Abstract

The result of a theoretical and experimental study on the phase fluctuations of a coupled optoelectronic oscillator is presented. We derive an analytical expression for the fundamental limit of phase noise of a radio-frequency signal generated in the oscillator and compare it with experimental data. We show that the noise can be extremely low, approaching 160dBc/Hz at 10 kHz offset for reasonable experimental parameters. The experimentally observed noise is 15 dB higher due to technical noise of the system.

© 2013 Optical Society of America

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  7. W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.
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  18. J. D. Kafka, M. L. Watts, and J. J. Pieterse, “Picosecond and femtosecond pulse generation in a regeneratively mode-locked Ti:sapphire laser,” IEEE J. Quantum Electron. 28, 2151–2162 (1992).
    [CrossRef]
  19. M. Nakazawa, E. Yoshida, and Y. Kimura, “Ultrastable harmonically and regeneratively modelocked polarization-maintaining erbium fiber laser,” Electron. Lett. 30, 1603–1605 (1994).
    [CrossRef]
  20. M. Nakazawa, E. Yoshida, E. Yamada, and Y. Kimura, “A repetition rate stabilized and tunable, regeneratively mode-locked fiber laser using an offset-locking technique,” Jpn. J. Appl. Phys. 35, L691–L694 (1996).
    [CrossRef]
  21. M. Nakazawa, E. Yoshida, and K. Tamura, “Ideal phase-locked-loop (PLL) operation of a 10  GHz erbium-doped fiber laser using regenerative mode-locking as an optical voltage controlled oscillator,” Electron. Lett. 33, 1318–1320 (1997).
    [CrossRef]
  22. B. Bakshi, P. A. Andrekson, and X. Zhang, “10  GHz mode-locked, dispersion-managed and polarization-maintaining erbium fiber ring laser with variable output coupling,” Electron. Lett. 34, 884–885 (1998).
    [CrossRef]
  23. K. K. Gupta, D. Novak, and H.-F. Liu, “Noise characterization of a regeneratively mode-locked fiber ring laser,” IEEE J. Quantum Electron. 36, 70–78 (2000).
    [CrossRef]
  24. K. K. Gupta and N. Onodera, “Regenerative mode locking via superposition of higher-order cavity modes in composite cavity fiber lasers,” Opt. Lett. 30, 2221–2223 (2005).
    [CrossRef]
  25. K. Koizumi, M. Yoshida, T. Hirooka, and M. Nakazawa, “10  GHz, 1.1  ps optical pulse generation from a regeneratively mode-locked Yb fiber laser in the 1.1  m band,” Opt. Express 19, 25426–25432 (2011).
    [CrossRef]
  26. A. Bekal, K. Vijayan, and B. Srinivasan, “Study of pulse stability enhancement in regeneratively mode-locked fiber laser,” in International Conference on Fibre Optics and Photonics, OSA Technical Digest (online) (Optical Society of America, 2012), paper TPo.1.
  27. D. A. Howe and A. Hati, “Low-noise X-band oscillator and amplifier technologies: comparison and status,” in Proceedings of 2005 Joint Mtg. IEEE Intl. Freq. Cont. Symp. and PTTI (IEEE, 2005), pp. 481–487.
  28. C. McNeilage, J. H. Searls, E. N. Ivanov, P. R. Stockwell, D. M. Green, and M. Mossammaparast, “A review of sapphire whispering gallery-mode oscillators including technical progress and future potential of the technology,” in Proceedings of 2004 IEEE International Frequency Control Symposium and Exposition (IEEE, 2004), pp. 210–218.
  29. J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41, 650–651 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  32. H. A. Haus, M. Margalit, and C. X. Yu, “Quantum noise of mode locked lasers,” J. Opt. Soc. Am. B 17, 1240–1256 (2000).
    [CrossRef]
  33. F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
    [CrossRef]
  34. F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30, 1775–1785 (2013).
    [CrossRef]
  35. F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen, and H. A. Haus, “Characterization of the noise and correlations in harmonically mode-locked lasers,” J. Opt. Soc. Am. B 19, 2609–2621 (2002).
    [CrossRef]
  36. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

2013 (2)

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30, 1775–1785 (2013).
[CrossRef]

2011 (1)

2009 (3)

2008 (1)

2007 (1)

E. Salik, N. Yu, and L. Maleki, “An ultralow phase noise coupled optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 444–446 (2007).
[CrossRef]

2006 (1)

2005 (3)

2004 (1)

