Abstract

This paper shows the experimental details of the stabilization scheme that allows full control of the repetition rate and the carrier-envelope offset frequency of a 10 GHz frequency comb based on a femtosecond Ti:sapphire laser. Octave-spanning spectra are produced in nonlinear microstructured optical fiber, in spite of the reduced peak power associated with the 10 GHz repetition rate. Improved stability of the broadened spectrum is obtained by temperature-stabilization of the nonlinear optical fiber. The carrier-envelope offset frequency and the repetition rate are simultaneously frequency stabilized, and their short- and long-term stabilities are characterized. We also measure the transfer of amplitude noise of the pump source to phase noise on the offset frequency and verify an increased sensitivity of the offset frequency to pump power modulation compared to systems with lower repetition rate. Finally, we discuss merits of this 10 GHz system for the generation of low-phase-noise microwaves from the photodetected pulse train.

© 2011 OSA

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  2. A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30, 667–669 (2005).
    [CrossRef] [PubMed]
  3. C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
    [CrossRef] [PubMed]
  4. S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
    [CrossRef] [PubMed]
  5. S. T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Opt. D: Applied Physics 35, R43 (2002).
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    [CrossRef]
  9. S. Zeller, T. Südmeyer, K. Weingarten, and U. Keller, “Passively modelocked 77 GHz Er:Yb:glass laser,” Electronics Letters 43, 32–33 (2007).
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  12. F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-Spaced Optical Frequency Comb Spanning ¿400 nm for Infrared Astronomical Spectrograph Calibration,” Rev. Sci. Ins. 81, 063105 (2010).
    [CrossRef]
  13. M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34, 872–874 (2009).
    [CrossRef] [PubMed]
  14. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hnsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Applied Physics B: Lasers and Optics 96, 251–256 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635–639 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
  22. A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz Self-Referenced Optical Frequency Comb,” Science 326, 681 (2009).
    [CrossRef] [PubMed]
  23. A. Bartels, D. Heinecke, and S. A. Diddams, “Passively mode-locked 10 GHz femtosecond Ti:sapphire laser,” Opt. Lett. 33, 1905–1907 (2008).
    [CrossRef] [PubMed]
  24. T. M. Fortier, A. Bartels, and S. A. Diddams, “Octave-spanning Ti:sapphire laser with a repetition rate ¿ 1 GHz for optical frequency measurements and comparisons,” Opt. Lett. 31, 1011–1013 (2006).
    [CrossRef] [PubMed]
  25. Mention of specific trade names is for technical information only and does not constitute an endorsement by NIST.
  26. For typical frequency counters the input frequency is limited to a few hundreds of megahertz. Thus, the frequencies to analyze in the range of gigahertz have to be converted to lower values to enable counter measurements. In the process of difference or sum frequency generation in a mixing device the actual frequency fluctuations of the input frequencies are preserved. Using a stable reference frequency this allows to shift frequencies without affecting the frequency stability. In contrast, in a frequency division process the noise density and therefore the frequency fluctuations are reduced by the division factor. This leads to an increase in frequency stability. For the offset frequency stabilization and analysis we use a frequency division step to reduce phase fluctuations making the phase lock more robust by extending the capture range of the phase detector. In the data evaluation we account for this division factor to recover the original offset frequency stability.
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    [CrossRef]
  30. R. P. Scott, T. D. Mulder, K. A. Baker, and B. H. Kolner, “Amplitude and phase noise sensitivity of modelocked Ti:sapphire lasers in terms of a complex noise transfer function,” Opt. Express 15, 9090–9095 (2007).
    [CrossRef] [PubMed]
  31. T. M. Fortier, J. Ye, S. T. Cundiff, and R. S. Windeler, “Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase,” Opt. Lett. 27, 445–447 (2002).
    [CrossRef]
  32. B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible Lasers with Subhertz Linewidths,” Phys. Rev. Lett. 82, 3799–3802 (1999).
    [CrossRef]
  33. T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
    [CrossRef]
  34. P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Transactions on Microwave Theory and Techniques47, 1297–1303 (1999).
    [CrossRef]
  35. S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
    [CrossRef] [PubMed]
  36. J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photonics Journal3, 140–151 (2011).
    [CrossRef]

