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Abstract
A novel fiber Bragg grating (FBG) sensing system, based on an optically injected distributed feedback laser diode (DFB-LD) with an optoelectronic oscillating (OEO) loop, is proposed and experimentally demonstrated for temperature measurements with high and tunable sensitivity. The FBG sensor device works as an edge filter to adjust the optical power of the injected beam in response to temperature variations. The optically injected DFB-LD works at Period-one (P1) oscillating state, and the central wavelength of the oscillating mode of the DFB-LD can be tuned by the variable power of the injected beam. Furthermore, an OEO loop is implemented to improve the signal quality of the generated P1 microwave signal. Hence, the sensing parameter of temperature is converted to the frequency variation of the generated P1 microwave signal in the proposed sensing system. In the proof-of-concept experiment, a series of P1 microwave signals are generated while different temperatures are applied to the FBG sensor. The sensitivity of the proposed FBG sensing system for temperature measurements can be tuned from 0.44322 GHz/°C to 1.25952 GHz/°C. The stability and repeatability experiments are also performed, demonstrating the high measurement accuracy (0.0629°C) and low error of the system. The proposed FBG-based sensing and interrogation system exhibits high sensitivity, large tunability, good linearity, and flexible sensing generality.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber Bragg grating (FBG) based sensors have gradually been developed into a mainstream type of fiber optic sensor in the past few decades due to their unique superiorities including suitability to on-chip integration, immunity to electromagnetic interference, serial multiplexing, and environment adaptability [1–4]. The variation of the sensing physical parameters can modify the structural parameter in the FBG, thus causing the characteristics variation in the transmission or reflection optical spectrum of the FBG, such as the peak reflectivity, full width at half maximum, side-slob suppression ratio, and the Bragg wavelength [4]. Hence, the sensing physical parameter can be obtained by interrogating the variation in the optical spectrum of the FBG. Typically, the interrogation systems for the FBG-based sensors operate based on analyzing the variations of the optical spectrums, e.g., spectral shifts or changes in the optical power. The optical spectrum-based interrogation systems are normally based on a broadband light source and an optical spectrum analyzer (OSA) or a spectrometer to trace the shift of the Bragg wavelength. However, the OSA is expensive, and the measuring accuracy and scanning speed of the OSA are respectively limited, for example, by 0.02 nm and tens of Hz, which hinders the application scope of this method [5–9]. The optical intensity-based interrogation systems are based on edge filtering to realize the conversion of the interrogating parameter from optical wavelength to optical intensity by using a single wavelength laser and a photodetector [10–12]. However, the nonlinear response and power jitter of the laser source will cause the interrogation inaccuracy of the optical intensity of the probing wavelength.
To enhance the measuring sensitivity and interrogating accuracy, microwave photonics (MWP) based sensing systems have been proven to greatly improve the sensing accuracy and measuring speed for fiber optic sensing [13–15]. MWP-based sensing technique converts the low-precision measurements of optical wavelength drift or optical power variation into the high-precision measurement of characteristics of microwave signals, such as frequency, phase, and delay. The microwave signal measuring instruments show high resolution and precision compared with an OSA, thus significantly improving the sensing accuracy and measurement speed of optical sensing systems. MWP-based sensing systems have two main categories: microwave photonic filter (MPF) based and optoelectronic oscillator (OEO) based. The FBG sensor in the MPF-based interrogation system is typically used as a wavelength selector in phase-to-intensity modulation-based single passband MPF [16] or limited taps-based periodic passband MPF [17]. However, the ultra-narrow linewidth of the FBG used in the phase-to-intensity modulation-based MPF is expensive and difficult to realize, and the periodic passbands of the periodic passband MPF-based interrogation systems show limited sensitivity. The OEO-based interrogation system can effectively improve the interrogation speed and ensure high measurement accuracy, benefiting from the high signal quality of the generated microwave signals [18,19]. Typically, the sensing FBG in the OEO-based sensor can change the time delay of the OEO loop or work as an MPF to convert the measurand of interest to the frequency shift or delay change of the generated electric signal. Many OEO-based sensing systems have been reported for measurements of temperature [20], pressure [21], refractive index [22], curvature [23], and magnetic field [24]. However, the limited free spectrum range in the time delay-based OEO sensor restricts the measurement range and sensitivity. The MPF-based OEO sensor shows a large measurement range and high sensitivity, but the ultra-narrow passband of the FBG used in the OEO loop increases the cost and complexity of the system.
