Temperature-Compensated Refractive-Index Sensing ... - IEEE Xplore

Temperature-Compensated Refractive-Index Sensing Using a Single Bragg Grating in an Abrupt Fiber Taper Volume 5, Number 2, April 2013 Yang Ran Long Jin Li-Peng Sun Jie Li Bai-Ou Guan

DOI: 10.1109/JPHOT.2013.2249504 1943-0655/$31.00 Ó2013 IEEE

IEEE Photonics Journal

Temperature-Compensated RI Sensing

Temperature-Compensated Refractive-Index Sensing Using a Single Bragg Grating in an Abrupt Fiber Taper Yang Ran, Long Jin, Li-Peng Sun, Jie Li, and Bai-Ou Guan Institute of Photonics Technology, Jinan University, Guangzhou 510632, China DOI: 10.1109/JPHOT.2013.2249504 1943-0655/$31.00 Ó2013 IEEE

Manuscript received January 17, 2013; revised February 13, 2013; accepted February 17, 2013. Date of publication March 7, 2013; date of current version March 12, 2013. This work was supported in part by the National Science Found for Distinguished Young Scholars of China under Grant 61225023, by the Research Fund for the Doctoral Program of Higher Education under Grant 20114401110006, by the Project of Science and Technology New Star of Zhujiang in Guangzhou city under Grant 2012J2200062, and by the Fundamental Research Funds for the Central Universities. Corresponding author: B.-O. Guan (e-mail: [email protected]).

Abstract: In this paper, temperature-compensated refractive-index (RI) sensing is realized by use of a single Bragg grating inscribed in a silica microfiber. The microfiber is tapered from a single-mode fiber with two short transition regions. The mode evolution and intermodal couplings are analyzed based on the coupled local-mode theory. Due to the sharp variation of transverse geometry along the fiber length, couplings between copropagating local modes are excited, and the energy of light can be distributed into different modes by the transition regions. The grating couples the incident light to phasematched backward fundamental and higher-order modes at the individual wavelengths. The coupled higher-order modes can be partially retrieved as a result of the abrupt taper. As a result, several reflection peaks can be observed in the reflection spectrum. The peaks present different responses to surrounding RI and identical temperature sensitivity. Therefore, the temperature cross-sensitivity can be removed by measuring the wavelength separations. Compared with previous reports, the proposed method is simpler and more practical. Index Terms: Fiber gratings, subwavelength structures, sensors.

1. Introduction Microscaled optical fiber has provided a superior platform for refractive-index (RI) measurement toward chemical and biomedical sensing applications, due to their strong evanescent field interaction with the surrounding medium and the natural compatibility with conventional single-mode fibers (SMFs) [1]–[4]. Interferometric, grating, and resonant sensors have been implemented with microfibers in the recent years [5]–[10]. Bragg gratings inscribed in the microfibers, i.e., the microfiber Bragg gratings, have been attracting increasing attention because of their compact size, high sensitivity, fast response, wavelength encoding operation, and multiplexing capability. In addition, an mFBG can act as a tip sensor because it provides a reflective signal. Bragg gratings have been effectively formed in microfibers by means of inducing index modulation with conventional UV illumination [11]–[13] or femtosecond (fs) laser exposure [14] and forming periodic structure variations with focus ion beam (FIB) [15]–[17] or fs lasers [18], as well as surface etching by plasma [19], which benefits further practical applications of these sensors. However, similar with the conventional FBGs in communication fibers, the mFBGs are sensitive to environmental temperature

Vol. 5, No. 2, April 2013

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Fig. 1. (a) Measured longitudinal diameter variation of the fiber taper. Inset: the microscope image of a section of micron-scaled fiber within the uniform region over which a Bragg grating is inscribed. (b) The azimuth distribution of the electric-field profiles of the HE11 and HE12 modes in microfiber.

due to the thermal expansion and thermooptic effect of the silica glass. Temperature cross-sensitivity is a key problem for practical applications of mFBG-based RI sensors and needs to be overcome. We have proposed a method to solve this problem by using an mFBG fabricated in a microfiber, which was drawn from a rectangular-cladded fiber [20]. Temperature-independent RI measurement can be carried out by recording the separation between the two resonant peaks because they have different RI sensitivities and identical temperature responses. In this paper, we demonstrate an alternative technique for temperature-compensated RI measurement by monitoring different resonant peaks of a single FBG in circular microfiber. The tapered fiber has relatively short transition regions so that the higher-order grating resonances can be excited. The coupled backward higher-order modes are then partially coupled into the fundamental mode when traveling through the transition region due to the variation in transverse geometry, and the corresponding reflective peak can be observed. The different peaks present different RI responses but almost identical temperature sensitivity. As a result, the effect of temperature can be compensated by measuring the wavelength separation for RI sensing.

