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Abstract
An in-line interferometer based on tapered multicore embedded into a flexible thermo-optical material is proposed and investigated, theoretically and experimentally. The device consists of a tapered multicore fiber spliced between two single-mode fibers covered with PDMS, with high thermo-optic coefficient. The temperature sensitivity improvement obtained from PDMS applied on a tapered multicore fiber (TMCF) interferometer has been fundamentally and experimentally verified. The experimental results show the temperature sensitivity can be improved by reducing the tapered waist diameter of TMCF. The sensor exhibits the high sensitivity of 5-25 nm/°C within the decreasing temperature range from 50 °C down to 10 °C. A sequence of simulations and corresponding experiments are performed to clarify the evolution of the interference fading and consequently build the criteria for sensor design and reachable lower limit of temperature sensing. The proposed sensor can be employed as photonic thermometer with ultra-high sensitivity for biological and deep-sea applications, particularly based on the claimed quantitative criteria.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber interferometers have been widely used for sensing in a broad range of applications, including temperature, refractive index (RI), liquid level, pressure, acoustic waves, strain, etc. Particularly for the temperature measurement, the interferometer based on Sagnac [1], Fabry-Perot [2], Michelson interferometer [3], or Mach-Zehnder [4] structures, or multimode interference [5,6] have been proposed and demonstrated. The surrounding refractive index (SRI) sensitivity and temperature of these structures have been investigated intensively.
Multicore fiber is a promising interferometer candidate, due to its compact structure comprising multiple optical paths in a limited cross-sectional space. An in-line interferometer based on the intermodal coupling of a tapered multicore fiber (TMCF) has been explored due to its easy fabrication, compact structure and its stable and highly-repeatable performance on temperature sensing [7,8] and RI [9]. The transmission spectrum of TMCF has obtained a sensitivity of 29 pm/°C at lower temperatures (100-300 °C) and 52 pm/°C at higher temperatures (300-1000 °C) through the thermo-optic effect and thermal expansion of MCF [7]. This structure as well presents high performance on RI sensing in a range of 1.34-1.43 RIU, with a different sensitivity related with the RI value and the waist diameter of tapered region.
Rather than depending on the thermo-optic coefficient of pure silica, a few researcher groups have reported the temperature measurements by employing materials with a high thermo-optic coefficient [10,11]. The poly-dimethylsiloxane (PDMS) is a polymeric silicone material widely used in the area of photonics [12]. PDMS has unique optical properties with transparency for a wide range of wavelength, an appropriate RI value slightly lower than silica, biocompatibility, low Young’s modulus, and especially high thermo-optic coefficient (TOC) (−4.66×10−4/°C) [13,14]. Integrated with the optical fiber sensors, PDMS has been utilized as an active mater ial for temperature sensing in Ref. [4–6], and has achieved a sensitivity of 3101.8 pm/°C [6].
The combination of PDMS and TMCF is a potential configuration for temperature sensing, by employing the high TOC and appropriate RI value from PDMS, the high RI sensitivity and longitudinal waist region from the TMCF to build strong relation between sensor setup and the environment. Moreover, the PDMS encapsulation can provide entire protection for the fragile photonic structure with excellent flexibility, biocompatibility, avoiding the surrounding influence on temperature sensing [15].
In this paper, a highly sensitive sensor of temperature based on the TMCF interferometer embedded in PDMS is experimentally demonstrated. The proposed structure takes advantage of the external evanescent field of the TMCF and the interaction between the evanescent field and surrounding PDMS. The experiments showed that the temperature sensitivity of the proposed sensor could be effectively improved by embedding the TMCF in PDMS. The temperature sensitivity of the proposed sensor with a diameter of 7 µm reaches 25676.8 pm/°C in the range of 10 °C to 50 °C.
