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Abstract
We have proposed and experimentally demonstrated an optical fiber strain sensor with high precision and extended dynamic range based on a coupled optoelectronic oscillator (COEO). The COEO is a combination of an OEO and a mode-locked laser, sharing one optoelectronic modulator. The feedback between the two active loops makes the oscillation frequency equal to the mode spacing of the laser. It is equivalent to a multiple of the natural mode spacing of the laser, which is affected by the applied axial strain to the cavity. Therefore, we can evaluate the strain by measuring the oscillation frequency shift. Higher sensitivity can be obtained by adopting higher frequency order harmonics owing to the accumulative effect. We carry out a proof-to-concept experiment. The dynamic range can reach 10000 $\mu \varepsilon $. Sensitivities of 6.5 ${{H\textrm{z}} / {\mu \varepsilon }}$ for 960 MHz and 13.8 ${{H\textrm{z}} / {\mu \varepsilon }}$ for 2700 MHz are obtained. The maximum frequency drifts of the COEO in 90 mins are within ±148.03 Hz for 960 MHz and ±303.907 Hz for 2700 MHz, which correspond to measurement errors of ±22 $\mu \varepsilon $ and ±20 $\mu \varepsilon $. The proposed scheme has the advantages of high precision and high speed. The COEO can generate an optical pulse whose pulse period is influenced by the strain. Therefore, the proposed scheme has potential applications in dynamic strain measurement.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Strain sensors based on fiber optics, which take merits of compact size, high sensitivity, low cost, immunity to electromagnetic interference, have attracted extensive research interest over the past few years due to their potential applications in structural health monitoring [1], pipeline security monitoring [2], saving lives [3], ocean-bottom seismic system [4] and so on. Much effort has been concentrated on the development of optical fiber strain sensors, for instance, sensors based on fiber Bragg grating (FBG) [5,6], optical interferometry [7,8], fiber bending attention [9], fiber Brillouin scattering [10,11], fiber long-period grating [12], polarimetric [13], etc. Unfortunately, the most common approach to exact the sensing information is employing optical spectrum analyzer, which suffers from poor resolution and low speed [14]. With the development of the microwave photonics (MWP) technology, optical fiber sensor interrogation proposals employing MWP have drawn lots of attention [15,16]. The fundamental principle of MWP-based interrogation method is to map optical variation into a change of electrical signal, such as frequency transmission response change of the microwave photonics link [15], intensity change [17] or phase shift [18] of the microwave signals [19]. Optoelectronic oscillator (OEO) can generate high frequency microwave signal with high spectrum purity, high stability and low phase noise. Cooperated with the OEO, the sensing resolution and interrogation speed can be improved effectively.
The operation principle of OEO-based optical sensor is to convert the optical variations which are induced by the sensing parameter into the oscillation frequency shift. The oscillation frequency determination mechanism can be categorized into two groups. One is determined by the passband of the microwave photonic filter (MPF). The MPF can be implemented by a phase modulator and an optical filter [20,21]. The bandwidth of the optical filter should be as narrow as several MHz, whose structure need to be special designed. It increases the system complexity and cost. The MPF also can be realized by a sliced broadband light and optoelectronic feedback loop. Optical interferometry is adopted to achieve the sinusoidal-shaped broadband light [22,23], while it is easily affected by the environmental perturbations. The other determination mechanism is the time delay of the OEO loop. In these methods, the measurand induces cavity length or refractive index change as well as the oscillation frequency [4,19,24]. In order to achieve the microwave signal with low phase noise, a long fiber is necessary to enhance the Q value of the oscillator loop. Long loop length (∼km) will cause multiple mode oscillation, which decreases the system stability and increase the error. Moreover, there exists a trade-off between the sensitivity and the measurement range.
