In this paper, we report two fiber-optic temperature sensors based on silica/polymer microfiber knot resonators (SMKR/PMKR). The structures of these sensors are composed of three layers, MgF2 crystal plate is adopted as the substrate, and the sensing knots are covered by a thin MgF2 slab to keep it steady and immunity to the environment fluctuations. Experimental results show that the temperature sensitivity of SMKR is ~52pm/°C within 30°C~700°C, while the sensitivity of PMKR is ~266pm/°C within 20°C~80°C. The temporal response of SMKR and PMKR sensors are less than 1 ms and 5 ms, respectively. These microfiber knot resonators can be used as miniature high temperature sensors with fast response. Higher resolution can be anticipated with further improvement of the Q factor of the microfiber knot resonators.
©2009 Optical Society of America
Optical resonators based on microfibers/nanofibers have been attracting great attention owing to their high Q-factor, large coupling coefficient, low loss, etc. They have been widely used in the areas of optical sensing, optical communication, and photonics devices . The characteristics of microfiber resonators (MRs) in the form of knot, loop and coil have been under intensive investigation in the recent published literatures. (Various structures of microfiber resonators (MRs), including knot, loop and coil, have been investigated [1–3].) In this paper, the microfiber knot resonators (MKRs) used for temperature sensing are proposed and demonstrated. As both the length and refractive index of the MKR vary with temperature, the resonance wavelength is tuned by the temperature change. The dynamic range and resolution of the MKR temperature sensors made of silica/polymer microfibers have been investigated by experiment, respectively. Compared with other fiber optic temperature sensors, such as fiber Bragg grating  and Fabry-Perot interferometer , these MKR temperature sensors have advantages such as smaller size, higher resolution, faster response time, and lower cost.
In this section, we discuss the relationship between temperature and the resonance wavelength of the MKRs. By solving the coupled mode equations, the transmission property of light propagating along the MKR can be obtained. The free spectral range (FSR) of MKR can be given as 
Here is the resonance wavelength and FWHM its full width at half-maximum. The typical Q of single-loop resonators is in the range 103–107 [7,8]. When the temperature changes, the length and index of the microfiber will be varied, leading to resonant wavelength shifts. In order to obtain the resonant wavelength in a dynamic temperature field, we calculate the derivative of Eq. (1) with respect to the temperature, thus the relationship can be evaluated as below
Where, α is the coefficient of thermal expansion(CTE) of the microfiber, is the thermal-optical coefficient(TOC) of the microfiber, n is the effective index of the mode propagating in the microfiber, and is refractive index variation with temperature. There,and represent the CTE and TOC of the bonding fluoropolymer respectively. According to Eq. (3), it is assumed that the resonance wavelength shift is small compared with wavelengthλ, so could be considered to change linearly with the temperature variance. For the silica microfiber, is about, and is ~. For the polymer microfiber, is about, and is~. Therefore, the resonance wavelength shift of the PMKR is more sensitive than that of SMKR for the same temperature change.
3. Sensor fabrication
The silica microfibers used in this work are fabricated by flame-heated taper-drawing of a single-mode fiber , while polymer (poly-methyl methacrylate, PMMA) microfibers are fabricated by direct drawing of solvated polymers that have been reported elsewhere . These microfibers with minimum diameter of <200 nm and length up to millimeters showed smooth outer surface morphology without pronounced bending or obvious structural defects. They can be bent with much smaller radius of curvature than that of standard optical fibers to form more compact optical structures. Figure 1(a) and (b) show the microscope images of a 190μm-diameter SMKR with 1.7μm-diameter silica microfiber and a 98μm-diameter PMKR with 2.1μm-diameter PMMA microfiber, respectively.
As the microfibers provide large proportion evanescent field outside the fiber core, it should be a low refractive index transmission medium to support the MKR. Therefore, a MgF2 crystal plate with refractive index of ~1.37 is adopted as the substrate of the MKR due to its low refractive index and good thermal conductivity. The MKRs are assembled by manipulating with two fiber-tapers under a microscope. A microfiber taper, which is used as the collecting fiber, is arranged adjacent to the freestanding end of SMKR to form a coupler. The two microfibers can attract tightly via Van Der Waals and electrostatic attractive force in the coupling region, as shown in Fig. 1(c). There need two microfiber tapers, each connected to one of the free-standing ends of the PMKR. The microfiber tapers serve as the launching and collecting fibers by evanescent wave coupling. Finally, the SMKR/PMKR structures were covered with a thin MgF2 slab with a thickness of 300μm, which providing a gentle means of holding the sensing structure in place and immunity to environment fluctuations.
