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Abstract
A new mechanism between the temperature sensitivity and the length ratio of PMMA coating to no-core fiber (NCF) is reported to realize an optical fiber temperature sensor with ultra-high sensitivity and compact size by PMMA-coated no-core fiber. By both theory and experiment, it is found that the sensitivity has a linear response to the length ratio of PMMA coating to NCF rather than the conventional viewpoint that it depends on the length of PMMA. Based on this conclusion and the high thermo-optic coefficient of PMMA, the temperature sensitivity is significantly enhanced as high as -9.582 nm/℃ through a simple, compact, and inexpensive sensor with 5 mm NCF and 3 mm PMMA coating. Our work opens a new avenue of a significant increase in the detection sensitivity of miniaturized fiber temperature sensors.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber sensors based on multimode interference have attracted extensive interest in recent years due to the advantages of simple structure, easy fabrication, and high sensitivity. [1–6] This kind of sensor is generally obtained by splicing a section of multimode fiber (MMF) into single-mode fiber (SMF) to form an SMF-MMF-SMF (SMS) structure. As a special MMF, no-core fiber (NCF) is an excellent sensing platform benefiting from its exposure to the evanescent field into the surrounding media. They have found applications in sensing various parameters such as temperature [7], refractive index (RI) [8], strain [9], and magnetic field [10]. Among them, the accurate and fast detection of temperature has great importance in chemistry [11], agriculture [12], medicine [13], and so on. Nevertheless, the intrinsic temperature sensitivity of an SMF-NCF-SMF (SNS) is only ∼0.01 nm/°C [14], which results from the low thermo-optic coefficient (TOC, ∼1×10−5/°C) [15] and thermal expansion coefficient of silica fiber [16].
To enhance the temperature sensitivity, one promising strategy is to coat a material with a high TOC around the multimode waveguides [17–19]. For example, Bhardwaj et al. sealed the NCF with the saline solutions with different RIs. They found the sensitivity increased with the surrounding RI, achieving the maximal sensitivity of 0.2 nm/°C when the solution RI is 1.40 [20]. Hu et al. further increased the RI of the surrounding liquid to 1.45, which is slightly lower than the RI of NCF, and the temperature sensitivity is dramatically enhanced to 5.15 nm/°C [18]. Moreover, solid materials with large TOCs, which possess the advantages of easy handling and assembling with fiber compared with liquid, have also been employed to enhance the sensitivity. For instance, the silicon rubber with a RI of 1.42 was coated around an SNS to increase the sensitivity to 0.25 nm/°C [21]. Fukano et al. coated the MMF core with epoxy resin, which has a RI of 1.438 at 1530 nm, significantly improving the sensitivity to -5.96 nm/°C [19]. All the above works employed the coating materials having a RI lower than the silica, where the light occurs total reflection at the interface of fiber core and coating. Recently, polymethyl methacrylate (PMMA) with a RI (∼1.48 at 1550 nm) higher than the fiber had been demonstrated as a sensitivity-enhanced coating material for SNS [22]. In this case, the light enters the PMMA coating with a high TOC, significantly enhancing the temperature sensitivity. Moreover, it has been shown that the anti-resonance of an individual mode can be generated by bending a PMMA-coated SNS, leading to the temperature sensitivity of -3.784 nm/°C [23]. Nevertheless, the anti-resonance requires a strict condition on phase matching, which is vulnerable to ambient randomness.
Our work focuses on the dependence of sensitivity on the lengths of NCF and PMMA coating theoretically and experimentally, even though the configuration of SNS with PMMA coating has been proposed previously. We discovered that the length ratio of PMMA to NCF (LRPN) determines the sensitivity, and they present a linearly proportional relation. Based on this conclusion, an ultra-compact sensor, where the NCF and PMMA lengths are 5 and 3 mm, respectively, with an ultra-high sensitivity of -9.582 nm/°C, is achieved. The size and sensitivity can be further optimized by reducing the NCF length and meanwhile increasing the LRPN.
