Abstract

An ultraflat self-oscillating optical frequency comb generator based on an optoelectronic oscillator employing cascaded modulators was proposed and experimentally demonstrated. By incorporating the optoelectronic oscillation loop with cascaded modulators into the optical frequency comb generator, 11 ultraflat comb lines would be generated, and the frequency spacing is equal to the oscillation frequency of the OEO. 10 and 12GHz optical frequency combs are demonstrated with the spectral power variation below 0.82dB and 0.93dB respectively. The corresponding spectral pure microwave source are also generated and evaluated. The corresponding single-sideband phase noise are as low as −122dBc/Hz and −115 dBc/Hz at 10 kHz offset frequency.

© 2015 Optical Society of America

1. Introduction

Optical frequency comb generators (OFC) have attracted great interests during the last two decades. Due to their accurate frequency spacings and fixed phase relationship, they cannot only provide high-frequency microwave sources for ultra high-speed communications [1], but also find wide applications in many fields, such as optical microwave signal processing [2], precise optical metrology [3], and optical arbitrary waveform generation [4].

Conventionally, mode-locked lasers [5], fiber nonlinearities [6], and external modulation [7] are the principal methods for OFC generation. A smooth spectral profile can be generated by passively mode-locked lasers, but the repetition rate is usually very low. To enlarge the wavelength spacing, methods based on cascaded electro-optical modulation have been widely adopted, which also provide high stability, precise comb spacing and low complexity. On account of these advantages, external modulation has been a popular candidate for researchers and many schemes have been proposed and experimentally demonstrated these years [8–11].

In [8], R. Wu demonstrates a 10 GHz comb based on a cascade of lithium niobate intensity and phase modulators. A very high spectral flatness is achieved via special tailored RF waveforms. Besides, a flat optical comb with tunable comb spacing and adjustable comb number is generated based on carrier suppressed intensity modulation and phase modulation [9]. Except for the normal intensity and phase modulators, C. Chen proposes and experimentally demonstrates a flat and tunable seven-line OFC generation scheme based on a single polarization modulator [10]. Moreover, cascaded polarization modulators have also been used to generate ultraflat and stable OFC with tunable frequency spacing [11].

Despite previous successful generation of OFC under different requirements in these studies, external high power microwave or millimeter-wave sources are always required to drive the various modulators, which may be poor in phase noise performance at high frequencies because of the multiplied phase noise. Due to the high Q value of the optical storage elements, the optoelectronic oscillator (OEO) can provide stable microwave or millimeter-wave signals with ultralow phase noise performance [12]. In [13], the microwave signal from the optoelectronic oscillator is used to drive the polarization modulator out of the oscillation loop. For the comb generation, part of the optical power should be separated from the oscillator and injected into the polarization modulated link. Moreover, the polarization modulation and demodulation architecture makes the whole system very sensitive to the polarization state. In [14], T. Sakamoto etc. propose the self-oscillating frequency comb based on the oscillation loop employing phase modulator and fiber bragg grating (FBG) filter. The FBG filter used as phase demodulator makes the scheme sensitive to the environment. Besides, the single stage modulation limits the flatness of the generated combs.

In this paper, we propose and experimentally demonstrate an ultraflat OFC generator without any external RF sources. An absolutely self-oscillating OFC is generated based on the optoelectronic oscillator loop employing cascaded commercial intensity and phase modulators. By simply converting the optical modulated signal to electrical domain via a fast photodetector and feeding back into the intensity modulator, a self-starting OEO is built to offer stable microwave signals for the generation of OFC. The phase modulator is used to broaden the number of comb lines. As a result, the proposed OFC generator is experimentally demonstrated. The 10GHz and 12GHz combs with eleven flat-topped lines are generated, whose spectral power variations are below 0.82 dB and 0.93 dB respectively. Besides, the performance of the relevant OEO is also evaluated, and the measured phase noise is −122 dBc/Hz and −115 dBc/Hz at 10 kHz frequency offset.