F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40, 41–56 (2004).
[CrossRef]

2002 (1)

2000 (3)

1998 (1)

B. Bakshi, P. A. Andrekson, and X. Zhang, “10  GHz mode-locked, dispersion-managed and polarization-maintaining erbium fiber ring laser with variable output coupling,” Electron. Lett. 34, 884–885 (1998).
[CrossRef]

1997 (2)

M. Nakazawa, E. Yoshida, and K. Tamura, “Ideal phase-locked-loop (PLL) operation of a 10  GHz erbium-doped fiber laser using regenerative mode-locking as an optical voltage controlled oscillator,” Electron. Lett. 33, 1318–1320 (1997).
[CrossRef]

X. S. Yao and L. Maleki, “Dual microwave and optical oscillator,” Opt. Lett. 22, 1867–1869 (1997).
[CrossRef]

1996 (1)

M. Nakazawa, E. Yoshida, E. Yamada, and Y. Kimura, “A repetition rate stabilized and tunable, regeneratively mode-locked fiber laser using an offset-locking technique,” Jpn. J. Appl. Phys. 35, L691–L694 (1996).
[CrossRef]

1994 (1)

M. Nakazawa, E. Yoshida, and Y. Kimura, “Ultrastable harmonically and regeneratively modelocked polarization-maintaining erbium fiber laser,” Electron. Lett. 30, 1603–1605 (1994).
[CrossRef]

1993 (1)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[CrossRef]

1992 (1)

J. D. Kafka, M. L. Watts, and J. J. Pieterse, “Picosecond and femtosecond pulse generation in a regeneratively mode-locked Ti:sapphire laser,” IEEE J. Quantum Electron. 28, 2151–2162 (1992).
[CrossRef]

1991 (2)

L. Turi and F. Krausz, “Amplitude modulation mode locking of lasers by regenerative feedback,” Appl. Phys. Lett. 58, 810–812 (1991).
[CrossRef]

D. E. Spence, J. M. Evans, W. E. Sleat, and W. Sibbett, “Regeneratively initiated self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 1762–1764 (1991).
[CrossRef]

1984 (2)

K. Y. Lau and A. Yariv, “Self-sustained picosecond pulse generation in a GaAlAs laser at an electrically tunable repetition rate by optoelectronic feedback,” Appl. Phys. Lett. 45, 124–126 (1984).
[CrossRef]

M. Nakazawa, T. Nakashima, and M. Tokuda, “An optoelectronic self-oscillatory circuit with an optical fiber delayed feedback and its injection locking technique,” J. Lightwave Technol. 2, 719–730 (1984).
[CrossRef]

1973 (1)

T. S. Kinsel, “A stabilized mode-locked Nd: YAG laser using electronic feedback,” IEEE J. Quantum Electron. 9, 3–8 (1973).
[CrossRef]

1968 (1)

G. R. Huggett, “Mode-locking of CW lasers by regenerative RF feedback,” Appl. Phys. Lett. 13, 186–187 (1968).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Andrekson, P. A.

B. Bakshi, P. A. Andrekson, and X. Zhang, “10  GHz mode-locked, dispersion-managed and polarization-maintaining erbium fiber ring laser with variable output coupling,” Electron. Lett. 34, 884–885 (1998).
[CrossRef]

Bakshi, B.

B. Bakshi, P. A. Andrekson, and X. Zhang, “10  GHz mode-locked, dispersion-managed and polarization-maintaining erbium fiber ring laser with variable output coupling,” Electron. Lett. 34, 884–885 (1998).
[CrossRef]

Bartels, A.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41, 650–651 (2005).
[CrossRef]

Bekal, A.

A. Bekal, K. Vijayan, and B. Srinivasan, “Study of pulse stability enhancement in regeneratively mode-locked fiber laser,” in International Conference on Fibre Optics and Photonics, OSA Technical Digest (online) (Optical Society of America, 2012), paper TPo.1.

Cai, S.

S. Cai, S. Pan, D. Zhu, and X. Chen, “Stabilize the coupled optoelectronic oscillator by an unpumped erbium-doped fiber,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2012), paper ATh2C.5.

Campbell, J. C.

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[CrossRef]

Chen, X.

S. Cai, S. Pan, D. Zhu, and X. Chen, “Stabilize the coupled optoelectronic oscillator by an unpumped erbium-doped fiber,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2012), paper ATh2C.5.

Choi, M. T.

Davis, L.

Delfyett, P. J.

