the heating/cooling cycle experiments. Therefore, the smaller RSD indicates a sensor with a better reversibility. From above experimental results, the RSD for the dip1~3 are, respectively, measured as ± 0.12%, ± 0.53% and ± 0.068%. It is worth noticing that such PDMSW-CSPF can have both the high reversibility of RSD=±0.068%, high linearity of 0.9974 and the high temperature sensitivity of −0.4409 nm/°C.

 figure: Fig. 8

Fig. 8 The cycle experiments to characterize the reversibility of the PDMSW-CSPF with RT = 43.26 μm when the chamber temperature is heating and cooling. The linear dependences of the dip wavelength on the temperature for the heat/cool cycle experiments when tracking dip1 (a), dip2 (b) and dip3 (c), respectively; (d) ‘sensitivity of the tracking dips.

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4.5 Long-term stability of the PDMSW-CSPF sensor

To investigate the long-term stability of the sensor experimentally, we choose the high sensitive PDMSW-CSPF with RT = 43.26 μm. In our experiment, the dip3 wavelength is recoded for 74 hours when the chamber temperature is circularly changed from 40°C to 80°C. The black, red, blue, green, and pink solid lines denotes the dip3 wavelength averaged in time, respectively, at 40°C,50°C,60°C,70°C and 80°C. From Fig. 9(b), the standard deviation of the dip wavelength at 40°C, 50°C, 60°C, 70°C and 80°C are, respectively, obtained as low as 0.141 nm, 0.135 nm, 0.088 nm, 0.069 nm and 0.085 nm. These low standard deviations of the dip wavelength indicate that the PDMSW-CSPF has high long-term stability.

 figure: Fig. 9

Fig. 9 The long-term stability of the PDMSW-CSPF. (a) the long-term variation of the dip wavelength and (b) standard deviation of the dip wavelength at 40°C, 50°C, 60°C, 70°C and 80°C, respectively.

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In Table 1, we compare the performance and fabrication of fiber temperature sensors in different fiber structures. It is shown that, unlike the fabrication of other fiber sensors involving chemical etching, precise alignment, splicing and tapering, the fabrication of the PDMSW-CSPF is much simpler and has a lower cost than the other temperature fiber sensors, since the PDMSW-CSPF requires only wheel side-polishing. Additionally, the PDMSW-CSPF sensor can work in relatively wide temperature range of 30~85°C, and has both high sensitivity of −0.4409 nm/°C, high linearity of 0.9974 and good reversibility of RSD=±0.068%. Although the PDMS-coated STF has very high sensitivity [19], the temperature range of 20~65 °C is slightly narrower than the PDMSW-CSPF. In Ref [19], the reversibility and linearity of the PDMS-coated STF were not investigated. Despite of the high sensitivity (−1.328 nm/°C) [20], the PDMS-grating fiber has more poor reversibility (RSD=±6.4%) than that of the PDMSW-CSPF, and the linearity of the PDMS-grating fiber were not investigated as well From the comparison in Table 1, it can be seen that the comprehensive performance of the PDMSW-CSPF is better than other fiber temperature sensors.

Tables Icon

Table 1. Performance and fabrication of different temperature fiber sensors.

In summary, to our best knowledge, a novel fiber structure of CSPF is, for the first time, exploited to realize a fiber temperature senor by wrapping the sensitive material PDMS. The temperature sensing characteristics are investigated numerically and experimentally. It is found that the dip in the transmitted spectrum is caused by the multimode interference in CSPF, and that the negative thermo-optic effect of the PDMS results in the blueshift of the dip. Both experimental and numerical results show that the temperature has highly linear correlation with the dip wavelength shift, allowing the PDMSW-CSPF to be a good temperature sensor. The fabricated PDMSW-CSPF with RT = 43.26 μm has high sensitivity of −0.4409 nm/°C, high linearity of 0.9974 and relative wide working range of 30~85 °C. Moreover, the influence of RT and RW of the PDMSW-CSPF on the sensitivity is also analyzed. The analysis shows that reducing the residual thickness and choosing the dip at a longer reference wavelength (RW) could further enhance the sensitivity of the PDMSW-CSPF and the temperature sensitivity has a linear correlation with the RW. Finally, the reversibility and stability of the PDMSW-CSPF with RT = 43.26 μm is investigated by heating/cooling cycle experiments. The relative deviation of sensitivity (RSD) is, for the first time, introduced to assess the reversibility of the fiber sensor. The results of the cycle experiments showRSD=±0.068%, and show that the sensor has high long-term stability with low standard deviation of less than 0.141 nm for 72 hours. Compared with other fiber structure sensor, we found that the PDMSW-CSPF has higher comprehension performance, although its sensitivity is not the highest. Due to the advantages of easy fabrication, low cost, compact size, relative wide range, high sensitivity, good linearity and reversibility, the PDMSW-CSPF has a great potential in practical applications where the high measurement precision is required.

