Abstract

In a harmonically mode-locked laser multiple optical pulses propagate inside the laser cavity. The noise in different pulses inside the laser cavity is in general correlated. Information regarding the sign and magnitude of the noise correlations is contained in the distribution of the spectral weight among the supermode noise peaks that appear in the pulse energy and timing noise spectral densities. We show that the supermode noise spectrum obtained experimentally by measurement of the photodetector current noise spectral density can be used to determine the correlations in the energy and the timing noise of different pulses in the laser cavity. We also present simple models for the timing noise in harmonically mode-locked lasers that demonstrate the relationship between the noise correlations and the supermode noise peaks.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2002

2001

D. A. Yanson, M. W. Street, S. D. McDougall, I. G. Thayne, J. H. Marsh, and E. A. Avrutin, “Ultrafast harmonic mode-locking of monolithic compound-cavity laser diodes incorporating photonic-bandgap reflectors,” IEEE J. Quantum Electron. 38, 1–11 (2001).
[CrossRef]

C. M. DePriest, A. Braun, J. H. Abeles, E. Park, and P. Delfyett, Jr., “10-GHz ultralow-noise optical sampling stream from a semiconductor diode ring laser,” IEEE Photonics Technol. Lett. 13, 1109–1111 (2001).
[CrossRef]

T. Yilmaz, C. M. DePriest, and P. Delfyett, Jr., “Complete noise characterisation of external cavity semiconductor laser hybridity modelocked at 10 GHz,” Electron. Lett. 37, 1338–1339 (2001).
[CrossRef]

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

2000

1999

T. R. Clark, T. F. Carruthers, P. J. Mathews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

E. Yoshida and M. Nakazawa, “Measurement of timing jitter and pulse energy fluctuation of a PLL regeneratively mode-locked fiber laser,” IEEE Photonics Technol. Lett. 11, 548–550 (1999).
[CrossRef]

1997

A. B. Grudinin and S. Gray, “Passive harmonic mode locking in soliton fiber lasers,” J. Opt. Soc. Am. B 14, 144–154 (1997).
[CrossRef]

T. Shimizu, I. Ogura, and H. Yokoyama, “860 GHz rate asymmetric colliding pulse modelocked diode lasers,” Electron. Lett. 33, 1868–1869 (1997).
[CrossRef]

J. S. Wey, J. Goldhar, and G. L. Burdge, “Active harmonic modelocking of an erbium fiber laser with intracavity Fabry-Perot filters,” J. Lightwave Technol. 15, 1171–1180 (1997).
[CrossRef]

N. Onodera, “Supermode beat suppression in harmonically mode-locked erbium-doped fiber lasers with composite cavity structure,” Electron. Lett. 33, 962–963 (1997).
[CrossRef]

1996

M. Nakazawa, K. Tamura, and E. Yoshida, “Supermode noise suppression in a harmonically modelocked fibre laser by selfphase modulation and spectral filtering,” Electron. Lett. 32, 461–463 (1996).
[CrossRef]

1995

J. F. Martins-Filho, E. A. Avrutin, C. N. Ironside, and J. S. Roberts, “Monolithic multiple colliding pulse mode-locked quantum-well lasers, experiment and theory,” IEEE J. Sel. Top. Quantum Electron. 1, 539–552 (1995).
[CrossRef]

1994

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

1993

X. Shan and D. M. Spirit, “Novel method to suppress noise in harmonically modelocked erbium fibre lasers,” Electron. Lett. 29, 979–981 (1993).
[CrossRef]

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

G. T. Harvey and L. F. Mollenauer, “Harmonically mode-locked fiber ring lasers with an internal Fabry-Perot stabilizer for soliton transmission,” Opt. Lett. 18, 107–109 (1993).
[CrossRef] [PubMed]

1992

D. R. Hjelme and A. R. Mickelson, “Theory of timing jitter in actively mode-locked lasers,” IEEE J. Quantum Electron. 28, 1594–1606 (1992).
[CrossRef]

H. A. Haus and A. Mecozzi, “Long term storage of a bit stream of solitons,” Opt. Lett. 17, 1500–1502 (1992).
[CrossRef]

1991

D. J. Derickson, P. A. Morton, and J. E. Bowers, “Comparison of timing jitter in external and monolithic cavity mode-locked semiconductor lasers,” Appl. Phys. Lett. 59, 3372–3374 (1991).
[CrossRef]

A. J. Lowery and I. W. Marshall, “Numerical simulations of 1.5 μm actively mode-locked semiconductor lasers including dispersive elements and chirp,” IEEE J. Quantum Electron. 27, 1981–1989 (1991).
[CrossRef]

1986

D. Von Der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[CrossRef]

1972

M. F. Becker, D. J. Kuizenga, and A. E. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron. 8, 687–693 (1972).
[CrossRef]

Abeles, J.

Abeles, J. H.