In this paper, a novel FBG sensing system with high sensitivity based on an optically injected distributed feedback laser diode (DFB-LD) with an OEO loop for temperature measurements is proposed and experimentally demonstrated. Optically injected DFB-LD has abundant nonlinear dynamics characteristics, such as the Period-one (P1) oscillating state in optically injected DFB-LD has been proven for microwave signal generation with a large frequency range and high signal quality [25–27]. In this work, the FBG sensor device works as an edge filter to linearly modify the optical power of the injected beam in response to temperature variations. The mode of the DFB-LD can be red-shifted to a new frequency due to the power variation of the injected beam, leading to a change in the frequency of the generated P1 microwave signal. In addition, an OEO structure with no electrical or optical filter in the loop is introduced to improve the signal quality of the generated P1 microwave signal and ensure the characteristics of a wide frequency tuning range. Hence, the proposed interrogation system realizes the mapping of optical power to microwave frequency for an FBG-based sensor. In the proof-of-concept experiment, a series of P1 microwave signals are generated at different settings of temperatures. The sensitivity of the proposed FBG sensing system can be tuned from 0.44322 GHz/°C to 1.25952 GHz/°C. Furthermore, the stability and repeatability experiments are carried out, demonstrating high stability and measurement accuracy of the system.
2. Principle and experimental setup
The experiment setup of the proposed FBG-based sensing system for temperature measurement based on an optically injected DFB-LD with an OEO loop is shown in Fig. 1(a). A tunable laser with a narrow linewidth (∼100 kHz) works as the master laser (ML) to generate a tunable laser beam with a wavelength of λm for optical injection to the DFB-LD. The generated laser beam with a suitable state of polarization after a polarization controller (PC) is sent to an FBG via an optical fiber circulator (Cir 1). The FBG is secured in a water bath kettle to work as the temperature sensor. It is noteworthy that the temperature variation of the water in the water bath kettle can cause the overall shift of the FBG-reflection spectrum. Hence, the FBG can work as an edge filter to tune the optical power of the injected beam in response to temperature variations, as conceptually illustrated in Fig. 1(b). The wavelength of the laser beam, λm, is properly set at the edge of the FBG-reflection spectrum so that the optical power of the reflected light can be quasi-linearly tuned when the temperature-caused FBG-reflection spectrum shifts. Then the reflected light from the FBG is sent back to the Cir1 and then injected into the DFB-LD via another circulator (Cir 2) after passing through a Mach-Zehnder modulator (MZM) with a polarization-maintaining optical input. The free-running DFB-LD works as the slave laser (SL) and has a single longitudinal mode with a center frequency of fs. The principle of optical injection into a DFB-LD is shown in Fig. 1(c). After stable optical injection, the frequency of SL is red-shifted from fs to fs’. The emission mode, fm, of the free-running DFB-LD can be expressed as:
where µ is the refractive index of the active layer, which depends on the number of the charge carrier N in the laser cavity, and L is the cavity length. As the laser beam from the ML is injected into the DFB-LD, parts of the carriers are consumed for stimulated radiation, which leads to increases in the refractive index of the active layer. According to Eq. (1), the frequency of the DFB-LD’s emission mode after optical injection is reduced, which is known as red-shift in the semiconductor lasers.
Fig. 1. (a) Block diagram of the proposed FBG sensor system for temperature measurements based on OEO structure with an optically injected DFB-LD; (b) FBG-based edge filter; (c) principle of the optical injection into DFB-LD. ML: master laser, PC: polarization controller, MZM: Mach-Zehnder modulator, Cir 1(2): optical fiber circulator, PD: photodetector, LNA: low noise amplifier, ESA: electric spectrum analyzer, OSA: optical spectrum analyzer. Note that the OSA is only used for the purpose of system characterization for better understanding, and it is not needed in real sensing applications.
Typically, the laser beam from the ML is injected into the SL with a negative frequency detuning under a wide range of Period-one (P1) oscillating state for single microwave signal generation, where the frequency of the ML, fm, is a little bigger than that of the SL, fs. The P1 oscillating state is one of the typical nonlinear dynamics in semiconductor lasers under external disturbance, which can be described as the rate equations of complex field amplitude and the density of the carriers of the DFB-LD [27]:
Fig. 2. Simulation results of optically injected DFB-LD with different injected optical power. (a) the output optical spectra; (b) the corresponding electric spectra in (a); and (c) the relationship of the P1 oscillating microwave signal’s frequency and the injection strength.