Diddams, S. A.

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30, 1775–1785 (2013).
[CrossRef]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41, 650–651 (2005).
[CrossRef]

Eliyahu, D.

Evans, J. M.

Fortier, T. M.

F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30, 1775–1785 (2013).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[CrossRef]

Fu, Y.

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[CrossRef]

Gee, S.

Green, D. M.

C. McNeilage, J. H. Searls, E. N. Ivanov, P. R. Stockwell, D. M. Green, and M. Mossammaparast, “A review of sapphire whispering gallery-mode oscillators including technical progress and future potential of the technology,” in Proceedings of 2004 IEEE International Frequency Control Symposium and Exposition (IEEE, 2004), pp. 210–218.

Grein, M.

W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.

Grein, M. E.

Gupta, K. K.

K. K. Gupta and N. Onodera, “Regenerative mode locking via superposition of higher-order cavity modes in composite cavity fiber lasers,” Opt. Lett. 30, 2221–2223 (2005).
[CrossRef]

K. K. Gupta, D. Novak, and H.-F. Liu, “Noise characterization of a regeneratively mode-locked fiber ring laser,” IEEE J. Quantum Electron. 36, 70–78 (2000).
[CrossRef]

Hati, A.

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[CrossRef]

D. A. Howe and A. Hati, “Low-noise X-band oscillator and amplifier technologies: comparison and status,” in Proceedings of 2005 Joint Mtg. IEEE Intl. Freq. Cont. Symp. and PTTI (IEEE, 2005), pp. 481–487.

Haus, H. A.

F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40, 41–56 (2004).
[CrossRef]

F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen, and H. A. Haus, “Characterization of the noise and correlations in harmonically mode-locked lasers,” J. Opt. Soc. Am. B 19, 2609–2621 (2002).
[CrossRef]

H. A. Haus, M. Margalit, and C. X. Yu, “Quantum noise of mode locked lasers,” J. Opt. Soc. Am. B 17, 1240–1256 (2000).
[CrossRef]

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[CrossRef]

Hirooka, T.

Hollberg, L.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41, 650–651 (2005).
[CrossRef]

Howe, D. A.

D. A. Howe and A. Hati, “Low-noise X-band oscillator and amplifier technologies: comparison and status,” in Proceedings of 2005 Joint Mtg. IEEE Intl. Freq. Cont. Symp. and PTTI (IEEE, 2005), pp. 481–487.

Huggett, G. R.

G. R. Huggett, “Mode-locking of CW lasers by regenerative RF feedback,” Appl. Phys. Lett. 13, 186–187 (1968).
[CrossRef]

Ippen, E. P.

Ivanov, E. N.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41, 650–651 (2005).
[CrossRef]

C. McNeilage, J. H. Searls, E. N. Ivanov, P. R. Stockwell, D. M. Green, and M. Mossammaparast, “A review of sapphire whispering gallery-mode oscillators including technical progress and future potential of the technology,” in Proceedings of 2004 IEEE International Frequency Control Symposium and Exposition (IEEE, 2004), pp. 210–218.

Izadpanah, H.

Jiang, H.

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[CrossRef]

F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30, 1775–1785 (2013).
[CrossRef]

Jiang, L. A.

Juodawlkis, P. W.

W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.

Kafka, J. D.

J. D. Kafka, M. L. Watts, and J. J. Pieterse, “Picosecond and femtosecond pulse generation in a regeneratively mode-locked Ti:sapphire laser,” IEEE J. Quantum Electron. 28, 2151–2162 (1992).
[CrossRef]

Kimura, Y.

M. Nakazawa, E. Yoshida, E. Yamada, and Y. Kimura, “A repetition rate stabilized and tunable, regeneratively mode-locked fiber laser using an offset-locking technique,” Jpn. J. Appl. Phys. 35, L691–L694 (1996).
[CrossRef]

M. Nakazawa, E. Yoshida, and Y. Kimura, “Ultrastable harmonically and regeneratively modelocked polarization-maintaining erbium fiber laser,” Electron. Lett. 30, 1603–1605 (1994).
[CrossRef]

Kinsel, T. S.

T. S. Kinsel, “A stabilized mode-locked Nd: YAG laser using electronic feedback,” IEEE J. Quantum Electron. 9, 3–8 (1973).
[CrossRef]

Klamkin, J.

W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.

Koizumi, K.

Koonath, P.

Krausz, F.

