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Abstract
A sensitivity enhanced temperature sensor with cascaded tapered two-mode fibers (TTMFs) based on the Vernier effect is proposed and experimentally demonstrated. It is confirmed that series connection exhibits higher extinction ratio than parallel one both by theory and experiments, which provides guidance for related experiments. In experiments, two TTMFs have the same single-mode fiber-TTMF-single-mode fiber configuration, while the free spectral ranges (FSRs) are chosen with slightly difference by modifying the parameters in the tapering process. Experimental results show that the proposed temperature sensor possesses sensitivity of −3.348 nm/°C in temperature measurement range from 25 °C to 60°C, 11.3 times sensitivity enhancement in comparison with single TTMF. Benefiting from advantages of high temperature sensitivity, simplicity of manufacture and long distance sensing, this novel sensitivity enhanced temperature sensor can be applied to various particular fields, such as oil wells, coal mines and so on.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Temperature is a fundamental and significant physical parameter in many fields, such as industrial manufacturing, biomedical science, fuel storage and so on. Since the optical fiber devices have the advantages of compact configuration and convenient fabrication, optical fiber sensors are developed vigorously for temperature monitoring currently, which convert the state of temperature into a measurable optical signal.
Nowadays, fiber grating [1–4], hollow-core fiber (HCF) [5–7] and other specific fibers [8–11] are commonly utilized methods for producing temperature sensors. In 2014, Tosi et al. proposed a fiber Bragg grating (FBG) array-based sensing probe installed on a device for radio frequency thermal ablation (RFTA), to provide quasi-distributed thermal pattern measurements [12]. Yadav et al. proposed a single-mode tapered optical fiber for temperature sensing application. The tapered fiber-based temperature sensor has sensitivity in the range from 0.01143 to 0.03406 nm/°C [13]. In 2018, Chen et al. used a PDMS-filled air-microbubble Fabry-Perot interferometer (FPI) in HCF as temperature sensor, which has the high temperature sensitivity of 2.7035 nm/°C with high linear response in the range of 51.2–70.5 °C [14]. Obviously, the sensor of single device is either of low sensitivity or complex to prepare.
To achieve higher sensitivity, the Vernier effect has been employed for sensitivity amplification [15–21]. Compared with a single structure, the sensitivity of the cascaded configurations can be increased several times. In 2014, Zhang et al. experimentally demonstrated a fiber-optic sensor based on two cascaded FPIs for high sensitive measurement of axial strain and magnetic field. FPIs were formed by a short section of hollow core photonic crystal fiber sandwiched by two single-mode fibers [22]. In 2019, Tian et al. reported a strain sensor based on the Vernier effect, which consists of a sensing FPI fabricated by splicing a section of microfiber between two single-mode fibers (SMFs) and a matched FPI formed by a section of HCF sandwiched between SMFs [23]. Recently, Jiang et al. proposed a refractive index (RI) sensor based on the Vernier effect in dual-microfiber coupler formations, and achieved an ultra-high sensitivity of 126,540 nm/RIU [24]. However, FPIs possess the extremely poor temperature sensitivity owing to the air cavity structure. Generally, tapered fiber is available for temperature measurement, because the change in ambient temperature can be observed by the shift of interference fringe pattern [13]. Nevertheless, temperature sensitivity for single tapered fiber sensor is too low to perform high-precision measurement of temperature. This dilemma would be resolved through assembling two tapered fibers with slightly different free spectrum ranges (FSRs), regarded as the fixed and sliding parts of Vernier caliper respectively, to induce Vernier effect.
In this paper, a simple, low-cost, high temperature sensitivity all-fiber sensor is demonstrated, the sensor consists of cascaded tapered two-mode fibers (TTMFs) based on Vernier effect. Both theory and experiment reveal that series connection exhibits higher extinction ratio than parallel connection. The experimental results show that the sensitivity of the cascaded TTMFs based sensor can be enhanced about 11.3 times compared with that of single TTMF based temperature sensor, and exhibits a high temperature sensitivity of −3.348 nm/°C in the temperature measurement range from 25 °C to 60 °C. The other great superiority of the proposed sensing framework is suitable for telemetry, as the sensing performance is independent of fiber length between the cascaded fiber tapers. It can be applied to remotely measure the amount of temperature change precisely, especially for occasions like oil wells, coal mines, etc.