C. M. DePriest, A. Braun, J. H. Abeles, E. Park, and P. Delfyett, Jr., “10-GHz ultralow-noise optical sampling stream from a semiconductor diode ring laser,” IEEE Photonics Technol. Lett. 13, 1109–1111 (2001).
[CrossRef]

Avrutin, E. A.

D. A. Yanson, M. W. Street, S. D. McDougall, I. G. Thayne, J. H. Marsh, and E. A. Avrutin, “Ultrafast harmonic mode-locking of monolithic compound-cavity laser diodes incorporating photonic-bandgap reflectors,” IEEE J. Quantum Electron. 38, 1–11 (2001).
[CrossRef]

J. F. Martins-Filho, E. A. Avrutin, C. N. Ironside, and J. S. Roberts, “Monolithic multiple colliding pulse mode-locked quantum-well lasers, experiment and theory,” IEEE J. Sel. Top. Quantum Electron. 1, 539–552 (1995).
[CrossRef]

Becker, M. F.

M. F. Becker, D. J. Kuizenga, and A. E. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron. 8, 687–693 (1972).
[CrossRef]

Betts, G. E.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

Blondel, M.

O. Pottiez, O. Deparis, R. Kiyan, M. Haelterman, P. Emplit, P. Megret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron. 38, 252–259 (2002).
[CrossRef]

Bowers, J. E.

D. J. Derickson, P. A. Morton, and J. E. Bowers, “Comparison of timing jitter in external and monolithic cavity mode-locked semiconductor lasers,” Appl. Phys. Lett. 59, 3372–3374 (1991).
[CrossRef]

Braun, A.

C. M. DePriest, T. Yilmaz, P. Delfyett, Jr., S. Etemad, A. Braun, and J. Abeles, “Ultralow noise and supermode suppression in an actively mode-locked external cavity semiconductor diode ring laser,” Opt. Lett. 27, 219–721 (2002).
[CrossRef]

C. M. DePriest, A. Braun, J. H. Abeles, E. Park, and P. Delfyett, Jr., “10-GHz ultralow-noise optical sampling stream from a semiconductor diode ring laser,” IEEE Photonics Technol. Lett. 13, 1109–1111 (2001).
[CrossRef]

Burdge, G. L.

J. S. Wey, J. Goldhar, and G. L. Burdge, “Active harmonic modelocking of an erbium fiber laser with intracavity Fabry-Perot filters,” J. Lightwave Technol. 15, 1171–1180 (1997).
[CrossRef]

Carruthers, T. F.

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling III, “Pulse dropout in harmonically mode-locked fiber lasers,” IEEE Photonics Technol. Lett. 12, 266–268 (2000).
[CrossRef]

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling, “Theoretical and experimental study of harmonically modelocked fiber lasers for optical communication systems,” J. Lightwave Technol. 18, 1565–1574 (2000).
[CrossRef]

T. R. Clark, T. F. Carruthers, P. J. Mathews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

Clark, T. R.

T. R. Clark, T. F. Carruthers, P. J. Mathews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

Delfyett Jr., P.

C. M. DePriest, T. Yilmaz, P. Delfyett, Jr., S. Etemad, A. Braun, and J. Abeles, “Ultralow noise and supermode suppression in an actively mode-locked external cavity semiconductor diode ring laser,” Opt. Lett. 27, 219–721 (2002).
[CrossRef]

T. Yilmaz, C. M. DePriest, and P. Delfyett, Jr., “Complete noise characterisation of external cavity semiconductor laser hybridity modelocked at 10 GHz,” Electron. Lett. 37, 1338–1339 (2001).
[CrossRef]

C. M. DePriest, A. Braun, J. H. Abeles, E. Park, and P. Delfyett, Jr., “10-GHz ultralow-noise optical sampling stream from a semiconductor diode ring laser,” IEEE Photonics Technol. Lett. 13, 1109–1111 (2001).
[CrossRef]

Deparis, O.

O. Pottiez, O. Deparis, R. Kiyan, M. Haelterman, P. Emplit, P. Megret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron. 38, 252–259 (2002).
[CrossRef]

DePriest, C. M.

C. M. DePriest, T. Yilmaz, P. Delfyett, Jr., S. Etemad, A. Braun, and J. Abeles, “Ultralow noise and supermode suppression in an actively mode-locked external cavity semiconductor diode ring laser,” Opt. Lett. 27, 219–721 (2002).
[CrossRef]

T. Yilmaz, C. M. DePriest, and P. Delfyett, Jr., “Complete noise characterisation of external cavity semiconductor laser hybridity modelocked at 10 GHz,” Electron. Lett. 37, 1338–1339 (2001).
[CrossRef]

C. M. DePriest, A. Braun, J. H. Abeles, E. Park, and P. Delfyett, Jr., “10-GHz ultralow-noise optical sampling stream from a semiconductor diode ring laser,” IEEE Photonics Technol. Lett. 13, 1109–1111 (2001).
[CrossRef]

Derickson, D. J.