2011

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

A. Martinez and S. Yamashita, “Multi-gigahertz repetition rate passively modelocked fiber lasers using carbon nanotubes,” Opt. Express 19, 6155–6163 (2011).
[CrossRef] [PubMed]

2010

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-Spaced Optical Frequency Comb Spanning ¿400 nm for Infrared Astronomical Spectrograph Calibration,” Rev. Sci. Ins. 81, 063105 (2010).
[CrossRef]

2009

D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, and S. A. Diddams, “Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in 87rubidium,” Phys. Rev. A 80, 053806 (2009).
[CrossRef]

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz Self-Referenced Optical Frequency Comb,” Science 326, 681 (2009).
[CrossRef] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hnsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Applied Physics B: Lasers and Optics 96, 251–256 (2009).
[CrossRef]

S. Xiao, L. Hollberg, and S. A. Diddams, “Generation of a 20 GHz train of subpicosecond pulses with a stabilized optical-frequency-comb generator,” Opt. Lett. 34, 85–87 (2009).
[CrossRef]

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
[CrossRef] [PubMed]

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34, 872–874 (2009).
[CrossRef] [PubMed]

2008

A. Bartels, D. Heinecke, and S. A. Diddams, “Passively mode-locked 10 GHz femtosecond Ti:sapphire laser,” Opt. Lett. 33, 1905–1907 (2008).
[CrossRef] [PubMed]

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full Stabilization of a Microresonator-Based Optical Frequency Comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable Optical Frequency Comb with a Crystalline Whispering Gallery Mode Resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef] [PubMed]

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

2007

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[CrossRef] [PubMed]

S. Zeller, T. Südmeyer, K. Weingarten, and U. Keller, “Passively modelocked 77 GHz Er:Yb:glass laser,” Electronics Letters 43, 32–33 (2007).
[CrossRef]

R. P. Scott, T. D. Mulder, K. A. Baker, and B. H. Kolner, “Amplitude and phase noise sensitivity of modelocked Ti:sapphire lasers in terms of a complex noise transfer function,” Opt. Express 15, 9090–9095 (2007).
[CrossRef] [PubMed]

2006

2005

2004

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

2002

2000

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

1999

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible Lasers with Subhertz Linewidths,” Phys. Rev. Lett. 82, 3799–3802 (1999).
[CrossRef]

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,” Applied Physics B: Lasers and Optics 69, 327–332 (1999).
[CrossRef]

1998

E. Yoshida and M. Nakazawa, “Wavelength tunable 1.0 ps pulse generation in 1.530–1.555 μm region from PLL, regeneratively modelocked fibre laser,” Electronics Letters 34, 1753–1754 (1998).
[CrossRef]

1996

1982

C. Harder, J. Katz, S. Margalit, J. Shacham, and A. Yariv, “Noise equivalent circuit of a semiconductor laser diode,” IEEE Journal of Quantum Electronics QE-18, 333–337 (1982).
[CrossRef]

Araujo-Hauck, C.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hnsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Applied Physics B: Lasers and Optics 96, 251–256 (2009).
[CrossRef]

Arcizet, O.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full Stabilization of a Microresonator-Based Optical Frequency Comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef] [PubMed]

Aschwanden, A.

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

Baker, K. A.

Bartels, A.

Benedick, A. J.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

Bergquist, J. C.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30, 667–669 (2005).
[CrossRef] [PubMed]

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible Lasers with Subhertz Linewidths,” Phys. Rev. Lett. 82, 3799–3802 (1999).
[CrossRef]

Braje, D.

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
[CrossRef] [PubMed]

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-Enhanced Hyperparametric Generation of an Optical Frequency Comb in a Monolithic Highly Nonlinear Fiber Cavity Pumped by a cw Laser,” Phys. Rev. Lett. 102, 193902 (2009).

Braje, D. A.

D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, and S. A. Diddams, “Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in 87rubidium,” Phys. Rev. A 80, 053806 (2009).
[CrossRef]

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34, 872–874 (2009).
[CrossRef] [PubMed]

Caraquitena, J.

