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Abstract
Optoelectronic oscillators (OEOs) are promising for radar, communication and electronic countermeasure systems. Among them, frequency-scanning OEOs with wide instantaneous bandwidth are needed for many advanced applications. In this work, we demonstrate a novel system to generate bandwidth-doubled linearly chirped microwave waveforms (LCMWs) based on bandwidth superposition using a Fourier domain mode-locked OEO (FDML OEO). In the proposed system, bandwidth-doubling is achieved by re-modulating the generated LCMW of the FDML OEO onto a frequency-scanning optical carrier signal with the help of an external Mach-Zehnder modulator. LCMWs with wide frequency scanning instantaneous bandwidth of 10 GHz are experimentally obtained. Meanwhile, these LCMWs are tunable in an ultra-wide frequency range from 1 to 39 GHz. Moreover, they are with high frequency sweep linearity of 0.5%. Our work presents a simple method to generate tunable wide-band LCMWs for potential microwave sources.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Frequency scanning microwave sources with large time-bandwidth product (TBWP) play an important role in wireless communications, modern radar and other military applications [1–8]. Although extensively used, traditional electrical microwave sources are with shortcomings such as narrow instantaneous bandwidth, low operating frequency, high complexity and high cost. On the other hand, a simple and cost-effective method, the photonics-assisted technique based on optoelectronic oscillator (OEO) has been introduced to generate microwave signals. Within the past decade, OEOs have attracted tremendous attention on account of their low phase noise, broad bandwidth, and the capacity to generate high-frequency signals [9–13].
Nevertheless, it is hard to generate a linearly chirped microwave waveform (LCMW) with a high chirp rate directly from the OEO cavity due to the limitation of mode building time. In [14–17], we proposed and demonstrated a novel Fourier domain mode-locked OEO to break the limitation of mode building time. Fourier domain mode-locking operation was achieved by using a frequency scanning microwave photonic filter (MPF) and synchronizing the scanning period of the filter to the cavity round-trip time. LCMWs with an instantaneous frequency scanning bandwidth of 7.5 GHz were achieved in [17]. However, the maximum achievable instantaneous frequency scanning bandwidth is limited by the bandwidth of laser diode (LD) in our previous work, and the frequency sweep linearity is also poor due to the nonlinear response of the LD to a linear saw-tooth driving signal. In recent years, several other FDML OEO structures have also been proposed to generate LCMWs, such as FDML-OEO based on optical injection, a frequency swept electronic filter and a dual-loop structure [18–20]. The generation of LCMWs with very high frequency scanning linearity and broad bandwidth has also been demonstrated using the FDML OEO [21,22]. To obtain an enhanced frequency scanning linearity and enlarged TBWP, which are of prime importance for LCMWs [23–26], we present a high linearity bandwidth-doubled FDML OEO in [27], where bandwidth-doubling is achieved by bandwidth superposition of the generated LCMW of the FDML OEO and high linearity is obtained with the help of an electrically pumped frequency scanning light source (FSLS). This scheme is easier to obtain FSLS with high linearity, and generates LCMWs with higher frequency and larger bandwidth beyond the limitation of FDML OEO.
The work reported in this paper is an extension of our earlier work reported in [27]. Here, a more detailed study, including the response of notch filter, the frequency sweep linearity and the reconfigurability of the system are conducted. We realized the generation of LCMWs with a frequency scanning instantaneous bandwidth of up to 10 GHz, together with an ultrawide tuning range from 1 to 39 GHz. Moreover, these LCMWs are with a high frequency distribution linearity of 0.5% and a large TBWP of about 220,000.