To further reveal the evolution of the interference spectrum under lower temperature, the consequent simulations were performed and analyzed. The relationship between the interference elimination and the design of the interferometer is constructed. A series of experiments were conducted to extend the conclusions from simulations to real world. Based on the combined results from simulations and experiments, the proposed highly sensitive temperature structure is thoroughly investigated and the design criteria of the temperature sensor is discussed, which is essential for applications with different requirements on temperature sensitivity or various range.
2. Fabrication and operation principle
A schematic of tapered multicore fiber (TMCF) structure with PDMS encapsulation is shown in Fig. 1(a). The interferometer was built by splicing tapered MCF of a few centimeters between two single-mode fibers. The cross-section of the un-tapered MCF (FIBERCORE, SM-7C1500) with cores diameter a, a cladding diameter, and a pitch size $\varLambda$ of 6.1 µm, 125 µm, and 35 µm as shown in Fig. 1(b). The flame heating technique was used to fabricate the tapered MCF. When the waist diameter is thinned, the core and the pitch size reduce in proportion with a constant ratio of the core diameter over the pitch size. The tapered MCF interferometer was encapsulated by completely immersing in PDMS and then baked in the thermostat for 1 h under 120 °C.
Fig. 1. (a) Schematic of TMCF structure with PDMS capsulation. (b) Cross section of the MCF. (c) The interference spectrum of TMCF structure with PDMS capsulation
The reduction of the core diameter and pitch size by tapering MCF mainly induces the inter-core coupling and interference between the central core and outer cores in the tapered region. Among the multiple cores region within the tapered waist, the strong evanescent field also contributes to the variation of the inter-core interference, resulting in the intermodal coupling between the surrounding and the multiple cores modes. The light is firstly launched from the center core of the MCF, and the inter-core coupling occurs between the distributed cores among the tapered region. The intensities of the normalized core modes for the interferometer can be written as [16]:
where z is the propagation direction of the fundamental core mode. C is the coupling coefficient, which is related to effective RIs of the core and the cladding modes, the core diameter (a), and the pitch size ($\varLambda$). From Eqs. (1)–(2), it is evident that the center core mode and the pth outer core mode can be oscillated periodically with a phase difference of π⁄2 [17], shown by the interference spectrum of the sensor in Fig. 1(c). When the MCF is tapered and thinned, the coupling coefficient, C, is greatly strengthened, and six Mach-Zehnder Interferometers (MZIs) based on the coupling between center core and six outer cores are constructed. For simplification, here the MZI between center core and one of outer cores is theoretically investigated.For a MZI structure, taking the initial phase difference as zero, the wavelength of the mth interference peak (${\mathrm{\lambda }_\textrm{m}}$) is:
where $\varDelta {n_{eff}}$ is the difference between the effective RI of two branches, i.e., the center core and outer core particularly for a TMCF. L is the Z-direction length of the thinned waist region. The temperature sensitivity can be obtained as:3. Experiment and discussions
In our previous work, the refractive index sensing characteristics of the TMCF sensing unit have been presented [8]. To provide a reference for temperature sensing based on thermo-optic effect, we refabricated and measured the refractive index sensor response of samples with waist diameters of 7, 9, and 11 µm within SRI range of 1.3333-1.430 (simulated by glycerin solutions). The RI value of glycerin solution was calibrated by Handheld Refractometer (KEM, RA-130) with a resolution of 0.0001 RIU.
Figure 2(a) illustrates the sensitivity response of the above three sensors, the highest RI sensitivity reached 21505.4, 14601.0, 9946.2 nm/RIU within the high RI range (1.333-1.430), respectively. With regard to the above refractive index sensitivity results, the TMCF sensing units exhibit ultra-sensitive when the refractive index is about higher than 1.4.
Fig. 2. (a) RI sensitivity responses of TMCF with 9, 11, 13 µm diameter. (b) The relationship between the refractive index of PDMS material and temperature measured by RA-130.