Coupled optoelectronic oscillator (COEO) has aroused significant research interest in recent years for their capacity of simultaneously generating optical pulses and high frequency microwave signal with high quality [25,26]. Different from the traditional OEO, the optical source is replaced by an additional optical feedback loop with an optical amplifier to simultaneously generate the light energy, as well. The COEO contains two coupled active feedback loops sharing an electro-optical modulator. The positive feedback between the OEO and the mode-locked fiber laser ensures the high spectral purity, high stability and low phase noise of the generated optical pulses and radiofrequency (RF) signals [27], which is appropriate for high-precision sensing. The quality factor of the optical loop transforms to the RF quality factor, and an effective RF Q factor exceeding 106 at 10 GHz has been reported [28,29]. Beside, short loop length (∼m) can ensure high sidemode suppression ratio, which can improve the system stability and increase the dynamic range.
In this paper, we have proposed and experimentally demonstrated optical fiber strain sensor with high precision and extended dynamic range based on coupled optoelectronic oscillator. The combination of the OEO and the mode-locked fiber laser makes the oscillation frequency equals to the mode spacing of the laser. It is equivalent to a multiple of the natural mode spacing of the laser, which is affected by the applied axial strain to the cavity. Therefore, the strain can be evaluated by measuring the oscillation frequency shift. Due to accumulative effect, the sensitivity can be improved by adopting higher order harmonics. A proof-to-concept experiment is carried out. The dynamic range can reach 10000 $\mu \varepsilon $. Sensitivities of 6.5 ${{H\textrm{z}} / {\mu \varepsilon }}$ for 960 MHz and 13.8 ${{H\textrm{z}} / {\mu \varepsilon }}$ for 2700 MHz are obtained. The maximum frequency drifts of the COEO in 90 mins are within ±148.03 Hz for 960 MHz and ±303.907 Hz for 2700 MHz, which correspond to measurement errors of ±22 $\mu \varepsilon $ and ±20 $\mu \varepsilon $. The proposed scheme has advantages of high precision and high speed. The COEO can generate optical pulse, whose pulse period is influenced by the strain. Therefore, the proposed scheme has potential application for dynamic strain measurement.
2. Principle
Figure 1 schematically illustrates the proposed COEO-based strain sensor. The COEO is a combination of an OEO and a mode-locked laser sharing an electro-optical modulator. A traditional OEO contains an optical source and an optoelectronic feedback loop. In the COEO, the optical source is replaced by an additional optical feedback loop with an optical amplifier to simultaneously generate the light energy, as well [25]. In the mode-locked loop, the output of an EDFA connectes a length of SMF. Two ends of SMF are fixed on a tensioner, where strain can be introduced. After SMF, the light is divided into two parts through a 60/40 OC. One is delayed by a TODL, modulated by a MZM and fed back to the EDFA to form a ring fiber laser. The MZM, which acts as an active mode-locking device, is polarization dependent. Therefore, a PC is inserted in the laser loop to adjust the polarization state of light. One portion of light is extracted from the laser loop via a 90/10 OC, detected by PD1 and monitored by ESA1. In the OEO loop, the other light after 60/40 OC is detected by a PD, filtered by an EBPF, amplified by an EA and feedback to the MZM to form the OEO loop. The OEO output is monitored by ESA2 through an ES. The cavity length can be tuned by the TODL to make two loops match, which can improve mode locking efficiency. The COEO will oscillate when the loop gain is large enough via adjusting the magnification factors of the EDFA and EA.
Fig. 1. Schematic of the COEO-based strain sensor. EDFA: erbium-doped fiber amplifier; SMF: single mode fiber; OC: optical coupler; TODL: tunable optical delay line; MZM: Mach-Zehnder modulator; PC: polarization controller; PD: photodetector; ESA: electrical spectrum analyzer; EBPF: electrical band pass filter; EA: electrical amplifier; ES: electrical splitter.