2. Sensor Fabrication and Spectral Characteristics The microfiber is tapered from a communication SMF by use of a flame with a width of 2 mm. The fiber is stretched by use of two linear stages when the fiber is heated by the flame. The heat source does not move during the taper process. The moving speed of each linear stage is 0.3 mm/s, and the moving range is 5 mm. Fig. 1(a) shows the measured longitudinal profile of the whole fiber taper. The diameter of microfiber is measured every 0.2 mm along the longitudinal direction with microscope. The tapered fiber contains two transition regions, where the fiber diameter gradually decreased from 125 m to about 10 m, and a uniform region, where the grating is inscribed. The inset in Fig. 1(a) shows a microscope image of the microfiber, i.e., the uniform region. The diameter of the microfiber is about 12.9 m. Surface roughness can be observed from Fig. 1(a), which is a result of the fast tapering process. The diameter fluctuation over the uniform region is estimated as 0.5 m. This fluctuation can possibly weaken the grating coupling and causes broadening of reflective peaks when the microfiber is as thin as 3 m [12]. However, this effect is much weaker for the microfiber with a diameter of above 10 m. The geometry of the tapered fiber, including the diameter of the uniform region and the lengths of the transition regions, are determined by the moving ranges and the speeds of the linear stages and the heat source. It has been demonstrated that the mode evolution in the tapered fiber is largely determined by its geometrical parameters, especially the lengths of the transition regions. If the linear stages moves much more slowly and the heat source scans along the fiber back and forth, an adiabatic fiber taper can be obtained. Its transmission can be considered lossless and the propagating light can maintain a fundamental mode profile, even the microfiber is not a single-mode


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waveguide [21], [22]. In contrast, if the transition region is shorter than 2 cm, the fundamental mode can be partially coupled to higher-order modes [23]. In an extreme case, an abrupt taper is introduced in our experiment, and a large fraction of energy can be coupled into higher-order modes. Consequently, the incident light onto the mFBG contains multiple-mode components, and the spectral characteristics of the grating can be changed. The whole mode couplings in the device and the spectral characteristics are described as follows:

2.1. Local-Mode Coupling Over the Transition Region Light transmission in the transition regions can be described based on the coupled local-mode theory [24]. A local mode refers to an eigenmode of the fiber transverse geometry at a certain longitudinal position. The local modes are not exact solutions of the Maxwell equations but can be considered as an excellent approximation for the slowly varying waveguides. When propagating in a nonuniform waveguide, the energy cannot be perfectly maintained in the fundamental mode due to the variation of local-mode profiles. Couplings to copropagating higher-order local modes are therefore excited. The couplings are described by the coupled local-mode equations [24] X dbj ij bj ¼ Cjl bl dz l

(1)

where bj and bl are complex amplitudes, which contain modal amplitudes and phase variations, Cjl is the coupling coefficient between the local modes of the jth and lth orders, which is defined by ) Z ( ^l ^l 1 @ e @ h ^j ^j h e Cjl ¼ ^zdA; j 6¼ l: (2) 4 @z @z A1

The second term at the left side of (1) represents the phase change and does not contribute to the intermodal couplings. Based on (2), we can deduce that the coupling strength is determined by two factors: First, it is determined by the mode-field profiles of the intercoupling modes. Assuming that the fiber can keep cylindrical symmetry, only the couplings to HE1m local modes, which have circularly symmetrical electric-field distributions, are allowed. Second, it is determined by how rapidly the mode field changes along the fiber. Here, only the HE11 and HE12 modes are involved in the local-mode coupling, since the couplings to HE1m modes with m 9 3 are much weaker. The radiation-mode couplings are not included either. Equation (2) explains the adiabatic transmission over a long transition region because the mode-field variation is extremely slow. In contrast, for a nonuniform waveguide, the fundamental HE11 local mode is partially coupled into HE12 local mode over the transition region, which means the incident unity mode energy is redistributed at the end of ^HE11 þ b2 e ^HE12 , where e ^HE11 and e ^HE12 are the the transition region as the composition E ¼ b1 e normalized eigen electrical fields of the HE11 and HE12 modes for the 12.9-m microfiber. Due to the energy conservation, the complex amplitudes of the two modes should satisfy jb1 j2 þ jb2 j2 ¼ 1. The coupled HE12 mode decays with propagation and causes a certain insertion loss. The typical insertion loss of the taper is about 0.5 dB, which indicates that jb2 j2 jb1 j2 . Note that this localmode coupling is almost wavelength independent over a certain wavelength range. The above analysis suggests that the effect of the transition region is to redistribute the energy of light into modes of different orders.

