A miniature all-fiber temperature sensor is demonstrated by using a Michelson interferometer formed with a short length of Germania-core, silica-cladding optical fiber (Ge-fiber) fusion-spliced to a conventional single-mode fiber (SMF). Thanks to the large differential refractive index of the Ge-fiber sensing element, a reasonably small free spectral range (FSR) of 18.6 nm is achieved even with an as short as 0.9 mm Ge-fiber that may help us increase the measurement accuracy especially in point sensing applications and, at the same time, keep large measurement temperature range without overlapping reading problem. Experimental results show that high sensitivity of 89.0 pm/°C is achieved and the highest measurement temperature is up to 500°C.
© 2015 Optical Society of America
In past decades, optical fiber temperature sensors have been intensively studied due to their many intrinsic advantages such as electrically passive operation, long life-time and immunity to electromagnetic interference. Several configurations such as fiber Bragg gratings (FBGs) [1,2 ], long period fiber gratings (LPFGs) [3,4 ] and fiber interferometers have been employed. All of them, FBG-based temperature sensors are widely used in some industrial areas but the sensitivity is relatively low, ~10 pm/°C . LPFG-based temperature sensors have relatively high sensitivity but they are cross sensitive to fiber bending and surrounding materials. Optical fiber interferometers including Fabry-Perot (F-P) interferometers [6–9 ], Mach-Zenhder interferometers (MZIs) [10–13 ], Sagnac fiber loops  and Michelson interferometers  are good candidates for highly sensitive temperature sensors. However, these sensors are mostly based on conventional silica fibers or silica-based microstructure fibers. Their sensitivities are usually limited by the relatively a low thermal-optical coefficient of silica material. Recently, an optical fiber Michelson interferometer-based temperature sensor was demonstrated with a 4-mm-long dispersion compensation fiber. The sensitivity is up to 68.6 pm/°C and the maximum temperature for measurement is up to 600°C . A Mach-Zenhder interferometer (MZI) based on a 25 mol.% Germania-doped core optical fiber sandwiched between two single mode fibers was reported, which demonstrated high temperature sensitivity of 98 pm/°C from room temperature to 90°C . However, the MZI configuration was operated in transmission mode that is inconvenient in practical applications and the relatively small (less than 5 nm) free spectral range (FSR) makes tracking the transmission minimum/maximum difficult.
In this work, a miniature all-fiber temperature sensor is proposed and experimentally demonstrated by using a Michelson interferometer formed by a 0.9 mm-long 75 mol.% Germania-doped core, silica-cladding optical fiber (Ge-fiber) fusion-spliced to a normal single-mode fiber (SMF). Due to the higher differential refractive index of the Ge-fiber compared to that of the conventional step-index fibers, a suitable FSR of 18.6 nm is obtained even with such a short Ge-fiber. That helps to maintain relatively high wavelength reading accuracy in measurement and simultaneously, keeps the sensor head miniature. Good linear response with sensitivity of 89.0 pm/°C is realized in a large measurement range from room temperature to 500°C.
2. Sensor fabrication and principle
The Ge-fiber has a core and cladding diameters of 4 and 125 μm, respectively. The core of the fiber contains 75 mol.% germania (i.e., GeO2) and 25 mol.% silica (i.e., SiO2). The cladding is made from pure silica. The parameters including diameters and material refractive indices for the core and cladding of Ge-fiber and SMF respectively are shown in Table 1 . To fabricate the sensor head, we spliced the Ge-fiber to a normal SMF by using a fusion splicer in an automatic mode, and then cut the Ge-fiber at certain distance away from the splicing point as shown in the details of Fig. 1(a) . We fabricated seventeen samples and measured their lengths of Ge-fiber and FSRs at around 1550 nm by microscopy (Nikon, Eclipse, TS100) and an optical spectrum analyzer (OSA, Yokogawa, AQ6370C), respectively.
When light propagates from the SMF to the Ge-fiber, various modes may be excited at the splicing point due to the large mismatch of core and mode field diameters between the two fibers. Figure 1(b) and (c) shows the simulated light intensity distribution around the splicing point based on the beam propagation method. It indicates that about two third of the incident light is coupled into core of the Ge-fiber and the rest is into cladding. Note that the color in most of the core area in the Ge-fiber is white in Fig. 1(b), because the calculated normalized intensity in the core area of the Ge-fiber is higher than 1, the maximum value normalized based on the optical intensity in the input SMF. There is an equivalent convergent effect when light propagates from the SMF to the Ge-fiber  because the Ge-fiber has a much smaller mode field diameter than the SMF. In addition, it can be seen that there is a periodical fluctuation on the intensity in the core of Ge-fiber. It is caused by the self-imaging effect because the Ge-fiber is multimode at this wavelength range .
When the excited modes are reflected from the cleaved end of the Ge-fiber and recoupled back into the core of the SMF, interference occurs because different modes experience different optical paths. A Michelson interferometer is therefore formed and FSR of the interference pattern, depending on optical path difference between the two involved modes, can be described as
Figure 2(a) and (b) show respectively the measured spectra of three samples with 0.493, 0.599 and 1.300 mm of Ge-fiber and the dependence of FSR on length of Ge-fiber for all the twelve samples. The data in Fig. 2(b) fit well to the inverse function y = 16.02/x with a high R-squared value of 0.9713. According to Eq. (1), the calculated differential effective refractive index is 0.07498. It is much larger than that in normal single-mode fibers so length of the sensing fiber can be greatly reduced in our sensor.