2. Principle and design
Figure 1 shows the schematic diagram of the sensor, which is composed of a piece of PMMA-coated NCF (YOFC Ltd.) spliced between two SMFs (SMF-28e, Corning Inc.). The coating and cladding diameters of the SMF are 9 and 125 μm, respectively. The diameters of the NCF and PMMA coating are 125 and 250 μm, respectively.
Fig. 1. (a) Schematic diagram of the proposed sensor. (b) Beam propagation method presents the light propagation inside the sensor.
The working principles of the sensor are multimode interference and the large TOC of PMMA, -1.35×10−4/°C [24]. When the fundamental mode in the lead-in SMF propagates to the NCF without PMMA, the light couples into a serial of modes in NCF owing to the mismatch of the core diameters between SMF and NCF. The modes in various propagation constants interfere with each other if a specific phase difference is satisfied, that is, multimode interference occurs as shown by red arrows in Fig. 1(a). In the section of NCF with PMMA coating, the light beam is partly reflected and transmits stably in the coating as the black arrows shown in Fig. 1(a). The high-temperature sensitivity can be achieved as expected for the large TOC of PMMA. For simplicity, we assume that two guided modes are dominated in the whole propagation process. Considering only these two dominant modes, the phase difference Φ, which is a function of wavelength λ and temperature T, between the two dominant modes can be expressed by
The sensor was first analyzed by simulation using the beam propagation method (BeamProp, RSoft Synopsys Inc.), as shown in Fig. 1(b). The RIs of the SMF, NCF, and PMMA were set as 1.44, 1.444, and 1.488, respectively. The length of NCF was set as 25 mm. Considering the TOCs of PMMA and NCF as -1.35×10−4/°C and 1×10−5/°C, respectively [24], the transmission spectra of the sensors with different PMMA coating lengths in the temperature range from 25 to 37 °C were simulated in Figs. 2(a)-(c). For the PMMA-coated SNSs, all the spectra exhibit a blueshift with the increase of temperature. However, the 4 mm coating presents a larger shift than the 2 mm, and the spectra present a slight redshift for a bare SNS. The reason is that the PMMA has a negative TOC while NCF has a positive one, and the TOC of PMMA is much larger than that of NCF in the absolute value. As a result, the temperature sensitivity increases with the PMMA length, as shown in Fig. 2(d). The simulations present the dependence of sensitivity and the length of PMMA, partly confirming the conclusion suggested by Eqs. (2) and (3). Furthermore, a series of experiments will be carried out to demonstrate the conclusion in the following section.
Fig. 2. Simulated spectra of the proposed sensors with the coating lengths of (a) 0 mm, (b) 2 mm, and (c) 4 mm, respectively. (d) Wavelength shifts of dips as a function of temperature for the sensors with different PMMA coating lengths.
3. Experiments and results analysis
To verify the proposed sensor experimentally, we fabricated a series of PMMA-coated SNS sensors. The schematic diagram of the experimental setup for the sensors test is depicted in Fig. 3. The fabricated sensors were fixed on a silica plate with a similar thermal expansion coefficient to the fibers. Two ends of the sensor were connected to a supercontinuum light source (SCL, YSL photonics SC-5) and an optical spectral analyzer (OSA, AQ6370D) set with a resolution of 0.1 nm. The sensors were placed into a temperature-controllable chamber to characterize the temperature response.
Because of the multimode interference, there are a series of peaks and dips in the transmission. As mentioned below, the PMMA coating can significantly enhance the sensitivity so that the wavelength shift will be even much more than the free spectral range, leading to one-dimensional transmittance spectra overlapped. Figure 4(a) presents a messy fashion when the ambient temperature changes from 25 to 45 °C in steps of 1 °C. Therefore, we alternatively used a two-dimensional spectra evolution in Fig. 4(b) to display the response. The spectra exist in the form of a color-cell plane array. For a particular color unit, its’ position in the coordinate shows the environment temperature. The chromaticity represents the intensity in the corresponding wavelength. In this paper, larger chromaticity corresponds to more significant intensity. In this case, by tracking the position of chromaticity in continuous temperature change, as the dashed line shown, peaks or dips in the spectra depending on temperature can be easily distinguished and tracked.
