A dual-frequency optoelectronic oscillator (OEO) incorporating a polarization-maintaining fiber Bragg grating (PMFBG) Fabry-Perot filter for high-sensitivity and high-speed axial strain and temperature sensing is proposed and experimentally demonstrated. In the OEO loop, two oscillation frequencies are determined by a PMFBG Fabry-Perot filter with two ultra-narrow notches and two laser sources which operate as a dual-passband microwave photonic filter. The fiber birefringence affected by axial strain is far less than the temperature. Through monitoring the variations of two oscillating frequencies and beat frequency, the simultaneous measurement for the axial strain and temperature is realized. The sensitivities of the proposed OEO sensor for axial strain and temperature are experimentally measured to be as high as 100.6 or 100.5 MHz/με and −41 MHz/°C, respectively.
© 2017 Optical Society of America
Fiber Bragg grating (FBG) sensors have attracted significant attention for their intrinsic advantages such as immunity to electromagnetic interference, resistance to corrosion, compact size, potential low cost, and low dependence on environmental parameters [1–3]. In recent years, extensive fiber sensors based on a variety of FBGs such as tapered phase shifted FBG (PS-FBG) , microstructure FBG , tilted FBG  and Hi-Bi FBG  have been carried out for measuring axial strain, temperature, pressure, refractive index, twist, and so on. But FBG sensors have also intrinsic disadvantages such as cross sensitivity, complex and slow demodulation, and low resolution.
Optoelectronic oscillator (OEO) for optical sensing is to translate the physical, chemical or biological parameters applied to the narrow-band optical filter to the change of the frequency in the microwave domain instead of the change of the wavelength in the optical domain, which can use a digital signal processing (DSP) module to realize high-speed and high-resolution interrogation [8,9]. In addition, the microwave signal generated by an OEO has also low phase noise, high Q factor, and much higher signal-to-noise ratio . Meanwhile, the equivalent PS-FBG can be used to form a microwave photonic filter (MPF) which is the key device in an OEO-based optical sensor. Thus, in the last few years, lots of exploratory efforts have been directed to the design and implementation of new OEO structures based on different FBGs for strain, temperature or pressure sensing and numerous solutions have been reported.
M. Li et al. proposed a high-speed and high-resolution strain sensor using an OEO with its oscillation frequency determined by the frequency spacing between the carrier frequency and the notch center frequency of PS-FBG, and the measured strain sensitivity was as high as 206.83 MHz/με . F. Q. Kong et al. reported a dual-frequency OEO incorporating a dual passband MPF by jointly operating a PS-FBG and a polarization modulator for temperature-insensitive transverse load sensing. The sensitivity and the minimal detectable transverse load were 9.73 GHz/(N/mm) and 2.06 × 10−4 N/mm, respectively . O. Xu et al. proposed a dual-frequency OEO by utilizing two PS-FBGs and two laser sources to realize dual-frequency oscillation for temperature-insensitive strain sensing. The measured strain sensitivity and resolution were 119.2 MHz/με and 0.83με, respectively .
In addition, a broadband light source has also been used in the OEO sensor for overcoming the existed frequency drift problem of the laser source in the above approaches . A single-band MPF implemented by a broadband light source and Mach-Zehnder interferometer followed by a dispersion compensating fiber was incorporated into a fiber loop to realize an OEO sensor with a temperature sensitivity of 3.7 MHz/°C . X. H. Zou et al. reported an OEO sensor using an amplified spontaneous emission source for measuring optical length changes. The sensitivity of −28 kHz/cm, and the resolution of nanometer scale were obtained .
In this paper, we report an approach to realize simultaneous measurement for axial strain and temperature with high-sensitivity and high-speed interrogation based on a dual-frequency OEO incorporating a polarization-maintaining FBG (PMFBG) Fabry-Perot filter. A PMFBG Fabry-Perot filter has two ultra-narrow notches along two orthogonal polarization directions. The joint use of a PMFBG Fabry-Perot filter and two laser sources operates as a dual-passband MPF with the passband center frequencies equaling the differences between the two notches and optical carriers of laser sources. By imbedding the MPF into an OEO loop, a dual-frequency OEO whose two oscillation frequencies are equal to two passband center frequencies of the dual-passband MPF is realized. Due to the nonlinearity, an additional beat signal is also generated by two OEO-generated microwave signals. Because the fiber birefringence affected by axial strain is far less than the temperature, the strain and temperature can be simultaneously measured by monitoring the beat frequency and two oscillating frequencies of microwave signals. A theoretical analysis is performed, which is verified by an experiment. The sensitivities of axial strain are experimentally measured to be as high as 100.6 MHz/με and 100.5 MHz/με, and the sensitivity −41 MHz/°C of temperature sensing is obtained.
