Abstract

An actively mode-locked optoelectronic oscillator (OEO) is proposed and demonstrated to generate chirp-free microwave pulse trains with variable repetition rates. Time-domain mode locking is realized by using an electric signal modulator to achieve amplitude modulation of the generated microwave signal in the OEO cavity. Through setting the externally applied electric signal frequency to be equal to the integral multiple of the free spectral range, a microwave pulse train with a low close-to-carrier phase noise is generated. In the experiment, microwave pulse trains with repetition rates of 179.94 and 360.00 kHz are generated through fundamental mode locking and 2nd-order harmonic mode locking, respectively. Under fundamental mode locking, the phase noise of the actively mode-locked OEO at 100 Hz frequency offset is measured to be 30 dB lower than that in a free-running OEO.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Optoelectronic oscillators (OEOs) can generate high-frequency microwave signals with ultra-low phase noise [13]. This feature makes it a promising candidate in various applications, such as radar [4] and broadband wireless communication [5]. In an OEO, oscillation starts from white noise in the cavity. There is no fixed phase relationship among different longitudinal modes. A strong mode competition effect only allows one dominant mode to stably oscillate at a time. Therefore, a single-tone microwave signal is generally generated in a conventional OEO. This process is analogous to a free-running laser, which generates a monochrome light wave.

Mode locking is a well-known technique to generate broadband optical waveforms by locking the laser cavity modes in either a Fourier or time domain [69]. Since an OEO architecture is similar to a fiber ring laser, mode locking has also been recently introduced into OEOs to generate microwave waveforms [1014]. In 2018, a Fourier-domain mode-locked OEO was first demonstrated to generate a periodic broadband linearly frequency-modulated signal with an ultra-large time-bandwidth product, where tens of thousands of longitudinal modes at different frequencies oscillate with a continuous phase in a time-division multiplexing way in the ring cavity [10]. This new type of OEO is beneficial for improving the range resolution of a long-range pulse compression radar.

As an alternative, periodic microwave pulses with low phase noise and short durations are favorable for improving the velocity detection sensitivity and the range resolution of a pulse Doppler radar. This kind of signal can be generated by introducing a time-domain mode locking (TDML) technique into OEOs. A passively mode-locked OEO was demonstrated to generate a single-cycle radio-frequency (RF) pulse train, in which a fixed phase relationship among the cavity modes was realized by using a saturable RF amplifier as the mode-locking component [12]. In this scheme, an RF pulse train with a carrier frequency of 650 MHz, a 5 dB bandwidth of 440 MHz, and a repetition rate of 1.0543 MHz was obtained. The main limitation of a passively mode-locked OEO is that the repetition rate of the generated RF pulse train is equal to the free spectral range (FSR) of the OEO cavity, which can only be varied by changing the loop length.

In this Letter, a TDML OEO scheme based on active mode locking is proposed and experimentally demonstrated. In this scheme, an electric signal modulator is inserted into the OEO cavity to act as the mode-locking component. The phase of the longitudinal modes is locked through modulating the generated microwave signal in the OEO cavity by an external electric signal with a frequency equal to the integral multiple of the FSR. Hence, phase-locked multi-mode oscillation can be realized in the OEO cavity to form a short microwave pulse train with a high carrier frequency and a low phase noise. Compared with the passively mode-locked OEO, the superiority of the proposed actively mode-locked OEO is that a reconfigurable repetition rate can be achieved by simply varying the externally applied electric signal frequency, which is favorable for realizing a high-speed pulse Doppler radar with a large velocity measurement range and a high velocity detection sensitivity [15].