L. Turi and F. Krausz, “Amplitude modulation mode locking of lasers by regenerative feedback,” Appl. Phys. Lett. 58, 810–812 (1991).
[CrossRef]

Lau, K. Y.

K. Y. Lau and A. Yariv, “Self-sustained picosecond pulse generation in a GaAlAs laser at an electrically tunable repetition rate by optoelectronic feedback,” Appl. Phys. Lett. 45, 124–126 (1984).
[CrossRef]

Lee, H. L. T.

Lee, W.

Liu, H.-F.

K. K. Gupta, D. Novak, and H.-F. Liu, “Noise characterization of a regeneratively mode-locked fiber ring laser,” IEEE J. Quantum Electron. 36, 70–78 (2000).
[CrossRef]

Loh, W.

W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.

Madison, S.

W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.

Maleki, L.

Margalit, M.

Matsko, A. B.

McFerran, J. J.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41, 650–651 (2005).
[CrossRef]

McNeilage, C.

C. McNeilage, J. H. Searls, E. N. Ivanov, P. R. Stockwell, D. M. Green, and M. Mossammaparast, “A review of sapphire whispering gallery-mode oscillators including technical progress and future potential of the technology,” in Proceedings of 2004 IEEE International Frequency Control Symposium and Exposition (IEEE, 2004), pp. 210–218.

Mecozzi, A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[CrossRef]

Mossammaparast, M.

C. McNeilage, J. H. Searls, E. N. Ivanov, P. R. Stockwell, D. M. Green, and M. Mossammaparast, “A review of sapphire whispering gallery-mode oscillators including technical progress and future potential of the technology,” in Proceedings of 2004 IEEE International Frequency Control Symposium and Exposition (IEEE, 2004), pp. 210–218.

Nakashima, T.

M. Nakazawa, T. Nakashima, and M. Tokuda, “An optoelectronic self-oscillatory circuit with an optical fiber delayed feedback and its injection locking technique,” J. Lightwave Technol. 2, 719–730 (1984).
[CrossRef]

Nakazawa, M.

K. Koizumi, M. Yoshida, T. Hirooka, and M. Nakazawa, “10  GHz, 1.1  ps optical pulse generation from a regeneratively mode-locked Yb fiber laser in the 1.1  m band,” Opt. Express 19, 25426–25432 (2011).
[CrossRef]

M. Nakazawa, E. Yoshida, and K. Tamura, “Ideal phase-locked-loop (PLL) operation of a 10  GHz erbium-doped fiber laser using regenerative mode-locking as an optical voltage controlled oscillator,” Electron. Lett. 33, 1318–1320 (1997).
[CrossRef]

M. Nakazawa, E. Yoshida, E. Yamada, and Y. Kimura, “A repetition rate stabilized and tunable, regeneratively mode-locked fiber laser using an offset-locking technique,” Jpn. J. Appl. Phys. 35, L691–L694 (1996).
[CrossRef]

M. Nakazawa, E. Yoshida, and Y. Kimura, “Ultrastable harmonically and regeneratively modelocked polarization-maintaining erbium fiber laser,” Electron. Lett. 30, 1603–1605 (1994).
[CrossRef]

M. Nakazawa, T. Nakashima, and M. Tokuda, “An optoelectronic self-oscillatory circuit with an optical fiber delayed feedback and its injection locking technique,” J. Lightwave Technol. 2, 719–730 (1984).
[CrossRef]

Nelson, C.

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[CrossRef]

Novak, D.

K. K. Gupta, D. Novak, and H.-F. Liu, “Noise characterization of a regeneratively mode-locked fiber ring laser,” IEEE J. Quantum Electron. 36, 70–78 (2000).
[CrossRef]

O’Donnell, F. J.

W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.

Oates, C. W.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41, 650–651 (2005).
[CrossRef]

Onodera, N.

Ozdur, I.

Ozharar, S.

Pan, S.

S. Cai, S. Pan, D. Zhu, and X. Chen, “Stabilize the coupled optoelectronic oscillator by an unpumped erbium-doped fiber,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2012), paper ATh2C.5.

Pieterse, J. J.

J. D. Kafka, M. L. Watts, and J. J. Pieterse, “Picosecond and femtosecond pulse generation in a regeneratively mode-locked Ti:sapphire laser,” IEEE J. Quantum Electron. 28, 2151–2162 (1992).
[CrossRef]

Plant, J.

W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.

Quinlan, F.

Ram, R.

W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.

Ram, R. J.