2. Principle
Figure 1(a) shows the structure of the proposed system. This system mainly consists of a FSLS, a closed optoelectronic feedback loop and a bandwidth doubling module. In order to implement the FSLS, we load a highly-linear frequency scanning microwave signal ${f_R}$, generated by a homemade frequency scanning radio frequency (RF) source, onto the single-frequency optical signal ${f_{carrier}}$ generated by LD. The MZM is adjusted to work at the minimum bias point to achieve the carrier suppressed double sideband modulation, thus two sidebands that named as up-conversion signal ${f_{up}}$ and the down-conversion signal ${f_{down}}$ are obtained. To construct the FSLS, the up-conversion signal ${f_{up}}$ or the down-conversion signal ${f_{down}}$ is picked out from the modulated lightwave utilizing an optical filter. The generated FSLS can retain the excellent properties of high linearity of ${f_R}$, which can avoid the influence of the nonlinear response of the LD to a linear saw-tooth driving signal in our previous work.
Fig. 1. Schematic illustration of the bandwidth-doubling system based on the FDML OEO. (a) System architecture. (b) The principle on the MPF based on PM-IM conversion. FSLS: frequency scanning light source; RF: radio frequency source; LD: laser diode; OC: optical coupler; PM: phase modulator; PS-FBG: phase-shifted fiber Bragg grating; EDFA: erbium-doped fiber amplifier; PD: photodetector; EA: electrical amplifier; EC: electric coupler; MZM: Mach-Zehnder modulator; SMOS: single mode optical signal.
As for the OEO, a fast frequency-tuning MPF is constructed based on phase-modulation to intensity-modulation (PM-IM) conversion technology. The detailed structure is shown in Fig. 1(a). To further clarify its working principle, an MPF working at the single-frequency mode is first discussed as follows. When the single-frequency optical carrier signal is inputted into the phase modulator (PM), two 1-st order sidebands with equal amplitude and opposite phase, accompanied with the optical signal, are generated. After passing through a notch filter, the phase and the amplitude of the optical signal are changed at the certain wavelength (the green sideband in Fig. 1(b)). The filtered optical signal is converted into a single-frequency electrical one by the photodetector 1 (PD1), thus a PM-IM conversion is achieved [17]. The generated signal is then returned to the PM to form an optoelectronic oscillation loop. The generated signal is stable when the gain equals to the loss within the resonant cavity. However, a long mode-building time is needed to generate a single-frequency microwave signal in OEO. Due to the limitation of the long mode-building time, it is difficult to realize a continuous fast frequency tuning for the microwave signal. Therefore, we assemble a MPF with a high frequency-tuning speed. The frequency of the electrical signal generated by OEO equals to the central frequency of the MPF, i.e., ${f_{OEO}} = {f_{MPF}}$. The central wavelength of MPF can be expressed as ${f_{MPF}} = |{{f_{notch}} - {f_{FSLS}}} |$, where ${f_{notch}}$ means the center frequency of notch filter, and ${f_{FSLS}}$ is the center frequency of FSLS. The center frequency of the MPF can be tuned at a high speed by rapidly changing the center frequency of the optical carrier or the center frequency of the notch filter.
In this scheme, a FSLS with a periodically-swept frequency is adopted to realize a fast frequency-tunable MPF. The tuning period of MPF is the same as that of the FSLS. In order to achieve the vibrations of multiple modes in the cavity simultaneously, the tuning period of MPF should match with the time delay of the OEO loop to achieve Fourier domain mode locking operation. That is, the time it takes for the signal to propagate in the cavity within a cycle equals to several tuning periods of MPF, as expressed as ${T_{O + E}} = n \times {T_{MPF}}({n \in {N_ + }} )$. The optical signal can be preserved in the long fiber of an OEO loop to obtain a high quality-factor (Q-factor) with low phase noise. Furthermore, the signal is amplified by an erbium-doped fiber amplifier (EDFA) and electrical amplifiers (EA) for a high loop gain.
