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Abstract
By using an external injection locking method, for what we believe to be the first time, we experimentally demonstrate continuous ultra-wideband signal regeneration in random optoelectronic oscillators, achieving more adaptable signal processing capabilities than self-oscillation methods. Supported by theoretical analysis and experimental evidences, this system can regenerate any signal with sufficient gain in a random-feedback cavity, independent of cavity filters. Remarkably, enhanced phase noise performance with over 35.2 dB side mode suppression and a phase noise better than −86 dBc@1 kHz at higher injecting powers are demonstrated. Additionally, we successfully process complex multi-frequency communication signals, indicating potential applications in radar, remote sensing, and data communications.
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1. Introduction
The emergence and evolution of wideband and multi-channel signals are expected to play a pivotal role in the next generation of wireless communications, as well as in civil and military radar applications, and various wireless sensor network scenarios [1–6], marking a key challenge in the development of radio frequency transmission, sensing, and cognition technologies. Photonic-assisted microwave generation systems can overcome the shortcomings of narrow bandwidth and high power consumption in all-electronic technologies and have been applied to generate higher-quality radiofrequency signals [7–10], demonstrating outstanding capabilities in high-performance transmitter preparation and low-noise signal transmission for communication links.
An optoelectronic oscillator (OEO) structure is a representative photonic-assisted approach to realize a stable and low-phase noise optoelectronic oscillation [11–13]. However, ordinary OEOs are based on a fixed-length cavity, in which only a discrete set of cavity modes that meet the phase conditions of resonance can oscillate in the cavity, featuring a very limited frequency oscillation range. To increase the operating frequency range of the wideband target signals, many attempts have been reported over the past year [14–17]. The random OEO structure [18–21] can efficiently generate and process resonant signals with randomly distributed time delays, achieving ultra-wideband continuous resonance without any discrete mode interval ($\Delta f \approx 0$). To date, most of the related research on random OEO structure focuses on the generation of various wideband random signals [22–24], and improving certain applications of self-oscillated signals in ultra-wideband communications, electronic countermeasures, and high-speed neuromorphic computing. However, the flexibility for the application of broadband complex signals is limited in the self-oscillating working state. In communication applications such as long-distance links, communication signals usually need to go through pre-amplification and relay amplification while still maintaining high signal-to-noise ratio characteristics. The injection-locking technology has been widely studied to achieve high-quality regeneration of many complex signals in typical OEO structures [25,26], but the study in the random OEO remains fancy.
In this work, we use injection-locking technology to achieve continuous wideband signal regeneration in a random OEO. To the best knowledge of the authors, it is the first study of experimental implementation of an injection-locking random OEO. Both theoretical and experimental results show that any signal meeting the gain condition could be locked and regenerated in the random OEO, with or without a cavity filter. Higher injection powers yield output signals with improved noise characteristics, achieving over 35.2 dB of side-mode suppression and over −86 dBc@1 kHz of phase noise across the entire continuous frequency band. Additionally, we inject complex communication signals into this random OEO and explore the synchronous amplification and regeneration of multi-frequency signals.
2. System design and analysis
2.1 Experimental setup
The block diagram of the injection-locking random OEO is shown in Fig. 1. The OEO is composed of a narrow-bandwidth laser diode (LD), a polarization controller (PC), a high-speed Mach-Zehnder modulator (MZM), two Erbium-doped fiber amplifiers (EDFAs), an optical circulator (OCR), a section of single-mode fiber (SMF), a high-speed photodetector (PD), a broadband low-noise electrical amplifier (LNA), an electrical filter, power amplifier (EA), and three broadband electrical couplers (ECs).
Fig. 1. Schematic diagram of the injection-locking broadband random OEO. LD: tunable laser source; PC: polarization controller; MZM: Mach-Zehnder modulator, EDFA: Erbium-doped fiber amplifier; OCR: optical circulator; SMF: single-mode fiber; PD: high-speed photodetector; LNA: low-noise electrical amplifier, EA: the power electrical amplifier, EC: electrical coupler; OSC: oscilloscope, ESA: electrical spectrum analyzer.