Fig. 4. Spectral response to the temperature changing from 25 to 45 °C for the sensor with 40 mm NCF and 16 mm PMMA coating in the form of (a) one-dimensional fashion and (b) two-dimensional fashion.
Using this novel approach, we implement the temperature sensitivity in different lengths of PMMA, as shown in Fig. 5. By linearly fitting the wavelength shift of a peak or a dip varying with temperature, the sensitivity increases from 0.259 to -4.390, -5.150, and -6.179 nm/°C when the PMMA coating length increases from 0 to 8, 16, and 24 mm. We find that the experimental results are consistent with the simulations in Fig. 2(d): the spectra of the sensors without PMMA shows a slight redshift with the increase of temperature, whereas the addition of PMMA coating merits the sensors a significant blueshift to the temperature increase; moreover, a longer PMMA coating results in a larger blueshift, indicating that the temperature sensitivity increases with the PMMA coating length.
Fig. 5. Transmittance spectra of the sensors, with the PMMA length of (a) 0 mm, (b) 8 mm, and (c) 24 mm, varying with temperature presented in the form of two-dimensional spectra evolution. (d) Dependence of the dips shifts to temperature for the sensor with 40 mm NCF and different PMMA lengths.
To verify the conclusion suggested by Eq. (3) that the sensitivity is determined by the LRPN, several sensors with a constant LRPN but different NCF lengths were fabricated. Specifically, three sensors with a fixed ratio of 60%, where the NCF lengths are 20, 30, and 40 mm with the corresponding PMMA lengths of 12, 18, and 24 mm, were fabricated. The experimental results in Fig. 6 confirm that once the LRPN is fixed, the sensitivities are nearly the same, although their spectra present a remarkable difference. Three sensors have similar sensitivities of -6.029, -6.437, and -6.179 nm/°C with a standard deviation (SD) of 0.206 nm/°C. Although the lengths of PMMA and NCF are inaccurate in the confirmation experiments, the neglectable SD in sensitivities indicates that the same LRPN of the sensors contributes a similar sensitivity in temperature.
Fig. 6. Spectral responses to temperature for the sensors with a fixed LRPN of 60% but different NCF lengths of (a) 20 mm, (b) 30 mm, and (c) 40 mm. (d) The dependence of wavelength shift on temperature.
The dependence of the sensitivity on the LRPN is investigated. The LRPN can be achieved from 20% to 60% in steps of 10% by altering the NCF lengths of 20, 30, and 40 mm, and then changing the PMMA coating length. From the measurement results in Fig. 7, we can find that for a given LRPN, the sensitivity almost remains unchanged and is independent of the lengths of NCF and PMMA coating. More importantly, the sensitivity presents an excellent linear relationship with the increase of LRPN in Fig. 7(f), which agrees with the simulated results in the above theoretical analysis. The error bars in Fig. 7(f) indicate the standard deviations of the measured sensitivities keeping the LRPN unchanged while varying NCF and PMMA lengths, which verify that the conclusion is established regardless of the NCF length or PMMA.
Fig. 7. Sensitivities of LRPN taking (a) 20%, (b) 30%, (c) 40%, and (d) 50%. (e) Dependence of sensitivity on the LRPN and the NCF length. (f) Sensitivity versus the LRPN.
The repeatability of the proposed sensor in temperature sensing is evaluated by repeatedly varying the chamber temperature for two cycles between 24 °C and 42 °C in steps of 2 °C. In this experiment, a 20 mm NCF and a 10 mm PMMA coating sensor was employed. Figure 8(a) shows that the spectrum presents a regular shift with the temperature varying cycle. By tracking the peak in the spectra shown by the black dot line in Fig. 8(a), the results in Fig. 8(b) suggest that the sensor has a neglectable hysteresis to ambient temperature. The excellent repeatability allows us to obtain the closeness of the results, which is one of the most desired features in practical applications.
