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A multimode fiber laser sensor system for simultaneous measurement of strain and temperature is proposed and demonstrated. Because of the long cavity and birefringence, longitudinal mode beat frequency and polarization mode beat frequency are achieved in the beat frequency signals of the multimode fiber laser. The strain and temperature can be obtained by monitoring both of them for their different strain and temperature responses. The experimental measurement errors are within ± 16.2με and ± 1.9°C. The usage of only one fiber laser and one demodulation system makes the system simple, cost-effective and portable.
©2012 Optical Society of America
1. Introduction
Beat frequency demodulation arouses much interest in fiber laser sensor systems for its compactness, low cost and high stability. To get beat frequency signals, there should be at least two modes. Traditionally, polarimetric fiber laser is used to generate polarization mode beat frequency (PMBF) by beating the two polarization modes, and strain, temperature, load, ultrasound, hydrostatic pressure or bend can be measured by monitoring the PMBF [1–6]. However, as PMBF is sensitive to several parameters, it brings the problem of cross-sensitivity between these parameters in practical applications, especially, the cross-sensitivity between strain and temperature. To discriminate or simultaneously measure strain and temperature, a few schemes have been proposed with beat frequency demodulation. The wavelength of the polarimetric fiber laser is also a function of strain and temperature, and it has different responses with those of PMBF. Therefore, strain and temperature can be achieved by measuring them at the same time [7,8]. However, the wavelength and PMBF have to be detected with different equipment, which increase the complexity and cost of the demodulation system. When two polarimetric fiber lasers with different strain and temperature responses are incorporated together, strain and temperature can be obtained simultaneously [9]. But, the combination of two lasers makes the sensor system more complex. In Ref [10], a special distributed-feedback fiber laser with four modes is employed to realize the simultaneous measurement of strain and temperature, which is smart and compact. However, the fiber laser with four modes is difficult to fabricate, and expensive high-frequency photodetector (PD) and electrical spectrum analyzer (ESA) are required. In addition, there might be mode hopping, which will make the beat frequency signals unstable. Recently, another beat frequency demodulation based, multi-longitudinal mode fiber laser sensor system was reported [11–14]. The laser cavity is formed by two reflectors and a section of erbium-doped fiber (EDF). The longitudinal mode beat frequency (LMBF) is produced by beating two different longitudinal modes in the long laser cavity. The LMBF changes linearly with strain and temperature. It is also difficult to discriminate strain and temperature in the applications of multi-longitudinal mode fiber laser sensors.
In this paper, a multimode fiber laser sensor system is presented and demonstrated for simultaneous measurement of strain and temperature based on beat frequency demodulation. It is a combination of polarimetric fiber laser sensor system and multi-longitudinal mode fiber laser sensor system. In the multimode fiber laser, each longitudinal mode is split into two polarization modes due to the birefringence of cavity. The LMBF is achieved by beating two different modes with the same polarization direction, and the PMBF is obtained by beating two different modes with different polarization directions after the polarization controller (PC). As a result, the strain and temperature can be measured simultaneously by detecting the LMBF and PMBF for their different strain and temperature response characteristics. In the experiment, only one fiber laser and one demodulation system are used. Therefore, the sensor system is simple, cost-effective and portable. In addition, the measurement is immune to mode hopping.
2. Principle
The laser cavity is shown in Fig. 1 . In the long-cavity fiber laser, there are plenty of longitudinal modes. Each longitudinal mode is split into two polarization modes because of the birefringence as Fig. 2 shows.
The LMBF is generated by two different modes in the same polarization direction, as shown in Fig. 2, and it can be expressed by
where c is the light velocity in vacuum, n is the effective refractive index, l is the whole cavity length, and N is used to denote the mode spacing.The PMBF is generated by two modes in different polarization directions, as shown in Fig. 2, and it is given as [13]
where B is the effective birefringence of the cavity, and p is mode number.For example, the vL 1can be generated by two adjacent modes in the same polarization direction, and the vB can be generated by two adjacent modes in different polarizations directions.
When the strain and temperature applied on the laser cavity is changed, the LMBF and PMBF will both shift, and the responses of them can be written in a matrix form, shown as
where k11, k12, k21 and k22 are the strain and temperature sensitivities of LMBF and PMBF, and they can be determined in the experiment. Then, if |K|≠0, the strain and temperature can be achieved by taking the inverse operation of the sensitivity matrix K, and monitoring the shifts of LMBF and PMBF.Figure 2 also shows that the LMBF and PMBF are both the sum of many beat signals with the same frequency. Therefore, the LMBF and PMBF still exist, even when some of the beat signals disappear due to mode hopping. As a result, the mode hopping has little effect on the measurement.
3. Experiment and results
Figure 1 shows the schematic configuration of the multimode fiber laser sensor system. The pump light from a 980-nm laser diode is launched into the multimode fiber laser cavity through a wavelength division multiplexer (WDM). Then, the laser is sent into by a coupler. One output port of the coupler is connected to an optical spectrum analyzer (OSA), where the optical spectrum of the multimode laser is monitored. The other output port of the coupler is injected into a PC, which is used to control the polarization state of the multimode laser before it is sent into a PD. The LMBF and PMBF are generated at the PD, and they are measured by an ESA. The multimode fiber laser cavity includes an FBG with the central wavelength, 3-dB bandwidth and reflectivity of 1549.49 nm, 210pm, and 90%, a broadband optical reflector (BOR) with the central wavelength, 3-dB bandwidth and reflectivity of 1550nm, 80nm and 96.4%, and a section of fiber. Part of the fiber is EDF to serve as gain medium with the length and absorption coefficient of 0.8m and 40 dB/m @ 1530 nm. A section of the laser cavity with the length of 5.4m is rolled between two copper columns for strain sensing. The two columns are fixed on a stationary stage (SS) and a translation stage (TS), respectively. The strain applied on the laser cavity is changed by moving the TS. In addition, another section of the laser cavity with the length of 4.1m is coiled and put in an oven for temperature sensing. The temperature in the oven can be adjusted by the temperature controller, precisely.