Figure 1 shows the schematic diagram of the proposed actively mode-locked OEO. A continuous-wave (CW) light from a laser diode (LD), whose power is controlled by an optical variable attenuator, enters an electro-optic Mach–Zehnder modulator (MZM) biased at its quadrature point. In the MZM, the CW light is modulated by the feedback oscillating microwave signal centered at ${f_0}$. After passing through a section of single-mode fiber (SMF), the intensity-modulated optical signal is detected by a high-speed photodetector. Subsequently, a broadband electronic amplifier and a bandpass filter centered at ${f_0}$ are employed to compensate for the power loss in the cavity and select the oscillating microwave signal, respectively.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the proposed actively mode-locked OEO. LD, laser diode; V-Att, variable attenuator; MZM, Mach–Zehnder modulator; PD, photodetector; EA, electrical amplifier; AM, amplitude modulation; FG, function generator; ESA, electrical spectrum analyzer; OSC, oscilloscope.

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In order to achieve mode locking, an electric signal modulator is inserted into the cavity after the bandpass filter. The oscillating microwave signal in the cavity is amplitude modulated by an external electric signal at $\Omega$ applied to the modulator. After amplitude modulation (AM), the output signal can be expressed as

$$\begin{split}&V\left(t \right) = {V_0}\!\left[{1 + m{\rm \cos}\left({2\pi \Omega t} \right)} \right]\cos \left({2\pi {f_0}t + {\varphi _0}} \right)\\ &\quad = {V_0}\!\left\{\begin{array}{l}\cos \left({2\pi {f_0}t + {\varphi _0}} \right)\\ + \frac{m}{2}\! \cos\!\left[{2\pi\! \left({{f_0} + \Omega} \right)t + {\varphi _0}} \right] + \frac{m}{2}\! \cos\!\left[{2\pi\! \left({{f_0} - \Omega} \right)t + {\varphi _0}} \right]\end{array} \right\}\end{split},$$
where $m$ is the modulation index, and ${V_0}$ and ${\varphi _0}$ are the amplitude and the initial phase of the microwave carrier, respectively. It can be seen from Eq. (1) that the phase of the modulation sidebands is identical to that of the microwave carrier. If the externally applied electric signal frequency $\Omega$ is set to be equal to the FSR of the OEO cavity $\Delta {f_{{\rm FSR}}}$, the modulation sidebands act as new microwave carriers to excite more phase-locked longitudinal modes after obtaining sufficient gain from the OEO cavity. As a result, all of the longitudinal modes within the net gain spectrum of the OEO cavity can simultaneously oscillate, which are coherently superposed in the time domain to form a microwave pulse train with a center frequency of ${f_0}$ and a repetition rate of $\Delta {f_{{\rm FSR}}}$ (i.e., fundamental mode locking) as shown in Fig. 1. To further increase the repetition rate of the generated microwave pulse train, a harmonic mode-locking technique can be used in the proposed actively mode-locked OEO [16]. By setting $\Omega$ to be equal to $N\Delta {f_{{\rm FSR}}}$ ($N$ is integer and $N \ge 2$), the longitudinal modes with a frequency interval of $\Omega = N\Delta {f_{{\rm FSR}}}$ are phase locked. These modes oscillate in the cavity instead of the ones originating from white noise, which are coherently superposed in the time domain to form a microwave pulse train with a center frequency of ${f_0}$ and a repetition rate of $\Omega = N\Delta {f_{{\rm FSR}}}$ (i.e., harmonic mode locking) as shown in Fig. 1. Therefore, a long fiber can be employed in the OEO cavity to decrease the phase noise of the generated microwave signal, and a high repetition rate can be guaranteed by using high-order harmonic mode locking.

