Abstract

We characterize the timing jitter of passively mode-locked, femtosecond, erbium fiber lasers with unprecedented resolution, enabling the observation of quantum-origin timing jitter up to the Nyquist frequency. For a pair of nearly identical 79.4MHz dispersion-managed lasers with an output pulse energy of 450pJ, the high-frequency jitter was found to be 2.6fs [10kHz, 39.7MHz]. The results agree well with theoretical noise models over more than three decades, extending to the Nyquist frequency. It is also found that unexpected noise may occur if care is not taken in optimizing the mode-locked state.

© 2010 Optical Society of America

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2010

2009

2008

2007

2006

2005

2003

2002

2001

W. Ng, R. Stephens, D. Persechini, and K. V. Reddy, Electron. Lett. 37, 113 (2001).
[CrossRef]

1997

S. Namiki and H. A. Haus, IEEE J. Quantum Electron. 33, 649 (1997).
[CrossRef]

C. X. Yu, S. Namiki, and H. A. Haus, IEEE J. Quantum Electron. 33, 660 (1997).
[CrossRef]

1995

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

1993

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

1989

Abeles, J.

Benkler, E.

Bergquist, J. C.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Braun, A.

Byun, H.

Callicoatt, B. E.

Chen, J.

Chen, Y. F.

Coddington, I.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Coq, Y. L.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Cotcutt, M.

Cox, J.

Cox, J. A.

J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, Nat. Photon. 2, 733 (2008).
[CrossRef]

Delfyett, P. J.

DePriest, C. M.

Diddams, S. A.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Feder, K. S.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Foreman, S. M.

Grein, M. E.

Hall, J. L.

Haus, H. A.

F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen, and H. A. Haus, J. Opt. Soc. Am. B 19, 2609(2002).
[CrossRef]

M. E. Grein, L. A. Jiang, H. A. Haus, E. P. Ippen, C. Mcneilage, J. H. Searls, and R. S. Windeler, Opt. Lett. 27, 957 (2002).
[CrossRef]

C. X. Yu, S. Namiki, and H. A. Haus, IEEE J. Quantum Electron. 33, 660 (1997).
[CrossRef]

S. Namiki and H. A. Haus, IEEE J. Quantum Electron. 33, 649 (1997).
[CrossRef]

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

E. P. Ippen, H. A. Haus, and L. Y. Liu, J. Opt. Soc. Am. B 6, 1736 (1989).
[CrossRef]

Haverkamp, N.

Ippen, E. P.

Jiang, J.

Jiang, L. A.

Jones, D.

Jones, D. J.

Kapteyn, H. C.

Kärtner, F. X.

Kim, J.

Kracht, D.

Krainer, L.

Lee, H. L. T.

Liu, L. Y.

Loehl, F.

Lorini, L.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Ma, L. S.

Mcneilage, C.

Mecozzi, A.

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

Mirin, R. P.

Morgner, U.

Murnane, M. M.

Namiki, S.

S. Namiki and H. A. Haus, IEEE J. Quantum Electron. 33, 649 (1997).
[CrossRef]

C. X. Yu, S. Namiki, and H. A. Haus, IEEE J. Quantum Electron. 33, 660 (1997).
[CrossRef]

Nelson, L. E.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Neumann, J.

Newbury, N. R.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Ng, W.

W. Ng, R. Stephens, D. Persechini, and K. V. Reddy, Electron. Lett. 37, 113 (2001).
[CrossRef]

Nicholson, J. W.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Oates, C. W.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Paschotta, R.

Persechini, D.

W. Ng, R. Stephens, D. Persechini, and K. V. Reddy, Electron. Lett. 37, 113 (2001).
[CrossRef]

Prochnow, O.

Pudo, D.

Quraishi, Q.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Ram, R. J.

Rana, F.

Reddy, K. V.

W. Ng, R. Stephens, D. Persechini, and K. V. Reddy, Electron. Lett. 37, 113 (2001).
[CrossRef]

Rudin, B.

Sanford, N. A.

Schlager, J. B.

Schlarb, H.

Schlatter, A.

Searls, J. H.

Shelton, R. K.

Sickler, J. W.

Spühler, G. J.

Stephens, R.

W. Ng, R. Stephens, D. Persechini, and K. V. Reddy, Electron. Lett. 37, 113 (2001).
[CrossRef]

Swann, W. C.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Tamura, K.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Telle, H. R.

Wandt, D.

Westbrook, P. S.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

Windeler, R. S.

Wong, F. N. C.

Ye, J.

Yilmaz, T.

Yu, C. X.

C. X. Yu, S. Namiki, and H. A. Haus, IEEE J. Quantum Electron. 33, 660 (1997).
[CrossRef]

Zeller, S. C.

Zhang, Z.

Electron. Lett.

W. Ng, R. Stephens, D. Persechini, and K. V. Reddy, Electron. Lett. 37, 113 (2001).
[CrossRef]

IEEE J. Quantum Electron.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

S. Namiki and H. A. Haus, IEEE J. Quantum Electron. 33, 649 (1997).
[CrossRef]

C. X. Yu, S. Namiki, and H. A. Haus, IEEE J. Quantum Electron. 33, 660 (1997).
[CrossRef]

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photon.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photon. 1, 283 (2007).
[CrossRef]

J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, Nat. Photon. 2, 733 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (2)

Fig. 1
Fig. 1

Schematic of the timing jitter measurement based on BOC with a PPKTP crystal. The repetition rates of a pair of similar ultrafast lasers are tightly locked with a kilohertz feedback loop via direct optical detection of the signal from the BOC. The jitter beyond the loop bandwidth, known as the out-of-loop timing jitter, is measured at the BOC and reveals the timing jitter between the two lasers. DM-1, dichroic mirror coating (T, 775 nm ; R, 1550 nm ); DM-2, dichroic mirror (T, 1550 nm ; R, 775 nm ); Er, erbium-doped fiber; ISO, Faraday isolator; PBS, polarizing beam splitter; PZT, piezo mirror actuator.

Fig. 2
Fig. 2

(a) and (b) Jitter spectral density for the 79.4 MHz stretched pulse fiber lasers (divided by 2 for the equivalent noise of a single laser) and the integrated timing jitter (divided by 2 . (a) shows that the integrated jitter is 2.6 fs [ 10 kHz , 40 MHz ], and only 0.7 fs [ 100 kHz , 40 MHz ]. Also shown are the combined detector and instrument noise floor and the theoretical shot noise. For comparison, the theoretical slope, 1 / f 2 , described by Eq. (1) is shown. Note that the measurement extends to the Nyquist frequency ( f rep / 2 ) without being limited by the instrument, detector, or shot noise. (b) shows the measured jitter [ 1 kHz , 50 MHz ] for the same lasers in a noisier mode-locked state, with a spike at f rep / 2 contributing 5.5 fs to the jitter.

Equations (1)

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S Δ t ( f ) = σ t 2 2 ( 1 cos ( 2 π T R f ) ) .

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