As shown in Fig. 1(a), the electrical signal generated by FDML OEO is re-modulated to the FSLS through a Mach-Zehnder modulator (MZM) in the bandwidth-doubling module. In order to achieve bandwidth doubling or superposition, the LCMW generated by the OEO and the FSLS should be inputted into MZM synchronously. As mentioned above, ${f_{OEO}}$ is proportional to ${f_{FSLS}}$ when the center wavelength of notch filter ${f_{notch}}$ is constant (${f_{OEO}} = {f_{MPF}} = |{{f_{notch}} - {f_{FSLS}}} |$). It is crucial to ensure that the time difference between FSLS and LCMW transfer into MZM equals to an integral multiple of the OEO ring cavity delay, i.e., $\Delta t = |{{t_a} + {t_d} - {t_b} - {t_c}} |= m \times {T_{o + e}}({m \in {N_ + }} )$, where ${t_a},{\; }{t_b}$ represent the durations for FSLS from optical coupler (OC) transmitting to MZM and PM, respectively, while ${t_c},{\; }{t_d}$ means the transmission time for signal from electric coupler (EC) to MZM and PM, respectively (the propagation paths are labeled as a, b, c, d in Fig. 1(a)). The real-time frequency distributions of the electrical signal generated by OEO and the optical signal of the FSLS are depicted using blue and red lines in Fig. 2, respectively. By modulating the chirped electrical signal ${f_{LCMW}}$ to the frequency-scanning optical signal ${f_{FSLS}}$, a bandwidth-doubled signal, expressed as ${f_{FSLS}} + {f_{LCMW}}$, and a single-frequency signal (${f_{FSLS}} - {f_{OEO}}$) can be generated. When the two signals are superimposed synchronously, the bandwidth of the 1 sideband is doubled as the one of signals in FDML OEO, which can be expressed as ${f_1} = {f_{FSLS}} + {f_{OEO}}$, as shown in Fig. 2(a). The first-order sideband with doubled bandwidth becomes narrower, when the delay does not match, and the single-frequency first-order sideband becomes dual-frequency first-order sideband, which is presented in Fig. 2(b). The bandwidth-doubled signal can be picked out utilizing a narrowband optical filter. A LCMW can generated at the output of PD2 by mixing the bandwidth-doubled signal with a single mode optical signal (SMOS). The output LCMWs can be expressed a ${f_{LCMW}} = |{{f_{SMOS}} - {f_1}} |= |{{f_{SMOS}} - 2{f_{FSLS}} + {f_{notch}}} |$.
Fig. 2. Real-time frequency distributions of periodically-chirped electrical and optical signals. (a) the delay is matched; (b) the delay is dismatched.
3. Experiment results
Experiments are performed based on the schematic diagram shown in Fig. 1(a) to verify the feasibility of the proposed bandwidth-doubling system. Figure 3 shows the typical spectra for optical signals at different positions in this system. The frequency scanning microwave signal ${f_R}$ is first loaded onto the optical carrier signal and a carrier-suppressed modulated signal is generated. By filtering out by an optical filter, the FSLS with a sweep period of about 22 µs is obtained and is used as the input signal of OEO. The optical spectrum of the FSLS is shown in Fig. 3(a). Optical spectrum before PD1 in FDML OEO is shown in Fig. 3(b), and the point of notch is marked. The LCMW generated by the FDML OEO is re-modulated to the FSLS and the spectrum is given in Fig. 3(c) and (d), in which the delay is matched or dismatched respectively. In particular, Fig. 3(d) is measured when a 2.5 km single-mode fiber is added between the OC and MZM in Fig. 1(a). As can be seen from Fig. 3(c) and (d), the first-order sideband with doubled bandwidth becomes narrower, when the delay does not match, and the single-frequency first-order sideband becomes dual-frequency first-order sideband, which is corresponded to the condition shown in Fig. 2(b). After amplified and filtered, a bandwidth-doubled first-order sideband is obtained as shown in Fig. 3(e) and then mixed with the SMOS. The spectra before PD2 is shown in Fig. 3(f).
Fig. 3. Typical spectra for optical signals at different positions of the link. Spectrum for (a) FSLS. (b) Optical signals before PD1. (c) Optical signals after the Mach-Zehnder modulator (satisfy the delay matching condition). (d) Optical signals after the Mach-Zehnder modulator (delay matching condition is not met). (e) Optical signals at the output of the filter. (f) Optical signals before PD2.