C.-B. Huang, Z. Jiang, D. Leaird, J. Caraquitena, and A. Weiner, “Spectral line-by-line shaping for optical and microwave arbitrary waveform generations,” Laser & Photonics Reviews2, 227–248 (2008).
[CrossRef] [PubMed]

Carruthers, T. F.

Cruz, F. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible Lasers with Subhertz Linewidths,” Phys. Rev. Lett. 82, 3799–3802 (1999).
[CrossRef]

Cundiff, S. T.

T. M. Fortier, J. Ye, S. T. Cundiff, and R. S. Windeler, “Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase,” Opt. Lett. 27, 445–447 (2002).
[CrossRef]

S. T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Opt. D: Applied Physics 35, R43 (2002).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Datta, S.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photonics Journal3, 140–151 (2011).
[CrossRef]

Del’Haye, P.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full Stabilization of a Microresonator-Based Optical Frequency Comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef] [PubMed]

Delfyett, P. J.

Diddams, S.

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-Enhanced Hyperparametric Generation of an Optical Frequency Comb in a Monolithic Highly Nonlinear Fiber Cavity Pumped by a cw Laser,” Phys. Rev. Lett. 102, 193902 (2009).

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photonics Journal3, 140–151 (2011).
[CrossRef]

Diddams, S. A.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-Spaced Optical Frequency Comb Spanning ¿400 nm for Infrared Astronomical Spectrograph Calibration,” Rev. Sci. Ins. 81, 063105 (2010).
[CrossRef]

D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, and S. A. Diddams, “Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in 87rubidium,” Phys. Rev. A 80, 053806 (2009).
[CrossRef]

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz Self-Referenced Optical Frequency Comb,” Science 326, 681 (2009).
[CrossRef] [PubMed]

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34, 872–874 (2009).
[CrossRef] [PubMed]

S. Xiao, L. Hollberg, and S. A. Diddams, “Generation of a 20 GHz train of subpicosecond pulses with a stabilized optical-frequency-comb generator,” Opt. Lett. 34, 85–87 (2009).
[CrossRef]

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
[CrossRef] [PubMed]

A. Bartels, D. Heinecke, and S. A. Diddams, “Passively mode-locked 10 GHz femtosecond Ti:sapphire laser,” Opt. Lett. 33, 1905–1907 (2008).
[CrossRef] [PubMed]

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[CrossRef] [PubMed]

T. M. Fortier, A. Bartels, and S. A. Diddams, “Octave-spanning Ti:sapphire laser with a repetition rate ¿ 1 GHz for optical frequency measurements and comparisons,” Opt. Lett. 31, 1011–1013 (2006).
[CrossRef] [PubMed]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30, 667–669 (2005).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Duling, I. N.

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,” Applied Physics B: Lasers and Optics 69, 327–332 (1999).
[CrossRef]

Esman, R. D.

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Transactions on Microwave Theory and Techniques47, 1297–1303 (1999).
[CrossRef]

Fendel, P.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

Fortier, T.

Fortier, T. M.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, and S. A. Diddams, “Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in 87rubidium,” Phys. Rev. A 80, 053806 (2009).
[CrossRef]

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34, 872–874 (2009).
[CrossRef] [PubMed]

T. M. Fortier, A. Bartels, and S. A. Diddams, “Octave-spanning Ti:sapphire laser with a repetition rate ¿ 1 GHz for optical frequency measurements and comparisons,” Opt. Lett. 31, 1011–1013 (2006).
[CrossRef] [PubMed]

T. M. Fortier, J. Ye, S. T. Cundiff, and R. S. Windeler, “Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase,” Opt. Lett. 27, 445–447 (2002).
[CrossRef]

Frankel, M. Y.

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Transactions on Microwave Theory and Techniques47, 1297–1303 (1999).
[CrossRef]

Gee, S.

Glenday, A. G.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Harder, C.

C. Harder, J. Katz, S. Margalit, J. Shacham, and A. Yariv, “Noise equivalent circuit of a semiconductor laser diode,” IEEE Journal of Quantum Electronics QE-18, 333–337 (1982).
[CrossRef]

Hati, A.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photonics Journal3, 140–151 (2011).
[CrossRef]

Heinecke, D.