2.2. Resonant Couplings in the mFBG In the mFBG, the incident HE11 and HE12 modes are coupled into phase-matched counterpropagating modes. The coupling wavelengths are determined by the phase matching conditions


1 ¼ 2nHE11

(3-a)

2 ¼ ðnHE11 þ nHE12 Þ 3 ¼ 2nHE12

(3-b) (3-c)

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where is the grating pitch, and nHE11 and nHE12 are the effective indexes of the HE11 and HE12 modes of the microfiber. The coupling coefficient is defined as [25] Z n ^forward e ^backward dA ¼ e (4) Ge

^forward and e ^backward are the electric where n represents the amplitude of index modulation, and e fields of the incident and coupled HE11 =HE12 eigenmodes. Fig. 1(b) shows the calculated spatial electric-field profiles of the HE11 and HE12 modes of the 12.9-m microfiber. With the calculated mode fields, the individual overlap integrals and the coupling coefficients can be estimated. The calculated coupling coefficients for the three resonant couplings are 3:9 102 =cm for HE11 mode coupling, 5:74 102 =cm for HE11 HE12 mode coupling, and 8:42 102 =cm for HE12 mode coupling, with the index modulation n ¼ 1 104 at the wavelength ¼ 1570 nm. In the calculation, we have assumed that the index modulation only takes place over the Ge-doped region and the spread of Ge3þ at high temperature is not taken into consideration in the context. The coupling strengths at 1 and 3 can be simply expressed by 1;3 ¼ tanh2 j1;3 jL : (5) The backward coupled energy at 1 is P1 ¼ jb1 j2 1 in terms of HE11 mode and P3 ¼ jb3 j2 3 in terms of HE12 mode at 3 . The mode coupling at 2 is much more complicated since four modes are involved, including forward and backward HE11 and HE12 modes. Therefore, four differential equations can be established to describe this coupling. However, the mFBG is relatively weak since the Ge-doped region is small, which means the variation in mode amplitude is slow. As a result, at 2 , the four-mode coupling can be considered as the composition of two independent couplingsVone is between the forward HE11 and backward HE12 modes, the other is between forward HE12 and backward HE11 modes. The coupled mode energy can be simply expressed by P2 ¼ ðjb1 j2 þ jb2 j2 Þ2 .

2.3. Local-Mode Coupling Over the Transition Region Back to the SMF The backward light coupled by the grating contains HE11 mode component at 1 and 2 , and HE12 mode component at 2 and 3 . The HE11 mode tends to keep its fundamental mode profile, and most it energy is retrieved. However, a small fraction of mode energy is coupled to HE12 local modes in transition region back to the SMF. This energy fraction is eventually lost since the propagation of HE12 mode is not supported in the SMF. On the other hand, a small fraction of the backward HE12 mode is coupled to HE11 local mode when traveling over the transition region. This fraction can be retrieved by the OSA, and it is possible to observe the corresponding resonant peak at 3 . These processes are also determined by the coupled local-mode theory and described by (1) and (2). In contrast, for an mFBG with adiabatic transition regions, one cannot observe higher-order resonant peaks in the reflection spectrum. Although the incident fundamental HE11 mode can be coupled to higher-order modes by the grating, since the overlap integrals are nonzero, the reflective higher-order modes totally decay with propagation and cannot be converted into retrievable signal. The mFBGs were inscribed into the 12.9-m microfiber by use of a 193-nm ArF excimer laser and a phase mask with period of 1089.2 nm. Hydrogen loading or other photosensitization treatment is not performed. The spacing between the phase mask and the microfiber is 60 m. The energy density and repetition rate of laser are about 300 mJ/cm2 and 200 Hz, respectively. The length of the FBGs was 3 mm, which is determined by the aperture of the laser beam. The reflection spectrum of the mFBG is monitored by use of a broadband SLED and an optical spectrum analyzer (OSA) with a resolution of 0.02 nm. The central wavelength, spectral width, and output power of the SLED are 1450 nm, 400 nm, and 7 dBm, respectively. Fig. 2. shows the reflection spectrum of the mFBG. Three resonance peaks are clearly observed. The measured resonant wavelengths are 1 ¼ 1570:8 nm (peak1), 2 ¼ 1564:12 nm (peak2), and


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Fig. 2. Measured reflection spectrum of the Bragg grating inscribed in the 12.9-m microfiber.