Figure 2(a) shows the simulation results of the optical spectra after optical injection into the DFB-LD under the P1 oscillating state with different injected power, which is essentially the Fourier transform of the complex field amplitude, A, in Eq. (2). The frequency offset in Fig. 2(a) is ω-ω0, where ω is the frequency of the injected beam or the red-shifted angular frequency of SL after optical injection. In the simulation, the optical power of the injected beam is gradually increased, which is represented by the dimensionless injection strength, ξi = k|A1|/|A0|, where k is a constant value and A0 is the complex field amplitude of the free-running DFB-LD. In Fig. 2(a), as ξi is increased from 0.090 to 0.120 with a step of 0.005, the frequency of the DFB-LD’s optical beam is gradually red-shifted from low to high. Figure 2(b) shows the corresponding electrical spectra of the optical spectra in Fig. 2(a). It can be observed that several P1 microwave signals are generated with different frequencies and the relationship of the generated P1 microwave signal’s frequency and the injection strength is shown in Fig. 2(c). It shows that within a certain range, there is an almost linear relationship between the frequency of the P1 oscillating microwave signal generated by the optically injected DFB-LD and the injected optical power. The linear relationship offers great potential for applications in the field of optical fiber sensing by varying the injected power through sensing mediums, such as FBG. In addition, if the power variation range and the wavelength of the injected beam is unchanged, the initial frequency of the DFB-LD’s mode is changed as the working current or temperature of the DFB-LD is changed, thus the ability of the red-shift range of the mode is different. The bigger the initial frequency detuning, the smaller the red-shift range with the same injection strength range [27]. Hence, the sensing sensitivity of the proposed sensing system is proportional to the red-shift ability of the DFB-LD’s mode.
Furthermore, as shown in Fig. 1(a), an OEO loop is implemented to feedback the generated P1 oscillating microwave signal on the MZM to modulate the injected beam. Benefiting from the gain and high quality of the optoelectronic feedback loop, OEO can significantly improve the stability and quality of the generated microwave signal [28]. On the other hand, the generated microwave signal is continuously modulated to the injected beam through the OEO feedback, and the generated first-order sideband forms injection-locking to the mode of the DFB-LD, so that the coherence of the injected beam and the mode of DFB-LD is greatly improved, which in turn improves the stability of the whole system. Hence, the proposed FBG sensor for temperature measurements based on the OEO structure with the optically injected DFB-LD converts a variation of FBG-reflection spectrum caused by a temperature change into a change in the injected beam’s optical power and then transforms it into a frequency change in the generated microwave signal through optical injection into DFB-LD. Meanwhile, the signal quality and stability of the generated microwave signal are further enhanced through the OEO structure. The sensing system has the advantages of high sensitivity, high precision, and high stability.
3. Experimental results
In the experiment, the optical power of the injected beam is edge-filtered by the FBG sensor, where the central wavelength of the injected beam is set at the edge of the FBG-reflection spectrum. The experimental results are shown in Fig. 3(a). The red dotted line is part of the FBG-reflection spectrum under a temperature setting of 31 °C in the water bath kettle. The central wavelength and optical power of the injected beam are set as 1553.734 nm and 15.0 dBm, respectively. After optical injection into the DFB-LD under the P1 oscillating state, the output optical spectrum of the DFB-LD is shown as the red line in Fig. 3(a) with the same temperature of 31 °C, where the central wavelength of the oscillating mode in the DFB-LD is red-shifted to 1553.862 nm, and the frequency detuning of two P1 modes is denoted as fP1. As the temperature is increased from 31 °C to 38 °C with a step of 1.0 °C, the reflection spectrum of the FBG is gradually red-shifted, thus the optical power of the injected beam keeps increasing due to the power-edge filtering of the FBG. The increasing optical power of the injected beam makes the central wavelength of the DFB-LD mode increase due to red-shift in the laser cavity of the DFB-LD, where the measured optical spectra in the output of the DFB-LD with different temperatures are given in Fig. 3(a). As can be seen, the frequency detuning of the two P1 modes is changed from fP1 to fP1’ as the temperature applied to the FBG is increased from 31 °C to 38 °C. The relationship between the water temperature and the optical power of the injected beam/central wavelength of the DFB-LD mode is illustrated in Fig. 3(b). The sensitivity of the directly measured optical power of the injected beam and the central wavelength of the DFB-LD mode are 0.99119 dB/°C and 0.00592 nm/°C, respectively. It is shown that the optical interrogation method shows limited sensitivity and precision due to the limited resolution (e.g., 0.05 nm in terms of wavelength) of the OSA used in the experiment. Hence, MWP-based interrogation by monitoring the beating frequency of the P1 mode is an effective method to improve the sensitivity and accuracy of the FBG-based sensor.