Funding

This work is supported by the National Natural Science Foundation of China (Grant Nos.61675092, 61475066, 61771222, 61405075, 61401176, 61505069, 61575084); Natural Science Foundation of Guangdong Province (Grant No. 2016A030313079, 2014A030313377, 2015A030306046, 2015A030313320, 2016A030311019, 2016A030310098, 2014B010120002); Science and technology projects of Guangdong Province (Grant Nos. 2017A010102006, 2015A020213006, 2015B010125007, 2016B010111003, 2016A010101017); Science & Technology Project of Guangzhou (Grant Nos. 201707010396, 201506010046, 201605030002, 201607010134, 201707010253) and the Fundamental Research Funds for the Central Universities of China (No, 21617333).

Acknowledgment

The authors thank to Huazhuo Dong for helping design the simulation model of PDMSW-CSPF, and YeLin He for drawing Fig. 4.

References and links

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Figures (9)

Fig. 1
Fig. 1 Schematic diagrams of PDMS-wrapped CSPF: (a) three-dimensional view and (b) vertical section.
Fig. 2
Fig. 2 Simulated results of the PDMSW-CSPF with a residual thickness (RT) of 43.26μm. (a) Transmission spectra with temperature (30~85°C); (b)~(g) field evolutions in vertical sections (yz-plane) along the PDMSW-CSPF with temperatures of 30°C (b), 40°C (c), 50°C (d), 60°C (e), 70°C (f) and 80°C (g).
Fig. 3
Fig. 3 (a) Microscopic image of the flat section of the CSPF with a RT of 51.27 μm; (b) Microscopic image of polished surface of the CSPF; (c) Variations of residual thicknesses for the three fabricated CSPFs.
Fig. 4
Fig. 4 Schematic of experimental setup to investigate the temperature sensing characteristics of the PDMSW-CSPF.
Fig. 5
Fig. 5 The shift of transmitted spectra of the PDMSW-CSPF with RT = 57.81 μm with temperature increase from 30 °C to 85 °C for (a) experiment and (b) simulation.
Fig. 6
Fig. 6 The measured transmitted spectra of the PDMSW-CSPFs with RTs of (a) 43.26 μm, (c) 51.27 μm and (e) 57.81 μm; Simulated transmission spectra of the PDMSW-CSPFs with RTs of (b) 43.26 μm, (d)51.27 μm and (f) 57.81 μm; Measured (g) and simulated (h) dependencies of dip wavelength on temperature of PDMSW-CSPFs; Measured (i) and simulated (j) dependencies of dip wavelength on temperature sensitivity.
Fig. 7
Fig. 7 Influence of the RW on the sensitivity of the PDMSW-CSPF results for the CSPF with a RT of 43.26μm. Transmission spectrum: (a) the measured spectra, (b) the simulated spectra. Shift of the dip with temperature at different RWs: (c) measured, (d) simulated. The corresponding sensitivities in the temperature ranges: (e) measured, (f) simulated.
Fig. 8
Fig. 8 The cycle experiments to characterize the reversibility of the PDMSW-CSPF with RT = 43.26 μm when the chamber temperature is heating and cooling. The linear dependences of the dip wavelength on the temperature for the heat/cool cycle experiments when tracking dip1 (a), dip2 (b) and dip3 (c), respectively; (d) ‘sensitivity of the tracking dips.
Fig. 9
Fig. 9 The long-term stability of the PDMSW-CSPF. (a) the long-term variation of the dip wavelength and (b) standard deviation of the dip wavelength at 40°C, 50°C, 60°C, 70°C and 80°C, respectively.

Tables (1)

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Table 1 Performance and fabrication of different temperature fiber sensors.

Equations (4)

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ϕ = 2 π L λ ( n j e f f n k e f f ) = c o n s t ,
Δ ϕ = ϕ λ Δ λ + ϕ n P D M S Δ n P D M S = 0.
S T = Δ λ Δ T = γ λ P D M S ( n j e f f n k e f f ) ( n j e f f n k e f f ) λ λ ( n j e f f n k e f f ) ,
S T = γ λ P D M S ( n j e f f n k e f f ) n j e f f n k e f f .
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