Abstract

There is great interest in developing high performance optical frequency metrology based around mode-locked fibre lasers because of their low cost, small size and long-term turnkey operation when compared to the solid-state alternative. We present a method for stabilising the offset frequency of a fibre-based laser comb using a 2f – 3f technique based around a unique fibre that exhibits strong resonant dispersive wave emission. This fibre requires lower power than conventional highly non-linear fibre to generate a suitable signal for offset frequency stabilisation and this in turn avoids the complexity of additional nonlinear steps. We generate an offset frequency signal from the mixing of a wavelength-shifted second harmonic comb with a third harmonic of the comb. Additionally, we have stabilised the repetition rate of the laser to a level better than 10-14τ, limited by the measurement system noise floor. We present the means for complete and precise measurement of the transfer function of the laser frequency controls.

© 2009 Optical Society of America

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  1. L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
    [CrossRef] [PubMed]
  2. S. Cundiff and J. Ye, "Colloquium: femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325 - 342 (2003).
    [CrossRef]
  3. H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, "Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327 - 332 (1999).
    [CrossRef]
  4. R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hansch, "Optical Clockworks and Measurement of Laser Frequencies with a Mode-Locked Frequency Comb," IEEE J. of Quantum Electron. 37, 1493 - 1501 (2001).
    [CrossRef]
  5. J. Hall, "Nobel Lecture: Defining and measuring optical frequencies," Rev. of Mod. Phys. 78, 1279 - 1295 (2006).
    [CrossRef]
  6. J. Ye, H. Schnatz, and L. Hollberg, "Optical Frequency Combs: From Frequency Metrology to Optical Phase Control," IEEE J.Sel. Top. in Quantum Electron. 9, 1041 - 1058 (2003).
    [CrossRef]
  7. W. Swann, J. J. McFerran, I. Coddington, N. Newbury, I. Hartl, M. Fermann, P. Westbrook, J. Nicholson, K. Feder, C. Langrock, and M. M. Fejer, "Fibre-laser frequency combs with subhertz relative linewidths," Opt. Lett. 31, 3046 - 3048 (2006).
    [CrossRef] [PubMed]
  8. J. J. McFerran, W. Swann, B. Washburn, and N. Newbury, "Elimination of pump-indced frequency jitter on fibre-laser frequency combs," Opt. Lett. 31, 1997 - 1999 (2006).
    [CrossRef] [PubMed]
  9. TOPTICA Photonics AG Lochhamer Schlag 19 82166 Graefelfing (Munich) Germany.
  10. F. Benabid, F. Biancalana, P. S. Light, F. Couny, A. N. Luiten, P. J. Roberts, J. Peng, and A. Sokolov, "Fourthorder dispersion mediated solitonic radiations in HC-PCF cladding," Opt. Lett. 332680 - 2682 (2008).
    [CrossRef] [PubMed]
  11. N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602 - 2607 (1995).
    [CrossRef] [PubMed]
  12. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124 - 135 (2004).
    [CrossRef] [PubMed]
  13. S. Dawkins, J. J. McFerran, and A. N. Luiten, "Considerations on the Measurement of the Stability of Oscillators with Frequency Counters," IEEE Trans. Ultrason., Ferroelectr. Freq. Control. 54, 918 - 925 (2007).
    [CrossRef]
  14. P. Kubina, P. Adel, F. Adler, G. Grosche, T. H¨ansch, R. Holzwarth, A. Leitenstorfer, B. Lipphardt, and H. Schnatz, "Long term comparison of two fiber based frequency comb systems," Opt. Express 13904 - 909 (2005).
    [CrossRef] [PubMed]
  15. N. Newbury, W. Swann, I. Coddington, L. Lorini, J. Bergquist, and S. Diddams, "Fiber laser-based frequency combs with high relative frequency stability," 2007 Joint Frequency Control Symposium and 21st European Frequency and Time Forum, 980 - 983(2007).
  16. F.-L. Hong, K. Minoshima, A. Onae, H. Inaba, H. Takada, A. Hirai, H. Matsumoto, T. Sugiura, and M. Yoshida, "Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by secondharmonic generation of a mode-locked fiber laser," Opt. Lett. 28, 1516 - 1518 (2003).
    [CrossRef] [PubMed]
  17. N. Newbury and B. Washburn, "Theory of the frequency comb output from a femtosecond fiber laser," IEEE J.of Quantum Electron. 41, 1388 - 1402 (2005).
    [CrossRef]