2. Operation principle

The schematic diagram of the proposed self-oscillating optical frequency comb generator is shown in Fig. 1. The key part of the scheme consists of an optoelectronic oscillation loop and cascaded modulators. Firstly, the light from a distributed feedback laser (DFB) source is fed to the cascade of Mach-Zehnder modulator (MZM) and phase modulator (PM), which is driven by the oscillating radio frequency (RF) signals. If the oscillation signal v1=V1coswct is injected into the MZM with push-pull architecture, the output of the first stage intensity modulator E1 can be expressed as [15]:

E1=22Eoeiwot[ei(φ1+γ1coswct)+eiγ1coswct]
where wo and wc are the angular frequencies of the optical carrier and the driven oscillation signal respectively, Eo is amplitude of the optical carrier, γ1=πV1/Vπ1 is the modulation index in which V1 is the amplitude of the driven signal and Vπ1 is the half-wave voltage of the MZM. Finally, φ1=πVdc/Vπ1is the phase shift induced by the DC bias voltage.

 

Fig. 1 Schematic diagram of the proposed optical frequency comb generator. LD: laser diode. MZM: Mach-Zehnder modulator. PM: phase modulator. OSA: optical spectrum analyzer. SMF: single mode fiber. PD: photodetector. EA: electrical amplifier. BPF: bandpass filter. PS: phase shifter. VA: variable attenuator. ESA: electrical spectrum analyzer.

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After introducing E1 into the following phase modulator, the optical signal will be modulated by the same oscillating signal with different phase and amplitude v2=V2cos(wct+Δϕ). Therefore, the output of the second stage PM can be obtained as:

E2=E1eiγ2cos(ωct+Δϕ)=22E0eiwot[ei(φ1+γ1coswct)+eiγ1coswct]eiγ2cos(ωct+Δϕ)
where γ2=πV2/Vπ2 is the modulation index in which V2 is the amplitude of the driven signal and Vπ2 is the half-wave voltage of the PM, while Δϕ is the phase difference between the driven signals injected into the cascaded modulators.

Based on the Jacobi–Anger expansion of E2, the output optical signal can be derived as:

E2=22Eoeiwotn=(eiφ1+einπ)inJn(γ1)einwctk=ikJk(γ2)eik(ωct+Δϕ)=22Eoeiwotn=k=(eiφ1+einπ)inJn(γ1)einwctikJk(γ2)eik(ωct+Δϕ)=22Eoeiwotn=k=eikΔϕ(eiφ1+einπ)in+kJn(γ1)Jk(γ2)ei(n+k)wct
where Jn and Jk both denote the nth and kth order of the Bessel function, n and k are the orders of the modulation sidebands induced by the intensity and phase modulators respectively. From Eq. (3), we can see that the harmonic components can be generated with the frequency spacing of wc/2π which equals to the oscillating frequency. For the Nth order comb line, the optical power can be expressed as:
P=12Po|M=(ei(NM)Δϕ(eiφ1+eiMπ)iNJn(γ1)JNM(γ2))|2
where Po is the power of the optical carrier, N and M are the orders of the modulation sidebands. The intensity of the Nth comb line is the synthesis of many modulation sidebands. Since the driven oscillating signal is limited by the saturation input power of the intensity modulator, the modulation index of the MZM is fixed accordingly. Therefore, the intensiy of each comb line is maily influenced by the DC bias voltage, the phase difference between the driven signals, and the modulation index of the PM. We can improve the smoothness of the comb lines by delicately tuning these parameters.

After going through the long optical fiber and photodetector, the optical signal will be converted back to electrical domain which can be derived as:

I12LoE02[ei(φ1+2γ1coswct)+ei(φ1+2γ1coswct)]=LoP0n=Jn(2γ1)cos[(φ1+nwct)+12nπ]
where Po is the power of the optical carrier, while Lo is the transmission loss induced by the modulators, optical fiber and optical to electrical conversion. The fundamental item of the output detected signal can be expressed as:

I1stL0P0[J1(2γ1)cos(φ1+wct+π2)+J1(2γ1)cos(φ1wctπ2)]=2L0P0J1(2γ1)sinφ1coswct

From Eq. (5), we can see that the fundamental item is related with the DC bias and the modulation index of the MZM. It’s obviously that the phase modulation process would not affect the final detected microwave signal. Therefore, the gain of the optical link is just as shown:

Go=2π2L02P02sin2φ1Vπ2

After filtered by a band pass filter with a center frequency of wc/2π, RF signals with a fundamental frequency of wc are filtered out and fed back into the loop. In order for the OEO to oscillate, the open loop gains must exceed losses for the circulating waves in the loop. That is to say, the gain of the RF chain should satisfied such condition:

Ge>Vπ22π2L02P02sin2φ1

If we want to make the oscillation frequency equal to the frequency spacing of the optical frequency comb, the loop length should satisfy such condition by tuning the electronic phase shifter in the oscillation loop:

wc(τo+τe)=2mπm=0,1,2.....
where m is the mode number, while τo and τe are the time delays induced by the optical link and electronic chain respectively. When the gain and phase of the oscillation loop satisfy the required conditions simultaneously, an ultraflat and self-oscillating optical frequency comb would be generated.

3. Experiment results

The proposed OFC generator has been theoretically analyzed above. In order to demonstrate it, an experiment has been conducted. In the experiment, a narrow-linewidth laser was launched by a DFB laser source with the wavelength set at 1550nm. Behind the laser source was the cascaded MZM (Photoline) and PM (EOspace) with half-wave voltages of 7V and 3.5V respectively. A 3km single mode fiber was also used to improve the Q factor of the self-oscillating loop.

In the electrical feedback path, optical-to-microwave conversion was achieved by a high-speed PD (~0.8 A/W responsivity and 20 GHz bandwidth). In order to compensate the gain loss from the optical link, two stage RF amplifiers with both 30dB gain were employed as well. Moreover, oscillation frequency selection was realized by a bandpass filter with the center frequency of 10 GHz and 12GHz respectively. Then the filtered signal was divided by a 9:1 coupler, and 1/10 went to an electronic signal analyzer to measure the spectrum and phase noise of the microwave signal. Meanwhile, the rest was fed back into the modulators to build the self-oscillating OFC generator. The final oscillation power was determined by the half voltage of the MZM. Before the PM, a variable attenuator and a phase shifter were employed to adjust the driven signal. Finally, the third stage amplifier with 10 dB gain and 24 dBm saturation output power is used to broaden the number and improve the smoothness of the generated comb lines.

To increase the number and improve the flatness of the OFC lines in the experiment, we delicately tuned the DC bias voltage of the MZM, the phase shifter and variable attenuator before the PM. As a result, 11-lines flat-topped optical frequency combs were generated. The optical output was divided by a 95:5 optical coupler and measured by an optical spectrum analyzer (YOKOGAWA). The optical spectrums of the comb lines are shown as Fig. 2. As these figures depict, the frequency spacing of the generated OFCs are 10 GHz and 12 GHz respectively, and a flatness of 0.82 dB and 0.93dB could also be observed.

 

Fig. 2 Optical spectra of the generated eleven-line optical frequency comb with frequency spacing of (a) 10 GHz and (b) 12 GHz.

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Figure 3 shows the electrical spectrum of the generated oscillation signal at 10 GHz and 12GHz. A zoom-in view of the spectrum with a span of 100 kHz is shown as an inset respectively. As the figures show, the power of 10 GHz and 12 GHz oscillating microwave signals are about −15 dBm and −13 dBm respectively. Take consideration of the 10dB coupler, the phase shifter, the second stage amplifier and the 3 dB power divider, we can conclude that the power of the driven signal for the MZM is about 15dBm and 17dBm. Therefore, the power of the driven signal for the PM is about 24dBm accordingly. The single-sideband phase noise of the oscillating signal was measured by N9030A PXA signal analyzer (Agilent Technologies), just as Fig. 4 depicts. The phase noise at 10 kHz offset frequency are −122 dBc/Hz and −115 dBc/Hz for the 10GHz and 12GHz oscillating signals respectively. Besides, the spurious suppression ratio reach more than 70 dBc and it can be improved or removed by many methods, including multi-loops [16]. The long term frequency stability of the oscillation loop can be resolved by locking to the reference crystal oscillator, and lots of relative works have been done previously [17,18].