2. Device fabrication and theoretical principle
2.1 Fabrication of temperature sensor
The sensitivity enhanced temperature sensor, as schematically shown in Fig. 1(a), consists of two TTMF structures. The former TTMF is looked upon as a reference, and the latter one is considered for sensing probe. The schematic structure of single TTMF is constructed with SMF-TTMF-SMF conformation, which is manufactured by three main steps. Initially, the SMF-TMF (two-mode fiber)-SMF configuration should be established, and next the TMF component is tapered through the flame tapering method. Last, the architecture is solidified and encapsulated with UV glue after tapering, to guarantee the firmness and easy access. The UV glue only plays a fixed role in the SMF part and does not contact and affect the tapered portion. Figure 1(b) shows the images of the untapered TMF, the transition zone, and the taper waist portion under the microscope. As the fiber is stretched, the tapered waist becomes thinner. At the tapering process, it is tried to ensure that only LP01 and LP11 modes propagate in the waveguide, resulting in a smooth comb spectrum [25]. The TMF employed has a particular RI profile, as mentioned in [26]. It can be seen from Fig. 1(c) that the core radius (r1), the radius of second layer (r2), the radius of third layer (r3), the radius of the outer cladding (r4) of the used TMF are 7 µm, 13 µm, 19 µm and 62.5 µm, respectively. Their corresponding RIs are n1 (1.4485), n2 (1.444), n3 (1.435336) and n4 (1.444), respectively.
Fig. 1. (a) Schematic structure of cascaded TTMFs based sensor, (b) image of the TTMF under the microscope, (c) RI profile of the used TMF.
The superposition of two spectra with slightly different FSR engenders periodic envelope, the shift of which with temperature change can be magnified by a certain factor. In the experiments, the FSRs of the sensing and reference TTMFs can be manipulated by adjusting the length and diameter of the taper waist [25]. The spectrum relationship between the cascaded structure and two single TTMFs is characterized through simulation and experiment. As shown in Fig. 2(a) and Fig. 2(b), the FSRs of the sensing and reference TTMFs are 3.28 nm and 3.08 nm at 1550 nm, respectively. And their extinction ratios (ERs) are 10.3 dB and 10.5 dB, respectively. The ratio of their ERs is about 1.02, which meets the requirements of the Vernier effect for better visibility.
Benefiting from the periodic comb-like transmission spectrum of single TTMF, the spectrum can be approximately set as a cosine function without negative axis. The black dotted line in Fig. 3 shows the result obtained by adding the two spectra with simulation, and the measured spectrum of cascaded TTMFs in series in experiment is depicted by the red curve. Although the ER in the experiment result did not reach the sum of the ERs of the two separate structures, it is slightly larger than that of a single TTMF. By contradistinguishing simulation and experiment curves, it can be seen that the upper envelopes of the both simulation and experiment spectra are similar, reaching the maximum at the same wavelength. Since the experimental spectrum is not a standard sine curve, the lower envelope of the spectrum is slightly jagged. But this does not affect the conclusion. The comparison illustrates that although cascading connection leads to simply added spectrum, periodic interference fringes are generated, due to the double filtering of two TTMFs. The fringes with envelope will alter sharply due to the disturbance of the surrounding physical parameters, which is the basis of the Vernier effect applied to high sensitivity sensing.
Fig. 3. Transmission spectra of the cascaded TTMFs based sensor from simulation calculation (black dashed line) and experiment measurement (red solid line).
2.2 Theoretical principle
It can be comprehended that as the TTMF gradually tapered, the core almost disappears, and the cladding becomes a new core, which results in LP01 and LP11 modes become waveguide cladding modes [25]. After cascading the TTMFs, they will be combined into a high temperature sensitivity sensor. So as to further understand this phenomenon, the working principle is deliberated.