Referring to Eq. (5), since the refractive indexes of silica fiber and PDMS are close, and PDMS has a high TOC, high temperature sensitivity is theoretically achievable in this temperature range. To obtain the accurate TOC value of PDMS material employed in the sensor fabrication, we measured the TOC value of the refractive index response at different temperatures by KEM-RA-130, as shown in Fig. 2(b), which is close to the TOC value given by [13,14]. In a temperature range from 0 to 50 °C, the RI range of PDMS material roughly corresponds to the most sensitive RI range of the TMCF sensing unit.
The schematic of temperature sensing setup for the proposed TMCF with PDMS-encapsulation is shown in Fig. 3(a). An amplified spontaneous emission (ASE) light source and an optical spectrum analyzer (OSA, AQ6370B) are employed to stimulate and collect the transmission spectrum, respectively. The heating and cooling process for temperature measuring is implemented by a temperature controllable bath filled with water.
Fig. 3. (a) The experimental setup of the temperature sensor. (b) Temperature sensitivity responses of TMCF with 9, 11, 13µm diameter. (c) wavelength red shift of 7 µm sensor and the fading interference phenomenon (red area).
The sensitivity responses of these three sensors with different waist diameters in the temperature range of 0 °C-50 °C is shown as Fig. 3(b), which can be achieved with high repeatability. The proposed interferometer with PDMS has achieved rather high temperature sensitivity, compared with the interferometer without PDMS encapsulation with a sensitivity of 29-50 pm/°C, since the silica TOC is low. The PDMS capsulation has played an important role in the improvement of temperature sensing. The longitudinal crosslink between the waist of the TMCF and the PDMS protection, as well as the high TOC of PDMS, has increased its temperature sensitivity. The fundamental reason can be as well explained by the substantial difference of TOC value between outer core (dominated by PDMS) and the center core ($\widetilde {TO{C_2}} - \widetilde {TO{C_1}}$), referring to Eq. (5).
From the sensitivity responses, it can be observed that the thinner the waist diameter is, the higher temperature sensitivity is achieved. When MCF is tapered to obtain thinner waist, stronger evanescent field on the surface of the cladding is extremely close to the outer core. Hence, the waist diameter influences the value of ${\tilde{n}_{eff2}}$ and $\widetilde {TO{C_2}}$ in Eq. (5), thereby higher sensitivity is achieved for the interferometers with thinner waist.
The sensitivity of the sensor increases exponentially as the temperature decreases, and the sensitivity of the sensor with a waist diameter of 7 µm reaches 5-25 nm/°C in the low temperature range of 10-20 °C. When the RI of PDMS at lower temperature is closer to the effective RI of the center core, consequently the effective RI of outer core is closer to that of center core, i.e., ${\tilde{n}_{eff2}}$→${\tilde{n}_{eff1}}$, greater sensitivity of interferometer can be achieved, which can be inferred theoretically from Eq. (5). As shown in Table 1, compared with many reported optical fiber sensors, the sensor has a high temperature sensitivity.
Table 1. The Simulated attenuation value of samples at the lower limit temperature
Figure 3(c) illustrates the red-shift of the transmission spectrum wavelengths of the sensor with a 7 µm waist diameter as the temperature decreases. For simplification, here only one period of the whole interference spectrum corresponding to decreased temperature is presented. It is easily found that the period of the interference becomes shorter and the redshift of the spectrum trough increases as the temperature decreases.
However, this outstanding temperature sensing performance cannot be enhanced as the temperature continues to decrease below 10 °C. Because we found that when the measured temperature reaches down a certain threshold, the RI of the thermo-optic material will increase to a limited value resulting in interference fading. As a result, the interference spectrum becomes irregular and difficult to be traced for sensing applications, as shown in the red area of Fig. 3(c).
Due to the influence of the strengthened evanescent field in the thinned area of the MCF, the sensor can get ultra-high sensitivity. But the enhancement of the evanescent field to a certain extent will also destroy the existence of interference itself. It is contradictory to achieve ultra-high sensitivity and the interference fading, which is difficult to be inferred directly from equations. It is necessary to investigate the process between the good temperature sensing performance and invalidation of the sensor. By building the criteria on the sensor design, we can employ the sensors in diverse applications with high performance and sensitivity.