After that, the long-term stability of the sensor was evaluated by maintaining a constant chamber temperature. A sensor with a 20 mm NCF and a 4 mm PMMA coating was placed for 10 hours at 25, 28, 31, and 34 °C, respectively, and the transmittance spectra were recorded every 0.5 hours. The measured results in Fig. 9(a) show that the spectrum almost remains unchanged at a constant temperature during the test. The central wavelengths around 1550 nm varying with the ambient temperatures are displayed by the red dash line in Fig. 9(a). To gain a better insight into the long-term stability, we carried out the statistical analysis and presented the results in Fig. 9(b). The dip wavelengths are 1570.3, 1555.3, 1544.5, and 1528.2 nm with a neglectable SD of 0.9298, 0.6390, 0.6685, and 0.7242 nm for the temperatures of 25, 28, 31, and 34 °C, respectively. The fluctuation is mainly attributed to the temperature instability of the chamber with a maximal amplitude of ±0.2 °C, which can induce a wavelength fluctuation of ±0.936 nm according to the high sensitivity of -4.68 nm/°C. Therefore, the excellent long-term stability of the proposed sensor allows us to implement long-time sensing, which will benefit many essential applications such as battery monitoring and sensitive electronic devices.
3. Ultrahigh-sensitive and compact sensor
Based on the conclusion mentioned above—the temperature sensitivity is proportional to the LRPN—it is possible to achieve a sensor featuring high sensitivity and compact size if we choose a shorter NCF with a larger LRPN. To verify this, we fabricated a sensor with 5 mm NCF and 3 mm PMMA. The temperature response of the sensor was tested three times, and the results show good repeatability, as shown in Figs. 10(a)-(c). The sensitivities obtained from three repeated experiments are -9.416, -9.557, and -9.772 nm/°C with an expectation of -9.582 nm/°C and an SD of 0.179 nm, as shown in Fig. 10(d). The sensitivity increases ∼60% compared to the former experiments presented in Fig. 8. This can be attributed to the change of physical properties of the PMMA coating, such as RI, thickness, and morphology, during the process of fusion splice between PMMA-coated-NCF and SMF, as shown in Fig. 11. The physical properties change of PMMA coating is inevitable if a compact sensor with large LRPN is pursued because the distance between the PMMA and fusion splice point is so close, 1 mm in the current case, that the PMMA will be highly heated by the heat transferred from the splice point.
Fig. 10. Spectral response to temperature for the sensor with 5 mm NCF and 3 mm PMMA the (a) 1st, (b) 2nd, and (c) 3rd testing. (d) Dip wavelength dependence on temperature.
We categorize several typical SNS- or SMS-based temperature sensors in Table 1 regarding the detection range, sensitivity, and size. The most direct comparisons are the Refs. [26] and [23]. Even though SNS configuration with PMMA was used, their sensitivities were only -3.195 nm/°C and -3.784 nm/°C, respectively. Perfluorinated graded-index plastic optical fiber was used to enhance the sensitivity to incredible levels in Ref. [27], whereas size of 1000 mm reduces the spatial resolution and increases the cost and loss, which is inconvenient in practice.
Table 1. Comparison of the SNS- or SMS-based temperature fiber sensors.
4. Conclusion
In summary, an interesting study is reported to prove that the LRPN determines the sensitivity of PMMA-coated NCF from theory and experiments. By splicing the PMMA-coated NCF between two SMFs and comparing the sensitivities of a series of sensors with different LRPNs, it can be found that they present a linearly proportional relationship. Based on this conclusion and the large TOC of PMMA, the temperature sensitivity can be significantly improved. As a result, an SNS comprising a 5-mm-long PMMA-coated NCF is employed, and sensitivity of -9.582 nm/°C is achieved. Moreover, the tests demonstrate that the sensor possesses excellent repeatability and long-term stability in the measurements. Our work may open a new route to realize an ultrahigh-sensitive SMS-based fiber temperature sensor and simultaneously push the spatial resolution to new heights.
Funding
National Natural Science Foundation of China (61805108, 61904067, 62075088, 62175094); Fundamental Research Funds for the Central Universities (21620328, 21621405); Basic and Applied Basic Research Foundation of Guangdong Province (2017A010101013, 2020A1515011498); Science & Technology Project of Guangzhou (201605030002, 201704030105, 201707010500, 201807010077).
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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