F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40, 41–56 (2004).
[CrossRef]

F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen, and H. A. Haus, “Characterization of the noise and correlations in harmonically mode-locked lasers,” J. Opt. Soc. Am. B 19, 2609–2621 (2002).
[CrossRef]

Rana, F.

F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40, 41–56 (2004).
[CrossRef]

F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen, and H. A. Haus, “Characterization of the noise and correlations in harmonically mode-locked lasers,” J. Opt. Soc. Am. B 19, 2609–2621 (2002).
[CrossRef]

Salik, E.

E. Salik, N. Yu, and L. Maleki, “An ultralow phase noise coupled optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 444–446 (2007).
[CrossRef]

N. Yu, E. Salik, and L. Maleki, “Ultralow-noise mode-locked laser with coupled optoelectronic oscillator configuration,” Opt. Lett. 30, 1231–1233 (2005).
[CrossRef]

Searls, J. H.

C. McNeilage, J. H. Searls, E. N. Ivanov, P. R. Stockwell, D. M. Green, and M. Mossammaparast, “A review of sapphire whispering gallery-mode oscillators including technical progress and future potential of the technology,” in Proceedings of 2004 IEEE International Frequency Control Symposium and Exposition (IEEE, 2004), pp. 210–218.

Seidel, D.

Sibbett, W.

Sleat, W. E.

Spence, D. E.

Srinivasan, B.

A. Bekal, K. Vijayan, and B. Srinivasan, “Study of pulse stability enhancement in regeneratively mode-locked fiber laser,” in International Conference on Fibre Optics and Photonics, OSA Technical Digest (online) (Optical Society of America, 2012), paper TPo.1.

Stockwell, P. R.

C. McNeilage, J. H. Searls, E. N. Ivanov, P. R. Stockwell, D. M. Green, and M. Mossammaparast, “A review of sapphire whispering gallery-mode oscillators including technical progress and future potential of the technology,” in Proceedings of 2004 IEEE International Frequency Control Symposium and Exposition (IEEE, 2004), pp. 210–218.

Tamura, K.

M. Nakazawa, E. Yoshida, and K. Tamura, “Ideal phase-locked-loop (PLL) operation of a 10  GHz erbium-doped fiber laser using regenerative mode-locking as an optical voltage controlled oscillator,” Electron. Lett. 33, 1318–1320 (1997).
[CrossRef]

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M. Nakazawa, T. Nakashima, and M. Tokuda, “An optoelectronic self-oscillatory circuit with an optical fiber delayed feedback and its injection locking technique,” J. Lightwave Technol. 2, 719–730 (1984).
[CrossRef]

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L. Turi and F. Krausz, “Amplitude modulation mode locking of lasers by regenerative feedback,” Appl. Phys. Lett. 58, 810–812 (1991).
[CrossRef]

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A. Bekal, K. Vijayan, and B. Srinivasan, “Study of pulse stability enhancement in regeneratively mode-locked fiber laser,” in International Conference on Fibre Optics and Photonics, OSA Technical Digest (online) (Optical Society of America, 2012), paper TPo.1.

Watts, M. L.

J. D. Kafka, M. L. Watts, and J. J. Pieterse, “Picosecond and femtosecond pulse generation in a regeneratively mode-locked Ti:sapphire laser,” IEEE J. Quantum Electron. 28, 2151–2162 (1992).
[CrossRef]

Williams, C.

Wilpers, G.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41, 650–651 (2005).
[CrossRef]

Yamada, E.

M. Nakazawa, E. Yoshida, E. Yamada, and Y. Kimura, “A repetition rate stabilized and tunable, regeneratively mode-locked fiber laser using an offset-locking technique,” Jpn. J. Appl. Phys. 35, L691–L694 (1996).
[CrossRef]

Yao, X. S.

Yariv, A.

K. Y. Lau and A. Yariv, “Self-sustained picosecond pulse generation in a GaAlAs laser at an electrically tunable repetition rate by optoelectronic feedback,” Appl. Phys. Lett. 45, 124–126 (1984).
[CrossRef]

Yegnanarayanan, S.

W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.

Yimaz, T.

Yoshida, E.