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz Self-Referenced Optical Frequency Comb,” Science 326, 681 (2009).
[CrossRef] [PubMed]

A. Bartels, D. Heinecke, and S. A. Diddams, “Passively mode-locked 10 GHz femtosecond Ti:sapphire laser,” Opt. Lett. 33, 1905–1907 (2008).
[CrossRef] [PubMed]

Heinecke, D. C.

D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, and S. A. Diddams, “Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in 87rubidium,” Phys. Rev. A 80, 053806 (2009).
[CrossRef]

Hnsch, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hnsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Applied Physics B: Lasers and Optics 96, 251–256 (2009).
[CrossRef]

Hollberg, L.

D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, and S. A. Diddams, “Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in 87rubidium,” Phys. Rev. A 80, 053806 (2009).
[CrossRef]

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17, 3331–3340 (2009).
[CrossRef] [PubMed]

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34, 872–874 (2009).
[CrossRef] [PubMed]

S. Xiao, L. Hollberg, and S. A. Diddams, “Generation of a 20 GHz train of subpicosecond pulses with a stabilized optical-frequency-comb generator,” Opt. Lett. 34, 85–87 (2009).
[CrossRef]

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[CrossRef] [PubMed]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30, 667–669 (2005).
[CrossRef] [PubMed]

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-Enhanced Hyperparametric Generation of an Optical Frequency Comb in a Monolithic Highly Nonlinear Fiber Cavity Pumped by a cw Laser,” Phys. Rev. Lett. 102, 193902 (2009).

Holzwarth, R.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hnsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Applied Physics B: Lasers and Optics 96, 251–256 (2009).
[CrossRef]

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full Stabilization of a Microresonator-Based Optical Frequency Comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef] [PubMed]

Huang, C.-B.

C.-B. Huang, Z. Jiang, D. Leaird, J. Caraquitena, and A. Weiner, “Spectral line-by-line shaping for optical and microwave arbitrary waveform generations,” Laser & Photonics Reviews2, 227–248 (2008).
[CrossRef] [PubMed]

Ilchenko, V. S.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable Optical Frequency Comb with a Crystalline Whispering Gallery Mode Resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef] [PubMed]

Itano, W. M.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible Lasers with Subhertz Linewidths,” Phys. Rev. Lett. 82, 3799–3802 (1999).
[CrossRef]

Jiang, Y.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

Jiang, Z.

C.-B. Huang, Z. Jiang, D. Leaird, J. Caraquitena, and A. Weiner, “Spectral line-by-line shaping for optical and microwave arbitrary waveform generations,” Laser & Photonics Reviews2, 227–248 (2008).
[CrossRef] [PubMed]

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Joshi, A.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photonics Journal3, 140–151 (2011).
[CrossRef]

Kärtner, F. X.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

Katz, J.

C. Harder, J. Katz, S. Margalit, J. Shacham, and A. Yariv, “Noise equivalent circuit of a semiconductor laser diode,” IEEE Journal of Quantum Electronics QE-18, 333–337 (1982).
[CrossRef]

Keller, U.

S. Zeller, T. Südmeyer, K. Weingarten, and U. Keller, “Passively modelocked 77 GHz Er:Yb:glass laser,” Electronics Letters 43, 32–33 (2007).
[CrossRef]

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

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,” Applied Physics B: Lasers and Optics 69, 327–332 (1999).
[CrossRef]

Kippenberg, T. J.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full Stabilization of a Microresonator-Based Optical Frequency Comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef] [PubMed]

Kirchner, M.

Kirchner, M. S.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34, 872–874 (2009).
[CrossRef] [PubMed]

Kolner, B. H.

Krainer, L.

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

Leaird, D.

C.-B. Huang, Z. Jiang, D. Leaird, J. Caraquitena, and A. Weiner, “Spectral line-by-line shaping for optical and microwave arbitrary waveform generations,” Laser & Photonics Reviews2, 227–248 (2008).
[CrossRef] [PubMed]

Lecomte, S.

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

Lemke, N.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

Li, C.-H.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

Liu, P.-L.

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Transactions on Microwave Theory and Techniques47, 1297–1303 (1999).
[CrossRef]

Lorenser, D.