Fig. 3. (a) Measured optical spectra of the optically injected DFB-LD with different temperatures, (b) the relationship between water temperature and the optical power of the injected beam/central wavelength of the DFB-LD mode.
In the experiment, the beating P1 signal, fP1, after photoelectric conversion in PD is feedback to the MZM through an EA, as shown in Fig. 1(a). An MWP-based interrogation system is established by monitoring the beating P1 frequency through an ESA. The measured electrical spectra of the generated P1 microwave signals under different settings of temperatures are shown in Fig. 4(a). The frequency of the generated P1 signal is gradually enhanced as the temperature increases from 32.1 °C to 40.1 °C in steps of approximately 1 °C. The relationship between the frequency of the generated microwave signal and temperature is given in Fig. 4(b), and a linear curve fit model is applied. A high sensitivity ST of 1.02198 GHz/°C and a good linearity of 0.99735 for temperature measurements in the calibrated range are revealed. The FSR in the experiment is about 188 kHz due to the OEO length of ∼1 km, the corresponding resolution of the sensing system is FSR/ ST =1.84 × 10−4 °C, which provides a good resolution performance. The reason for the limited temperature range measured in the experiment is mainly because the edges of the FBG are too steep, resulting in the amount of variation of the injected optical power is already maximized in a temperature drift range of 10 °C. If the spectral edge filtering of the sensing element can be designed to be smoother or the temperature sensitivity of the sensing element can be reduced, the measurement range can be substantially improved.
Fig. 4. (a) Electrical spectra of the measured P1 microwave signals with different temperatures, and (b) the relationship between the frequency of the P1 microwave signal and the temperature.
Then, the tunability of the sensing sensitivity for temperature measurements is analyzed. In the experiment, the initial optical power and central wavelength of the injected beam are kept constant to match the reflection spectrum of the FBG for edge filtering. The working current and temperature of the DFB-LD can influence the red-shift ability of its oscillating mode. As the controlled temperature of the DFB-LD is changed to increase the initial wavelength of its oscillating mode, the initial frequency of the P1 signal is increased, but the red-shift ability of the oscillating mode is decreased. As a result, the frequency-changing range of the P1 signal becomes weaker with the same sensing temperature range. The experimental results are shown in Fig. 5. It shows that as the working temperature of the DFB-LD is increased from 21.0 °C to 26.5 °C, the frequency of the initial P1 signal is increased from 14.4875 GHz to 20.2483 GHz under a temperature setting of 31 °C for the FBG sensor. As the sensing temperature is increased from 31 °C to 36 °C with a step of 1 °C, the frequency of the generated microwave signal increases in all three cases. The sensitivity of the FBG sensor with optically injected DFB-LD under three different working temperatures is 1.25952 GHz/°C, 0.85971 GHz/°C, and 0.44322 GHz/°C, respectively. It indicates that the proposed FBG sensing system has a flexible and tunable sensitivity for temperature measurements.
Fig. 5. Tunability of the sensing sensitivity of the proposed FBG sensing system with different working temperatures of the DFB-LD (black line: 21.0 °C; blue line: 22.0 °C; red line: 26.5 °C).
Figure 6 shows the stability test results of the FBG sensing system at a temporal duration of 10 min at each setting of temperature. The frequency deviation and the corresponding measurement accuracy at different temperatures are shown. Each column in Fig. 6 shows the maximum frequency offset of the P1 signals measured under the same temperature at the temporal duration of 10 min with a data-recording step of 1 min. The measured maximum frequency offsets are about 70 MHz, 60 MHz, 70 MHz, 70 MHz, 60 MHz, and 80 MHz from 31 °C to 36 °C, which effectively reduce the frequency jitter (∼200 MHz in 10 mins) of the generated microwave signal based on optically injected DFB-LD without the OEO structure. Considering the sensitivity to be 0.954 GHz/°C, the corresponding measurement accuracy at different temperatures from 31 °C to 36 °C are 0.0734 °C, 0.0629 °C, 0.0734 °C, 0.0734 °C, 0.0629 °C, and 0.0839 °C, as shown in the right axis of Fig. 6. Note that during the stability test, the temperature in the water bath is kept constant by the assistance of a thermocouple. However, due to the limited resolution of the thermocouple of 0.1 °C, we also anticipate slight temperature fluctuations (e.g., within 0.1 °C) in the water bath during the 10-min serial experiments, which might also contribute to the fluctuations of the frequency of the measured microwave signals. Hence, we believe that the real measurement accuracy of the FBG sensing system is better than the calculated values.