In the laser loop, there are many longitudinal modes which have random phase shown in Fig. 2(a). The longitudinal mode space is
where c is the speed of light in vacuum; n1 and L1 are the refractive index and length of the optical fiber in the fiber ring laser loop, respectively.Fig. 2. (a) All possible laser modes with a mode spacing of $\Delta {f_o} = {c / {{n_1}{L_1}}}$ and random phase; (b) The mode beat frequencies of the laser modes after EBPF; (c) The oscillating modes existed in the OEO loop without mode-locking; (d) The existed laser modes with a mode spacing of $\Delta {f_N} = {{Nc} / {{n_1}{L_1}}}$, which is in phase; (e) The final existed modes in the OEO loop.
In the OEO loop, the PD2 convert the optical signal into electric signal. The longitudinal modes will beat. Seen from Fig. 2(b), some beating signals will be filtered according to the passband of EBPF. The mode spacing of OEO is
where n2 and L2 are the refractive index and length of the fiber in the OEO loop, respectively.Since the loop lengths of the laser and OEO are different, there exists difference between their mode spacing, which is demonstrated in in Fig. 2(a) and 2(c). In the bandwidth of EBPF, there are a few OEO modes. Because of the mode competition, only the mode which gets the most energy from the laser will win. Therefore, the final oscillation mode is closest to a beat frequency of the laser’s longitudinal modes. When the MZM is driven by this mode to modulate the gain of the ring laser, the mode-locking can be achieved. It makes the mode spacing of the laser and the OEO equal, which is a multiple of the natural mode spacing of the laser. The oscillation frequency can be expressed as
where N is positive integer.Seen from Eq. (3), the oscillation frequency ${f_{osc}}$ is inversely proportional to the fiber length ${L_1}$ and the refractive index ${n_1}$. When the axial strain is applied to the fiber, the fiber length as well as the refractive index change due to the elastic optical effect. The oscillation frequency shift is the combined effect of the variations of the fiber length and the refractive index. Therefore, the oscillation frequency shift can be described as
According to Ref. [30], the refractive index corresponding to the stress is given by
where C is the stress- optical constant, $\sigma $ is the axial stress. In the single mode fiber, the strain can be evaluated from the stress. Therefore, the refractive index variation still has a linear relationship with the strain.The frequency shift $\Delta {f_{osc}}$ of ${f_{osc}}$ induced by strain can be deduced as
where $\xi $ is the axial strain, $\alpha $ is a constant. Equation (5) indicates that the frequency shift of each harmonic has a linear relationship with the axial strain applied to the fiber, and higher order harmonics have higher sensitivities (${{\Delta {f_{osc}}} / {\alpha \xi }}$).Moreover, the COEO can generate optical pulse and RF signal simultaneously, which has a relationship of ${T_{osc}}\textrm{ = }{1 / {{f_{osc}}}}$. Seen from Fig. 3, the strain also can be evaluated from the optical pulse period. In the time domain, the optical pulse period can give not only the strength of stain but also the time information. Therefore, the proposed scheme has potential applications in the dynamic strain measurement. This part of the study will be accomplished in our future work.
3. Experimental results and discussions
We carry out an experiment based on the setup shown in Fig. 1 to verify the effectiveness of the conception and explore the sensor performance. The MZM has a 10 GHz bandwidth and half-wave voltage of 4.1 V (JDSU X5). The PD has a bandwidth of 15 GHz (CETC GD45220R). The EBPF has a center frequency of 960 MHz and a 40 MHz bandwidth. The tunable range of TODL is 300 ps (VDL-001-35-33-SS-FC/PC).
In order to explore the performance of COEO, we measure the pulse from the output of PD1 by a digital sampling oscilloscope (Tektronix DSA72004B, 20 GHz, 50 GS/s), which is depicted in Fig. 4(a). According the measured results, the pulse period is 1.085 ns and pulse width is 60 ps, respectively. The optical spectrum of the pulse, whose bandwidth is 0.132 nm, is measured by an optical spectrum analyzer (AQ6370D, 0.02 nm). For comparison, the optical spectrum of the laser without OEO loop is also given, which is shown in Fig. 4(b). The bandwidth is 0. 016 nm. Cooperated with the OEO, the optical spectrum bandwidth has been broadened effectively. This is because of that the MZM, which is driven by the OEO oscillation mode, can modulate the gain of the ring fiber. It forces the longitudinal modes to be in phase. The mode spacing of the laser changes to a multiple of the natural mode spacing of the laser. The beat signal between any two neighboring laser modes will add up in phase, which reinforces the OEO oscillation. This enhanced oscillation mode in turn to realize mode-locking. Hence, the optical spectrum will be broadened and optical pulse is obtained.