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

Ludlow, A.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

Maleki, L.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable Optical Frequency Comb with a Crystalline Whispering Gallery Mode Resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef] [PubMed]

Margalit, S.

C. Harder, J. Katz, S. Margalit, J. Shacham, and A. Yariv, “Noise equivalent circuit of a semiconductor laser diode,” IEEE Journal of Quantum Electronics QE-18, 333–337 (1982).
[CrossRef]

Martinez, A.

Matsko, A. B.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable Optical Frequency Comb with a Crystalline Whispering Gallery Mode Resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef] [PubMed]

Mbele, V.

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[CrossRef] [PubMed]

Mulder, T. D.

Nakazawa, M.

E. Yoshida and M. Nakazawa, “Wavelength tunable 1.0 ps pulse generation in 1.530–1.555 μm region from PLL, regeneratively modelocked fibre laser,” Electronics Letters 34, 1753–1754 (1998).
[CrossRef]

Nelson, C.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photonics Journal3, 140–151 (2011).
[CrossRef]

Oates, C. W.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30, 667–669 (2005).
[CrossRef] [PubMed]

Oskay, W. H.

Osterman, S.

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-Spaced Optical Frequency Comb Spanning ¿400 nm for Infrared Astronomical Spectrograph Calibration,” Rev. Sci. Ins. 81, 063105 (2010).
[CrossRef]

Ozharar, S.

Paschotta, R.

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

Phillips, D. F.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

Quinlan, F.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-Spaced Optical Frequency Comb Spanning ¿400 nm for Infrared Astronomical Spectrograph Calibration,” Rev. Sci. Ins. 81, 063105 (2010).
[CrossRef]

F. Quinlan, S. Gee, S. Ozharar, and P. J. Delfyett, “Ultralow-jitter and -amplitude-noise semiconductor-based actively mode-locked laser,” Opt. Lett. 31, 2870–2872 (2006).
[CrossRef] [PubMed]

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photonics Journal3, 140–151 (2011).
[CrossRef]

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Rosenband, T.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

Sasselov, D.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

Savchenkov, A. A.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable Optical Frequency Comb with a Crystalline Whispering Gallery Mode Resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef] [PubMed]

Schliesser, A.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full Stabilization of a Microresonator-Based Optical Frequency Comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef] [PubMed]

Scott, R. P.

Seidel, D.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable Optical Frequency Comb with a Crystalline Whispering Gallery Mode Resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef] [PubMed]

Shacham, J.

C. Harder, J. Katz, S. Margalit, J. Shacham, and A. Yariv, “Noise equivalent circuit of a semiconductor laser diode,” IEEE Journal of Quantum Electronics QE-18, 333–337 (1982).
[CrossRef]

Solomatine, I.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable Optical Frequency Comb with a Crystalline Whispering Gallery Mode Resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef] [PubMed]

Spühler, G. J.

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

Steinmetz, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hnsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Applied Physics B: Lasers and Optics 96, 251–256 (2009).
[CrossRef]

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,” Applied Physics B: Lasers and Optics 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,” Applied Physics B: Lasers and Optics 69, 327–332 (1999).
[CrossRef]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Südmeyer, T.

S. Zeller, T. Südmeyer, K. Weingarten, and U. Keller, “Passively modelocked 77 GHz Er:Yb:glass laser,” Electronics Letters 43, 32–33 (2007).
[CrossRef]

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,” Applied Physics B: Lasers and Optics 69, 327–332 (1999).
[CrossRef]

Szentgyorgyi, A.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

Taylor, J.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photonics Journal3, 140–151 (2011).
[CrossRef]

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,” Applied Physics B: Lasers and Optics 69, 327–332 (1999).
[CrossRef]

Udem, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hnsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Applied Physics B: Lasers and Optics 96, 251–256 (2009).
[CrossRef]

Unold, H. J.

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

Walsworth, R. L.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

Weiner, A.

C.-B. Huang, Z. Jiang, D. Leaird, J. Caraquitena, and A. Weiner, “Spectral line-by-line shaping for optical and microwave arbitrary waveform generations,” Laser & Photonics Reviews2, 227–248 (2008).
[CrossRef] [PubMed]

Weiner, A. M.