A proof-of-concept experiment is carried out to demonstrate the proposed actively mode-locked OEO. In the experiment, a narrow-linewidth CW light at 1560 nm and with a power of 16 dBm is generated by a distributed feedback semiconductor LD. The optical power injected into the MZM is controlled by using an optical variable attenuator to adjust the net gain in the OEO cavity. A 20 Gb/s electro-optic MZM (EOSPACE) biased at its quadrature point is used to feed the oscillating microwave signal back to the optical transmission link. After passing through a spool of SMF (YOFC), the intensity-modulated optical signal is detected by a 20 Gb/s photodetector (HP 11982A). An electronic amplifier (Qotana) with an operation frequency range from 1 to 20 GHz and a gain of 25 dB is employed to compensate for the power loss in the OEO cavity, and an electronic bandpass filter with a center frequency of 4 GHz and a 3 dB bandwidth of 70 MHz is used to select the oscillating longitudinal modes. The oscillating microwave signal is divided into two paths by an electronic power divider (GTPD-COMB50G), where one output port is connected to the input port of an electric signal modulator (HP 11665B), and the other one is connected to the input port of an electrical spectrum analyzer (ESA, R&S FSU50, 20 Hz–50 GHz) or a high-speed real-time oscilloscope (OSC, Tektronix DPO75002SX, 100 GS/s, 33 GHz) to measure the spectrum and the waveform of the generated microwave signal, respectively. In order to achieve active mode locking, the electric signal modulator is driven by an external signal from a function generator (Hantek HDG2022B), where the signal frequency is set to be equal to the integral multiple of the FSR.

First, a spool of SMF with a length of 1.1 km is inserted into the OEO cavity, which corresponds to a FSR of 179.94 kHz. Figures 2(a) and 2(b) exhibit the measured spectra of the generated microwave signals without and with external modulation, respectively. When the external modulation is turned off, the OEO is working as a free-running one. Due to the mode competition effect, only one dominant mode at the vicinity of the filter passband center can oscillate in the cavity as shown in Fig. 2(b). When the external modulation is turned on, and the externally applied electric signal frequency is set to be equal to 179.94 kHz, the phase of the longitudinal modes is locked. Therefore, all of the longitudinal modes within the net gain spectrum of the OEO (mainly determined by the passband of the filter in the experiment) oscillate simultaneously as shown in Fig. 2(a). The criterion of judging a good mode-locking status is obtaining a stable and smooth envelop in the frequency domain. The zoom-in view in Fig. 2(b) shows that the mode spacing is 179.94 kHz, indicating that the OEO is working in fundamental mode-locking mode (i.e., $N = {1}$). It should be pointed out that the 3 dB bandwidth of the generated microwave signal is not wide enough, which is attributed to the relatively narrow bandwidth of the electronic bandpass filter employed in the experiment. In order to realize mode locking in a large frequency range, an electronic bandpass filter with a large 3 dB bandwidth should be employed. In addition, the open-loop frequency response of the OEO should be optimized to have a good in-band flatness in the operation bandwidth.

 figure: Fig. 2.

Fig. 2. Measured spectra of the generated microwave signals from the proposed actively mode-locked OEO (a) without and (b) with external modulation. RBW, resolution bandwidth.

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Figure 3 presents the measured temporal waveform of the generated microwave pulse train. The pulse period is about 5.557 µs, which corresponds to a repetition rate of 179.94 kHz. The pulse width (i.e., full width at half-maximum) is measured to be about 222 ns, which can be further decreased by employing an electronic bandpass filter with a wider passband. The zoom-in view of the oscillation in a single microwave pulse indicates that the generated microwave pulse is with a center frequency of about 4.01 GHz.

 figure: Fig. 3.

Fig. 3. Measured temporal waveform of the generated microwave pulse train.

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The chirp characteristic of a single-microwave pulse is also analyzed by using Hilbert transform. Figure 4 shows the retrieved phase (solid line) and instantaneous frequency (dashed line) versus time in a single pulse. In can be seen that there is only a tiny linear frequency chirp (i.e., instantaneous versus time), which is mainly induced by the small dispersion of the electronic devices in the OEO cavity. The frequency chirp has no influence on mode locking.

 figure: Fig. 4.

Fig. 4. Retrieved phase (solid line) and instantaneous frequency (dashed line) versus time in a single-microwave pulse.