Due to imperfect fiber manufacturing, the internal refractive index of SMF is non-uniform, leading to inherent Rayleigh scattering (RS) in all directions, where weak backscattering can be recaptured by the fiber again, and propagate in the opposite direction. The EDFA1 before the OCR is used to amplify the incident light. Together with the long fibers, they both contribute to larger Rayleigh scattering and Brillouin scattering (BS) coefficients. Backscattered scattered parts of the light generated in the long fibers will then propagate in the opposite direction to incident light, providing randomly delayed feedback to the oscillations. Then the backpropagating light experienced further amplification by EDFA2 placed after Port 3 of the OCR.
The filter is an optional component and will be explained in detail in Chapter 3. Experimental results. Therefore, the operation bandwidth of the OEO cavity is mainly determined by the other electronic devices (especially the electrical amplifier and the modulator) in the cavity, indicating a broadband processing characteristic. The ECs are used to inject external signals at different locations for subsequent injection-locking analysis of the regenerated signals in the cavity.
2.2 Theoretical model
Meeting the two conditions that the signals can add coherently and that the loop gain exceeds the losses is essential for an OEO to be able to self-oscillate. The resonant mode interval in a conventional single-loop OEO is given by $\Delta f = c/nL$. While in a random OEO, the production of the backpropagating RS and BS signals [27–29] will provide random long-delayed feedback, thus the length of the OEO loop is,
where ${L_0}$ is the length of the OEO cavity excluding the long fibers, and ${z_i}$ is the location of Rayleigh backscattering or Brillouin scattering in the fiber, which changes continuously, leading to continuous microwave signal oscillating in the random OEO without any fixed longitudinal mode ($\Delta f \approx 0$). However, non-constant gain caused by the superposition of all these statistically independent backscattered sections with random fluctuations will cause inevitable random fluctuations in the power of the intracavity oscillation signals.To explore the injection locking mechanism in a random OEO through broadband signal injection, we refer to the injection locking theory of traditional single-ring OEO structure [25,30–34], in which $\varphi (t )$ and $\Omega $ denote to instantaneous phase difference and frequency difference between the injection signal ${V_{in}}(t )$ and the perturbed output signal ${V_o}(t )$, respectively. ${K_i} = \left( {\frac{{{V_{in}}}}{{{V_o}}}} \right)$ is the injection amplitude ratio. The oscillator phase dynamics equation of the single-loop OEO under the influence of the signal injection can be expressed as
The phase difference $\varphi $ between the oscillator signal and the injection signal decreases exponentially and approaches zero with a time constant of $\left( {\frac{{\mu {K_i}}}{{{K_i} + 1}}} \right)$. For signals injected with low power, ${K_i} \ll 1$, the time constant is approximately equal to F, which is dependent on the bandwidth of the filter and injection signal amplitude. While as the power of the injected signal gradually increases, Kican no longer be ignored.
When the injection locking is achieved in the OEO, the phase difference $\varphi (t )$ becomes constant, i.e., $\frac{{\textrm{d}\varphi }}{{\textrm{d}t}} = 0$. The steady-state phase difference ${\varphi _s}$ after injection-locking process is
Since frequency difference $\Omega \approx 0$ in an injection-locking random OEO, it can be rewritten as
Note that steady-state phase difference ${\varphi _s}$ is inversely proportional to ${K_i}$, thus higher injection power for target signals will lead to lower phase perturbation. In addition, since the random OEO system can operate without a filter, i.e., with a very large half-bandwidth $\mu $, it can achieve better noise performance than a system with a bandpass filter.
3. Experimental results
A proof-of-concept experiment is carried out to verify the feasibility of the proposed scheme to generate injection-locking oscillation. A tunable narrow-bandwidth laser source (Agilent, 8168F) is used to generate a continuous light signal with a wavelength of 1549.836 nm, which is sent to a MZM (Optilab, IM-1550-12-PM). The output is then amplified and coupled into ∼5 km SMFs set through an OCR. A homemade EDFA1 (with a maximum output power of 21.5 dBm) is used as the gain mechanism to amplify incident narrowband light and produce larger Rayleigh scattering and Brillouin scattering coefficients in long fibers. The backpropagating scattering parts of the signal are then further amplified in EDFA2 placed after port 3 of the OCR and converted to an electrical signal in a PD (Newport, BB-35F).