 

Fig. 3 Electrical spectrum of the generated oscillation signals (a) 10 GHz and (b) 12 GHz.

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Fig. 4 Corresponding measured single-sideband phase noise versus offset frequency.

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4. Conclusion

In this paper, we proposed an ultraflat self-oscillating OFC generator based on an optoelectronic oscillator employing cascaded modulators. A self-starting OEO was built to offer stable microwave signals for the generation of OFC. A cascade of Mach-Zehnder modulator and phase modulator was employed to generate flat-topped OFC. As a result, we experimentally demonstrated the proposed OFC generator, and 11-line flat-topped OFCs were generated with the frequency spacings of 10 GHz and 12 GHz respectively. The corresponding flatness are within 0.82 dB and 0.93 dB. Besides, the phase noise of the embedded OEO was also measured, and the corresponding results were −122 dBc/Hz and −115 dBc/Hz at 10 kHz offset frequency.

Acknowledgments

This work was supported in part by National 973 Program (2012CB315705), NSFC Program (61501051, 61271042, 61302016, 61335002), and NCET-13-0682.

References and links

1. J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014). [CrossRef]   [PubMed]  

2. T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011). [CrossRef]  

3. J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1041–1058 (2003). [CrossRef]  

4. Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13(25), 10431–10439 (2005). [CrossRef]   [PubMed]  

5. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). [CrossRef]   [PubMed]  

6. Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F. L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010). [CrossRef]   [PubMed]  

7. J. Zhang, J. Yu, N. Chi, Z. Dong, X. Li, Y. Shao, J. Yu, and L. Tao, “Flattened comb generation using only phase modulators driven by fundamental frequency sinusoidal sources with small frequency offset,” Opt. Lett. 38(4), 552–554 (2013). [CrossRef]   [PubMed]  

8. R. Wu, V. R. Supradeepa, C. M. Long, D. E. Leaird, and A. M. Weiner, “Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms,” Opt. Lett. 35(19), 3234–3236 (2010). [CrossRef]   [PubMed]  

9. X. Zou, W. Pan, and J. Yao, “Tunable optical comb generation based on carrier-suppressed intensity modulation and phase modulation,” Chin. Opt. Lett. 8(5), 468–470 (2010). [CrossRef]  

10. C. Chen, C. He, D. Zhu, R. Guo, F. Zhang, and S. Pan, “Generation of a flat optical frequency comb based on a cascaded polarization modulator and phase modulator,” Opt. Lett. 38(16), 3137–3139 (2013). [CrossRef]   [PubMed]  

11. C. He, S. Pan, R. Guo, Y. Zhao, and M. Pan, “Ultraflat optical frequency comb generated based on cascaded polarization modulators,” Opt. Lett. 37(18), 3834–3836 (2012). [CrossRef]   [PubMed]  

12. X. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996). [CrossRef]  

13. M. Wang and J. Yao, “Tunable Optical Frequency Comb Generation Based on an Optoelectronic Oscillator,” in IEEE,” IEEE Photonics Technol. Lett. 25(21), 2035–2038 (2013). [CrossRef]  

14. T. Sakamoto, T. Kawanishi, and M. Izutsu, “Optoelectronic oscillator using a LiNbO3 phase modulator for self-oscillating frequency comb generation,” Opt. Lett. 31(6), 811–813 (2006). [CrossRef]   [PubMed]  

15. G. L. Li and P. K. L. Yu, “Optical intensity modulators for digital and analog applications,” J. Lightwave Technol. 21(9), 2010–2030 (2003). [CrossRef]  

16. X. S. Yao and L. Maleki, “Multi-loop optoelectronic oscillator,” IEEE J. Quantum Electron. 36(1), 79–84 (2000). [CrossRef]  

17. D. Eliyahu, K. Sariri, M. Kamran, and M. Tokhmakhian, “Improving short and long term frequency stability of the opto-electronic oscillator,” in Proceedings of 2002 IEEE International Frequency Control Symposium, 580–583 (2002). [CrossRef]  