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Then, the externally applied electric signal frequency is set to be equal to 360.00 kHz to achieve 2nd-order harmonic mode locking (i.e., ${N} = {2}$). Figures 5(a) and 5(b) show the spectrum and the temporal waveform of the generated microwave pulse train, where the mode spacing is increased to 360.00 kHz, and the pulse period is decreased to about 2.778 µs. In Fig. 5(a), besides the dominant oscillating longitudinal modes, there are weak modes located at the vacant longitudinal mode frequencies, which are also with a frequency interval of 360.00 kHz. These modes are called supermode noise, referring to the definition in a harmonic mode-locked laser [17,18]. The origination of the supermode noise is the phase locking among weak oscillating modes at the initial stage of oscillation. Since these is a gain competition between oscillating modes and supermode, the existence of supermode noise has an innegligible impact on the stability of the generated microwave pulse train. Various methods have been proposed to suppress supermode noise in a fiber ring laser, such as employing an injection-locking technique [17] and using a composite cavity structure [18]. These methods can also be introduced in the proposed OEO to suppress the supermode noise.

 figure: Fig. 5.

Fig. 5. Measured (a) spectrum and (b) temporal waveform of the generated microwave pulse train under 2nd-order harmonic mode locking.

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Figures 6(a) and 6(b) present the spectrum and the temporal waveform of the generated microwave pulse train when the length of the SMF is increased to 2.05 km, and the externally applied electric signal frequency is set to be 96.90 kHz (i.e., $N = {1}$). Compared with Fig. 2, the pulse period is increased to about 10.35 µs. Thus, by inserting a longer optical fiber into the OEO cavity, a microwave pulse train with a lower repetition rate can be obtained by using the proposed scheme. This kind of signal plays an important role in moving target indication radar to avoid ambiguous range detection [15].

 figure: Fig. 6.

Fig. 6. Measured (a) spectrum and (b) temporal waveform of the generated microwave pulse train under fundamental mode locking, when the length of the SMF is increased to 2.05 km.

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Figure 7 shows the single-sideband phase noise of the generated microwave signals at 4.01 GHz from a free-running and an actively mode-locked OEO with different loop lengths, which are measured by using the phase noise analysis module of the ESA. It can be seen from Fig. 7 that, through increasing the loop length, the phase noise of either a free-running or an actively mode-locked OEO can be decreased. The close-to-carrier phase noise of the microwave signal from the actively mode-locked OEO is much smaller than that of the microwave signal from the free-running OEO. This is attributed to the periodic high-pass filtering effect induced by superposition between each mode and its delayed duplicate during AM process. This phenomenon is similar to a free-running voltage-controlled oscillator (VCO) and a VCO with a phase-locked loop (PLL). In a PLL VCO, the close-to-carrier phase noise can be obviously decreased compared with that in a free-running VCO [19]. The contribution of mode locking to greatly decreasing the close-to-carrier phase noise is beneficial for improving the velocity detection sensitivity of a pulse Doppler radar. It should also be pointed out that the flattop beyond frequency offset of 200 kHz in Fig. 7 is attributed to the rough frequency resolution of the phase noise analysis module and the small mode frequency interval.

 figure: Fig. 7.

Fig. 7. Measured single-sideband phase noise of the generated microwave signals at 4.01 GHz from a free-running and an actively mode-locked OEO with different loop lengths.

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Finally, it should be pointed out that an actively mode-locked OEO with a tunable carrier frequency and a variable pulse width can be realized by employing a reconfigurable microwave photonics filter (MPF) in the proposed OEO to replace the electronic bandpass filter. To date, various kinds of MPF have been proposed to achieve an OEO with a flexible tunability, such as the one based on stimulated Brillouin scattering [20] and the OEO based on optical spectrum slicing [21]. The above-mentioned MPF schemes can be utilized to realize a frequency- and bandwidth-reconfigurable actively mode-locked OEO.