2008 (1)

2007 (1)

S. Dawkins, J. J. McFerran, and A. N. Luiten, "Considerations on the Measurement of the Stability of Oscillators with Frequency Counters," IEEE Trans. Ultrason., Ferroelectr. Freq. Control. 54, 918 - 925 (2007).
[CrossRef]

2006 (3)

2005 (1)

2004 (2)

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124 - 135 (2004).
[CrossRef] [PubMed]

2003 (2)

2001 (1)

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hansch, "Optical Clockworks and Measurement of Laser Frequencies with a Mode-Locked Frequency Comb," IEEE J. of Quantum Electron. 37, 1493 - 1501 (2001).
[CrossRef]

1999 (1)

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, "Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327 - 332 (1999).
[CrossRef]

1995 (1)

N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602 - 2607 (1995).
[CrossRef] [PubMed]

Adel, P.

Adler, F.

Akhmediev, N.

N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602 - 2607 (1995).
[CrossRef] [PubMed]

Bartels, A.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

Benabid, F.

Bi, Z.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

Biancalana, F.

Coddington, I.

Couny, F.

Cristiani, I.

Cundiff, S.

S. Cundiff and J. Ye, "Colloquium: femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325 - 342 (2003).
[CrossRef]

Dawkins, S.

S. Dawkins, J. J. McFerran, and A. N. Luiten, "Considerations on the Measurement of the Stability of Oscillators with Frequency Counters," IEEE Trans. Ultrason., Ferroelectr. Freq. Control. 54, 918 - 925 (2007).
[CrossRef]

Degiorgio, V.

Diddams, S. A.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

Dunlop, A.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, "Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327 - 332 (1999).
[CrossRef]

Feder, K.

Fejer, M. M.

Fermann, M.

Grosche, G.

H¨ansch, T.

H¨ansch, T. W.

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hansch, "Optical Clockworks and Measurement of Laser Frequencies with a Mode-Locked Frequency Comb," IEEE J. of Quantum Electron. 37, 1493 - 1501 (2001).
[CrossRef]

Hall, J.

J. Hall, "Nobel Lecture: Defining and measuring optical frequencies," Rev. of Mod. Phys. 78, 1279 - 1295 (2006).
[CrossRef]

Hartl, I.

Hirai, A.

Hollberg, L.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

J. Ye, H. Schnatz, and L. Hollberg, "Optical Frequency Combs: From Frequency Metrology to Optical Phase Control," IEEE J.Sel. Top. in Quantum Electron. 9, 1041 - 1058 (2003).
[CrossRef]

Holzwarth, R.

P. Kubina, P. Adel, F. Adler, G. Grosche, T. H¨ansch, R. Holzwarth, A. Leitenstorfer, B. Lipphardt, and H. Schnatz, "Long term comparison of two fiber based frequency comb systems," Opt. Express 13904 - 909 (2005).
[CrossRef] [PubMed]

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hansch, "Optical Clockworks and Measurement of Laser Frequencies with a Mode-Locked Frequency Comb," IEEE J. of Quantum Electron. 37, 1493 - 1501 (2001).
[CrossRef]

Hong, F.-L.

Inaba, H.

Karlsson, M.

N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602 - 2607 (1995).
[CrossRef] [PubMed]

Keller, U.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, "Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327 - 332 (1999).
[CrossRef]

Kubina, P.

Langrock, C.