The configuration of the simultaneous axial strain and temperature sensor based on dual-frequency OEO incorporating a PMFBG Fabry-Perot filter is shown in Fig. 1. Two optical carriers from two tunable laser sources (TLSs) via the polarization controllers (PCs) (modulating the polarization state of optical carrier) are combined by a 3dB coupler, and sent to a phase modulator (PM). Then two phase-modulated optical signals generated by PM are sent to the PMFBG Fabry-Perot filter which has two ultra-narrow notches along two orthogonal polarization directions via PC3 and optical circulator. Phase-modulation to intensity-modulation conversion and single-sideband optical signals are achieved by filtering out one 1st-order sideband of the phase-modulated optical signals using the PMFBG Fabry-Perot filter. The reflected single-sideband optical signals are converted to electrical signals by a high-speed photodetector (PD). After that, the detected electrical signal via electrical amplifier (EA) which provides a sufficient gain is fed back to the PM to close the OEO loop. The PMFBG Fabry-Perot filter in conjunction with the PM and two TLSs perform as a high-Q, dual-passband MPF. The operating principle of the MPF, oscillating principle of the OEO and the sensing principle for axial strain and temperature are shown in Fig. 2. The generated microwave signals and beat signal of the OEO loop from the PD are monitored by an electrical spectrum analyzer (ESA).
Assuming the frequency or wavelength of the TLS is or , and the frequency or wavelength of the filter’s transmission peak is or (X and Y represent the fast axis and slow axis of PMF). The center frequencies of the dual-passband MPF and the difference between the oscillating frequencies of the dual-frequency OEO can be expressed as 
When the PMF is introduced by an axial strain ε, no extra birefringence is induced because of the fiber symmetry. In consideration of material elastic-optic coefficient , fiber axial symmetry, and ignoring the higher order term, the refractive index change of X or Y polarization direction can be simplified to formulas (1), (2), and (3), it can be estimated that the difference between the axial strain sensitivities of two oscillating microwave signals is less than 0.1 MHz/με, which is far less than the axial strain sensitivities of each oscillating microwave signal and the difference between the temperature sensitivities of two oscillating microwave signals. So, the difference between two oscillating microwave signals by the reason of the applied axial strain can be ignored (). Our experimental results (in section 3) will demonstrate the above analysis.
In the case of the normal PMF in our experiment, the geometrical component induced by the asymmetric shape of the core and the anisotropic thermal expansion of the asymmetric core are neglected for convenience. Thus, when only axial strain and temperature are applied to the fiber, the total birefringence of PMF is described as formulas (1), (2), and (4), is insensitive to the axial strain, and only determined by the environmental temperature of sensor element.
Thus, the shifts of two oscillating microwave signals and the beat frequency of OEO sensor subjected to an applied axial strain and temperature change are respectively given by
It can be seen that axial strain and temperature applied to the PMFBG Fabry-Perot filter is mapped to the change of the frequency in the microwave domain instead of the change of the wavelength in the optical domain. Therefore, through inversely solving the above equations, a high-resolution and high-sensitivity simultaneous axis strain and temperature sensing can be achieved by monitoring oscillating signal frequency shifts and the calculated coefficients.
3. Experiment results and discussion
The key component in the proposed dual-frequency OEO-based interrogation system is the PMFBG Fabry-Perot filter. In our experiment, the PMFBG Fabry-Perot filter which is formed by two identical PMFBGs is directly written in a14-day hydrogen-loaded (10Mpa; at room temperature) germanium-doped PMF using a 14 cm long uniform phase mask with a period 1075nm scanned by 248nm KrF excimer laser. In order to introduce an equivalent phase shift at the center of the filter, the space between two PMFBGs is controlled by switching the excimer laser and adjusting the writing position. The transmission spectrum of the PMFBG Fabry-Perot filter with the ultra-narrow notches are measured by an optical spectrum analyzer (OSA; ANDO AQ6317C resolution 0.01nm) at X and Y polarization directions, as shown in Fig. 3. The transmission peak wavelengths of the PMFBG Fabry-Perot filter are 1556.185nm and 1556.624nm, respectively. Note that the real optical power level of the narrow transmission peak should be same as the optical power level outside the optical transmission band of filter, which is underestimated in Fig. 3 due to the limited scanning resolution of the OSA (0.01nm). At the output of PMFBG Fabry-Perot filter along each polarization direction, one sideband of the phase modulated signal is removed, and a single-sideband with optical signal is obtained.