In conclusion, we have proposed and demonstrated an actively mode-locked OEO scheme for microwave pulse generation. Through inserting an electronic signal modulator into the OEO cavity and setting the externally applied electric signal frequency to be equal to the integral multiple of the FSR, a nearly transform-limited microwave pulse train with a repetition rate equal to the modulation frequency can be generated. In a proof-of-concept experiment, microwave pulse trains with a center frequency of 4.01 GHz and repetition rates of 197.94 and 360.00 kHz were generated based on fundamental and 2nd-order harmonic mode locking, respectively. The phase noise of the actively mode-locked OEO below 1 kHz frequency offset is much lower than that of the free-running OEO, where a phase noise reduction reaches beyond 30 dB at 100 Hz frequency offset. Therefore, the proposed actively mode-locked OEO is a promising candidate to greatly enhance the velocity detection sensitivity of a pulse Doppler radar.

Funding

National Key Research and Development Program of China (2019YFB2203800); National Natural Science Foundation of China (61421002, 61575037, 61927821); Fundamental Research Funds for the Central Universities (ZYGX2020ZB012).

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. X. S. Yao and L. Maleki, IEEE J. Quantum Electron. 32, 1141 (1996). [CrossRef]  

2. L. Maleki, Nat. Photonics 5, 728 (2011). [CrossRef]  

3. T. F. Hao, J. Tang, D. Domenech, W. Li, N. H. Zhu, J. Capmany, and M. Li, J. Lightwave Technol. 36, 4565 (2018). [CrossRef]  

4. J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, Bell Syst. Tech. J. 39, 745 (1960). [CrossRef]  

5. M. Z. Win and R. A. Scholtz, IEEE Trans. Commun. 48, 679 (2000). [CrossRef]  

6. R. Huber, M. Wojtkowski, and J. G. Fujimoto, Opt. Express 14, 3225 (2006). [CrossRef]  

7. H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000). [CrossRef]  

8. V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992). [CrossRef]  

9. S. P. Li and K. T. Chan, Appl. Phys. Lett. 74, 2737 (1999). [CrossRef]  

10. T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018). [CrossRef]  

11. Z. Zeng, L. J. Zhang, Y. W. Zhang, Z. Y. Zhang, S. J. Zhang, Y. L. Zhang, B. Sun, and Y. Liu, Opt. Express 28, 13861 (2020). [CrossRef]  

12. E. C. Levy and M. Horowitz, Opt. Express 19, 17599 (2011). [CrossRef]  

13. E. C. Levy and M. Horowitz, J. Opt. Soc. Am. B 30, 107 (2013). [CrossRef]  

14. A. Sherman and M. Horowitz, J. Opt. Soc. Am. B 30, 2980 (2013). [CrossRef]  

15. M. I. Skolnik, Radar Handbook (McGraw-Hill, 2008).

16. G. T. Harvey and L. F. Mollenauer, Opt. Lett. 18, 107 (1993). [CrossRef]  

17. C. Williams, F. Quinlan, and P. J. Delfyett, IEEE Photonics Technol. Lett. 21, 94 (2009). [CrossRef]  

18. N. Onodera, Electron. Lett. 33, 962 (1997). [CrossRef]  

19. B. Razavi, Phase-Locking in High-Performance Systems: From Devices to Architectures (Wiley-IEEE, 2003).

20. H. F. Peng, C. Zhang, X. P. Xie, T. Sun, P. Guo, X. Q. Zhu, L. X. Zhu, W. W. Hu, and Z. Y. Chen, J. Lightwave Technol. 33, 2707 (2015). [CrossRef]  