To obtain the frequency scanning MPF, a phase-shifted fiber Bragg grating (PS-FBG) with an ultra-narrow notch is used to serve as the optical notch filter, and its reflection spectrum (at room temperature, 25 °C) is shown in Fig. 4. The inset of Fig. 4 shows details of the magnitude response as a function of the wavelength nearby the notch. Obviously, it has a narrow notch response with 3-dB bandwidth of about 80 MHz, which can contribute to better filtering results. According to Fig. 4, the reflection bandwidth of PS-FBG is about 1.0 nm from 1550.2 nm to 1551.2 nm with the notch of 1550.7 nm. Regardless of other factors, the bandwidth of LCMWs generated by the FDML OEO is up to about 30 GHz. However, it is difficult to generate LCMWs which such a large bandwidth in the experiment due to the limited flatness of the reflection spectrum and phase response of the PS-FBG.
Fig. 4. The reflection spectrum of the phase-shifted fiber Bragg grating (PS-FBG). The inset shows details of the magnitude response as a function of wavelength nearby the notch, which is measured by vector network analyzer
Figure 5 exhibits the time domain waveform of the generated microwave signal, which is measured by a high-speed digital phosphor oscilloscope (Tektronix) with a sampling rate of 50 GS/s. The waveform has a temporal period of about 22 µs and a bandwidth of 8 GHz, and thus its TBWP is 176000. It should be mentioned that the uneven waveform is mainly caused by the different responsivities of optoelectronic devices to signals with different frequencies, and also related to the suppression of optical filters in the link. Besides, the inset in Fig. 5 shows the detail of the generated waveform with a duration of 5 ns, indicating its continuity in the time domain.
Fig. 5. Temporal waveform of the periodically and continuously chirped microwave waveform, the inset shows a section of the waveform.
A real-time frequency distribution of the generated microwave waveform is obtained by calculating the short-time Fourier transform of the generated LCMW, and the result is shown in Fig. 6. It can be observed that the frequency distribution of the generated chirped waveform will be partially discontinuous if the time difference between FSLS and LCMW transfer into MZM is not well-matched, as demonstrated in Fig. 6(a), And there are some high-order frequency-multiplicated spurious signals in the real-time frequency distribution, which is caused mainly by the nonlinearity of the modulator. By precisely controlling the length of the optical fiber, we adjust the difference between the transmission time of the optical signal and that of the electric signal in the bandwidth-doubling module, to satisfy the superposition condition. By doing so, LCMW with a continuous real-time frequency distribution can be realized, and the result is shown in Fig. 6(b). It can be observed that the instantaneous frequency periodically changes from 13 GHz to 21 GHz with a high speed. Clearly, a linearly chirped signal with a bandwidth of 8 GHz and a period of about 22 µs is experimentally obtained. Real-time frequency distribution of LCMWs generated by FDML OEO is presented in Fig. 6(c), the frequency span is about from 14.5 GHz to 18.5 GHz. The chirp direction of the generated signal depends on the relative positions of the center frequency of FSLS, notch and SMOS. And Fig. 7 shows the spectrum of the LCWM generated by the FDML OEO and the proposed bandwidth-doubled scheme. As Fig. 7(b) shown, the bandwidth of LCMWs generated by FDML OEO is about 4 GHz. And the bandwidth of LCMWs by the proposed scheme is about 8 GHz in Fig. 7(a). It is obvious that the bandwidth of LCMWs generated by the proposed scheme is doubled than that of FDML OEO.
Fig. 6. Real-time frequency distributions for LCMWs with different time difference between the FSLS and LCMW transfer into MZM and generated by FDML OEO. (a) Real-time frequency distribution when time difference between FSLS and LCMW transfer into MZM is not well-matched. (b) Real-time frequency distribution when time difference is well-matched. (c) Real-time frequency distribution of FDML OEO.
Fig. 7. The spectrum of LCMWs generated by the FDML OEO to compare the bandwidth-doubled LCMW with it. (a) The bandwidth-doubled LCMW. (b) LCMW generated by FDML OEO.