18. Y. L. Zhang, D. Hou, and J. Y. Zhao, “Long-term frequency stabilization of an optoelectronic oscillator using phase-locked loop,” J. Lightwave Technol. 32(13), 2408–2414 (2014). [CrossRef]  

References

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  1. J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
    [Crossref] [PubMed]
  2. T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
    [Crossref]
  3. J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1041–1058 (2003).
    [Crossref]
  4. Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13(25), 10431–10439 (2005).
    [Crossref] [PubMed]
  5. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
    [Crossref] [PubMed]
  6. Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F. L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010).
    [Crossref] [PubMed]
  7. J. Zhang, J. Yu, N. Chi, Z. Dong, X. Li, Y. Shao, J. Yu, and L. Tao, “Flattened comb generation using only phase modulators driven by fundamental frequency sinusoidal sources with small frequency offset,” Opt. Lett. 38(4), 552–554 (2013).
    [Crossref] [PubMed]
  8. R. Wu, V. R. Supradeepa, C. M. Long, D. E. Leaird, and A. M. Weiner, “Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms,” Opt. Lett. 35(19), 3234–3236 (2010).
    [Crossref] [PubMed]
  9. X. Zou, W. Pan, and J. Yao, “Tunable optical comb generation based on carrier-suppressed intensity modulation and phase modulation,” Chin. Opt. Lett. 8(5), 468–470 (2010).
    [Crossref]
  10. C. Chen, C. He, D. Zhu, R. Guo, F. Zhang, and S. Pan, “Generation of a flat optical frequency comb based on a cascaded polarization modulator and phase modulator,” Opt. Lett. 38(16), 3137–3139 (2013).
    [Crossref] [PubMed]
  11. C. He, S. Pan, R. Guo, Y. Zhao, and M. Pan, “Ultraflat optical frequency comb generated based on cascaded polarization modulators,” Opt. Lett. 37(18), 3834–3836 (2012).
    [Crossref] [PubMed]
  12. X. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996).
    [Crossref]
  13. M. Wang and J. Yao, “Tunable Optical Frequency Comb Generation Based on an Optoelectronic Oscillator,” in IEEE,” IEEE Photonics Technol. Lett. 25(21), 2035–2038 (2013).
    [Crossref]
  14. T. Sakamoto, T. Kawanishi, and M. Izutsu, “Optoelectronic oscillator using a LiNbO3 phase modulator for self-oscillating frequency comb generation,” Opt. Lett. 31(6), 811–813 (2006).
    [Crossref] [PubMed]
  15. G. L. Li and P. K. L. Yu, “Optical intensity modulators for digital and analog applications,” J. Lightwave Technol. 21(9), 2010–2030 (2003).
    [Crossref]
  16. X. S. Yao and L. Maleki, “Multi-loop optoelectronic oscillator,” IEEE J. Quantum Electron. 36(1), 79–84 (2000).
    [Crossref]
  17. D. Eliyahu, K. Sariri, M. Kamran, and M. Tokhmakhian, “Improving short and long term frequency stability of the opto-electronic oscillator,” in Proceedings of 2002 IEEE International Frequency Control Symposium, 580–583 (2002).
    [Crossref]
  18. Y. L. Zhang, D. Hou, and J. Y. Zhao, “Long-term frequency stabilization of an optoelectronic oscillator using phase-locked loop,” J. Lightwave Technol. 32(13), 2408–2414 (2014).
    [Crossref]

2014 (2)

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Y. L. Zhang, D. Hou, and J. Y. Zhao, “Long-term frequency stabilization of an optoelectronic oscillator using phase-locked loop,” J. Lightwave Technol. 32(13), 2408–2414 (2014).
[Crossref]

2013 (3)

2012 (1)

2011 (1)

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

2010 (3)

2006 (1)

2005 (1)

2003 (2)

J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1041–1058 (2003).
[Crossref]

G. L. Li and P. K. L. Yu, “Optical intensity modulators for digital and analog applications,” J. Lightwave Technol. 21(9), 2010–2030 (2003).
[Crossref]

2002 (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

2000 (1)

X. S. Yao and L. Maleki, “Multi-loop optoelectronic oscillator,” IEEE J. Quantum Electron. 36(1), 79–84 (2000).
[Crossref]

1996 (1)

Bergquist, J. C.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Brasch, V.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Chen, C.