The converted signal is then amplified by an LNA (MITEQ, ASF2-00010600) and filtered by an electrical filter. The filter is one of the following cases: (1) a fixed bandpass filter, K&L, 5C50-7560/E75; (2) a tunable YIG band-pass filter, frequency adjustment range 2.00-12.40 GHz, bandwidth 30 MHz; (3) a lowpass filter, Mini-Circuits, SLP-450; (4) No filter. To supply sufficient electrical gain in the resonator, two EAs (JDSU, H301-1210 and 1510) are also used after the EC1, which is used to import external signal (port ②, if any). Then the amplified signal is split into a fraction of the microwave signals to a spectrum analyzer (Keysight, N9020A) and a real-time oscilloscope (Rigol, DS1104) for analysis. The remainder of the signal combined with the signal imported from port ① (if any) are then injected into the MZM to close the loop. The injected signals are generated by a microwave signal generator (HP, 83623B) or a function/arbitrary waveform generator (Agilent, 33522A).
3.1 Injection locking of broadband microwave signals
The proposed broadband signal regeneration system based on random OEO was assembled and experimentally tested. The spectrum of the back-propagated optical signal obtained from Port 3 of the optical circulator is shown in Fig. 2(a), which is also the subsequent resonant light spectrum in the cavity. Both RS and BS gains are related to the optical power pumped into the long fibers. Due to the gain limitation of our homemade EDFA, we are just able to achieve the condition that the powers of the Rayleigh scattering signal and the Brillouin scattering signal are equal. For higher input optical powers, the BS coefficient increases faster than the RS coefficient in long fibers, thereby reducing the impact of the beat signal of the Brillouin scattering and Rayleigh backscattering signals.
Fig. 2. Injection-locking results of the microwave signals using the fixed bandpass filter (centered at 7.56 GHz) in the cavity. (a) The optical spectrum of the light obtained at port 3 of the OCR (resolution 0.01 nm). (b) Spectrum results of signals oscillating in the OEO. All frequencies in the passband oscillate in the OEO without a discrete mode interval. And spectrum results of the regenerated signals which were injected into (c) port ① with a power of 0.0 dBm or (d) port ② with a power of −20.0 dBm, respectively.
Initially, a fixed bandpass filter with a center frequency of 7.56 GHz and a 3 dB bandwidth of 75 MHz (case (1)) was used in the cavity to clearly distinguish the noise floor and the oscillation frequencies by the difference in power. The frequency response curve of the filter was shown in Fig. 2(b), demonstrating a full-passband output rather than a periodic single-frequency signal, and indicating all the frequencies contained in the passband of the filter oscillate in OEO at the same time. However, inconspicuous periodic unevenness at the curve is seen, which may be due to the close-loop effect of the resonant cavity caused by some inevitable interface reflection. Then the unevenness in the frequency response curve is further amplified by cavity gain and mode competition in the optoelectronic link and has a certain impact on the output spectrum result. If the end faces of device pigtails are well-spliced, a broadband signal with a flat spectrum can be generated.
We continuously changed the frequency of the injected microwave signal at a frequency interval of 1 MHz, while maintaining the signal power at 0.0 dBm, and then injected it into port ①. Figure 2(c) is the superimposed spectrum of the measured regenerated signal, showing a power jitter of 5.7 dB, and a side mode suppression ratio (SMSR) better than 29.3 dB over the tuning range. In contrast, the injected signal outside the filtered passband (green line in Fig. 2(c)) shows obvious non-resonant characteristics and the output power is low.
To improve the modulation efficiency and quality of the intracavity regenerated signals, the injection port of the microwave signal was changed to port ②, and the power of the injected signal was reduced to -20.0 dBm, which was amplified before entering the MZM. Figure 2(d) shows the superimposed spectrum of the measured regenerated signal again, with a power jitter of 8.8 dB and an SMSR better than 41.1 dB. The results show that the powers of the regenerated oscillation signals here are ∼15 dB higher than those in Fig. 2 (c), and ∼41 dB higher than the noise floor from DC to about 20.00 GHz, indicating that all injected signals in this range have good injection resonance characteristics.