D. J. Derickson, P. A. Morton, and J. E. Bowers, “Comparison of timing jitter in external and monolithic cavity mode-locked semiconductor lasers,” Appl. Phys. Lett. 59, 3372–3374 (1991).
[CrossRef]

Duling, I. N.

Duling III, I. N.

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling III, “Pulse dropout in harmonically mode-locked fiber lasers,” IEEE Photonics Technol. Lett. 12, 266–268 (2000).
[CrossRef]

T. R. Clark, T. F. Carruthers, P. J. Mathews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

Emplit, P.

O. Pottiez, O. Deparis, R. Kiyan, M. Haelterman, P. Emplit, P. Megret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron. 38, 252–259 (2002).
[CrossRef]

Etemad, S.

Goldhar, J.

J. S. Wey, J. Goldhar, and G. L. Burdge, “Active harmonic modelocking of an erbium fiber laser with intracavity Fabry-Perot filters,” J. Lightwave Technol. 15, 1171–1180 (1997).
[CrossRef]

Gray, S.

Grein, M. E.

Gross, M. C.

Grudinin, A. B.

Haelterman, M.

O. Pottiez, O. Deparis, R. Kiyan, M. Haelterman, P. Emplit, P. Megret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron. 38, 252–259 (2002).
[CrossRef]

Hargreaves, J. J.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

Harvey, G. T.

Haus, H. A.

Hjelme, D. R.

D. R. Hjelme and A. R. Mickelson, “Theory of timing jitter in actively mode-locked lasers,” IEEE J. Quantum Electron. 28, 1594–1606 (1992).
[CrossRef]

Horowitz, M.

M. Horowitz and C. R. Menyuk, “Analysis of pulse dropout in harmonically mode-locked fiber lasers by use of the Lyapunov method,” Opt. Lett. 40, 40–42 (2000).
[CrossRef]

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling III, “Pulse dropout in harmonically mode-locked fiber lasers,” IEEE Photonics Technol. Lett. 12, 266–268 (2000).
[CrossRef]

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling, “Theoretical and experimental study of harmonically modelocked fiber lasers for optical communication systems,” J. Lightwave Technol. 18, 1565–1574 (2000).
[CrossRef]

Ippen, E. P.

Ironside, C. N.

J. F. Martins-Filho, E. A. Avrutin, C. N. Ironside, and J. S. Roberts, “Monolithic multiple colliding pulse mode-locked quantum-well lasers, experiment and theory,” IEEE J. Sel. Top. Quantum Electron. 1, 539–552 (1995).
[CrossRef]

Jiang, L. A.

Juodawlkis, P. W.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

T. G. Ulmer, M. C. Gross, K. M. Patel, J. T. Simmons, and P. W. Juodawlkis, “160-Gb/s optically time-division multiplexed link with all-optical demultiplexing,” J. Lightwave Technol. 18, 1964–1977 (2000).
[CrossRef]

Kimura, Y.

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

Kiyan, R.

O. Pottiez, O. Deparis, R. Kiyan, M. Haelterman, P. Emplit, P. Megret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron. 38, 252–259 (2002).
[CrossRef]

Kuizenga, D. J.

M. F. Becker, D. J. Kuizenga, and A. E. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron. 8, 687–693 (1972).
[CrossRef]

Lowery, A. J.

A. J. Lowery and I. W. Marshall, “Numerical simulations of 1.5 μm actively mode-locked semiconductor lasers including dispersive elements and chirp,” IEEE J. Quantum Electron. 27, 1981–1989 (1991).
[CrossRef]

Margalit, M.

Marsh, J. H.

D. A. Yanson, M. W. Street, S. D. McDougall, I. G. Thayne, J. H. Marsh, and E. A. Avrutin, “Ultrafast harmonic mode-locking of monolithic compound-cavity laser diodes incorporating photonic-bandgap reflectors,” IEEE J. Quantum Electron. 38, 1–11 (2001).
[CrossRef]

Marshall, I. W.

A. J. Lowery and I. W. Marshall, “Numerical simulations of 1.5 μm actively mode-locked semiconductor lasers including dispersive elements and chirp,” IEEE J. Quantum Electron. 27, 1981–1989 (1991).
[CrossRef]

Martins-Filho, J. F.

J. F. Martins-Filho, E. A. Avrutin, C. N. Ironside, and J. S. Roberts, “Monolithic multiple colliding pulse mode-locked quantum-well lasers, experiment and theory,” IEEE J. Sel. Top. Quantum Electron. 1, 539–552 (1995).
[CrossRef]

Mathews, P. J.

T. R. Clark, T. F. Carruthers, P. J. Mathews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

McDougall, S. D.

