Abstract

We report on experimental studies of coherence and fluctuations in noise-like pulse trains generated by ultrafast fiber oscillators. By measuring the degree of first-order coherence using a Young’s-type interference experiment, we prove the lack of phase coherence across the seemingly regular array of pulses. We further quantify the pulse-to-pulse fluctuations by recording the single-shot spectra of the megahertz pulse train, and experimentally demonstrate the existence of spectral fluctuations that remain unresolved in conventional time-averaged ensemble measurements. Phase incoherence and spectral fluctuations are contrasted with quantified coherence and spectral stability when the laser is soliton mode-locked.

© 2013 Optical Society of America

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C. Aguergaray, N. G. R. Broderick, M. Erkintalo, J. S. Y. Chen, and V. Kruglov, Opt. Express 20, 10545 (2012).
[CrossRef]

M. Erkintalo, C. Aguergaray, A. Runge, and N. G. R. Broderick, Opt. Express 20, 22669 (2012).
[CrossRef]

S. Smirnov, S. Kobtsev, S. Kukarin, and A. Ivanenko, Opt. Express 20, 27447 (2012).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).
[CrossRef]

A. Boucon, B. Barviau, J. Fatome, C. Finot, T. Sylvestre, M. W. Lee, P. Grelu, and G. Millot, Appl. Phys. B 106, 283 (2012).
[CrossRef]

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, Phys. Rev. A 85, 013828 (2012).
[CrossRef]

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

2011

2010

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

2009

2008

D. R. Solli, J. Chou, and B. Jalali, Nat. Photonics 2, 48 (2008).
[CrossRef]

2007

L. M. Zhao, D. Y. Tang, J. Wu, X. Q. Fu, and S. C. Wen, Opt. Express 15, 2145 (2007).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

2006

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

2004

2003

2002

J. M. Dudley and S. Coen, Opt. Lett. 27, 1180 (2002).
[CrossRef]

Th. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef]

2001

M. Onorato, A. R. Osborne, M. Serio, and S. Bertone, Phys. Rev. Lett. 86, 5831 (2001).
[CrossRef]

1999

P. Kelkar, F. Coppinger, A. S. Bhushan, and B. Jalali, Electron. Lett. 35, 1661 (1999).
[CrossRef]

1997

Y. C. Tong, L. Y. Chang, and H. K. Tsang, Electron. Lett. 33, 983 (1997).
[CrossRef]

M. Horowitz, Y. Barad, and Y. Silberberg, Opt. Lett. 22, 799 (1997).
[CrossRef]

1996

J. M. Dudley, C. M. Loh, and J. D. Harvey, Quantum Semiclass. Opt. 8, 1029 (1996).
[CrossRef]

1988

1970

M. A. Duguay, J. W. Hansen, and S. L. Shapiro, IEEE J. Quantum Electron. QE-6, 725 (1970).
[CrossRef]

Aguergaray, C.

Akhmediev, N.

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).
[CrossRef]

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

J. M. Soto-Crespo, Ph. Grelu, and N. Akhmediev, Phys. Rev. E 84, 016604 (2011).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Barad, Y.

Barviau, B.

A. Boucon, B. Barviau, J. Fatome, C. Finot, T. Sylvestre, M. W. Lee, P. Grelu, and G. Millot, Appl. Phys. B 106, 283 (2012).
[CrossRef]

Ben Salem, A.

Bertone, S.

M. Onorato, A. R. Osborne, M. Serio, and S. Bertone, Phys. Rev. Lett. 86, 5831 (2001).
[CrossRef]

Bhushan, A. S.

P. Kelkar, F. Coppinger, A. S. Bhushan, and B. Jalali, Electron. Lett. 35, 1661 (1999).
[CrossRef]

Boucon, A.

A. Boucon, B. Barviau, J. Fatome, C. Finot, T. Sylvestre, M. W. Lee, P. Grelu, and G. Millot, Appl. Phys. B 106, 283 (2012).
[CrossRef]

Broderick, N. G. R.