To further verify the key characteristic that the system was capable of providing ultra-wideband oscillation, we applied a tunable YIG bandpass filter (case (2)) and then continuously changed the frequency of the injected microwave signal at a frequency interval of 500 MHz, and then injected it into port ① (with an injection power of 0.0 dBm) or port ② (with an injection power of −20.0 dBm) of the random OEO system, respectively, as showing in Figs. 3(a−c). The frequency tuning range are increased to 6.00 GHz, and the output SMSRs of both are still better than 35.2 dB, proving the high quality of the regenerated microwave signals. More gain non-uniformity can be seen in these two regenerated spectra due to the unevenness of the YIG filter response curve and the aging attenuation of the microwave devices in the high frequency band. However, it should be noted that for the amplification and regeneration of the injecting signal, this gain unevenness will not affect the injection-locking process in the OEO.
Fig. 3. Injection-locking results of the broadband microwave signals using the tunable YIG filter or no filter in the cavity. Spectrum results of the regenerated signals which were injected at (a, b) port ① with a power of 0.0 dBm and (c) port ② with a power of −20.0 dBm, respectively. The red curve in (b) is the output of the randomly selected injecting-regenerated signal (dot-dash line in (a)), in order to verify the continuous resonance characteristics of the system. (d) Spectrum results of the regenerated signals injected at port ② with no filter in the cavity. The dot-dash line circled the continuous resonant bandwidth of the system.
Although the cavity filter can help to obtain pure microwave signals, its bandwidth will also limit the operating bandwidth of the random OEO. Therefore, measuring the output signal spectrum without a cavity filter can better demonstrate the ultra-wideband output characteristics of the random OEO (case (4)), as shown in Fig. 3(d), where the signal is also injected at port ② with a power of −20.0 dBm. It can be seen that the power of the oscillating signal is ∼32 dB higher than the noise floor ranging from DC to 10.00 GHz, and the operating bandwidth is only limited by the bandwidths of the electrical amplifiers and the modulator. Due to the lack of filtering, some self-oscillated modes can be observed in the high-gain resonant cavity, resulting in an increase in the power jitter of the regenerated signal and a decrease in the output spectral purity. However, for injected signals with powers as low as −20.0 dBm, they can still satisfy the resonance conditions in the random OEO.
3.2 Measurement of phase noise for regenerated microwave signals
To analyze the output noise characteristics of broadband oscillation signals in the random OEO system, we selected several regenerated microwave signals discussed above to analyze their phase noise. The results were shown in Fig. 4, in which a microwave signal directly amplified by the LNA was also used for comparison under roughly the same signal gain conditions.
Fig. 4. Phase noise results of regenerated signals under different conditions. The blue and red lines are the phase noises of the regenerated signals injected into port ① and port ② (as shown in Fig. 2(c) and (d)). The green line is the phase noise of the signal injected outside the filter bandwidth. The black line is the phase noise of the signal injected into port ② with no cavity filter (as shown in Fig. 3(d)). The purple line is the phase noise of the signal directly amplified by an LNA.
For the microwave signal injected into port ②, regardless of whether there is a cavity filter or not, the regenerated output signals can both achieve the best signal quality of −86 dBc@1 kHz, as shown by the red and black lines in Fig. 4. However, due to the low modulation efficiency, the overall phase noise of regenerated output signal injected into port ① (blue line) is 20∼30 dB worse than that injected into port ②. Even it only has better phase noise characteristics than the signal amplified directly by an LNA (purple line) in the frequency offset range of <4 kHz and >37 MHz. It is worth noting that a signal injected into port ② but not locked (outside the filtering bandwidth) has the worst phase noise information (green line), which may be due to the fact that there were not only LNA but also the EA with relatively high noise in the OEO cavity. Therefore, to regenerate weak injected signals with high quality in a random OEO, the resonant gain condition must be satisfied.