D. A. Yanson, M. W. Street, S. D. McDougall, I. G. Thayne, J. H. Marsh, and E. A. Avrutin, “Ultrafast harmonic mode-locking of monolithic compound-cavity laser diodes incorporating photonic-bandgap reflectors,” IEEE J. Quantum Electron. 38, 1–11 (2001).
[CrossRef]

McNeilage, C.

Mecozzi, A.

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

H. A. Haus and A. Mecozzi, “Long term storage of a bit stream of solitons,” Opt. Lett. 17, 1500–1502 (1992).
[CrossRef]

Megret, P.

O. Pottiez, O. Deparis, R. Kiyan, M. Haelterman, P. Emplit, P. Megret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron. 38, 252–259 (2002).
[CrossRef]

Menyuk, C. R.

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling, “Theoretical and experimental study of harmonically modelocked fiber lasers for optical communication systems,” J. Lightwave Technol. 18, 1565–1574 (2000).
[CrossRef]

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling III, “Pulse dropout in harmonically mode-locked fiber lasers,” IEEE Photonics Technol. Lett. 12, 266–268 (2000).
[CrossRef]

M. Horowitz and C. R. Menyuk, “Analysis of pulse dropout in harmonically mode-locked fiber lasers by use of the Lyapunov method,” Opt. Lett. 40, 40–42 (2000).
[CrossRef]

Mickelson, A. R.

D. R. Hjelme and A. R. Mickelson, “Theory of timing jitter in actively mode-locked lasers,” IEEE J. Quantum Electron. 28, 1594–1606 (1992).
[CrossRef]

Mollenauer, L. F.

Morton, P. A.

D. J. Derickson, P. A. Morton, and J. E. Bowers, “Comparison of timing jitter in external and monolithic cavity mode-locked semiconductor lasers,” Appl. Phys. Lett. 59, 3372–3374 (1991).
[CrossRef]

Nakazawa, M.

E. Yoshida and M. Nakazawa, “Measurement of timing jitter and pulse energy fluctuation of a PLL regeneratively mode-locked fiber laser,” IEEE Photonics Technol. Lett. 11, 548–550 (1999).
[CrossRef]

M. Nakazawa, K. Tamura, and E. Yoshida, “Supermode noise suppression in a harmonically modelocked fibre laser by selfphase modulation and spectral filtering,” Electron. Lett. 32, 461–463 (1996).
[CrossRef]

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

O’Donnell, F. J.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

Ogura, I.

T. Shimizu, I. Ogura, and H. Yokoyama, “860 GHz rate asymmetric colliding pulse modelocked diode lasers,” Electron. Lett. 33, 1868–1869 (1997).
[CrossRef]

Onodera, N.

N. Onodera, “Supermode beat suppression in harmonically mode-locked erbium-doped fiber lasers with composite cavity structure,” Electron. Lett. 33, 962–963 (1997).
[CrossRef]

Park, E.

C. M. DePriest, A. Braun, J. H. Abeles, E. Park, and P. Delfyett, Jr., “10-GHz ultralow-noise optical sampling stream from a semiconductor diode ring laser,” IEEE Photonics Technol. Lett. 13, 1109–1111 (2001).
[CrossRef]

Patel, K. M.

Pottiez, O.

O. Pottiez, O. Deparis, R. Kiyan, M. Haelterman, P. Emplit, P. Megret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron. 38, 252–259 (2002).
[CrossRef]

Ray, K. G.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

Roberts, J. S.

J. F. Martins-Filho, E. A. Avrutin, C. N. Ironside, and J. S. Roberts, “Monolithic multiple colliding pulse mode-locked quantum-well lasers, experiment and theory,” IEEE J. Sel. Top. Quantum Electron. 1, 539–552 (1995).
[CrossRef]

Searls, J. H.

Shan, X.

X. Shan and D. M. Spirit, “Novel method to suppress noise in harmonically modelocked erbium fibre lasers,” Electron. Lett. 29, 979–981 (1993).
[CrossRef]

Shimizu, T.

T. Shimizu, I. Ogura, and H. Yokoyama, “860 GHz rate asymmetric colliding pulse modelocked diode lasers,” Electron. Lett. 33, 1868–1869 (1997).
[CrossRef]

Siegman, A. E.

M. F. Becker, D. J. Kuizenga, and A. E. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron. 8, 687–693 (1972).
[CrossRef]

Simmons, J. T.

Spirit, D. M.

X. Shan and D. M. Spirit, “Novel method to suppress noise in harmonically modelocked erbium fibre lasers,” Electron. Lett. 29, 979–981 (1993).
[CrossRef]

Street, M. W.

D. A. Yanson, M. W. Street, S. D. McDougall, I. G. Thayne, J. H. Marsh, and E. A. Avrutin, “Ultrafast harmonic mode-locking of monolithic compound-cavity laser diodes incorporating photonic-bandgap reflectors,” IEEE J. Quantum Electron. 38, 1–11 (2001).
[CrossRef]

Tamura, K.