Chabchoub, A.

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).
[CrossRef]

Chang, L. Y.

Y. C. Tong, L. Y. Chang, and H. K. Tsang, Electron. Lett. 33, 983 (1997).
[CrossRef]

Chen, J. S. Y.

Chen, K. P.

Chen, T.

Chou, J.

D. R. Solli, J. Chou, and B. Jalali, Nat. Photonics 2, 48 (2008).
[CrossRef]

Coen, S.

Coppinger, F.

P. Kelkar, F. Coppinger, A. S. Bhushan, and B. Jalali, Electron. Lett. 35, 1661 (1999).
[CrossRef]

Dias, F.

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Doran, N. J.

Dudley, J. M.

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

M. Erkintalo, G. Genty, and J. M. Dudley, Opt. Lett. 34, 2468 (2009).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

X. Gu, M. Kimmel, A. Shreenath, R. Trebino, J. M. Dudley, S. Coen, and R. Windeler, Opt. Express 11, 2697 (2003).
[CrossRef]

J. M. Dudley and S. Coen, Opt. Lett. 27, 1180 (2002).
[CrossRef]

J. M. Dudley, C. M. Loh, and J. D. Harvey, Quantum Semiclass. Opt. 8, 1029 (1996).
[CrossRef]

Duguay, M. A.

M. A. Duguay, J. W. Hansen, and S. L. Shapiro, IEEE J. Quantum Electron. QE-6, 725 (1970).
[CrossRef]

Egorov, O.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, Phys. Rev. A 85, 013828 (2012).
[CrossRef]

Erkintalo, M.

Fatome, J.

A. Boucon, B. Barviau, J. Fatome, C. Finot, T. Sylvestre, M. W. Lee, P. Grelu, and G. Millot, Appl. Phys. B 106, 283 (2012).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Finot, C.

A. Boucon, B. Barviau, J. Fatome, C. Finot, T. Sylvestre, M. W. Lee, P. Grelu, and G. Millot, Appl. Phys. B 106, 283 (2012).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Fu, X. Q.

Genty, G.

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

M. Erkintalo, G. Genty, and J. M. Dudley, Opt. Lett. 34, 2468 (2009).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Goda, K.

K. Goda and B. Jalali, Nat. Photonics 7, 102 (2013).
[CrossRef]

Godin, T.

Grajales-Coutiño, R.

Grelu, P.

A. Boucon, B. Barviau, J. Fatome, C. Finot, T. Sylvestre, M. W. Lee, P. Grelu, and G. Millot, Appl. Phys. B 106, 283 (2012).
[CrossRef]

Grelu, Ph.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

J. M. Soto-Crespo, Ph. Grelu, and N. Akhmediev, Phys. Rev. E 84, 016604 (2011).
[CrossRef]

Gu, X.

Hänsch, T. W.

Th. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef]

Hansen, J. W.

M. A. Duguay, J. W. Hansen, and S. L. Shapiro, IEEE J. Quantum Electron. QE-6, 725 (1970).
[CrossRef]

Harvey, J. D.

J. M. Dudley, C. M. Loh, and J. D. Harvey, Quantum Semiclass. Opt. 8, 1029 (1996).
[CrossRef]

Heberle, A. P.

Herink, G.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

Hernández-García, J.

Hoffmann, N.

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).
[CrossRef]

Holzwarth, R.

Th. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef]

Horowitz, M.

Ibarra-Escamilla, B.

Iliew, R.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, Phys. Rev. A 85, 013828 (2012).
[CrossRef]

Ivanenko, A.

Jalali, B.

K. Goda and B. Jalali, Nat. Photonics 7, 102 (2013).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, Nat. Photonics 2, 48 (2008).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

P. Kelkar, F. Coppinger, A. S. Bhushan, and B. Jalali, Electron. Lett. 35, 1661 (1999).
[CrossRef]

Kelkar, P.