4. Simulation and analysis
A sequence of simulations has been performed to explore the changes in the light field distribution and beam propagation among the sensor when the fading interference phenomenon occurs, and to determine the parameters associated with the lower limit of temperature sensing.
Figure 4 exhibits the simulation model for the PDMS-encapsulated TMCF device, built by Rsoft BeamPROP with the following parameters: length of TMCF cone - 9 mm, waist length - 6 mm, waist diameter - 7 µm. The RI of the core and cladding in MCF are 1.4457 and 1.4378, respectively. The background material is set to be PDMS with a RI changing by temperature (TOC=−4.58×10-4), same as in the experimental section. The simulation is performed at a wavelength of 1550 nm, and the light is launched from the bottom to the top.
Fig. 4. The simulation model and parameters for the PDMS-encapsulated TMCF device built by Rsoft BeamPROP.
In order to reproduce the process of interference fading of the 7 µm sensor while decreasing temperature. The parametric sweep of the temperature from −50°C to 30°C was performed.
Four simulated distributions were selected from this series of simulation results to represent four typical stages, as shown in Fig. 5(a)–5(d). It can be obviously seen that as the temperature decreases, more and more light fields in the sensor leak into the PDMS material, causing the inter-core interference in the waist area to gradually fading, eventually to elimination. At the same time, the transmission spectrum (white window) in the wavelength range of 1.3-1.7 µm also evolves from interference existence (Fig. 5(a)) to weak interference (Fig. 5(b)), and then fading (Fig. 5(c)) to disappear (Fig. 5(d)).
Fig. 5. The distribution of modal field power among the 7 µm sensor at the temperature of (A) 20 °C, (B) 5 °C, (C) −15 °C, (D) −40 °C respectively. Normalized power of pathway monitor at the temperature of (a)20 °C, (b)5 °C, (c)−15 °C, (d)−40 °C respectively.
From a quantitative perspective, the normalized power values of different pathways are shown in Fig. 5(e)–5(h). As the temperature decreases, the normalized power values of the center core and the outer core of the waist coupling area decrease gradually.
Another more intuitive data is the attenuation of the interferometer, which can be defined as the ratio of output power to input power. According to the red line in Fig. 5(e)–5(h), when the interference fades to disappear, the attenuation of the model is correspondingly intensified.
Figure 6 shows the continuous graph of the attenuation value of the sensor with a waist diameter of 7 µm as a function of temperature. Through the simulation results, the fading interference phenomenon process shown in Fig. 6. can be divided into four stages: stable interference, weak interference, no interference with light propagation, and no light propagation, represented by four distributions in Fig. 5. At the same time, the attenuation value has presented corresponding evolution in these four stages, which can be utilized as interference fading indicator.
Fig. 6. The Attenuation of interferometer at the temperature range of −50 °C−30 °C. The four stages of the fading interference phenomenon process.
Based on the above simulation results, we can clearly understand the mechanism of the light field distribution change in the sensor and its four stages during the interference fading.
By linking this simulation parameter with the lower temperature limit (LTL) in the experiment, the threshold of LTL setting at different waist diameters can be guided by simulations.