Fig. 4. (a) Time domain measurement of the optical pulses. (b) Optical spectrum of the ring laser with and without optoelectronic oscillation.
Figure 5 demonstrated the measured electrical spectra of the radiofrequency (RF) signals. In the OEO loop, the center frequency and sidemode suppression ratio of RF output signal are 963.804 MHz and 43.69 dB, respectively. The cavity length of OEO loop is about 27 m, which determines the mode spacing mode of OEO is ∼10. 89 MHz. Such large mode spacing ensures that the sidemodes are removed by the narrowband EBPF, which can improve the sidemode suppression ratio. Figure 5(b) illustrates the generated RF signal by directly detecting the optical pulses. The length of the fiber laser cavity is ∼26 m. The corresponding mode spacing is 8 MHz. The signal frequency is 963.804 MHz. The sidemode suppression ratio is 33.41 dB.
Fig. 5. (a) The measured electrical spectra of the RF signal (a) from the OEO loop and (b) of the optical pulses.
We investigate the capacity of the COEO-based strain sensor. The applied strain range is from 0 to 10000 $\mu \varepsilon $. We use the output signal from the optoelectronic loop as the tracking signal. Figure 6(a) displays the measured frequency response of the COEO under different applied axial strain. With the increment of axial strain, the oscillation frequency shifts towards lower frequency range. This is because of that the axial strain increases the cavity length. Seen from Eq. (3), the oscillation frequency become lower. The relationship between the oscillation frequency and the axial strain is demonstrated in Fig. 6(b). The sensitivity by linearly fitting the measured results is 6.5 ${{H\textrm{z}} / {\mu \varepsilon }}$. The R2 coefficient of determination is 0.99981, indicating the regression line fits the data well. Figure 6(c) shows the measured strain as a function of the applied strain and the measured errors. The maximum error is 80.196 $\mu \varepsilon $.
Fig. 6. (a) The measured frequency responses under different axial strains; (b) The relationship between the frequency shift and the axial strain; (c) The axial strain as a function of the applied axial strain and the measured errors.
We investigate the stability of the COEO-based sensor. The system operates at room temperature with a fixed strain for a period of 90 minutes. The oscillation frequency of the COEO is recorded with a step of 5 mins, which is depicted in Fig. 7. The measured results show that the maximum frequency variation of the tracking signal is ±148.03 Hz, which correspond to ± 22 $\mu \varepsilon $ measurement error. The measurement error may be induced by the environmental perturbations which cause the mode hopping in the laser cavity as well as the oscillating frequency.
According to Eq. (5), the sensitivity can be greatly improved by adopting high-order resonant frequency due to the accumulative effect. In order to generate high frequency microwave signal, we replace the electronic filter with a bandpass filter whose center frequency and bandwidth are around 2700 MHz and 80 MHz, respectively. Figure 8 illustrates the optical pulse and optical spectrum of the ring laser. According the measured results, the pulse period is 0.371 ns and pulse width is 59.5 ps, respectively. The bandwidths of optical spectrum are 0.096 nm with OEO loop and 0.016 nm without OEO loop.
Fig. 8. (a) Time domain measurement of the optical pulses. (b) Optical spectrum of the ring laser with and without optoelectronic oscillation.