Leitenstorfer, A.

Light, P. S.

Lipphardt, B.

Luiten, A. N.

F. Benabid, F. Biancalana, P. S. Light, F. Couny, A. N. Luiten, P. J. Roberts, J. Peng, and A. Sokolov, "Fourthorder dispersion mediated solitonic radiations in HC-PCF cladding," Opt. Lett. 332680 - 2682 (2008).
[CrossRef] [PubMed]

S. Dawkins, J. J. McFerran, and A. N. Luiten, "Considerations on the Measurement of the Stability of Oscillators with Frequency Counters," IEEE Trans. Ultrason., Ferroelectr. Freq. Control. 54, 918 - 925 (2007).
[CrossRef]

Ma, L. S.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

Matsumoto, H.

McFerran, J. J.

Minoshima, K.

Newbury, N.

Nicholson, J.

Oates, C.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

Onae, A.

Peng, J.

Roberts, P. J.

Robertsson, L.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

Schnatz, H.

P. Kubina, P. Adel, F. Adler, G. Grosche, T. H¨ansch, R. Holzwarth, A. Leitenstorfer, B. Lipphardt, and H. Schnatz, "Long term comparison of two fiber based frequency comb systems," Opt. Express 13904 - 909 (2005).
[CrossRef] [PubMed]

J. Ye, H. Schnatz, and L. Hollberg, "Optical Frequency Combs: From Frequency Metrology to Optical Phase Control," IEEE J.Sel. Top. in Quantum Electron. 9, 1041 - 1058 (2003).
[CrossRef]

Sokolov, A.

Steinmeyer, G.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, "Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327 - 332 (1999).
[CrossRef]

Stenger, J.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, "Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327 - 332 (1999).
[CrossRef]

Sugiura, T.

Sutter, D.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, "Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327 - 332 (1999).
[CrossRef]

Swann, W.

Takada, H.

Tartara, L.

Tediosi, R.

Telle, H.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, "Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327 - 332 (1999).
[CrossRef]

Udem, T.

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hansch, "Optical Clockworks and Measurement of Laser Frequencies with a Mode-Locked Frequency Comb," IEEE J. of Quantum Electron. 37, 1493 - 1501 (2001).
[CrossRef]

Washburn, B.

J. J. McFerran, W. Swann, B. Washburn, and N. Newbury, "Elimination of pump-indced frequency jitter on fibre-laser frequency combs," Opt. Lett. 31, 1997 - 1999 (2006).
[CrossRef] [PubMed]

N. Newbury and B. Washburn, "Theory of the frequency comb output from a femtosecond fiber laser," IEEE J.of Quantum Electron. 41, 1388 - 1402 (2005).
[CrossRef]

Westbrook, P.

Wilpers, G.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

Windeler, R. S.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

Ye, J.

S. Cundiff and J. Ye, "Colloquium: femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325 - 342 (2003).
[CrossRef]

J. Ye, H. Schnatz, and L. Hollberg, "Optical Frequency Combs: From Frequency Metrology to Optical Phase Control," IEEE J.Sel. Top. in Quantum Electron. 9, 1041 - 1058 (2003).
[CrossRef]

Yoshida, M.

Zimmermann, M.

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hansch, "Optical Clockworks and Measurement of Laser Frequencies with a Mode-Locked Frequency Comb," IEEE J. of Quantum Electron. 37, 1493 - 1501 (2001).
[CrossRef]

Zucco, M.