In the proposed system, radio-frequency electrical signals with a high frequency scanning linearity is modulated onto the optical carrier signal, and the intensity modulator is adjusted to work at the minimum bias point to achieve the carrier suppression double sideband modulation to construct the FSLS. Furthermore, the positive/negative 1-st order sideband signal is filtered out as FSLS by an ultranarrow-band optical filter. Under this circumstance, the nonlinear response of the laser diode to a linear saw-tooth driving signal [17] can be avoided, and thus the highly linear LCMWs can be generated. Figure 8 shows the linearity of generated microwave waveforms within a single sweep period. The real-time frequency distribution of the measured waveform and the fitting result (calculated by an ordinary least square method) are depicted using blue and red lines in Fig. 8(a), respectively. As can be seen, the fitting result almost coincides with the measured one. Figure 8(b) shows the absolute value of the difference between the measured frequency and the fitted one. It is demonstrated that the maximum difference value is less than 0.04 GHz, and thus, the nonlinear error of the measured LCMW is lower than 0.5%. According to the expressions of LCMWs ${f_{LCMW}} = |{{f_{SMOS}} - 2{f_{FSLS}} + {f_{notch}}} |$ and the expression of FSLS ${f_{FSLS}} = {f_C} \pm {f_R}$, the nonlinear error of the generated LCMWs is impacted by the frequency stability of two lasers (${f_C},{f_{SMOS}}$) and FS-FBG (${f_{notch}}$) as well as the linearity of ${f_R}$.
Fig. 8. The linearity of generated microwave waveforms within a single sweep period. (a) Real-time frequency distribution of measured waveform and the fitting result. (b) The difference between the measured frequency and the fitted one.
Figure 9 exhibits the reconfigurability of the generated LCMW. The bandwidth of the microwave waveform generated by the FDML OEO is changed accordingly by tuning the bandwidth of the low-frequency electrical signal from 1.5 GHz to 5 GHz. After the bandwidth-doubling process, the instantaneous bandwidth of generated LCMWs varies from 3 GHz to 10 GHz, as shown in Fig. 9(a). The maximum bandwidth of tunable LCMWs reaches up to 10 GHz, and the corresponding chirp rate and TBWP are 0.45 GHz/µs and 220,000, respectively. The center frequency of LCMWs can be controlled by adjusting the center frequency of SMOS or by changing the center frequency of FSLS. The center frequency of the generated LCMWs varies with the SMOS wavelength from 5 GHz to 35 GHz, as exhibited in Fig. 9(b). Furthermore, these LCMWs possess a bandwidth of 8 GHz. It can be inferred that the frequency of generated LCMWs covers the range from 1 to 39 GHz, which is larger than those reported by our previous work [27]. It is noted that the maximum bandwidth and the frequency tuning range is limited by the optoelectronic devices [28,29] adopted in our experiments, and LCMWs with better performances are expected by optimizing the discrete devices.
Fig. 9. Tuning of the generated LCMWs. (a) The scanning range is tuned from 3 GHz to 10 GHz with a center frequency of 23 GHz. (b) The center frequency is tuned from 5 GHz to 35 GHz.
Performance results of generated LCMWs and single frequency signal are presented in Fig. 10. As shown in Fig. 10(a), the autocorrelation of LCMWs generated by the proposed scheme is given and compared to that of the LCMWs generated by FDML OEO. The full-width at half maximum of the autocorrelation peak of LCMWs generated by the proposed scheme is about 0.138 ns, which is half that of FDML OEO (0.275 ns). The compression ratio achieves 159420, which is close to the time-bandwidth product of 176000. Figures 10(b) and (c) show the frequency overlapping Allan deviation (ADEV) and the phase noise of single frequency signal generated by the FDML OEO respectively. As shown in Fig. 10(c), the phase noise of single frequency signal generated by the FDML OEO is as low as -123.4dBc/Hz@10kHz at the center of 10 GHz. As shown in Fig. 10(b), the frequency overlapping ADEV of FDML OEO reach 5.14×10–10 at 1 s and 2.51×10–9 at 100 s. Due to the introduce of SMOS, the phase noise and the frequency stability of single frequency signal generated by the proposed scheme are worse compared with that of FDML OEO. Thus, single-frequency signals with low phase noise and good frequency stability can be output from EC, and broad-band LCMWs can be output from PD2.