21. C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018). [CrossRef]  

References

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  1. X. S. Yao and L. Maleki, IEEE J. Quantum Electron. 32, 1141 (1996).
    [Crossref]
  2. L. Maleki, Nat. Photonics 5, 728 (2011).
    [Crossref]
  3. T. F. Hao, J. Tang, D. Domenech, W. Li, N. H. Zhu, J. Capmany, and M. Li, J. Lightwave Technol. 36, 4565 (2018).
    [Crossref]
  4. J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, Bell Syst. Tech. J. 39, 745 (1960).
    [Crossref]
  5. M. Z. Win and R. A. Scholtz, IEEE Trans. Commun. 48, 679 (2000).
    [Crossref]
  6. R. Huber, M. Wojtkowski, and J. G. Fujimoto, Opt. Express 14, 3225 (2006).
    [Crossref]
  7. H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
    [Crossref]
  8. V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
    [Crossref]
  9. S. P. Li and K. T. Chan, Appl. Phys. Lett. 74, 2737 (1999).
    [Crossref]
  10. T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
    [Crossref]
  11. Z. Zeng, L. J. Zhang, Y. W. Zhang, Z. Y. Zhang, S. J. Zhang, Y. L. Zhang, B. Sun, and Y. Liu, Opt. Express 28, 13861 (2020).
    [Crossref]
  12. E. C. Levy and M. Horowitz, Opt. Express 19, 17599 (2011).
    [Crossref]
  13. E. C. Levy and M. Horowitz, J. Opt. Soc. Am. B 30, 107 (2013).
    [Crossref]
  14. A. Sherman and M. Horowitz, J. Opt. Soc. Am. B 30, 2980 (2013).
    [Crossref]
  15. M. I. Skolnik, Radar Handbook (McGraw-Hill, 2008).
  16. G. T. Harvey and L. F. Mollenauer, Opt. Lett. 18, 107 (1993).
    [Crossref]
  17. C. Williams, F. Quinlan, and P. J. Delfyett, IEEE Photonics Technol. Lett. 21, 94 (2009).
    [Crossref]
  18. N. Onodera, Electron. Lett. 33, 962 (1997).
    [Crossref]
  19. B. Razavi, Phase-Locking in High-Performance Systems: From Devices to Architectures (Wiley-IEEE, 2003).
  20. H. F. Peng, C. Zhang, X. P. Xie, T. Sun, P. Guo, X. Q. Zhu, L. X. Zhu, W. W. Hu, and Z. Y. Chen, J. Lightwave Technol. 33, 2707 (2015).
    [Crossref]
  21. C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018).
    [Crossref]

2020 (1)

2018 (3)

T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
[Crossref]

T. F. Hao, J. Tang, D. Domenech, W. Li, N. H. Zhu, J. Capmany, and M. Li, J. Lightwave Technol. 36, 4565 (2018).
[Crossref]

C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018).
[Crossref]

2015 (1)

2013 (2)

2011 (2)

2009 (1)

C. Williams, F. Quinlan, and P. J. Delfyett, IEEE Photonics Technol. Lett. 21, 94 (2009).
[Crossref]

2006 (1)

2000 (2)

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[Crossref]

M. Z. Win and R. A. Scholtz, IEEE Trans. Commun. 48, 679 (2000).
[Crossref]

1999 (1)

S. P. Li and K. T. Chan, Appl. Phys. Lett. 74, 2737 (1999).
[Crossref]

1997 (1)

N. Onodera, Electron. Lett. 33, 962 (1997).
[Crossref]

1996 (1)

X. S. Yao and L. Maleki, IEEE J. Quantum Electron. 32, 1141 (1996).
[Crossref]

1993 (1)

1992 (1)

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
[Crossref]

1960 (1)

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, Bell Syst. Tech. J. 39, 745 (1960).
[Crossref]

Albersheim, W. J.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, Bell Syst. Tech. J. 39, 745 (1960).
[Crossref]

Capmany, J.

Cen, Q. Z.

T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
[Crossref]

Chan, K. T.

S. P. Li and K. T. Chan, Appl. Phys. Lett. 74, 2737 (1999).
[Crossref]

Chen, Z. Y.

Dai, Y. T.

T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
[Crossref]

Darlington, S.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, Bell Syst. Tech. J. 39, 745 (1960).
[Crossref]

Delfyett, P. J.

C. Williams, F. Quinlan, and P. J. Delfyett, IEEE Photonics Technol. Lett. 21, 94 (2009).
[Crossref]

Domenech, D.

Fujimoto, J. G.