Fig. 6. Stability test of the FBG sensing system. The left axis shows the maximum frequency offset of the P1 signals and the right axis gives the corresponding accuracy in temperature measurements.
Finally, a series of repeated experiments are carried out to verify the repeatability of the proposed FBG sensing system for temperature measurements. Figure 7(a) shows measured electrical spectra of the generated P1 signals under different temperatures from 31 °C to 37 °C with a step of 1 °C during the first set of experiment. As can be expected, the frequency increases with increasing temperatures. Five sets of experiments are performed, and the results of the P1 microwave frequencies and linear fitting are shown in Fig. 7(b). It shows that the sensitivities for the five sets of experiments are 0.96964 GHz/°C, 0.95643 GHz/°C, 0.96679 GHz/°C, 0.97286 GHz/°C, and 0.95571 GHz/°C, indicating that the proposed FBG sensing system has good repeatability and stability.
Fig. 7. Results of five repeated experiments within the same temperature range. (a) The electrical spectra of the generated P1 signals at temperatures from 31 °C to 37 °C with a step of 1 °C, (b) the corresponding relationship between the frequency of the P1 microwave signal and the temperature for five different sets of experiments.
4. Conclusions
To conclude, a high-sensitivity FBG sensing system based on an optically injected DFB-LD with an OEO loop for temperature measurements has been proposed and experimentally demonstrated. The FBG sensor device works as an edge filter to adjust the optical power of the injected beam in response to temperature variations. As a result, the central wavelength of the oscillating mode in the optically injected DFB-LD can be modified by temperature variations applied to the FBG device. The optically injected DFB-LD operates under a P1 oscillating state. Hence, a tunable P1 microwave signal can be generated after photoelectric conversion. An OEO feedback loop is introduced to improve the signal quality of the generated P1 signal. In the proof-of-concept experiment, a series of P1 microwave signals have been successfully generated with different temperatures from 31 °C to 40 °C. The sensitivity of the proposed FBG sensing system can also be tuned from 0.44322 GHz/°C to 1.25952 GHz/°C with good linearity in all cases. Furthermore, the stability and repeatability of the sensing system have been demonstrated. The proposed FBG sensing system shows high sensitivity, large tunability, good linearity, and flexible sensing generality, and can be further explored for ultra-high speed detection due to the MWP-based interrogation.
Funding
Project of Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing University of Aeronautics and Astronautics) (No. NJ20220007); National Natural Science Foundation of China (No. 62301495).
Acknowledgment
Researchers Supporting Project number (RSPD2024R654), King Saud University, Riyadh, Saudi Arabia.
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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.
References
1. Y. J. Rao, Y. P. Wang, and T. Zhu, “Principle and application of fiber grating” (Science Press, 2006).
2. S. Mihailov, “Fiber Bragg grating sensors for harsh environments,” Sensors 12(2), 1898–1918 (2012). [CrossRef]
3. J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg grating sensors,” Laser Photon. Rev. 7(1), 83–108 (2013). [CrossRef]
4. J. K. Sahota, N. Gupta, and D. Dhawan, “Fiber Bragg grating sensors for monitoring of physical parameters: A comprehensive review,” Opt. Eng. 59(06), 1–060901 (2020). [CrossRef]
5. L. Sun, C. Li, C. W. Zhang, et al., “The strain transfer mechanism of fiber Bragg grating sensor for extra large strain monitoring,” Sensors 19(8), 1851 (2019). [CrossRef]
6. J. Peng, S. H. Jia, H. Q. Yu, et al., “Design and experiment of FBG sensors for temperature monitoring on external electrode of lithium-ion batteries,” IEEE Sens. J. 21(4), 4628–4634 (2021). [CrossRef]
7. J. B. Rosolem, R. S. Penze, C. Floridia, et al., “Dynamic effects of temperature on FBG pressure sensors used in combustion engines,” IEEE Sens. J. 21(3), 3020–3027 (2021). [CrossRef]
8. B. Rente, M. Fabian, M. Vidakovic, et al., “A fiber Bragg grating (FBG) -based sensor system for anaerobic biodigester humidity monitoring,” IEEE Sens. J. 21(2), 1540–1547 (2021). [CrossRef]
9. T. L. Li, J. X. Guo, Y. G. Tan, et al., “Recent advances and tendency in fiber Bragg grating-based vibration sensor: a review,” IEEE Sens. J. 20(20), 12074–12087 (2020). [CrossRef]
10. S. M. Melle, K. X. Liu, and R. M. Measures, “A passive wavelength demodulation system for guided-wave Bragg grating sensors,” IEEE Photonics Technol. Lett. 4(5), 516–518 (1992). [CrossRef]
11. B. Liu, Z. R. Tong, S. H. Chen, et al., “A novel method of edge filter linear demodulation using long-period grating in fiber sensor system,” Acta Opt. Sin. 24(2), 199–202 (2004).