The experimental schematic diagram of the dual-frequency OEO sensor system is shown in the Fig. 1. Through tuning the center wavelengths of two TLSs, two oscillating microwave signals at the frequencies of 1.79GHz and 3.33GHz are initially generated by the proposed OEO without the applied axial strain which agrees well with the previous theoretical analysis, as shown in Fig. 4. Meanwhile, the beating between the two oscillating microwave signals will generate a third microwave signal with its frequency being a function of the fiber birefringence because of the nonlinearity in the loop. The fundamental concept is to translate the axial strain and temperature applied to the PMFBG Fabry-Perot filter to the change of the frequency in the microwave domain instead of the change of the wavelength in the optical domain. Through measuring the beat frequency and the two oscillating frequencies of microwave signals, the variations of axial strain and temperature applied to the PMFBG Fabry-Perot filter can be monitored simultaneously. In our experiment, the responses of the sensor to temperature and axial strain are recorded separately.
For the axial strain measurement, the sensing PMFBG Fabry-Perot filter is fixed by two fiber clamps, and axial strain is increased from 0 to 40με at a constant room temperature. In our experiment, the distance between two fiber clamps is 20cm, and the fiber is elongated by the high-precision translation stage with a step of 0.001mm corresponding to an axial strain of 5με. The superimposed frequency spectra of the generated microwave signals and beat signal measured by an ESA (Agilent N9010A, 9kHz~26.5GHz) are shown in Fig. 4 at different axial strains. The frequency spectrum of the OEO sensor shifts to higher frequency as the axial strain increases, and the frequency of beat signal is almost invariant. Our experimental results are in good agreement with the theoretical analysis in section 2. Figure 5(a) shows that the axial strain sensitivities of two microwave signals are 100.6 MHz/με and 100.5 MHz/με linearly up to 40με from 0με by fitting the experimental data based on linear regression. And the axial strain sensitivity of beat signal is approximate 0.1 MHz/με, as shown in Fig. 5(b). Thus, the difference between two microwave signal shifts by the reason of the applied axial strain can be ignored.
For the temperature measurement, the sensing element of OEO is placed in the temperature controlled chamber which adjusts the temperature to increase from 20°C to 21°C with a step of 0.1°C. Figure 6 shows the superimposed frequency spectra of the generated microwave signals and beat signal which are measured by ESA at different temperatures without axial strain. The frequency spectrum of the OEO sensor shifts to higher frequency as the temperature increases, but the frequency of beat signal is decreasing. Figure 7 shows the relationship between the temperature and the oscillating frequencies of two microwave signals and the beat signal. Through plotting the experimental data and linear fitting, the temperature slopes of two microwave signals are as high as 1.152 GHz/°C and 1.193 GHz/°C respectively. At the same time, a temperature sensitivity −41 MHz/°C of the beat signal is obtained as illustrated in Fig. 7(b).
By analyzing the slopes of the beat signal and two microwave signals, the axial strain and temperature applied to the PMFBG Fabry-Perot filter can be measured simultaneously. The axial strain sensitivities of two microwave signals are approximately same as 101 MHz/με. Thus, the coefficient matrix between two microwave signals of OEO sensor and the change of axial strain and temperature are given by
In conclusion, we have proposed and experimentally demonstrated an axial strain and temperature simultaneous fiber-optic sensor based on a dual-frequency OEO incorporating a PMFBG Fabry-Perot filter with high-speed and high-sensitivity. The fundamental concept is to translate the axial strain and temperature applied to the PMFBG Fabry-Perot filter to the change of the frequency in the microwave domain instead of the change of the wavelength in the optical domain, which uses a DSP module to realize high-speed and high-resolution interrogation. By monitoring the beat frequency and the oscillating frequencies of two microwave signals, the strain and temperature were simultaneously measured. The axial strain sensitivities of two microwave signals were measured to be as high as 100.6 MHz/με and 100.5 MHz/με, and the temperature sensitivities of two microwave signals were as high as 1.152 GHz/°C and 1.193 GHz/°C respectively. Compared to the temperature dependence of beat signal with a sensitivity of −41 MHz/°C, the beat signal can be considered insensitive to axial strain with a coefficient of 0.1 MHz/με, which verified that the fiber birefringence affected by axial strain was far less than the temperature.
5. Funding and Acknowledgments
This work was supported by the National High Technology Research and Development Program of China (No. 2014AA09A511), the National Natural Science Foundation of China (NSFC) (No. 61475015, 41471309, 41375016), and the Postdoctoral Science Foundation of China (No. 2017M612350).
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