Although we had achieved locking and regeneration of the injected signals through intracavity gain competition, the phase noise results in Fig. 4 were still slightly lower than the results of the injection-locked output in a traditional OEO [25,29,34–36]. This may be due to the highly dynamic resonant cavity length in the random OEO system, which resulted in the inability to select the resonant mode by the cavity length, showing obvious limitations in the narrow-linewidth resonant output. However, on the other hand, the highly dynamic resonant cavity length in the random OEO system also demonstrates its great potential in high-quality processing of ultra-wideband or multi-frequency signals due to its higher adaptability to the resonant frequency. Therefore, this random OEO system can not only generate ultra-wideband signals [18] but also perform efficient signal processing in wideband sensing and communication fields such as 5 G communication, satellite link, weather monitoring, etc., without causing obvious deterioration of the transmitted signals.
3.3 Injection locking of multi-frequency signals
The regenerated waveforms of the complex communication signals were also measured with a real-time oscilloscope at a sampling rate of 100 GS/s and a broadband spectrum analyzer. The filter used here is a low-pass filter (case (3)). A 20 MHz Pseudo-Random Binary Sequence (PRBS) signal, a 15 MHz square wave (SW) signal, and a 10 MHz pulsed wave (PW) signal with a duty circle of 16% were injected into the random OEO cavity, respectively. They are composed of multi-order frequency signals [37] and commonly used in communication systems, which can further verify the simultaneous high-quality processing for multi-frequency signals in the cavity.
The time domain waveforms of the regenerated signals are shown in Figs. 5(a−c), where the amplitudes of the signals are increased by 140∼180 times, showing obvious amplification effects for multi-frequency communication signals. Due to the operating bandwidth limitation of the arbitrary waveform signal generator, only waves within 30 MHz have been studied, and the time-domain waveforms of the injection signals still exhibit certain distortions. However, regardless of whether the injected signals are standard or distorted, they are all locked and amplified in the proposed random OEO system. The corresponding frequency domain waveforms are shown in Figs. 5(d−f). The noise floor of the output spectrum shows an increase near the 10 MHz frequency since the LNA has gain non-uniformity at the 10 MHz low-frequency cutoff point, but the measured spectrum still has an SMSR better than 19.0 dB. Adopting optical and electrical amplifiers with lower noise will efficiently reduce the noise floor and increase the SMSR.
Fig. 5. Injection-locking results of multi-frequency communication signals using a lowpass filter in the cavity. (a-c) are the time-domain waveforms of a 20 MHz PRBS signal, a 15 MHz square wave signal, and a 10 MHz electrical pulse signal, respectively: input signal (red) and regenerated signal (black). (d-f) are their corresponding frequency domain spectrum. The insert in (d) shows the zoomed-in spectrum details in the 15.00 ∼17.00 GHz band (red box).
This study has demonstrated the ability of the random OEO to lock and regenerate the ultra-wide and multi-frequency signals with high quality. Since the key characteristic is that the oscillation frequencies in a random OEO are continuous with $\Delta f \approx 0$, three different filter cases and one no-filter case are used to adjust the gain bandwidth of the cavity and have achieved continuous injection locking of broadband microwave signals. Results show that locking and regeneration of any signal in random OEO can be achieved by ensuring sufficient resonant gain, breaking through the limitation of the length of the resonant cavity, and showing no mode hopping problem. However, highly dynamic resonator length also limits its application in scenarios with ultra-narrow linewidth and ultra-low noise. For higher injection power, the regenerated output signals have better phase noise characteristics with or without a cavity filter. Additionally, the random OEO system can achieve injection locking and amplification of complex multi-frequency signals, verifying its potential in the generation and processing of complex multi-frequency signals.
4. Conclusion
In summary, we have demonstrated the continuous ultra-wideband signal regeneration in a random OEO without discrete mode intervals. Both theoretical and experimental results show that any signal meeting resonant gain conditions could be effectively locked and regenerated in the random OEO, irrespective of the presence of a cavity filter. Notably, the quality of the regenerated signal improves at higher injection powers, showing an SMSR of over 35.2 dB and a phase noise surpassing −86 dBc@1 kHz within a 10.00 GHz operating bandwidth. Although the random resonator length in our system slightly compromises resonant phase noise compared to the typical OEOs [25,29,34–36], it introduces a unique adaptability to continuous resonant frequencies, showing great potential in the high-quality processing of ultra-wideband and multi-frequency communication signals. This study is the first-ever experimental demonstration of the injection-locking approach in broadband random OEOs, and we believe our work may find practical application in modern communication and sensing technologies.