A sequence of experiments was performed to build the relationship between the actually reachable LTL and the simulated attenuation values, based on the simulated models with the waist diameters as same as the actual samples from the experiments. For the actual experiments, the tracing of LTL is defined by the failing of demodulation within C-band (1525-1565 nm), which is suitable for most portable optical spectra analyzer (OSA), different from laboratory-adopted OSA. The failing of the demodulation can be determined by visibility of interference spectrum, defined by V=(IM-Im)/ (IM-Im), where IM and Im are the intensity of crest and trough of the transmission spectrum, respectively [21]. Based on the experience from these experiments, we designated the simulation setting wavelength (λ=1550 nm) as the watershed between visible interference spectrum (V>0.2, green window) and invisible interference spectrum (V≈0, pink window). The temperature at this turning point can be defined as the LTL value for the actual temperature sensing range. When the temperature decreased further down, the visible trough as to the portable OSA had red-shifted to invisible area, the range beyond C-band. Table 2 summarizes five examples of the experimental sequence the simulated attenuation of these models at the turning temperature point, i.e., the RI value of the simulated background material (PDMS) is set to be the value at LTL from actual experiments. It can be easily found that all of the attenuation values at the LTL are approximate to be 95%. Therefore, we can trust the effectiveness of our simulation models to extent and enlarge the actual experimental range, since it is impossible to perform ergodic experiments. Correspondingly, we can designate the attenuation greater than 95% from the simulations as the empirical threshold for the LTL of the sensors for temperature sensing of actual experiments.
Table 2. The Simulated attenuation value of samples at the lower limit temperature
By tracing the corresponding temperature of the sensor models with different waist diameters when the calculated attenuation is 95%, the relationship between the simulated LTL and the waist diameters of the sensors can be quantitatively built as plotted in the red line of Fig. 7. The pink area in Fig. 7. is corresponding to the sensing temperature lower than LTL, where the interference fading and invalidation occurs for the sensor.
Fig. 7. The relationship between the simulated lower limit of temperature sensing and the diameter of the sensor waist, serving as sensor fabrication criteria.
The sensitivity of the sensor can also be qualitatively obtained by calculating the effective refractive index and effective TOC to substitute into Eq. (5). The calculated sensitivity at a wavelength of 1550 nm is shown in the thermogram in Fig. 7. As the sensitivity increases, the color of the heat map transitions from cyan to dark blue, and the area where the calculated sensitivity is greater than 5 nm/°C is defined as the sweet area (between red line and green line). In the sweet area, the RI range and high TOC of the PDMS material are well adapted to the optimal sensing performance conditions of the TMCF interferometer. The sweet area can be regarded as the criteria for the sensor fabrication to match the temperature range for diverse applications.
The above simulations and analysis with consequent experiments have discovered the evolution of four typical stages, the relationship between the attenuation value and the interference fading, and workable temperature range for the sensors with different waist diameters. The determination of sweet area is essential and worthwhile for sensor design with different temperature requirements, which has been rarely investigated, however, in most literatures about optical fiber temperature sensing. For instance, when the sensor is designed for the deep sea monitoring, it can be preliminarily determined through simulation that the sensor with a waist diameter of 9 µm performs better in an environment higher than −5°C. In another condition, we can also design a sensor bunch including a few probes with different LTL, and realize ultra-high sensitivity sensing in a wide temperature range.
5. Conclusions
A high sensitivity temperature sensor has been investigated and demonstrated based on a TMCF interferometer embedded in thermo-optical polymer, PDMS. The temperature sensitivity improvement obtained from PDMS applying on a TMCF interferometer has been fundamentally and experimentally verified. The sensor exhibits the high sensitivity of 5-25 nm/°C within the decreasing temperature range from 50 °C down to 10 °C. To build the criteria between the reachable lower limit of temperature and the sensor design, a sequence of simulations and corresponding experiments are performed. The evolution of the interference fading is clarified, and the simulated lower limits of temperature sensing for TMCF with different waist diameters are continuously calculated, so as to choose a sensor with the appropriate waist diameter adapt to different temperature environments. The proposed sensor can be employed as photonic thermometer with ultra-high sensitivity for biological and deep-sea applications, as well with excellent flexibility and biocompatibility from PDMS encapsulation. Owing to the quantitative criteria claimed in the last section, the sensor can be delicately designed for diverse applications with different requirements on temperature range or sensitivity.
Funding
International Cooperation and Exchange Programme (62061136002); National Science Fund for Distinguished Young Scholars (62025505).
Disclosures
The authors declare no conflicts of interest.
Data availability
Date 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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