The multimode fiber laser is produced when the pump reaches the threshold power of 2.11mW, and the optical spectrum of the laser at different pump power is shown in Fig. 3 . In the experiment, the pump power is 87mW.
The beat frequency signals are generated at the PD. The frequency spectrum of them is given in Fig. 4 . It can be found that, there are many LMBFs and PMBFs, and the PMBFs are at the symmetric positions of the LMBFs, in accordance with Eq. (2). The frequency interval between the LMBFs is 9.33MHz, which means that the whole cavity length is 11.1m. The high-frequency LMBFs have higher sensitivities but lower signal-to-noise ratios (SNRs) than low-frequency LMBFs, as shown in Ref [11,12] and Fig. 4(b). As a trade-off, the LMBF of 2088MHz is chosen as the sensing signal that will be detected, and the SNR and 3-dB bandwidth of it are 32.8dB and 20.1kHz. The low-frequency PMBFs have higher SNRs and the same effective sensitivities with high-frequency PMBFs, according to Fig. 2 and Eq. (2). Therefore, the low-frequency PMBF of 14.6MHz is selected for monitoring with the SNR and 3-dB bandwidth of 28.8dB and 19.8kHz.
Fig. 4 (a) Frequency spectrum of the beat frequency signals from (a) 0 to 25MHz, and (b) 0 to 3000MHz.
The strain applied on the laser cavity for strain sensing is changed from 0με to 1150με. The responses of LMBF and PMBF to strain are given in Fig. 5 . The strain sensitivities of them are −0.8kHz/με and 1.2kHz/με, respectively.
The temperature applied on the laser cavity for temperature sensing is increased from 20°C to 120°C. The responses of LMBF and PMBF to temperature are shown in Fig. 6 . The temperature sensitivities of them are −5.49kHz/°C and 5.68kHz/°C, respectively.
According to the obtained sensitivities, it can be found that |K|≠0. Hence, based on the experimental results above, the strain and temperature measurement matrix is given as
Finally, the strain and temperature can be achieved from the changes of LMBF and PMBF.The frequencies of LMBF and PMBF are measured every 10 minutes for 2 hours, when the strain and temperature keep unchanged. The maximum deviations of them are ± 1.8kHz and ± 1.6kHz. According to Eq. (4) and the stabilities, the estimated maximum errors of the simultaneously measured strain and temperature are ± 9.3με and ± 1.7°C, respectively. To evaluate the capability of the proposed sensor system in simultaneous measurement, the temperature applied on the fiber for temperature sensing is increased from 20°C to 120°C, and the strain applied on the fiber for strain sensing is varied randomly from 0με to 1150με. Figure 7 shows the comparison between the measured and applied parameters. The maximum experimental errors of strain and temperature obtained are within ± 16.2με and ± 1.9°C over ranges of 0-1150με and 20-120°C. The experimental errors are larger than estimated errors, which are caused by the resolution of the translation stage and the temperature controller in the oven. In our opinion, the measurement accuracy can be improved by two methods. Firstly, if the laser cavity is well packaged to avoid the experimental disturbance, the LMBF and PMBF will have higher stabilities, which will lead to higher measurement accuracy. Secondly, in the experiment, different parts of the cavity are used for strain and temperature measurement on account of the restriction of our experimental equipment. In real applications, when the whole cavity is used for both strain and temperature sensing, higher sensitivities can be achieved, and the measurement accuracy will be improved, accordingly.
Fig. 7 Comparison between simultaneously applied strain-temperature and measured strain-temperature.
4. Conclusion
In conclusion, we have proposed an approach for simultaneous measurement of strain and temperature with a multimode fiber laser using beat frequency demodulation. There are LMBF and PMBF in the beat frequency signals, because of the long cavity and birefringence. The strain and temperature can be achieved by monitoring the LMBF and PMBF, which have different strain and temperature responses. The experimental measurement errors are within ± 16.2με and ± 1.9°C. The sensor system proposed has several advantages over some of those previous works. Firstly, only one fiber laser is used, which is simple and easy to fabricate. Secondly, the beat frequency demodulation system avoids complex optical and electronic signal processing, and relatively cheap and low-frequency equipment is used. Moreover, the sensor system provides many LMBFs and PMBFs with different frequencies and sensitivities, and we can select a pair of them according to practical requirements and available equipment. The compact and low-cost multimode fiber laser sensor system is suitable for the applications of geological monitoring, railway monitoring, and so on.
Acknowledgments
This work was supported in part by the National Nature Science Foundation of China under Grant 60877043 and 61090392, the National High Technology Research and Development Program of China under Grant 2011AA010303, 2011AA010304, 2011AA010305, and 2011AA010306, the Fundamental Research Funds for the Central Universities, and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
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