Funding
Introduction of Talent Research Fund of Guizhou University (2022 No. 64); Shuguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education Commission (22SG44); Natural Science Foundation of Shanghai (21ZR1481100); National Natural Science Foundation of China (12304333, 62075131, 62122054).
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.
References
1. F. Zuo, Z. Chen, L. Hu, et al., “Multiple-node time synchronization over hybrid star and bus fiber network without requiring link calibration,” J. Lightwave Technol. 39(7), 2015–2022 (2021). [CrossRef]
2. L. Ye, Y. Ma, W. Wang, et al., “High-sensitivity angular velocity measurement based on bidirectional coupled optoelectronic oscillator,” Opt. Commun. 440, 201–206 (2019). [CrossRef]
3. S. Prager, M. Haynes, and M. Moghaddam, “Wireless subnanosecond RF synchronization for distributed ultrawideband software-defined radar networks,” IEEE Trans. Microwave Theory Tech. 68(11), 4787–4804 (2020). [CrossRef]
4. S. Wang, Z. Yin, D. He, et al., “Twin-field quantum key distribution over 830-km fibre,” Nat. Photonics 16(2), 154–161 (2022). [CrossRef]
5. W. Bai, P. Li, X. Zou, et al., “Millimeter-wave joint radar and communication system based on photonic frequency-multiplying constant envelope LFM-OFDM,” Opt. Express 30(15), 26407–26425 (2022). [CrossRef]
6. S. Jia, M. Lo, L. Zhang, et al., “Integrated dual-laser photonic chip for high-purity carrier generation enabling ultrafast terahertz wireless communications,” Nat. Commun. 13(1), 1388 (2022). [CrossRef]
7. L. Zmrzlak, A. Blatnik, M. Scaffardi, et al., “Transmitter and receiver amplifier chains in X- and Ku-bands of radio frequency front-end for frequency-agile microwave photonic radars,” in 2023 30th International Conference on Systems, Signals and Image Processing (IWSSIP) (2023), pp. 1–5.
8. X. Zou, F. Zou, Z. Cao, et al., “A multifunctional photonic integrated circuit for diverse microwave signal generation, transmission, and processing,” Laser Photonics Rev 13(6), 1800240 (2019). [CrossRef]
9. J. Zhao, H. Jeng, L. O. Conlon, et al., “Enhancing quantum teleportation efficacy with noiseless linear amplification,” Nat. Commun. 14(1), 4745 (2023). [CrossRef]
10. F. Zhang, B. Gao, and S. Pan, “Photonics-based MIMO radar with high-resolution and fast detection capability,” Opt. Express 26(13), 17529–17540 (2018). [CrossRef]
11. X. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996). [CrossRef]
12. T. Hao, J. Tang, D. Domenech, et al., “Toward monolithic integration of OEOs: From systems to chips,” J. Lightwave Technol. 36(19), 4565–4582 (2018). [CrossRef]
13. L. Maleki, “The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011). [CrossRef]
14. T. Hao, Q. Cen, Y. Dai, et al., “Breaking the limitation of mode building time in an optoelectronic oscillator,” Nat. Commun. 9(1), 1839 (2018). [CrossRef]
15. W. Zhang and J. Yao, “Silicon photonic integrated optoelectronic oscillator for frequency-tunable microwave generation,” J. Lightwave Technol. 36(19), 4655–4663 (2018). [CrossRef]
16. J. Zhang and J. Yao, “Parity-time-symmetric optoelectronic oscillator,” Sci. Adv. 4(6), eaar6782 (2018). [CrossRef]
17. Y. Liu, T. Hao, W. Li, et al., “Observation of parity-time symmetry in microwave photonics,” Light Sci. Appl. 7(1), 38 (2018). [CrossRef]
18. Z. Ge, T. Hao, J. Capmany, et al., “Broadband random optoelectronic oscillator,” Nat. Commun. 11(1), 5724 (2020). [CrossRef]
19. Y. Wang, A. Wang, X. Liu X, et al., “Broadband random optoelectronic oscillator based on stimulated Brillouin scattering,” in Advanced Optical Manufacturing Technologies and Applications 2022; and 2nd International Forum of Young Scientists on Advanced Optical Manufacturing (AOMTA and YSAOM 2022) (2023), pp. 632–637.