From previous experiments, it can be found that there are LP01 and LP11 modes in TTMF, and account for the vast majority. Thus, the transmission spectrum of single TTMFs can be derived as
where $I_1^{}$ and $I_2^{}$ are the intensities of LP01 and LP11 modes, respectively. $\Delta \varphi$ represents the phase difference between two modes. Since the refractive index difference of two modes ($\Delta n_{eff}^{} = n_1^{} - n_2^{}$) is the dominant factor, the phase difference can be given as where L is the effective length of the tapered part, and $\lambda$ is the central wavelength of the light source. Furthermore, the free spectral range (FSR) of single TTMF can be conjectured asTwo TTMFs with similar FSRs are connected, one of which serves as a reference and the other as a sensing structure. When the transmission peaks of the two periodic comb spectra coincide, the maximum transmission can be attained. Due to the slight difference in the FSR period of the two spectra, the transmission peaks will overlap again after several orders, which leads to periodic envelope in cascaded composition spectrum. As the spectrum of sensing TTMF drifts subtly, the position of aligned transmission peaks will change greatly, so that the period of the cascaded structure will alter. The FSR of the sensing TTMF is called $FSR_1^{}$, and the reference one is $FSR_2^{}$. In accordance with the Vernier effect, the FSR of the cascaded TTMFs sensor can be deduced as [22]
Moreover, compared to the wavelength shift of a single TTMF, the envelope shift of the cascaded TTMFs sensor can be expanded by a magnification factor of M under the influence of the Vernier effect. The magnification factor is [22]
From Eq. (2), it can be seen that when the central wavelength of the light source is unchanged, the phase difference is determined by both the refractive index difference and the length of the tapered waist. As thermo-optic effect refers to the physical effect that the optical properties of the optical medium change with temperature. When the temperature increases, the effective refractive index and tapered length of the fiber will change accordingly. The thermo-optic coefficient $\zeta ( = \left. {\frac{{d\Delta n}}{{dT}}} \right|_{T = T_0} = 0.5 \times {10^{ - 6}}/K$) is used to represent the rate of change of the effective refractive index. And the coefficient of thermal expansion can be used to indicate the relative change in the length of the fiber when the temperature increases by 1 K. Since the optical fiber is composed of silica, the coefficient $\alpha ( = \frac{1}{L}\left. {\frac{{dL}}{{dT}}} \right|_{T = T_0} = 5.5 \times 10^{ - 7}/K$) is obtained by referring to the parameters of silica. Therefore, the temperature sensitivity can be obtained by differential derivation:
Under the magnification of the Vernier effect, the temperature sensitivity of the cascaded TTMFs sensor can be expressed as
Equation (7) clearly reflects the principle for temperature sensitivity of proposed sensor based on Vernier effect. This effect can increase the sensing sensitivity in a multiple relationship, enabling high-sensitivity.
3. Experiments and discussion
3.1 Sensitivity study of TTMFs with different FSRs
The experimental setups for temperature measurement with series and parallel TTMFs are schematically depicted in Figs. 4(a) and 4(b). A broadband source (BBS) with wavelength range from 1250 to 1650 nm is used for engendering light into the sensing schemes. A column oven is used to change the ambient temperature. As the temperature of oven changes from 25°C to 65°C with a step size of 5°C, the spectrum measurement is illustrated and saved via an optical spectrum analyzer (OSA) individually. For Vernier-based configuration, only one of TTMFs is placed in the oven, the other TTMF acts as a reference.
To compare the two cases, i.e. single TTMF sensor and cascaded one, the relationship between temperature sensitivity and FSR of single TTMF was firstly investigated. The result is given in Fig. 5. It can be seen that as FSR decreases, the absolute value of sensitivity rises exponentially. The TTMFs with FSR less than 5 nm has greater sensitivity, and the wavelength shift can be directly seen by observing the OSA. While FSR is below 15 nm, the temperature sensitivity reaches 150 pm/°C. Within 40-100 nm of the FSR, the temperature sensitivity is less than 50 pm/°C, much lower than that of the TTMF with FSR less than 5 nm, and the slope growth rate is insignificant. In order to maximize sensitivity, TTMFs with a smaller FSR should be utilized for single TTMF sensor. However, for cascading case, it can be seen from Eq. (5) that small FSR will reduce the magnification factor. Therefore, TTMFs with ∼3 nm of FSR are chosen for cascade experiments.
3.2 Temperature sensing experiment of the cascaded TTMFs based sensor
Generally, there are two connection methods for cascading two structures, one is series connection and the other is parallel connection [24, 27–30]. Figure 4(a) shows that series connection is to successively link two TTMF structures. While, as depicted in Fig. 4(b), the way for TTMFs connected in parallel requires two 3 dB couplers. Figure 6 reveals that the transmission spectra obtained by series and parallel connection. Comparing the two spectra, it can be seen that the trends of the envelope curves are approximately the same, but the ER in parallel is just half of that in series. And the TTMFs in parallel have the coarser spectrum and higher loss. It is speculated that this phenomenon is the inherent defect of the parallel method by introducing two additional 3 dB couplers. Similar to the case the resistors are connected in parallel ($R = \frac{{{R_1}{\cdot}{R_2}}}{{{R_1} + {R_2}}}$), the ER is analogous to the resistor. Since the ratio of the two structures’ ERs is about 1: 1, the ER of the total spectrum should be half of a single TTMF structure. As mentioned in the previous part of the article, the ER of the cascaded TTMFs in series is slightly greater than a single TTMF, thus the intensity of ER in parallel is about 1/2 of that in series. For the purpose of acquiring clearer envelope curves and detecting the temperature more accurately, the series connection method was exploited in the experiment.