M. Nakazawa, E. Yoshida, and K. Tamura, “Ideal phase-locked-loop (PLL) operation of a 10  GHz erbium-doped fiber laser using regenerative mode-locking as an optical voltage controlled oscillator,” Electron. Lett. 33, 1318–1320 (1997).
[CrossRef]

M. Nakazawa, E. Yoshida, E. Yamada, and Y. Kimura, “A repetition rate stabilized and tunable, regeneratively mode-locked fiber laser using an offset-locking technique,” Jpn. J. Appl. Phys. 35, L691–L694 (1996).
[CrossRef]

M. Nakazawa, E. Yoshida, and Y. Kimura, “Ultrastable harmonically and regeneratively modelocked polarization-maintaining erbium fiber laser,” Electron. Lett. 30, 1603–1605 (1994).
[CrossRef]

Yoshida, M.

Yu, C. X.

Yu, N.

E. Salik, N. Yu, and L. Maleki, “An ultralow phase noise coupled optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 444–446 (2007).
[CrossRef]

N. Yu, E. Salik, and L. Maleki, “Ultralow-noise mode-locked laser with coupled optoelectronic oscillator configuration,” Opt. Lett. 30, 1231–1233 (2005).
[CrossRef]

Zhang, X.

B. Bakshi, P. A. Andrekson, and X. Zhang, “10  GHz mode-locked, dispersion-managed and polarization-maintaining erbium fiber ring laser with variable output coupling,” Electron. Lett. 34, 884–885 (1998).
[CrossRef]

Zhu, D.

S. Cai, S. Pan, D. Zhu, and X. Chen, “Stabilize the coupled optoelectronic oscillator by an unpumped erbium-doped fiber,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2012), paper ATh2C.5.

Appl. Phys. Lett. (3)

L. Turi and F. Krausz, “Amplitude modulation mode locking of lasers by regenerative feedback,” Appl. Phys. Lett. 58, 810–812 (1991).
[CrossRef]

G. R. Huggett, “Mode-locking of CW lasers by regenerative RF feedback,” Appl. Phys. Lett. 13, 186–187 (1968).
[CrossRef]

K. Y. Lau and A. Yariv, “Self-sustained picosecond pulse generation in a GaAlAs laser at an electrically tunable repetition rate by optoelectronic feedback,” Appl. Phys. Lett. 45, 124–126 (1984).
[CrossRef]

Electron. Lett. (4)

M. Nakazawa, E. Yoshida, and K. Tamura, “Ideal phase-locked-loop (PLL) operation of a 10  GHz erbium-doped fiber laser using regenerative mode-locking as an optical voltage controlled oscillator,” Electron. Lett. 33, 1318–1320 (1997).
[CrossRef]

B. Bakshi, P. A. Andrekson, and X. Zhang, “10  GHz mode-locked, dispersion-managed and polarization-maintaining erbium fiber ring laser with variable output coupling,” Electron. Lett. 34, 884–885 (1998).
[CrossRef]

M. Nakazawa, E. Yoshida, and Y. Kimura, “Ultrastable harmonically and regeneratively modelocked polarization-maintaining erbium fiber laser,” Electron. Lett. 30, 1603–1605 (1994).
[CrossRef]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low-noise synthesis of microwave signals from an optical source,” Electron. Lett. 41, 650–651 (2005).
[CrossRef]

IEEE J. Quantum Electron. (5)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[CrossRef]

J. D. Kafka, M. L. Watts, and J. J. Pieterse, “Picosecond and femtosecond pulse generation in a regeneratively mode-locked Ti:sapphire laser,” IEEE J. Quantum Electron. 28, 2151–2162 (1992).
[CrossRef]

F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40, 41–56 (2004).
[CrossRef]

K. K. Gupta, D. Novak, and H.-F. Liu, “Noise characterization of a regeneratively mode-locked fiber ring laser,” IEEE J. Quantum Electron. 36, 70–78 (2000).
[CrossRef]

T. S. Kinsel, “A stabilized mode-locked Nd: YAG laser using electronic feedback,” IEEE J. Quantum Electron. 9, 3–8 (1973).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

E. Salik, N. Yu, and L. Maleki, “An ultralow phase noise coupled optoelectronic oscillator,” IEEE Photon. Technol. Lett. 19, 444–446 (2007).
[CrossRef]

J. Lightwave Technol. (4)

J. Opt. A (1)

F. Quinlan, S. Ozharar, S. Gee, and P. J. Delfyett, “Harmonically mode-locked semiconductor-based lasers as high repetition rate ultralow noise pulse train and optical frequency comb sources,” J. Opt. A 11, 103001 (2009).
[CrossRef]

J. Opt. Soc. Am. B (4)

Jpn. J. Appl. Phys. (1)

M. Nakazawa, E. Yoshida, E. Yamada, and Y. Kimura, “A repetition rate stabilized and tunable, regeneratively mode-locked fiber laser using an offset-locking technique,” Jpn. J. Appl. Phys. 35, L691–L694 (1996).
[CrossRef]

Nat. Photonics (1)

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Other (6)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

S. Cai, S. Pan, D. Zhu, and X. Chen, “Stabilize the coupled optoelectronic oscillator by an unpumped erbium-doped fiber,” in Asia Communications and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2012), paper ATh2C.5.