20. B. Li, R. Wu, W. Hong, et al., “Correlation optical time domain reflectometry based on broadband random optoelectronic oscillator,” Opt. Laser Technol. 167, 109835 (2023). [CrossRef]
21. Y. Huang and J. Yao, “Microwave chaotic signal generation based on an optoelectronic oscillator with randomly distributed feedbacks,” in 2021 International Topical Meeting on Microwave Photonics (MWP) (2021), pp. 1–4.
22. Z. Ge, Y. Xiao, T. Hao, et al., “Tb/s fast random bit generation based on a broadband random optoelectronic oscillator,” IEEE Photon. Technol. Lett. 33(22), 1223–1226 (2021). [CrossRef]
23. H. Tian, L. Zhang, Z. Zeng, et al., “Externally-triggered spiking and spiking cluster oscillation in broadband optoelectronic oscillator,” J. Lightwave Technol. 41(1), 48–58 (2023). [CrossRef]
24. H. Tian, L. Zhang, Z. Zhang, et al., “Externally-excited short pulse train generation in a broadband nonlinear optoelectronic oscillator,” in 2022 IEEE 14th International Conference on Advanced Infocomm Technology (ICAIT) (2022), pp. 212–215.
25. Z. Fan, J. Su, Y. Lin, et al., “Injection locking and pulling phenomena in an optoelectronic oscillator,” Opt. Express 29(3), 4681–4699 (2021). [CrossRef]
26. J. Wang, T. Jia, S. Wang, et al., “Wavelength synchronization technology for UDWDM-PON transmitter based on injection locking,” Chin. Opt. Lett. 19(1), 010602 (2021). [CrossRef]
27. M. Nakazawa, “Rayleigh backscattering theory for single-mode optical fibers,” J. Opt. Soc. Am. 73(9), 1175–1180 (1983). [CrossRef]
28. Y. Aoki, K. Tajima, and I. Mito, “Input power limits of single-mode optical fibers due to stimulated Brillouin scattering in optical communication systems,” J. Lightwave Technol. 6(5), 710–719 (1988). [CrossRef]
29. Y. Ma, X. Jing, and F. Gu, “Stable and tunable optoelectronic oscillator with external stimulated Brillouin beat note injection,” IEEE Photon. Technol. Lett. 33(19), 1085–1088 (2021). [CrossRef]
30. R. Adler, “A study of locking phenomena in oscillators,” in Proceedings of the IRE (IEEE, 1946), pp. 351–357.
31. M. Hasan, A. Banerjee, and T. Hall, “Injection locking of optoelectronic oscillators with large delay,” J. Lightwave Technol. 40(9), 2754–2762 (2022). [CrossRef]
32. A. Banerjee, J. Sarkar, L. de Britto, et al., “On the transient behavior of single-loop optoelectronic oscillators under RF injection-locking,” IEEE J. Quantum Electron. 56(6), 1–13 (2020). [CrossRef]
33. A. Banerjee and J. Sarkar, “Improved analytical model of phase-locking dynamics in unlocked-driven optoelectronic oscillators under RF injection locking,” Opt. Commun. 437, 184–192 (2019). [CrossRef]
34. A. Banerjee, L. A. D. de Britto, and G. M. Pacheco, “A theoretical and experimental study of injection-locking and injection-pulling for optoelectronic oscillators under radio Frequency signal injection,” J. Lightwave Technol. 38(6), 1210–1220 (2020). [CrossRef]
35. T. Kan, K. Kasai, M. Yoshida, et al., “Injection-locked 256 QAM WDM coherent transmissions in the C- and L-bands,” Opt. Express 28(23), 34665–34676 (2020). [CrossRef]
36. Y. Wang, X. Li, J. Zhang, et al., “Spurious level and phase noise improved Fourier domain mode-locked optoelectronic oscillator based on a self-injection-locking technique,” Opt. Express 29(5), 7535–7543 (2021). [CrossRef]
37. Y. Ma, W. Wang, K. Song, et al., “Photonic microwave waveform generation based on dual-wavelength time domain synthesis technology,” Acta Phys. Sin. 68(17), 174203 (2019). [CrossRef]