As depicted in Fig. 4(a), the reference TTMF is exposed in air to maintain room temperature and the sensing TTMF is placed in oven to monitor the ambient temperature. The length of SMF applied to connect two TTMF is ∼0.5 m. The FSR of the sensing TTMF is 3.28 nm, and the other one is 3.08 nm. Figure 7 interprets the temperature sensitivity of the cascaded TTMFs based sensor. As indicated in Fig. 7(a), the dip of the upper envelope in the range of 1530-1570 nm is regarded as the reference point. The envelope is denoted by a red line, and the reference point is represented by an arrow. It can be seen from the spectrum that the visibility of the interference fringes increases for longer wavelengths. According to the Eq. (1) and Eq. (2), as the wavelength increases, the phase difference will decrease for same effective refractive index difference and length. The interference intensity will increase due to the increase of the cosine function with the phase difference decrease. In Fig. 7(b), the spectrum has a blue shift when the temperature increases. As the temperature gradually rises from 25°C to 65°C with a step size of 5°C, the arrowed point drifts to the left.
Fig. 7. (a) Transmission spectrum of the sensor (red line is the fitted upper envelope), (b) transmission spectra with temperature rises.
As it can be seen from the linear fitting red curve in Fig. 8, the temperature sensitivity of the cascaded TTMFs based sensor, is −3.348 nm/°C with R-square of 0.99983. In contrast, temperature sensitivity of single TTMF expressed by a blue line is −0.297 nm/°C. Distinctly, the sensitivity of the cascaded TTMFs based sensor is much higher than that of a single TTMF based sensor, exhibiting a sensitivity enhancement factor of 11.3. According to the theoretical analysis and Eq. (5), the theoretical amplification factor of sensitivity is about 15.4. The reason for the discrepancy is attributed to limited resolution of the used OSA and manually read FSR values.
Fig. 8. Linear fitting results of wavelength shift versus temperature for single TTMF and cascade TTMFs.
From the above experimental results, it can be concluded that, for a single TTMF based sensor, the narrower the FSR, the higher the sensitivity. Moreover, for a cascaded TTMFs based sensor, if the FSR of sensing TTMF and the FSR difference between the two TTMFs could be made both exceedingly small, higher sensitivity can be achieved. Nevertheless, in the actual manufacturing process, it is difficult to ensure that both are extremely small, so a compromise value should be taken. When the FSR of sensing TTMF is 3.28 nm, and the reference one is 3.08 nm, the temperature sensitivity of the cascaded TTMFs based sensor reaches −3.348 nm/°C from 25°C to 60°C, which is 11.3 times higher than the sensitivity of single TTMF based sensor. It is worth noting that the sensing performance is independent of fiber length between the cascaded fiber tapers. Thus, the great superiority of the proposed sensing framework based on series connection is suitable for telemetry.
4. Conclusions
A sensitivity enhanced temperature sensor with serial TTMFs based on the Vernier effect has been proposed and demonstrated in this paper. Both simulation and experiment results confirmed that the two cascaded TTMFs in series connection can bring about greater ER than parallel one, which provides guidance for related experiments. The proposed temperature sensor exhibits −3.348 nm/°C of sensitivity in the temperature measurement range of 25°C to 60°C, with 11.3 times sensitivity enhancement. Comparing with other sensors, cascaded TTMFs based sensor has quite a few advantages such as simple fabrication, compatibility with fiber-based system, and long distance sensing. Such superiority makes this temperature sensor a competitive candidate for special occasions like oil wells, coal mines, etc.
Funding
National Natural Science Foundation of China (91950105); 1311 talent plan of Nanjing University of Posts and Telecommunications; Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX19_0967); Natural Science Foundation of Jiangsu Province (19KJB510005); High-Level Training Fund project of Nanjing Xiaozhuang University (2019NXY18).
Disclosures
The authors declare no conflicts of interests.
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