Fig. 10. Performance results of generated LCMWs and single frequency signal. (a) the autocorrelation of LCMWs generated by the proposed scheme (down) and the FDML OEO (up). (b) the frequency overlapping Allan deviation of FDML OEO. (c) the phase noise of single frequency signal generated by the FDML OEO.
4. Conclusion
In summary, we have proposed, theoretically analyzed and experimentally demonstrated a novel signal generation system for broadband bandwidth-doubled LCMWs based on bandwidth superposition of a FDML OEO. It is proved that a high frequency-tuning speed can be realized utilizing a FSLS-based MPF. Bandwidth-doubled LCMWs can be obtained through an in-situ modulation method (re-modulation of the LCMW onto the input FSLS). The bandwidth of the first-order sideband signal has doubled. We experimentally realized LCMWs with a frequency scanning instantaneous bandwidth of up to 10 GHz. These LCMWs are tunable in an ultrawide tuning range from 1 to 39 GHz and they are with a high frequency sweep linearity of 0.5% and a large TBWP of 220,000. Our work presents the feasibility and superiority of FDML-OEO for the generation of broadband bandwidth-doubled LCMWs, bringing a new promise for frequency scanning microwave sources.
Funding
National Key Research and Development Program of China (2018YFB2201901, 2018YFB2201902, 2018YFB2201903); National Natural Science Foundation of China (61925505); Beijing Municipal Natural Science Foundation (Z210005).
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. L. Maleki, “Sources: The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011). [CrossRef]
2. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B. 13(8), 1725–1735 (1996). [CrossRef]
3. W. H. Tseng and K. M. Feng, “Enhancing long-term stability of the optoelectronic oscillator with a probe-injected fiber delay monitoring mechanism,” Opt. Express 20(2), 1597 (2012). [CrossRef]
4. M. Shin, V. S. Grigoryan, and P. Kumar, “Frequency-doubling optoelectronic oscillator for generating high-frequency microwave signals with low phase noise,” Electron. Lett. 43(4), 242–244 (2007). [CrossRef]
5. F. Kong, B. Romeira, J. Zhang, W. Li, and J. Yao, “A dual-wavelength fiber ring laser incorporating an injection-coupled optoelectronic oscillator and its application to transverse load sensing,” J. Lightwave Technol. 32(9), 1784–1793 (2014). [CrossRef]
6. F. Jiang, J. H. Wong, H. Q. Lam, J. Zhou, S. Aditya, P. H. Lim, K. E. K. Lee, P. P. Shum, and X. Zhang, “An optically tunable wideband optoelectronic oscillator based on a bandpass microwave photonic filter,” Opt. Express 21(14), 16381–16389 (2013). [CrossRef]
7. X. Xie, C. Zhang, T. Sun, P. Guo, X. Zhu, L. Zhu, W. Hu, and Z. Chen, “Wideband tunable optoelectronic oscillator based on a phase modulator and a tunable optical filter,” Opt. Lett. 38(5), 655–657 (2013). [CrossRef]
8. T. Hao, J. Tang, D. Domenech, W. Li, N. Zhu, J. Capmany, and M. Li, “Toward monolithic integration of OEOs: From systems to chips,” J. Lightwave Technol. 36(19), 4565–4582 (2018). [CrossRef]
9. H. Peng, C. Zhang, X. Xie, T. Sun, P. Guo, X. Zhu, L. Zhu, W. Hu, and Z. Chen, “Tunable DC-60 GHz RF generation utilizing a dual-loop optoelectronic oscillator based on stimulated Brillouin scattering,” J. Lightwave Technol. 33(13), 2707–2715 (2015). [CrossRef]
10. M. Li, W. Li, and J. Yao, “Tunable optoelectronic oscillator incorporating a high-Q spectrum-sliced photonic microwave transversal filter,” IEEE Photonics Technol. Lett. 24(14), 1251–1253 (2012). [CrossRef]
11. W. Li and J. Yao, “A wideband frequency tunable optoelectronic oscillator incorporating a 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(6), 1735–1742 (2012). [CrossRef]
12. W. Li and J. Yao, “An Optically Tunable Optoelectronic Oscillator,” J. Lightwave Technol. 28(18), 2640–2645 (2010).
13. D. Eliyahu and L. Maleki, “Low phase noise and spurious level in multi-loop opto-electronic oscillators,” in Proceedings of the 2003 IEEE International Frequency Control Symposium and PDA Exhibition (IEEE, 2003), 405–410.