M. Nakazawa, K. Tamura, and E. Yoshida, “Supermode noise suppression in a harmonically modelocked fibre laser by selfphase modulation and spectral filtering,” Electron. Lett. 32, 461–463 (1996).
[CrossRef]

Thayne, I. G.

D. A. Yanson, M. W. Street, S. D. McDougall, I. G. Thayne, J. H. Marsh, and E. A. Avrutin, “Ultrafast harmonic mode-locking of monolithic compound-cavity laser diodes incorporating photonic-bandgap reflectors,” IEEE J. Quantum Electron. 38, 1–11 (2001).
[CrossRef]

Twichell, J. C.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

Ulmer, T. G.

Von Der Linde, D.

D. Von Der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[CrossRef]

Wasserman, J. L.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

Wey, J. S.

J. S. Wey, J. Goldhar, and G. L. Burdge, “Active harmonic modelocking of an erbium fiber laser with intracavity Fabry-Perot filters,” J. Lightwave Technol. 15, 1171–1180 (1997).
[CrossRef]

Williamson, R. C.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

Windeler, R. S.

Yanson, D. A.

D. A. Yanson, M. W. Street, S. D. McDougall, I. G. Thayne, J. H. Marsh, and E. A. Avrutin, “Ultrafast harmonic mode-locking of monolithic compound-cavity laser diodes incorporating photonic-bandgap reflectors,” IEEE J. Quantum Electron. 38, 1–11 (2001).
[CrossRef]

Yilmaz, T.

C. M. DePriest, T. Yilmaz, P. Delfyett, Jr., S. Etemad, A. Braun, and J. Abeles, “Ultralow noise and supermode suppression in an actively mode-locked external cavity semiconductor diode ring laser,” Opt. Lett. 27, 219–721 (2002).
[CrossRef]

T. Yilmaz, C. M. DePriest, and P. Delfyett, Jr., “Complete noise characterisation of external cavity semiconductor laser hybridity modelocked at 10 GHz,” Electron. Lett. 37, 1338–1339 (2001).
[CrossRef]

Yokoyama, H.

T. Shimizu, I. Ogura, and H. Yokoyama, “860 GHz rate asymmetric colliding pulse modelocked diode lasers,” Electron. Lett. 33, 1868–1869 (1997).
[CrossRef]

Yoshida, E.

E. Yoshida and M. Nakazawa, “Measurement of timing jitter and pulse energy fluctuation of a PLL regeneratively mode-locked fiber laser,” IEEE Photonics Technol. Lett. 11, 548–550 (1999).
[CrossRef]

M. Nakazawa, K. Tamura, and E. Yoshida, “Supermode noise suppression in a harmonically modelocked fibre laser by selfphase modulation and spectral filtering,” Electron. Lett. 32, 461–463 (1996).
[CrossRef]

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

Younger, R. D.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

Yu, C. X.

Appl. Phys. B

D. Von Der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[CrossRef]

Appl. Phys. Lett.

D. J. Derickson, P. A. Morton, and J. E. Bowers, “Comparison of timing jitter in external and monolithic cavity mode-locked semiconductor lasers,” Appl. Phys. Lett. 59, 3372–3374 (1991).
[CrossRef]

Electron. Lett.

N. Onodera, “Supermode beat suppression in harmonically mode-locked erbium-doped fiber lasers with composite cavity structure,” Electron. Lett. 33, 962–963 (1997).
[CrossRef]

X. Shan and D. M. Spirit, “Novel method to suppress noise in harmonically modelocked erbium fibre lasers,” Electron. Lett. 29, 979–981 (1993).
[CrossRef]

T. Yilmaz, C. M. DePriest, and P. Delfyett, Jr., “Complete noise characterisation of external cavity semiconductor laser hybridity modelocked at 10 GHz,” Electron. Lett. 37, 1338–1339 (2001).
[CrossRef]

T. R. Clark, T. F. Carruthers, P. J. Mathews, and I. N. Duling III, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

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

M. Nakazawa, K. Tamura, and E. Yoshida, “Supermode noise suppression in a harmonically modelocked fibre laser by selfphase modulation and spectral filtering,” Electron. Lett. 32, 461–463 (1996).
[CrossRef]

T. Shimizu, I. Ogura, and H. Yokoyama, “860 GHz rate asymmetric colliding pulse modelocked diode lasers,” Electron. Lett. 33, 1868–1869 (1997).
[CrossRef]

IEEE J. Quantum Electron.