Figure 9 demonstrated the measured electrical spectra of the RF signals. In the OEO loop, the center frequency and sidemode suppression ratio of RF output signal are 2655.802 MHz and 43.67 dB, respectively. By directly detecting the optical pulse, the signal frequency is 2655.644 MHz. The sidemode suppression ratio is 27.9 dB.
Fig. 9. (a) The measured electrical spectra of the RF signal (a) from the OEO loop and (b) of the optical pulses.
Figure 10(a) shows the measured frequency response of the COEO under different applied axial strain. The tracking signal is the output signal of the optoelectronic loop. The applied strain range is from 0 to 10000 $\mu \varepsilon $. With the increase of the axial strain, the oscillation frequency becomes lower. The relationship between the oscillation frequency and the axial strain is demonstrated in Fig. 10(b). The sensitivity by linearly fitting the measured results is 13.8 ${{H\textrm{z}} / {\mu \varepsilon }}$. The R2 coefficient of determination is 0.9989. In this case, by tracking microwave signal with higher frequency, higher sensitivity can be achieved. Figure 10(c) shows the measured axial strain as a function of the applied strain and the measured errors. The maximum error is 146 $\mu \varepsilon $. The stability of the COEO-based sensor is demonstrated in Fig. 11. The measured results show that the maximum frequency variation of the tracking signal is 303.907 Hz, which correspond to ± 20 $\mu \varepsilon $ measurement error.
Fig. 10. (a) The measured frequency responses under different axial strains; (b) The relationship between the frequency shift and the axial strain; (c) The axial strain as a function of the applied axial strain and the measured errors.
Compared with the strain sensors based on traditional OEO, the proposed sensor has metrics of large dynamic range, high stability and high precision. The traditional OEO-based strain sensors can be classified into two types. One is the strain induced FBG wavelength shift which can be interrogated by the OEO. Since the FBG is sensitive to the strain, the sensitivities of this type are large, which are from ${{Hz} / {\mu \varepsilon }}$ to ${{MHz} / {\mu \varepsilon }}$ [19,20,31,32]. However, small spacing mode caused by long length fiber deteriorates the measurement range which are mostly around hundred $\mu \varepsilon $. The other one is the strain induced fiber length change which can be evaluated by the OEO. The sensitivity of this type is smaller than the former one, which is around about ${{Hz} / {\mu \varepsilon }}$ [4]. The proposed COEO-based sensor interrogates the strain via the fiber length change. The dynamic range and the stability have been greatly improved. The sensitivity can be improved by utilizing the chirped fiber Bragg gratting instead on the fiber.
4. Conclusion
In conclusion, we have proposed an optical fiber strain sensor with high precision and extended dynamic range based on COEO. We can obtain the applied axial strain by measuring the oscillation frequency shift of the COEO. The sensitivity can be further increased by adopting higher order harmonics. The dynamic range can reach 10000 $\mu \varepsilon $. Sensitivities of 6.5 ${{H\textrm{z}} / {\mu \varepsilon }}$ for 960 MHz and 13.8 ${{H\textrm{z}} / {\mu \varepsilon }}$ for 2700 MHz are obtained. The maximum frequency drifts of the COEO in 90 mins are within ±148.03 Hz for 960 MHz and ±303.907 Hz for 2700 MHz, which correspond to measurement errors of ±22 $\mu \varepsilon $ and ±20 $\mu \varepsilon $. Since the fundamental concept of this mode is to transform the equivalent optical length into the oscillation frequency shift, the proposed scheme can be applied to other sensors, such as temperature, refractive index sensors. Besides, the COEO can generate optical pulse, whose pulse period is influenced by the sensing parameters. The system can also be used in dynamic measurement.
Funding
National Natural Science Foundation of China (61905029, 62075022); Natural Science Foundation of Chongqing (2022NSCQ-MSX2481); Educational Department Foundation of He’nan Province (22A416014); Chongqing Technology Innovation and Development Project (cstc2020jscx-msxmX0216); Chongqing National Science Foundation of Innovative Reach Groups (cstc2020jcyj-cxttX0005).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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