14. T. Hao, J. Tang, W. Li, N. Zhu, and M. Li, “Fourier domain mode locked optoelectronic oscillator based on the deamplification of stimulated brillouin scattering,” OSA Continuum 1(2), 408–415 (2018). [CrossRef]
15. T. Hao, J. Tang, N. Shi, W. Li, N. Zhu, and M. Li, “Multiple-frequency measurement based on a Fourier domain mode-locked optoelectronic oscillator operating around oscillation threshold,” Opt. Lett. 44(12), 3062–3065 (2019). [CrossRef]
16. T. Hao, J. Tang, W. Li, N. Zhu, and M. Li, “Microwave photonics frequency-to-time mapping based on a fourier domain mode locked optoelectronic oscillator,” Opt. Express 26(26), 33582–33591 (2018). [CrossRef]
17. T. Hao, Q. Cen, Y. Dai, J. Tang, W. Li, J. Yao, N. Zhu, and M. Li, “Breaking the limitation of mode building time in an optoelectronic oscillator,” Nat. Commun. 9(1), 1839 (2018). [CrossRef]
18. Y. Wang, X. Li, J. Zhang, and J. Wo, “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]
19. P. Hao, H. Lu, R. Han, X. Wang, X. Liu, and X. S. Yao, “Fourier domain mode-locked opto-electronic oscillator with a diode-tuned bandpass filter,” Opt. Express 28(16), 23454–23466 (2020). [CrossRef]
20. P. Zhou, F. Zhang, and S. Pan, “Generation of Linear Frequency-Modulated Waveforms by a Frequency-Sweeping Optoelectronic Oscillator,” J. Lightwave Technol. 36(18), 3927–3934 (2018). [CrossRef]
21. H. Zhang, F. Z. Zhang, S. L. Pan, X. W. Ye, S. F. Liu, and H. Chen, “Photonic generation of linearly chirped microwave waveforms with tunable parameters,” IEEE Photonics Technol. Lett. 32(17), 1037–1040 (2020). [CrossRef]
22. Z. Zeng, L. J. Zhang, Y. W. Zhang, Z. Y. Zhang, S. J. Zhang, Y. L. Zhang, B. Sun, and Y. Liu, “Frequency-definable linearly chirped microwave waveform generation by a Fourier domain mode locking optoelectronic oscillator based on stimulated Brillouin scattering,” Opt. Express 28(9), 13861–13870 (2020). [CrossRef]
23. M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread spectrum impulse radio for wireless multiple-access communications,” IEEE Trans. Commun. 48(4), 679–689 (2000). [CrossRef]
24. J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39(4), 745–808 (1960). [CrossRef]
25. D. K. Barton, “Radar System Analysis and Modeling,” IEEE Aerosp. Electron. Syst. Mag. 20(4), 23–25 (2005). [CrossRef]
26. S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-thz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013). [CrossRef]
27. G. Li, T. Hao, Z. Ge, W. Li, and M. Li, “Broadband frequency-doubled linearly chirped microwave waveform generation based on Fourier domain mode-locked optoelectronic oscillator,”in Proceedings of the 2021 IEEE Electron Devices Technology and Manufacturing Conference (IEEE, 2021), 1–3.
28. Z. H. Yin, X. M. Hu, J. P. Zeng, Y. Zeng, and W. Peng, “Self-powered circularly polarized light detector based on asymmetric chiral metamaterials,” J. Semicond. 41(12), 122301 (2020). [CrossRef]
29. M. A. Rafiq, “Carrier transport mechanisms in semiconductor nanostructures and devices,” J. Semicond. 39(6), 061002 (2018). [CrossRef]