In order to analyze the detailed modes participated in the Michelson interferometer, we transformed the wavelength spectrum (Length = 1.3 mm) into the spatial frequency domain through fast Fourier transform (FFT). The achieved spatial frequency spectrum, as shown in Fig. 2(c), has only one clear peak, indicating that there are only two modes involving the interference. We then figured out the possible LP modes in the Ge-fiber by using the finite element method (FEM). Table 2 shows the effective refractive indices of these modes. We found that the LP02 mode is the only possible one because its effective refractive index is smaller than that of LP01 mode by 0.0754, which is very close to the above-achieved value from measurement data. The field profiles of two modes are shown in the inset of Fig. 2(c). Therefore, the Michelson interference in our design is most probably introduced by LP01 and LP02 modes of the Ge-fiber.
When temperature is changed, optical path difference of the Ge-fiber based Michelson interferometer will be changed due to thermal expansion and thermo-optic effects of the Ge-fiber. As a result, wavelength shift of the interference fringe pattern against temperature will be observed. It can be expressed by 
3. Experimental results and discussions
The experimental setup for temperature measurement is shown in Fig. 1(a). Light from a broadband source (BBS) with wavelength range from 1530 to 1630 nm was launched into the sensor head through an optical circulator. The reflected light was guided into the OSA with the wavelength resolution of 0.02 nm for measurement. We chose the sample with 0.9-mm-long Ge-fiber with a suitable FSR of 18.6 nm in experimental value as the sensor head, whose optical microscope image is shown in the inset of Fig. 1(a). The sensor head, free from any bending and vibration, was placed in a temperature-controlled oven with accuracy of 0.5°C and the maximum testing temperature is up to 600°C. A calibrated commercially available temperature meter was placed next to the sensor head for reference.
When temperature was changed from room temperature to 500°C, reflection pattern of the sensor head shifted towards longer wavelength as shown in Fig. 3 . Figure 4(a) shows the wavelengths shift against temperature for the three chosen fringe dips A, B and C with initial wavelengths of 1550.52, 1569.14 and 1588.02 nm, respectively. The temperature sensitivities are 87.2, 88.1 and 89.0 pm/°C for dip A to C, respectively. They are quite close but longer the dip wavelength locates at, higher the temperature sensitivity can achieve. That agrees well with the prediction by Eq. (2). The temperature test was repeated with ascending and descending orders several times and all the data fit well. The temperature measurement resolution of the proposed sensor is 0.25°C, based on the sensitivity of 89.0 pm/°C and the wavelength resolution, 0.02 nm, of the OSA.
The stability test was carried out under four temperature from 300 to 550 °C. The chamber temperature was first fixed at 300°C in time duration of 80 minutes and the reflection spectrum was recoded in every 10 minutes. Then temperature was changed to 400°C, 500°C and 550°C and at each temperature the testing was repeated. The experimental results (for dip B) are shown in Fig. 4(b). The maximum fluctuation under temperature of 300°C, 400°C and 500°C is only ± 0.08 nm, which corresponds to a maximum measurement error of less than ± 1°C, if we take the temperature sensitivity of 88.1 pm/°C into account. For temperature of 550°C, the dip wavelength was shifting to longer wavelength with time as shown in Fig. 4(b). It should be related to the phase transition of the Germania fiber core because it already reached the glass-transition temperature range of the GeO2 . Under this condition, the refractive index of fiber core will decrease with heat-absorption even at fixed temperature. Therefore, the proposed sensor is recommended to operate below the temperature 500°C to make sure good stability and repeatability.
As predicted by the theoretical analysis, experimental measurements also testified that length of Ge-fiber has no impact on temperature sensitivity. However, length of the sensing fiber determines FSR of the interference pattern and the latter affects the sensor performance significantly. For example, a too large FSR leads to bandwidth requirement for the light source while a too small one results in serious overlapping in wavelength between interference maxima or minima when the spectrum is shifted. For optical fiber sensors based on this particular Michelson interferometer configuration, normally long sensing fibers are required to decrease the FSR to a reasonable value because differential refractive indices of the normal used sensing fibers are usually much lower than that of the Ge-fiber we used. A comparative table is given in Table 3 , which compares the sensor head details and performances of our sensor with that of previously reported ones with similar sensor head designs, including Mach-Zehnder, mode-mode and Michelson interferometers relying on different kinds of fibers. It can be seen that the FSR of our sensor is medium but the sensing fiber is the shortest. It should be noticed that reducing length of the sensing fiber may enhance accuracy of the temperature measurement especially in point sensing applications. Our proposed temperature sensor is therefore the best choice if only this point is taken into consideration. For sensitivity and measurement range, our sensor is among the best for both parameters. And the reflection operation mode also contributes to more convenience in practical application than the transmission one.
A miniature all-fiber temperature sensor has been demonstrated by using a Michelson interferometer configuration formed by a Ge-fiber with a length of 0.9 mm. Due to the high differential refractive index of the Ge-fiber, a reasonable FSR of 18.6 nm has been achieved even with such a short sensing fiber. The achieved sensitivity is up to 89.0 pm/°C in the measurement range from room temperature to 500°C. It may have good potential applications in a wide range of temperature measurement, especially when point sensing is required.
This work was supported partially by Singapore A*STAR “Advanced Optics in Engineering” Program under Grant No. 1223600006, National Natural Science Foundation of China under Grant No. 61475147, National Natural Science Foundation of Zhejiang Province, China under Grant No. Z13F050003 and the Energy Market Authority (LA/Contract No. NRF2013EWT-EIRP001-006). We also appreciate Dr. Gengzhi Sun from School of Chemical and Biomedical Engineering of Nanyang Technological University for fruitful discussion.
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