4. Experiments and results
To investigate the performance of these MKR temperature sensors, firstly we tested the output spectrum of the MKRs. Figure 2 shows typical transmission spectra of the silica and polymer microfiber knots with diameters of 190μm and 98μm, respectively. The 190μm-diameter knot, assembled with 1.7μm-diameter silica microfiber (refractive index ~1.45), has a Q factor of ~12000 and a FSR of ~3.9nm. The 98μm-diameter knot, assembled with 2.1μm-diameter polymer microfiber (refractive index ~1.49),, shows a Q factor of ~8000 and a FSR of ~7.4nm. The Q factors obtained from these knot resonators are close to or higher than those reported for microfiber loop resonators .
4.1 Static temperature experiment
In order to investigate the static temperature resolution of the two MKRs, an experimental system was constructed firstly. A broadband ASE laser was used as the light source. Light passing through the MKRs will generate the resonant signals. An optical spectrum analyzer, OSA (ANDO-AQ6317B) was used for detecting the output spectra of these temperature sensors. While a hotplate with 0.5°C temperature resolution and range from 30°C to 850°C was used for heating the MKRs. The SMKR sensor was first heated by a temperature step of 1°C. The temperature sensitivity of the SMKR is about 52pm/°C. As shown in Fig. 3 , from 420°Cto 425°C, the total shift of the resonance wavelength is ~260pm and the maximum extinction ratio is >10dB. Figure 4 illustrates the relationship between temperature and resonance wavelength drift over the temperature range from 30°C to 700°C by heating the SMKR with 10°C in each step. The result shows good linearity between temperature and resonant wavelength shift.
For the PMKR, as shown in Fig. 5 , the experimental measured sensitivity of −266pm/°C, can be obtained over the temperature range from 20°C to 80°C in heating process is indicated by solid dots, and cooling process is indicated by hollow dots, as shown in Fig. 6 . Because the thermal expansion coefficient and thermal-optical coefficient of the polymer microfibers are larger than that of the silica microfibers, the temperature sensitivity of PMKR is more than five times larger than that of SMKR.
4.2 Temporal response experiments
At small diameters of the fibers, the previously derived thermal equation represented an insufficiently detailed model of the physical processes involved. Hence, the thermal equation is modeled using the approximation of a thin rod in the one-dimensional case. Validity using the 1-D case rather than the 3-D is verified by the thermal thinness condition. The relaxation time in heating and cooling processes of these sensors can be described by the lumped system equation . For these cylindrical microfibers with radius r, the relaxation time equation can be described as [13,14]:
Here ρis the density of the fiber material, is the specific heat, h is the convection heat-transfer coefficient. For the silica microfibers considered in this paper, we use the following values of parameters:, , , , which yields the relaxation time:. Comparing with the PMMA polymer microfiber, ,,, , so the relaxation time: . For a regular optical fiber having a diameter 100 times greater, the relaxation time is proportionally enlarged to 0.3s.
In the temporal response experiments, the MKRs were illuminated and heated periodically by controlling the tunable CO2 laser pulse (the maximum impulse frequency is 25kHz and single impulse relaxation time is less than 40µs) duration and repetition rate. The schematic diagram is shown in Fig. 7 . A tunable laser(Agilent 8164A) was tuned to 1576.5 nm, which corresponds to a steep resonance region near the slope is maximum, then we controlled the impulse ON/OFF of the CO2 laser beam to heat the MKRs and recorded the time dependence of transmitted power corresponding to this region of the spectrum, as shown in Fig. 8 . From the laser ON to reach thermal steady state, the experimental measured relaxation times are and respectively, which is in good agreement with the theoretical values. However, as we know, the characteristic intrinsic response time of a microfiber is , where K is the heat conductivity of silica or PMMA . For a 1.7μm diameter silica microfiber,, for the 2.1µm PMMA microfiber, . In order to model and approach the intrinsic temporal responses of the MKRs, we preheated them with a period of time by a thermostatic hot plate. After thermal equilibration, the SMKR was heated by the square-wave modulated CO2 laser beam with frequency of 50Hz and the duty cycle of 50%. Considering the relaxation time of PMKR is longer than that of SMKR, the PMKR was modulated by CO2 laser beam with frequency of 20Hz and the duty cycle is 20%. The approximate response times of the MKRs can be obtained, as shown in Fig. 9
In conclusion, we have demonstrated two novel fiber-optic temperature sensors based on microfiber knot resonators with high Q-factor made of silica and polymer microfibers. These tiny temperature sensors have advantages of high-resolution,fast response, compact size, and low cost. The silica microfiber knot resonators sensor has a temperature sensitivity of ~, and can stand high temperature of up to 700°C with the response time less than 1ms, while the polymer microfiber knot resonators sensor has a temperature sensitivity of ~, with achieved the response time about 5ms. Such types of miniature temperature sensors could find important applications where micro space, high-resolution and fast temperature response is essential, such as in thermal property study of nano-devices, chemical, biomaterial and MEMS.
This work is supported by the Key Project of National Natural Science Foundation of China under Grant 60537040.
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