W. Loh, S. Yegnanarayanan, J. Plant, F. J. O’Donnell, M. Grein, J. Klamkin, S. Madison, R. Ram, and P. W. Juodawlkis, “RF-amplifier-free coupled optoelectronic oscillator (COEO),” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTu3A.6.

A. Bekal, K. Vijayan, and B. Srinivasan, “Study of pulse stability enhancement in regeneratively mode-locked fiber laser,” in International Conference on Fibre Optics and Photonics, OSA Technical Digest (online) (Optical Society of America, 2012), paper TPo.1.

D. A. Howe and A. Hati, “Low-noise X-band oscillator and amplifier technologies: comparison and status,” in Proceedings of 2005 Joint Mtg. IEEE Intl. Freq. Cont. Symp. and PTTI (IEEE, 2005), pp. 481–487.

C. McNeilage, J. H. Searls, E. N. Ivanov, P. R. Stockwell, D. M. Green, and M. Mossammaparast, “A review of sapphire whispering gallery-mode oscillators including technical progress and future potential of the technology,” in Proceedings of 2004 IEEE International Frequency Control Symposium and Exposition (IEEE, 2004), pp. 210–218.

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagram of the COEO. Optical and RF loops are shown by solid black and red-dashed lines, respectively. Both loops include amplifiers and filters. The optical loop contains a semiconductor optical amplifier with gain g (SOA). The RF loop has an amplifier with gain G. Part of the light circulating in the optical loop (r1) is demodulated on a fast PD generating an RF signal with a carrier frequency equivalent to the optical pulse repetition rate. The amplified and filtered RF signal is fed into an electro-optical modulator (EOM). The phase of the RF signal is tuned via the phase rotator ϕ. The oscillator contains two optical delay lines, one in the optical and the other in the RF feedback loops. The dispersions of the delay lines, β2Σ and β˜2Σ, can be changed independently. The nonlinearity of the delay line in the optical loop, γΣ, should be taken into account, while the nonlinearity of the second delay line is generally not important because of the comparably low optical power in it.

Fig. 2.
Fig. 2.

Theoretical calculations of the phase noise of COEOs having a 300 m main optical loop (the other parameters are presented in the next section) with and without a dispersive element in front of the PD for chirp compensation.

Fig. 3.
Fig. 3.

Theoretically calculated phase noise of two COEOs with 300 and 30 m optical loops (the other parameters are discussed in the text). (a) Calculations for the complete model. (b) Calculations done with the simplified model [Eq. (30)].

Fig. 4.
Fig. 4.

Typical phase noise of experimentally demonstrated COEO (blue line) and the theoretical plot obtained using the theoretical model (red line). The peaks below 100 kHz in the experimental spectrum are artifacts of the measurement system.

Fig. 5.
Fig. 5.

Amplitude noise measured for COEO operating in mode-locked (blue line) and not-mode-locked (red line) regimes. The noise drops significantly when the mode-locked regime is achieved.

Fig. 6.
Fig. 6.

Typical optical pulses (a) and associated optical spectrum and (b) generated by a COEO. The pulse shape was measured using an Agilent wide-bandwidth oscilloscope.

Fig. 7.
Fig. 7.

Autocorrelation traces of optical pulses emitted by the COEO without (blue solid line) and with (red-dashed line) a 290 m of SMF-28 fiber link used to compensate for the pulse chirp. It is clearly seen that the fiber link results in reduction of the pulse duration and increase of the pulse peak power.

Fig. 8.
Fig. 8.

Phase noise of a COEO measured without (blue line) and with (red line) of a 500 m link of SMF28 optical fiber. The fiber insertion improves the phase noise of the oscillator. The results of analytical calculations are given by solid lines. Thermal noise limit of the phase noise of the oscillator is shown by the dashed line.