D. A. Yanson, M. W. Street, S. D. McDougall, I. G. Thayne, J. H. Marsh, and E. A. Avrutin, “Ultrafast harmonic mode-locking of monolithic compound-cavity laser diodes incorporating photonic-bandgap reflectors,” IEEE J. Quantum Electron. 38, 1–11 (2001).
[CrossRef]

M. F. Becker, D. J. Kuizenga, and A. E. Siegman, “Harmonic mode locking of the Nd:YAG laser,” IEEE J. Quantum Electron. 8, 687–693 (1972).
[CrossRef]

A. J. Lowery and I. W. Marshall, “Numerical simulations of 1.5 μm actively mode-locked semiconductor lasers including dispersive elements and chirp,” IEEE J. Quantum Electron. 27, 1981–1989 (1991).
[CrossRef]

D. R. Hjelme and A. R. Mickelson, “Theory of timing jitter in actively mode-locked lasers,” IEEE J. Quantum Electron. 28, 1594–1606 (1992).
[CrossRef]

O. Pottiez, O. Deparis, R. Kiyan, M. Haelterman, P. Emplit, P. Megret, and M. Blondel, “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity,” IEEE J. Quantum Electron. 38, 252–259 (2002).
[CrossRef]

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

IEEE J. Sel. Top. Quantum Electron.

J. F. Martins-Filho, E. A. Avrutin, C. N. Ironside, and J. S. Roberts, “Monolithic multiple colliding pulse mode-locked quantum-well lasers, experiment and theory,” IEEE J. Sel. Top. Quantum Electron. 1, 539–552 (1995).
[CrossRef]

IEEE Photonics Technol. Lett.

E. Yoshida and M. Nakazawa, “Measurement of timing jitter and pulse energy fluctuation of a PLL regeneratively mode-locked fiber laser,” IEEE Photonics Technol. Lett. 11, 548–550 (1999).
[CrossRef]

C. M. DePriest, A. Braun, J. H. Abeles, E. Park, and P. Delfyett, Jr., “10-GHz ultralow-noise optical sampling stream from a semiconductor diode ring laser,” IEEE Photonics Technol. Lett. 13, 1109–1111 (2001).
[CrossRef]

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling III, “Pulse dropout in harmonically mode-locked fiber lasers,” IEEE Photonics Technol. Lett. 12, 266–268 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49, 1840–1853 (2001).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Lett.

Other

C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, New York, 1996).

L. A. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

F. Rana and R. J. Ram, “Noise and timing jitter in active and hybrid mode-locked semiconductor lasers,” Conference on Lasers and Electro-optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 6–7.

A. V. Oppenheim, A. S. Willsky, and I. T. Young, Signals and Systems (Prentice Hall, Englewood Cliffs, N.J., 1983).

T. R. Clark, T. F. Carruthers, I. N. Duling III, and P. J. Mathews, “Sub-10 femtosecond timing jitter of a 10-GHz harmonically mode-locked fiber laser,” Proceedings of the Optical Fiber Communication Conference 1999 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. PD24/1–3 Supplement.

C. M. DePriest, P. Delfyett, Jr., J. H. Abeles, and A. Braun, “Ultrahigh-stability photonic sampling streams from an actively-modelocked semiconductor diode ring laser,” Conference on Lasers and Electro-optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 89–90.

J. J. Hargreaves, P. W. Juodawlkis, J. J. Plant, J. P. Donnelly, and J. C. Twichell, “Residual phase-noise measurements of actively mode-locked fiber and semiconductor lasers,” IEEE Lasers and Electro-optics Society 2001 Annual Meeting (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), pp. 115–116.

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Figures (6)

Fig. 1
Fig. 1

Timing noise correlation function Rtt[n] (normalized to the RMS timing jitter) plotted for the output pulses from a fundamentally mode-locked laser. TR is assumed to be 1 ns; γTR is 0.01π. The RMS timing jitter is assumed to be 100 fs.

Fig. 2
Fig. 2

Timing noise spectral density TRΦtt(Ω) (note the multiplication by TR to conform to the units used in the literature) plotted for a fundamentally mode-locked laser on a linear frequency scale and on a log frequency scale. The timing noise spectral density shown corresponds to the timing noise correlation function in Fig. 1. The cavity round-trip time TR is 1.0 ns; γTR equals 0.01π. The RMS timing jitter is assumed to be 100 fs. The spectral density has identical noise peaks at multiples of the pulse repetition frequency ΩR.

Fig. 3
Fig. 3

Timing noise correlation function Rtt[n] (normalized to the RMS timing jitter) plotted for the output pulses from a laser mode locked at the tenth harmonic (N=10) when the timing noise in different pulses inside the laser cavity is completely uncorrelated. The timing noise in every tenth pulse in the output is correlated. TR is assumed to be 1 ns; γTR is assumed to be 0.01π. The RMS timing jitter is assumed to be 100 fs.