Weingarten, K.

S. Zeller, T. Südmeyer, K. Weingarten, and U. Keller, “Passively modelocked 77 GHz Er:Yb:glass laser,” Electronics Letters 43, 32–33 (2007).
[CrossRef]

Weingarten, K. J.

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

Wilken, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hnsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Applied Physics B: Lasers and Optics 96, 251–256 (2009).
[CrossRef]

Williams, K. J.

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Transactions on Microwave Theory and Techniques47, 1297–1303 (1999).
[CrossRef]

Wilpers, G.

Windeler, R. S.

T. M. Fortier, J. Ye, S. T. Cundiff, and R. S. Windeler, “Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase,” Opt. Lett. 27, 445–447 (2002).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Xiao, S.

Yamashita, S.

Yariv, A.

C. Harder, J. Katz, S. Margalit, J. Shacham, and A. Yariv, “Noise equivalent circuit of a semiconductor laser diode,” IEEE Journal of Quantum Electronics QE-18, 333–337 (1982).
[CrossRef]

A. Yariv, Optical Electronics (Saunders College Publishing, Orlando, 1991), 4th ed.

Ycas, G.

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-Spaced Optical Frequency Comb Spanning ¿400 nm for Infrared Astronomical Spectrograph Calibration,” Rev. Sci. Ins. 81, 063105 (2010).
[CrossRef]

Ye, J.

Yoshida, E.

E. Yoshida and M. Nakazawa, “Wavelength tunable 1.0 ps pulse generation in 1.530–1.555 μm region from PLL, regeneratively modelocked fibre laser,” Electronics Letters 34, 1753–1754 (1998).
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Young, B. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible Lasers with Subhertz Linewidths,” Phys. Rev. Lett. 82, 3799–3802 (1999).
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Zeller, S.

S. Zeller, T. Südmeyer, K. Weingarten, and U. Keller, “Passively modelocked 77 GHz Er:Yb:glass laser,” Electronics Letters 43, 32–33 (2007).
[CrossRef]

Zeller, S. C.

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
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Applied Physics B: Lasers and Optics

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hnsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Applied Physics B: Lasers and Optics 96, 251–256 (2009).
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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,” Applied Physics B: Lasers and Optics 69, 327–332 (1999).
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Electronics Letters

E. Yoshida and M. Nakazawa, “Wavelength tunable 1.0 ps pulse generation in 1.530–1.555 μm region from PLL, regeneratively modelocked fibre laser,” Electronics Letters 34, 1753–1754 (1998).
[CrossRef]

S. Zeller, T. Südmeyer, K. Weingarten, and U. Keller, “Passively modelocked 77 GHz Er:Yb:glass laser,” Electronics Letters 43, 32–33 (2007).
[CrossRef]

IEEE Journal of Quantum Electronics

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J. Opt. D: Applied Physics

S. T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Opt. D: Applied Physics 35, R43 (2002).
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Nat. Photon.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photon. 5, 425–429 (2011).
[CrossRef]

Nature

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s−1,” Nature 452, 610–612 (2008).
[CrossRef] [PubMed]

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[CrossRef] [PubMed]

New Journal of Physics

R. Paschotta, L. Krainer, S. Lecomte, G. J. Spühler, S. C. Zeller, A. Aschwanden, D. Lorenser, H. J. Unold, K. J. Weingarten, and U. Keller, “Picosecond pulse sources with multi-GHz repetition rates and high output power,” New Journal of Physics 6, 174 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34, 872–874 (2009).
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A. Bartels, D. Heinecke, and S. A. Diddams, “Passively mode-locked 10 GHz femtosecond Ti:sapphire laser,” Opt. Lett. 33, 1905–1907 (2008).
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S. Xiao, L. Hollberg, and S. A. Diddams, “Generation of a 20 GHz train of subpicosecond pulses with a stabilized optical-frequency-comb generator,” Opt. Lett. 34, 85–87 (2009).
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A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30, 667–669 (2005).
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T. M. Fortier, A. Bartels, and S. A. Diddams, “Octave-spanning Ti:sapphire laser with a repetition rate ¿ 1 GHz for optical frequency measurements and comparisons,” Opt. Lett. 31, 1011–1013 (2006).
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Phys. Rev. A

D. C. Heinecke, A. Bartels, T. M. Fortier, D. A. Braje, L. Hollberg, and S. A. Diddams, “Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in 87rubidium,” Phys. Rev. A 80, 053806 (2009).
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Phys. Rev. Lett.