Equations (41)

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

TRAT+i2(β2Σ+iΩf2)2At2=iγΣ|A|2A+12(gΣαΣ)AAΔAM2ωm2(ttm)2+TRF(t,T),
A(T,t)=[Eπτ]1/2[exp(tξ2τ)2](1+iq)eiΩ(tξ),
F(t,T)F(t,T)=DFF+δ(tt)δ(TT),
F(t,T)F(t,T)=DF+Fδ(tt)δ(TT),
DFF+=ω0TR[gΣ(nsp1)+αΣ+1+q22τ2Ωf2+12ΔAMωm2τ2],
DF+F=ω0TRgΣnsp,
ξ(T)=1Et|A(T,t)|2dt,
Ω(T)=i2E[A*AtAA*t]dt,
dξdT=β2ΣΩf2qTRΩf2ΩΔAMωm2τ2TR(ξtm)+Fξ,
dΩdT=1+q2TRΩf2τ2Ω+ΔAMωm2qTR(ξtm)+FΩ.
Fξ(T)=1Et[A*F(t,T)+F(t,T)A]dt,
FΩ(T)=iE[A*tF(t,T)F(t,T)At]dt,
[A*F(t,T)t+A*tF(t,T)]dt=A*F(t,T)|=0.
Fξ(T)Fξ(T)=Dξξδ(TT)=τ22E[DFF++DF+F]δ(TT),
FΩ(T)FΩ(T)=DΩΩδ(TT)=1+q22Eτ2[DFF++DF+F]δ(TT),
Fξ(T)FΩ(T)=DξΩδ(TT)=12E[i(DFF+DF+F)q(DFF++DF+F)]δ(TT),
FΩ(T)Fξ(T)=DΩξδ(TT)=12E[i(DFF+DF+F)q(DFF++DF+F)]δ(TT).
tm(ω)eiωTmw1=ΔRFΔRF+2iω[ξ(ω)+Fshot(ω)]+Fmw(ω),
Fmw(T)Fmw*(T)=Dmwδ(TT),
Dmw=1ωm2FkBΘPmw|D,
Fshot(T)Fshot(T)=Dshotδ(TT),
Dshot=1ωm22ω0ηPpd,
T˜+=TRΔAMωm2τ2,
T=TRτ2Ωf21+q2,
qβ2ΣΩf2q21+q21.
tm(T)=tm(ω)eiωTdω2π,
tm(ω)=tm(T)eiωTdT,
tm(ω)=iω[Fξ(ω)τ2(β2ΣΩf2q)(1+q2)(1+iωT)FΩ(ω)+1+iωT˜+T˜+(Fshot(ω)+Fmw(ω))].
Stm(ω)=δtm*(T)δtm(T+T)eiωTdT
Stm(ω)1ω2[Dξξ+DΩΩ1+ω2T2τ4(β2ΣΩf2q)2(1+q2)2+(Dmw+Dshot)1+ω2T˜+2T˜+2τ2(β2ΣΩf2q)(1+q2)(1+iωT)DξΩτ2(β2ΣΩf2q)(1+q2)(1iωT)DΩξ].
Sϕ=1ω2[ω0PaveαΣωm2τ2TR2(1+β2Σ2Ωf4q2(1+q2)(1+ω2T2))+[2ω0ηPpd+FkBΘPmw|D]1+ω2T˜+2T˜+2].
tm(ω)eiωTmw1=ΔRFΔRF+2iω[ξ(ω)β˜2ΣΩ(ω)+Fshot(ω)]+Fmw(ω).
β˜2Στ2q1+q2
dξ(T)dT=ξ(T+TR)ξ(T)TR,
dΩ(T)dT=Ω(T+TR)Ω(T)TR.
ξ(T+TR)=(1ΔAMωm2τ2)ξ(T)+ΔAMωm2τ2tm(T)β2ΣΩf2qΩf2Ω(T)+F˜ξ(T),
Ω(T+TR)=(11+q2Ωf2τ2)Ω(T)+ΔAMωm2q[ξ(T)tm(T)]+F˜Ω(T).
F˜ξ(T)=Tmsinc(ωTm2)Fξ(ω)eiωTdω2π,
F˜Ω(T)=Tmsinc(ωTm2)FΩ(ω)eiωTdω2π,
(1eiωTRΔAMωm2τ2)ξ(ω)+ΔAMωm2τ2tm(ω)β2ΣΩf2qΩf2Ω(ω)+F˜ξ(ω)=0,
(1eiωTR1+q2Ωf2τ2)Ω(ω)+ΔAMωm2q[ξ(ω)tm(ω)]+F˜Ω(ω)=0.

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