Guo, P.

Hao, T. F.

T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
[Crossref]

T. F. Hao, J. Tang, D. Domenech, W. Li, N. H. Zhu, J. Capmany, and M. Li, J. Lightwave Technol. 36, 4565 (2018).
[Crossref]

Harvey, G. T.

Haus, H. A.

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[Crossref]

Horowitz, M.

Hu, W. W.

Huber, R.

Klauder, J. R.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, Bell Syst. Tech. J. 39, 745 (1960).
[Crossref]

Levy, E. C.

Li, C. X.

C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018).
[Crossref]

Li, M.

T. F. Hao, J. Tang, D. Domenech, W. Li, N. H. Zhu, J. Capmany, and M. Li, J. Lightwave Technol. 36, 4565 (2018).
[Crossref]

T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
[Crossref]

Li, S. P.

S. P. Li and K. T. Chan, Appl. Phys. Lett. 74, 2737 (1999).
[Crossref]

Li, W.

T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
[Crossref]

T. F. Hao, J. Tang, D. Domenech, W. Li, N. H. Zhu, J. Capmany, and M. Li, J. Lightwave Technol. 36, 4565 (2018).
[Crossref]

Liu, Y.

Maleki, L.

L. Maleki, Nat. Photonics 5, 728 (2011).
[Crossref]

X. S. Yao and L. Maleki, IEEE J. Quantum Electron. 32, 1141 (1996).
[Crossref]

Matsas, V. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
[Crossref]

Mollenauer, L. F.

Newson, T. P.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
[Crossref]

Onodera, N.

N. Onodera, Electron. Lett. 33, 962 (1997).
[Crossref]

Payne, D. N.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
[Crossref]

Peng, H. F.

Price, A. C.

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, Bell Syst. Tech. J. 39, 745 (1960).
[Crossref]

Quinlan, F.

C. Williams, F. Quinlan, and P. J. Delfyett, IEEE Photonics Technol. Lett. 21, 94 (2009).
[Crossref]

Razavi, B.

B. Razavi, Phase-Locking in High-Performance Systems: From Devices to Architectures (Wiley-IEEE, 2003).

Richardson, D. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
[Crossref]

Scholtz, R. A.

M. Z. Win and R. A. Scholtz, IEEE Trans. Commun. 48, 679 (2000).
[Crossref]

Sherman, A.

Skolnik, M. I.

M. I. Skolnik, Radar Handbook (McGraw-Hill, 2008).

Sun, B.

Sun, T.

Tang, D. S.

C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018).
[Crossref]

Tang, J.

T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
[Crossref]

T. F. Hao, J. Tang, D. Domenech, W. Li, N. H. Zhu, J. Capmany, and M. Li, J. Lightwave Technol. 36, 4565 (2018).
[Crossref]

Wang, H. T.

C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018).
[Crossref]

Wang, W.

C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018).
[Crossref]

Wang, Y.

C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018).
[Crossref]

Williams, C.

C. Williams, F. Quinlan, and P. J. Delfyett, IEEE Photonics Technol. Lett. 21, 94 (2009).
[Crossref]

Win, M. Z.

M. Z. Win and R. A. Scholtz, IEEE Trans. Commun. 48, 679 (2000).
[Crossref]

Wojtkowski, M.

Xie, X. P.

Xu, Z. H.

C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018).
[Crossref]

Yao, J. P.

T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
[Crossref]

Yao, X. S.

X. S. Yao and L. Maleki, IEEE J. Quantum Electron. 32, 1141 (1996).
[Crossref]

Zeng, Z.

Zhang, C.

Zhang, L. J.

Zhang, S. J.

Zhang, Y. L.

Zhang, Y. W.

Zhang, Z. Y.

Zhao, B.

C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018).
[Crossref]

Zhu, L. X.

Zhu, N. H.

T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
[Crossref]

T. F. Hao, J. Tang, D. Domenech, W. Li, N. H. Zhu, J. Capmany, and M. Li, J. Lightwave Technol. 36, 4565 (2018).
[Crossref]

Zhu, X. Q.