Fig. 4
Fig. 4

Pulse timing noise spectral density TNΦtt(Ω) (note the multiplication by TN to conform to the units used in the literature) plotted for a laser mode locked at the tenth harmonic (N=10) on linear and log frequency scales. The timing noise spectral density shown in the figure corresponds to the timing noise correlation function in Fig. 3. TR is 1.0 ns; TN is 0.1 ns; γNTR is assumed to be 0.01π. The RMS timing jitter is assumed to be 100 fs. The timing noise in different pulses inside the laser cavity is assumed to be completely uncorrelated and, consequently, the periodicity of the noise spectral density is reduced from the pulse repetition frequency (10 GHz) to the cavity round-trip frequency (1 GHz). Supermode noise peaks appear at multiples of the cavity round-trip frequency. All the noise peaks are identical.

Fig. 5
Fig. 5

Pulse timing noise spectral density TNΦtt(Ω) (solid curve) plotted for a laser mode locked at the tenth harmonic (N=10) in the presence of timing (or phase) noise in the RF oscillator (dashed curve) on linear and log frequency scales. TR is 1.0 ns; TN is 0.1 ns; γNTR and κTR are assumed to be 0.01π and 2π10-5, respectively. The RMS timing jitter in the RF oscillator is assumed to be 50 fs. The RMS timing jitter contribution from spontaneous emission and vacuum fluctuations is assumed to be 100 fs. The increased noise in the noise peak at Ω=0 is due to the phase noise of the RF oscillator. The figure shows that the noise contribution form the RF oscillator does not appear in any of the supermode noise peaks. All the supermode noise peaks are identical.

Fig. 6
Fig. 6

Timing noise correlation function Rtt[n] (normalized to the RMS timing jitter) for the output pulses shown for a laser mode locked at the tenth harmonic (N=10) in the presence of phase noise from the RF oscillator. The correlation function corresponds to the timing noise spectral density shown in Fig. 5. The timing noise in all the pulses inside the laser cavity is positively correlated, and therefore the timing noise in the output pulses is correlated at time scales shorter than the cavity round-trip time.

Equations (84)