Fig. 3. Measured wavelength shifts for the three resonant peaks of the mFBG as a function of ambient RI at 20 C.

3 ¼ 1557:58 nm (peak3), respectively. In order to identify the origin of the peaks, we carried out a calculation. A finite-element-method (FEM) model is set up to construct the transverse structure of the microfiber. The RIs of the Ge-doped and pure glass are 1.44922 and 1.44402 at around 1570 nm, respectively. We assume the transverse profile does not change during the tapering. The effective indexes are calculated with this model, and then, the resonant wavelengths are calculated based on (3a–c). The calculated resonant wavelengths are shown in Fig. 2 as the dashed lines and in good agreement with the measured result. The measured spectrum verifies the above theory in that the higher-order modes can be coupled by the grating and the reflective signals can possibly be retrieved. These peaks provide the feasibility for multiparameter measurement.

3. Temperature-Compensated RI Measurement The response to RI was measured by immersing the 12.9-m FBG into the sucrose solution. The temperature of the solution was maintained at 20 C. Its RI changed from 1.33 to 1.39 by changing the solution concentration. The wavelength shifts are monitored by use of the OSA with a resolution of 0.01 nm. Fig. 3 shows the measured wavelength shifts of the three peaks with surrounding RI. All the peaks red-shift with increasing RI due to the raised mode indices of the silica–liquid waveguide structure. The RI sensitivity of the peaks corresponding to the mode order coupling are about 4.5, 11.2, and 17.2 nm/RIU, respectively, at RI of 1.39. Fig. 4 shows the spatial energy distribution of the HE11 and HE12 modes at around the silica–liquid interface with different levels of surrounding RIs, respectively. The HE12 mode has larger energy fractions within the liquid and therefore has stronger evanescent–field interaction with the surrounding medium. As a result, the peak3 exhibits the highest RI sensitivity among the three peaks.


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Fig. 4. Calculated mode energy distributions of the HE11 and HE12 modes of 12.9-m microfiber at around the silica–liquid interface. The blue dashed curve represents the silica–liquid interface.

Fig. 5. Measured wavelength shifts for different peaks as functions of environmental temperature in air.

To characterize the response to temperature, the mFBG was put into a tube oven. A thermocouple was placed near the mFBG for temperature calibration. The temperature of the oven was set to 120 C for an hour to stabilize the grating and then the oven cools down to room temperature. Fig. 5 shows the peak wavelengths as a function of temperature. They exhibit identical temperature sensitivity of 11:9 pm= C. The difference in temperature sensitivities of the two selected peaks is estimated as only 0.1%. The temperature sensitivity can be expressed by d i d dni þ2 ¼ 2ni : dT dT dT

(6)

The former term denotes the effect of thermal-expansion, which is relatively weak because the thermal expansion coefficient has an order of only 107 . The latter one represents the thermooptic effect, which plays a dominant role in the temperature sensitivity. Considering that almost all of the energy of the HE11 and HE12 modes is confined in the silica microfiber, the two modes have nearly identical thermooptic coefficients, resulting identical value of dni =dT . As a result, the temperature sensitivities for the two peaks are identical. Figs. 3 and 5 suggest that the precision of the RI measurement can be significantly affected due to the temperature cross-sensitivity, if only a single peak is monitored for the measurement. The effect of temperature response should be removed in the RI measurement. This can be realized by monitoring the wavelength separation of the reflective peaks since the individual peaks present identical temperature response. Fig. 6(a) and (b) demonstrates the peak separation 1 3 as a function of RI and temperature, respectively. The separation decreases with the ambient RI with a sensitivity of 9.47 nm/RIU. The variation can be approximately considered a linear change. In


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Fig. 6. Peak separation between peak1 and peak3 : (a) as a function of ambient RI at 20 C; (b) versus temperature in the air.

contrast, the peak separation hardly changes with temperature, as shown in Fig. 5(b), which suggests the capability of the temperature-independent measurement of the surrounding RI. Note that the wavelength shift and the sensitivities are only determined by the modal property of the microfiber. The length change in transition regions only affects the reflective strengths at the individual resonant wavelengths.

4. Conclusion In conclusion, temperature-compensated RI sensing has been realized by use of a single Bragg grating in an abrupt fiber taper. The transition regions of the fiber taper have been greatly shortened compared with the adiabatic tapering, in order to excite resonant couplings to higher-order modes and retrieve the corresponding signals. Multiple resonant peaks can be observed in the reflection spectrum, which present different RI sensitivities and identical temperature response. As a result, temperature-compensated RI measurement can be carried out by monitoring the peak separation. The proposed method does not need microfibers with special geometry like [20] and is more simple and practical.

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