P. Kelkar, F. Coppinger, A. S. Bhushan, and B. Jalali, Electron. Lett. 35, 1661 (1999).
[CrossRef]

Kibler, B.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Kimmel, M.

Knox, W.

Kobtsev, S.

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Kruglov, V.

Kudlinski, A.

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Kukarin, S.

Kuzin, E.

Lacourt, P. A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Larger, L.

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Latkin, A.

Lecaplain, C.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

Lederer, F.

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, Phys. Rev. A 85, 013828 (2012).
[CrossRef]

Lee, M. W.

A. Boucon, B. Barviau, J. Fatome, C. Finot, T. Sylvestre, M. W. Lee, P. Grelu, and G. Millot, Appl. Phys. B 106, 283 (2012).
[CrossRef]

Loh, C. M.

J. M. Dudley, C. M. Loh, and J. D. Harvey, Quantum Semiclass. Opt. 8, 1029 (1996).
[CrossRef]

Lu, F.

Merolla, J. M.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Millot, G.

A. Boucon, B. Barviau, J. Fatome, C. Finot, T. Sylvestre, M. W. Lee, P. Grelu, and G. Millot, Appl. Phys. B 106, 283 (2012).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Mussot, A.

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Onorato, M.

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).
[CrossRef]

M. Onorato, A. R. Osborne, M. Serio, and S. Bertone, Phys. Rev. Lett. 86, 5831 (2001).
[CrossRef]

Osborne, A. R.

M. Onorato, A. R. Osborne, M. Serio, and S. Bertone, Phys. Rev. Lett. 86, 5831 (2001).
[CrossRef]

Pottiez, O.

Ratner, J.

M. Rhodes, G. Steinmeyer, J. Ratner, and R. Trebino, Laser Photon. Rev. 7, 557 (2013).
[CrossRef]

Rhodes, M.

M. Rhodes, G. Steinmeyer, J. Ratner, and R. Trebino, Laser Photon. Rev. 7, 557 (2013).
[CrossRef]

Ropers, C.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Runge, A.

Serio, M.

M. Onorato, A. R. Osborne, M. Serio, and S. Bertone, Phys. Rev. Lett. 86, 5831 (2001).
[CrossRef]

Shapiro, S. L.

M. A. Duguay, J. W. Hansen, and S. L. Shapiro, IEEE J. Quantum Electron. QE-6, 725 (1970).
[CrossRef]

Shreenath, A.

Silberberg, Y.

Smirnov, S.

Solli, D. R.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, Nat. Photonics 2, 48 (2008).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Soto-Crespo, J. M.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, Phys. Rev. Lett. 108, 233901 (2012).
[CrossRef]

J. M. Soto-Crespo, Ph. Grelu, and N. Akhmediev, Phys. Rev. E 84, 016604 (2011).
[CrossRef]

Stefani, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
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Figures (4)

Fig. 1.
Fig. 1.

Characteristics of the laser in the soliton (a), (c), (e) and NL (b), (d), (f) regimes. (a), (b) Output spectrum; (c), (d) autocorrelation trace, and (e), (f) output pulse trains measured with a photodiode (PD).

Fig. 2.
Fig. 2.

Experimental coherence setup.

Fig. 3.
Fig. 3.

Spectral interference pattern of consecutive pulses when the laser is operated in the (a) soliton and (b) NL regime. Solid curves show the spectrum at the output of the interferometer and dashed curves indicate the laser output spectrum for comparison.

Fig. 4.
Fig. 4.

Single-shot spectral results for (a) soliton and (b) NL regime. (Top) The solid curves show the mean spectrum computed from the single-shot measurements and the dashed curve shows an example of a single spectral realization. (Bottom) Linear scale density maps of the single-shot spectra over 1000 consecutive roundtrips. The spectral axis is derived from the oscilloscope timebase.

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