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Ip(t)=nEpf(t-nT),
I(t)=n(Ep+Δe[n])f(t-nT-Δt[n])n(Ep+Δe[n])f(t-nT)-EpnΔt[n]ddtf(t-nT).
Rαβ[n]=Δα[n]Δβ[0].
Φαβ(Ω)=n=-Rαβ[n]exp(-jΩTn).
Rαβ[n]=T-π/Tπ/T dΩ2πΦαβ(Ω)exp(jΩTn).
σe2=Ree[0]=T-π/Tπ/T dΩ2πΦee(Ω),
σt2=Rtt[0]=T-π/Tπ/T dΩ2πΦtt(Ω).
SII(Ω)(ηrP)21P2TΦee(Ω)+Ω2TΦtt(Ω)+jΩP[Φet(Ω)-Φet*(Ω)],
Δt[n+1]-Δt[n]=-γTRΔt[n]+F[n].
F[n]F[m]=Dδn,m.
Rtt[n]=D2γTR(1-γTR)|n|D2γTR exp(-γTR|n|),sinceγTR1.
σt2=Rtt[0]=D/2γTR.
Φtt(Ω)=σt2 2γTR1+(1-γTR)2-2(1-γTR)cos(ΩTR)
σt2TRn=-2γ(Ω-nΩR)2+γ2,
sinceγTR1.
σe2[measured]=-ΩR/2ΩR/2 dΩ2πTR2 SII(Ω)ηr2.
σt2[measured]=mΩR-ΩR/2mΩR+ΩR/2 dΩ2πSII(Ω)(ΩηrP)2.
Φαβ(Ω)=n=-Rαβ[n]exp(-jΩTNn)=k=-Rαβ[Nk]exp(-jΩTRk).
Δt[n+N]-Δt[n]=-γNTRΔt[n]+FN[n].
FN[n]FN[m]=DNδn,m.
Rtt[n]=DN2γNTR(1-γNTN)|n|DN2γNTR exp(-γNTN|n|)
ifnisanintergralmultipleofN,
Rtt[n]=0otherwise.
σt2=Rtt[0]=DN/2γNTR.
Φtt(Ω)=σt2 2γRTR1+(1-γNTR)2-2(1-γNTR)cos(ΩTR)
σt2NTNn=-2γN(Ω-nΩR)2+γN2,
sinceγNTR1.
σe2=TN-ΩN/2ΩN/2 dΩ2πΦee(Ω)
=NTN-ΩR/2ΩR/2 dΩ2πΦee(Ω),
σt2=TN-ΩN/2ΩN/2 dΩ2πΦtt(Ω)
=NTN-ΩR/2ΩR/2 dΩ2πΦtt(Ω).
σe2[measured]=-ΩN/2ΩN/2 dΩ2πTN2 SII(Ω)ηr2
=N-ΩR/2ΩR/2 dΩ2πTN2 SII(Ω)ηr2.
σt2[measured]=(m-1/2)ΩN(m+1/2)ΩN dΩ2πSII(Ω)(ΩηrP)2
=NmΩN-ΩR/2mΩN+ΩR/2 dΩ2πSII(Ω)(ΩηrP)2.
Rαβ[n]=TN-ΩN/2ΩN/2 dΩ2πΦαβ(Ω)exp(jΩTNn)
p=0N-1 expj2πpNnTN(p-1/2)ΩR(p+1/2)ΩR dΩ2πΦαβ(Ω)
=Rαβ[0]p=0N-1Wαβp expj2πpNn
=Rαβ[0]Cαβ[n],
Wαβp=(p-1/2)ΩR(p+1/2)ΩR dΩ2πΦαβ(Ω)-ΩN/2ΩN/2 dΩ2πΦαβ(Ω),
Cαβ[n]=Rαβ[n]Rαβ[0]=p=0N-1Wαβp expj2πpNn for|n|<N.
J(t)J(t)=σRF2 exp(-κ|t-t|),
Δt[n+N]-Δt[n]=-γNTRΔt[n]+γNTRΔJ[n]
+FN[n].
Φtt(Ω)
=11+(1-γNTR)2-2(1-γNTR)cos(ΩTR)
×DN+σRF2γN2TR2[1-exp(-2κTN)]1+exp(-2κTN)-2 exp(-κTN)cos(ΩTN)
1TNn=-2γN(Ω-nΩR)2+γN21NDN2γNTR+γNσRF22p=-2κ(Ω-pΩN)2+κ2.
σt2=DN2γNTR+σRF2.
Wttp=(1/N)(DN/2γNTR)+σRF2σt2
ifp=0(noisepeaksatmultiplesofΩN),
Wttp=(1/N)(DN/2γNTR)σt2
if1p(N-1)
(forallthesupermodenoisepeaks).
Ctt[n]=1ifn=0σRF2/σt2if1|n|(N-1).
I(t)=ηr-dtχ(t-t)Ip(t)=ηr-dtχ(t-t)n(Ep+Δe[n])f(t-nT-Δt[n])=ηrn(Ep+Δe[n])h(t-nT-Δt[n]),
h(t)=-dtχ(t-t)f(t),
SII(τ)=limT0 1T0
×-T0/2T0/2dt[I(t)-I(t)][I(t+τ)-I(t+τ)].
SII(Ω)=|H(Ω)|2(ηrP)21P2TΦee(Ω)+Ω2TΦtt(Ω)+jΩP[Φet(Ω)-Φet*(Ω)].
M(t)=I(t)a cos{Ωm[t-ΔJ(t)]+Φ},
SMM(Ω)=a2(cos2 ϕ)SII(Ω)+a2(sin2 ϕ)×(ηrP)2Ωm2TΦt-Jt-J(Ω)
-a2(cos ϕ)(sin ϕ)ηr2PΩm[Φet-J(Ω)+Φet-J*(Ω)].
Φt-Jt-J(Ω)=n=(Δt[n]-ΔJ[n])(Δt[0]-ΔJ[0])exp(-jΩTn).
SMM(Ω)|ϕ=π/2=a2(ηrP)2Ωm2TΦt-Jt-J(Ω).
TR ϕ(t, T)T=jν+B22ϕ(t, T)t2+12[G(t)+gm(t)-L(t)]ϕ(t, T)+Fsp(t, T)+Fv(t, T),
ϕ(t, T)npτ1/2Atτ+npτ1/2Δa(T)Atτ+jΔθ(T)Atτ-Δt(T)dAdt-jΔω(T)(t-t0)Atτ,
dΔt(T)dT=-γΔt(T)+F(T),
γ=12TR-dtdgm(t)dtA(t/τ)dA(t/τ)dt-dtdA(t/τ)dtdA(t/τ)dt=M2TRΩR2τ2--dxxA(x)A(x)-dxA(x)A(x)
=M2TRΩR2τ212-dxA(x)A(x).
F(T)F(T)=τ22npTR[(2nsp-1)G+L]12-dxA(x)A(x)δ(T-T),
F(T)F(T)=nspnp LTRτ212-dxA(x)A(x)δ(T-T).
Δt[n+1]-Δt[n]=-γTRΔt[n]+F[n].
F[n]=dTF(T),
F[n]F[m]=Dδn,m,
D=nspnpLτ212-dxA(x)A(x).
σt2=Δt2[n]=D/2γTR.
σt2=nspnpL1MΩR2.
Δt[n+N]-Δt[n]=-γNTRΔt[n]+FN[n],
γN=M2TRΩN2τN212-dxB(x)B(x).
FN[n]FN[m]=DNδn,m,
DN=nspnpLτN212-dxB(x)B(x).
σt2=Δt2[n]=DN/2γNTR.
σt2=nspnpL1MΩN2.

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