Chi, N.

Diddams, S. A.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Dong, Z.

Eliyahu, D.

D. Eliyahu, K. Sariri, M. Kamran, and M. Tokhmakhian, “Improving short and long term frequency stability of the opto-electronic oscillator,” in Proceedings of 2002 IEEE International Frequency Control Symposium, 580–583 (2002).
[Crossref]

Fortier, T. M.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Freude, W.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Guo, R.

Hänsch, T. W.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Hartinger, K.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

He, C.

Herr, T.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Hillerkuss, D.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Hollberg, L. W.

J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1041–1058 (2003).
[Crossref]

Holzwarth, R.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Hong, F. L.

Hosaka, K.

Hou, D.

Inaba, H.

Izutsu, M.

Jiang, Y.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Jiang, Z.

Kamran, M.

D. Eliyahu, K. Sariri, M. Kamran, and M. Tokhmakhian, “Improving short and long term frequency stability of the opto-electronic oscillator,” in Proceedings of 2002 IEEE International Frequency Control Symposium, 580–583 (2002).
[Crossref]

Katsuyama, T.

Kawanishi, T.

Kawato, S.

Kippenberg, T. J.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Kirchner, M. S.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Kobayashi, T.

Kohno, T.

Koos, C.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Lauermann, M.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Leaird, D. E.

Lemke, N.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Leuthold, J.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Li, G. L.

Li, J.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Li, X.

Long, C. M.

Ludlow, A.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Maleki, L.

X. S. Yao and L. Maleki, “Multi-loop optoelectronic oscillator,” IEEE J. Quantum Electron. 36(1), 79–84 (2000).
[Crossref]

X. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996).
[Crossref]

Minoshima, K.

Nakajima, Y.

Oates, C. W.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Onae, A.

Pan, M.

Pan, S.

Pan, W.

Pfeifle, J.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Quinlan, F.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Rosenband, T.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Sakamoto, T.

Sariri, K.

D. Eliyahu, K. Sariri, M. Kamran, and M. Tokhmakhian, “Improving short and long term frequency stability of the opto-electronic oscillator,” in Proceedings of 2002 IEEE International Frequency Control Symposium, 580–583 (2002).
[Crossref]

Schindler, P.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Schmogrow, R.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Schnatz, H.

J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1041–1058 (2003).
[Crossref]

Shao, Y.

Supradeepa, V. R.

Tao, L.

Taylor, J.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Tokhmakhian, M.

D. Eliyahu, K. Sariri, M. Kamran, and M. Tokhmakhian, “Improving short and long term frequency stability of the opto-electronic oscillator,” in Proceedings of 2002 IEEE International Frequency Control Symposium, 580–583 (2002).
[Crossref]

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Wang, M.

M. Wang and J. Yao, “Tunable Optical Frequency Comb Generation Based on an Optoelectronic Oscillator,” in IEEE,” IEEE Photonics Technol. Lett. 25(21), 2035–2038 (2013).
[Crossref]

Wegner, D.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Weimann, C.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Weiner, A. M.

Wu, R.

Yao, J.

M. Wang and J. Yao, “Tunable Optical Frequency Comb Generation Based on an Optoelectronic Oscillator,” in IEEE,” IEEE Photonics Technol. Lett. 25(21), 2035–2038 (2013).
[Crossref]

X. Zou, W. Pan, and J. Yao, “Tunable optical comb generation based on carrier-suppressed intensity modulation and phase modulation,” Chin. Opt. Lett. 8(5), 468–470 (2010).
[Crossref]

Yao, X.

Yao, X. S.

X. S. Yao and L. Maleki, “Multi-loop optoelectronic oscillator,” IEEE J. Quantum Electron. 36(1), 79–84 (2000).
[Crossref]

Yasuda, M.