Appl. Phys. Lett. (1)

S. P. Li and K. T. Chan, Appl. Phys. Lett. 74, 2737 (1999).
[Crossref]

Bell Syst. Tech. J. (1)

J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, Bell Syst. Tech. J. 39, 745 (1960).
[Crossref]

Electron. Lett. (2)

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, Electron. Lett. 28, 1391 (1992).
[Crossref]

N. Onodera, Electron. Lett. 33, 962 (1997).
[Crossref]

IEEE J. Quantum Electron. (1)

X. S. Yao and L. Maleki, IEEE J. Quantum Electron. 32, 1141 (1996).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[Crossref]

IEEE Photonics Technol. Lett. (2)

C. Williams, F. Quinlan, and P. J. Delfyett, IEEE Photonics Technol. Lett. 21, 94 (2009).
[Crossref]

C. X. Li, Y. Wang, W. Wang, Z. H. Xu, B. Zhao, H. T. Wang, and D. S. Tang, IEEE Photonics Technol. Lett. 30, 7 (2018).
[Crossref]

IEEE Trans. Commun. (1)

M. Z. Win and R. A. Scholtz, IEEE Trans. Commun. 48, 679 (2000).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

Nat. Commun. (1)

T. F. Hao, Q. Z. Cen, Y. T. Dai, J. Tang, W. Li, J. P. Yao, N. H. Zhu, and M. Li, Nat. Commun. 9, 1839 (2018).
[Crossref]

Nat. Photonics (1)

L. Maleki, Nat. Photonics 5, 728 (2011).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Other (2)

B. Razavi, Phase-Locking in High-Performance Systems: From Devices to Architectures (Wiley-IEEE, 2003).

M. I. Skolnik, Radar Handbook (McGraw-Hill, 2008).

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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Figures (7)

Fig. 1.
Fig. 1. Schematic diagram of the proposed actively mode-locked OEO. LD, laser diode; V-Att, variable attenuator; MZM, Mach–Zehnder modulator; PD, photodetector; EA, electrical amplifier; AM, amplitude modulation; FG, function generator; ESA, electrical spectrum analyzer; OSC, oscilloscope.
Fig. 2.
Fig. 2. Measured spectra of the generated microwave signals from the proposed actively mode-locked OEO (a) without and (b) with external modulation. RBW, resolution bandwidth.
Fig. 3.
Fig. 3. Measured temporal waveform of the generated microwave pulse train.
Fig. 4.
Fig. 4. Retrieved phase (solid line) and instantaneous frequency (dashed line) versus time in a single-microwave pulse.
Fig. 5.
Fig. 5. Measured (a) spectrum and (b) temporal waveform of the generated microwave pulse train under 2nd-order harmonic mode locking.
Fig. 6.
Fig. 6. Measured (a) spectrum and (b) temporal waveform of the generated microwave pulse train under fundamental mode locking, when the length of the SMF is increased to 2.05 km.
Fig. 7.
Fig. 7. Measured single-sideband phase noise of the generated microwave signals at 4.01 GHz from a free-running and an actively mode-locked OEO with different loop lengths.

Equations (1)

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$$\begin{split}&V\left(t \right) = {V_0}\!\left[{1 + m{\rm \cos}\left({2\pi \Omega t} \right)} \right]\cos \left({2\pi {f_0}t + {\varphi _0}} \right)\\ &\quad = {V_0}\!\left\{\begin{array}{l}\cos \left({2\pi {f_0}t + {\varphi _0}} \right)\\ + \frac{m}{2}\! \cos\!\left[{2\pi\! \left({{f_0} + \Omega} \right)t + {\varphi _0}} \right] + \frac{m}{2}\! \cos\!\left[{2\pi\! \left({{f_0} - \Omega} \right)t + {\varphi _0}} \right]\end{array} \right\}\end{split},$$