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

Appl. Phys. B (1)

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. Sutter, and U. Keller, "Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327 - 332 (1999).
[CrossRef]

IEEE J. of Quantum Electron. (1)

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hansch, "Optical Clockworks and Measurement of Laser Frequencies with a Mode-Locked Frequency Comb," IEEE J. of Quantum Electron. 37, 1493 - 1501 (2001).
[CrossRef]

IEEE Trans. Ultrason., Ferroelectr. Freq. Control. (1)

S. Dawkins, J. J. McFerran, and A. N. Luiten, "Considerations on the Measurement of the Stability of Oscillators with Frequency Counters," IEEE Trans. Ultrason., Ferroelectr. Freq. Control. 54, 918 - 925 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (1)

N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602 - 2607 (1995).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

S. Cundiff and J. Ye, "Colloquium: femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325 - 342 (2003).
[CrossRef]

Rev. of Mod. Phys. (1)

J. Hall, "Nobel Lecture: Defining and measuring optical frequencies," Rev. of Mod. Phys. 78, 1279 - 1295 (2006).
[CrossRef]

Science (1)

L. S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, "Optical Frequency Synthesis and Comparison with Uncertainty at the 10−19 Level," Science 303, 1843 - 1845 (2004).
[CrossRef] [PubMed]

Other (4)

N. Newbury, W. Swann, I. Coddington, L. Lorini, J. Bergquist, and S. Diddams, "Fiber laser-based frequency combs with high relative frequency stability," 2007 Joint Frequency Control Symposium and 21st European Frequency and Time Forum, 980 - 983(2007).

N. Newbury and B. Washburn, "Theory of the frequency comb output from a femtosecond fiber laser," IEEE J.of Quantum Electron. 41, 1388 - 1402 (2005).
[CrossRef]

J. Ye, H. Schnatz, and L. Hollberg, "Optical Frequency Combs: From Frequency Metrology to Optical Phase Control," IEEE J.Sel. Top. in Quantum Electron. 9, 1041 - 1058 (2003).
[CrossRef]

TOPTICA Photonics AG Lochhamer Schlag 19 82166 Graefelfing (Munich) Germany.

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Figures (6)

Fig. 1.
Fig. 1.

A micrograph of the Kagome fibre in cross section. In this experiment, we couple 780 nm light into any of the six equivalent intersections adjacent to the core (one of which has been labelled A), resulting in a comb with maximum intensity at 520 nm (green). If we couple into any of the intersection points B, we obtain a comb with a maximum at 570 nm (yellow). Similarly, launching into any of the points C results in 480 nm light (blue).

Fig. 2.
Fig. 2.

Three spectra showing the second harmonic comb of the laser (grey-heavy solid) with a peak at 780 nm; the spectrum from the Kagome fibre (red-dashed) when light is launched into the intersection adjacent to the core (labelled A in Fig. 1); the third harmonic comb (blue-solid) generated incidentally in the nonlinear crystal.

Fig. 3.
Fig. 3.

The experimental layout showing how the third harmonic comb from the laser is separated from the fundamental and second harmonic comb with dichroic mirrrors and temporally delayed so that its pulses will arrive at the photodetector at the same time as the lower wavelength component of the spectrally shifted pulses emitted by the Kagome fibre. The interference of these two pulses on the detector produces a beat note at the offset frequency of the comb. The inset shows the beat-note as it appears at the photodiode. The feedback paths for the repetition rate and offset frequency detection are also shown.

Fig. 4.
Fig. 4.

Amplitude transfer functions of (left) the PZT used to control the repetition rate, and (right) the pump laser current modulation used to control the offset frequency.

Fig. 5.
Fig. 5.

Square root Allan variance of repetition rate. Crosses represent the free running repetition rate and circles the noise floor of the measurement system. The measured repetition rate was indistinguishable from this noise floor; triangles represent the inferred repetition rate stability using the uncertainty values in the measurement system noise floor.

Fig. 6.
Fig. 6.

SRAV of unlocked (filled squares) and locked (hollow circles) offset frequency of the fibre laser, referred to a mode at 500 THz.

Equations (4)

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

f n 1560 = n f r + f ceo
f h 780 = h f r + 2 f ceo f m 520 = m f r + 3 f ceo
f j RDW 520 = j f r + 2 f ceo f p RDW 1620 = p f r + 2 f ceo
f m 520 f j RDW 520 = ( m j ) f r + f ceo

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