12. U. Tiwari, K. Thyagarajan, M. R. Shenoy, et al., “EDF-based edge-filter interrogation scheme for FBG sensors,” IEEE Sens. J. 13(4), 1315–1319 (2013). [CrossRef]
13. J. Hervas, A. L. Ricchiuti, W. Li, et al., “Microwave photonics for optical sensors,” IEEE J. Sel. Top. Quantum Electron. 23(2), 327–339 (2017). [CrossRef]
14. J. P. Yao, “Microwave photonic sensors,” J. Lightwave Technol. 39(12), 3626–3637 (2021). [CrossRef]
15. J. P. Yao, “Microwave photonic systems,” J. Lightwave Technol. 40(20), 6595–6607 (2022). [CrossRef]
16. W. Z. Li, M. Li, and J. P. Yao, “A narrow-passband and frequency-tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microwave Theory Tech. 60(5), 1287–1296 (2012). [CrossRef]
17. Z. W. Xu, X. W. Shu, and H. Y. Fu, “Sensitivity enhanced fiber sensor based on a fiber ring microwave photonic filter with the Vernier effect,” Opt. Express 25(18), 21559–21566 (2017). [CrossRef]
18. X. H. Zou, X. K. Liu, W. Z. Li, et al., “Optoelectronic oscillators (OEOs) to sensing, measurement, and detection,” IEEE J. Quantum Electron. 52(1), 1–16 (2016). [CrossRef]
19. J. P. Yao, “Optoelectronic oscillators for high speed and high resolution optical sensing,” J. Lightwave Technol. 35(16), 3489–3497 (2017). [CrossRef]
20. L. Wang, T. F. Hao, G. Y. Li, et al., “Microwave photonic temperature sensing based on Fourier domain mode-locked OEO and temperature-to-time mapping,” J. Lightwave Technol. 40(15), 5322–5327 (2022). [CrossRef]
21. Z. W. Xu, X. W. Shu, and H. Y. Fu, “Fiber Bragg grating sensor interrogation system based on an optoelectronic oscillator loop,” Opt. Express 27(16), 23274–23281 (2019). [CrossRef]
22. Y. G. Yang, M. G. Wang, Y. Shen, et al., “Refractive index and temperature sensing based on an optoelectronic oscillator incorporating a Fabry–Perot fiber Bragg grating,” IEEE Photonics J. 10(1), 1–9 (2018). [CrossRef]
23. T. T. Xie, Z. W. Xu, X. Cai, et al., “Highly Sensitive Fiber Bragg Grating Sensing System Based on a Dual-Loop Optoelectronic Oscillator with the Enhanced Vernier Effect,” J. Lightwave Technol. 40(14), 4871–4877 (2022). [CrossRef]
24. D. R. Xiao, G. Q. Wang, F. H. Yu, et al., “Highly stable and precise demodulation of an FBG-based optical current sensor using a dual-loop optoelectronic oscillator,” J. Lightwave Technol. 39(18), 5962–5972 (2021). [CrossRef]
25. S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. 46(3), 421–428 (2010). [CrossRef]
26. S. L. Pan and J. P. Yao, “Wideband and frequency-tunable microwave generation using an optoelectronic oscillator incorporating a Fabry–Perot laser diode with external optical injection,” Opt. Lett. 35(11), 1911–1913 (2010). [CrossRef]
27. S. C. Chan, S. K. Hwang, and J. M. Liu, “Period-one oscillation for photonic microwave transmission using an optically injected semiconductor laser,” Opt. Express 15(22), 14921–14935 (2007). [CrossRef]
28. P. Zhou, F. Z. Zhang, D. Zhang, et al., “Performance enhancement of an optically-injected-semiconductor-laser-based optoelectronic oscillator by subharmonic microwave modulation,” Opt. Lett. 43(21), 5439–5442 (2018). [CrossRef]