Ye, J.

J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1041–1058 (2003).
[Crossref]

Yu, J.

Yu, P. K. L.

Yu, Y.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Zhang, F.

Zhang, J.

Zhang, Y. L.

Zhao, J. Y.

Zhao, Y.

Zhu, D.

Zou, X.

Chin. Opt. Lett. (1)

IEEE J. Quantum Electron. (1)

X. S. Yao and L. Maleki, “Multi-loop optoelectronic oscillator,” IEEE J. Quantum Electron. 36(1), 79–84 (2000).
[Crossref]

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

J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1041–1058 (2003).
[Crossref]

IEEE Photonics Technol. Lett. (1)

M. Wang and J. Yao, “Tunable Optical Frequency Comb Generation Based on an Optoelectronic Oscillator,” in IEEE,” IEEE Photonics Technol. Lett. 25(21), 2035–2038 (2013).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Nat. Photonics (2)

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, etc., “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Nature (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (5)

Other (1)

D. Eliyahu, K. Sariri, M. Kamran, and M. Tokhmakhian, “Improving short and long term frequency stability of the opto-electronic oscillator,” in Proceedings of 2002 IEEE International Frequency Control Symposium, 580–583 (2002).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Schematic diagram of the proposed optical frequency comb generator. LD: laser diode. MZM: Mach-Zehnder modulator. PM: phase modulator. OSA: optical spectrum analyzer. SMF: single mode fiber. PD: photodetector. EA: electrical amplifier. BPF: bandpass filter. PS: phase shifter. VA: variable attenuator. ESA: electrical spectrum analyzer.
Fig. 2
Fig. 2 Optical spectra of the generated eleven-line optical frequency comb with frequency spacing of (a) 10 GHz and (b) 12 GHz.
Fig. 3
Fig. 3 Electrical spectrum of the generated oscillation signals (a) 10 GHz and (b) 12 GHz.
Fig. 4
Fig. 4 Corresponding measured single-sideband phase noise versus offset frequency.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

E 1 = 2 2 E o e i w o t [ e i( φ 1 + γ 1 cos w c t ) + e i γ 1 cos w c t ]
E 2 = E 1 e i γ 2 cos( ω c t+Δϕ ) = 2 2 E 0 e i w o t [ e i( φ 1 + γ 1 cos w c t ) + e i γ 1 cos w c t ] e i γ 2 cos( ω c t+Δϕ )
E 2 = 2 2 E o e i w o t n= ( e i φ 1 + e inπ ) i n J n ( γ 1 ) e in w c t k= i k J k ( γ 2 ) e ik( ω c t+Δϕ ) = 2 2 E o e i w o t n= k= ( e i φ 1 + e inπ ) i n J n ( γ 1 ) e in w c t i k J k ( γ 2 ) e ik( ω c t+Δϕ ) = 2 2 E o e i w o t n= k= e ikΔϕ ( e i φ 1 + e inπ ) i n+k J n ( γ 1 ) J k ( γ 2 ) e i( n+k ) w c t
P= 1 2 P o | M= ( e i(NM)Δϕ ( e i φ 1 + e iMπ ) i N J n ( γ 1 ) J NM ( γ 2 ) ) | 2
I 1 2 L o E 0 2 [ e i( φ 1 +2 γ 1 cos w c t ) + e i( φ 1 +2 γ 1 cos w c t ) ] = L o P 0 n= J n ( 2 γ 1 )cos[ ( φ 1 +n w c t )+ 1 2 nπ ]
I 1st L 0 P 0 [ J 1 ( 2 γ 1 )cos( φ 1 + w c t+ π 2 )+ J 1 ( 2 γ 1 )cos( φ 1 w c t π 2 ) ] =2 L 0 P 0 J 1 ( 2 γ 1 )sin φ 1 cos w c t
G o = 2 π 2 L 0 2 P 0 2 sin 2 φ 1 V π 2
G e > V π 2 2 π 2 L 0 2 P 0 2 sin 2 φ 1
w c ( τ o + τ e )=2mπ m=0,1,2.....

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