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Rev. Sci. Ins.

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-Spaced Optical Frequency Comb Spanning ¿400 nm for Infrared Astronomical Spectrograph Calibration,” Rev. Sci. Ins. 81, 063105 (2010).
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Science

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz Self-Referenced Optical Frequency Comb,” Science 326, 681 (2009).
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J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photonics Journal3, 140–151 (2011).
[CrossRef]

Mention of specific trade names is for technical information only and does not constitute an endorsement by NIST.

For typical frequency counters the input frequency is limited to a few hundreds of megahertz. Thus, the frequencies to analyze in the range of gigahertz have to be converted to lower values to enable counter measurements. In the process of difference or sum frequency generation in a mixing device the actual frequency fluctuations of the input frequencies are preserved. Using a stable reference frequency this allows to shift frequencies without affecting the frequency stability. In contrast, in a frequency division process the noise density and therefore the frequency fluctuations are reduced by the division factor. This leads to an increase in frequency stability. For the offset frequency stabilization and analysis we use a frequency division step to reduce phase fluctuations making the phase lock more robust by extending the capture range of the phase detector. In the data evaluation we account for this division factor to recover the original offset frequency stability.

Analog Devices, Ultrahigh Speed Phase/Frequency Discriminator AD9901.

A. Yariv, Optical Electronics (Saunders College Publishing, Orlando, 1991), 4th ed.

C.-B. Huang, Z. Jiang, D. Leaird, J. Caraquitena, and A. Weiner, “Spectral line-by-line shaping for optical and microwave arbitrary waveform generations,” Laser & Photonics Reviews2, 227–248 (2008).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Compact setup for the supercontinuum generation. The zoom in shows the 10 GHz Ti:sapphire laser cavity. AOM: acousto-optic modulator, PZT: piezo-electric transducer to modulate cavity mirror, CL: collimation lens, GTI: negative dispersion Gires-Tournois interferometric mirrors for pulse recompression, λ/2: half-wave plate, M: 60x microscope objective, TS: xyz-translation stage, PCF: 1.5 m of microstructured fiber, CP: temperature-stabilized copper plate, SC: generated supercontinuum.

Fig. 2
Fig. 2

Laser spectrum and octave-spanning spectrum (supercontinuum) generated in microstructured fiber. To further demonstrate the possibility of expanding the spectral coverage of the comb, the direct laser output of the laser was doubled in a 50 μm thick BBO crystal and is also shown as the isolated peak near 390 nm.

Fig. 3
Fig. 3

(a) Setup for offset frequency detection, locking and analysis consisting of the f-2f interferometer and electronics for signal processing. PCF: microstructured fiber on a temperature-stabilized copper plate, DCM: dichroic mirror, KNbO3: 1 mm long nonlinear potassium niobate crystal, IF: interference filter as optical bandpass at 532 nm with 3 nm bandwidth, PD: SI PIN diode with 2 GHz bandwidth, M: double-balanced mixer, synth I: synthesizer at f = f 0 + 925 MHz, div: frequency divider with N = 46, split: −3 dB/−3 dB signal splitter, VSA: vector signal analyzer. For clarity signal microwave filters and amplifiers are not shown. (b) Repetition rate phase-locked loop and characterization scheme. PD: high-speed photodetector with 10 GHz bandwidth, M: double-balanced mixers for phase detection and frequency down-conversion, synth I: synthesizer at f = fR +10 MHz, synth II: synthesizer at f = fR .

Fig. 4
Fig. 4

Offset frequency beat signal for the free-running system. (a) Microwave spectra of the unlocked and undivided offset frequency signal at 2.7 GHz taken with 1 MHz resolution bandwidth. The red trace (oe-19-19-18440-i001.jpg) shows a spectrum where the pump laser exhibits excessive amplitude noise. (b) High-resolution zoom (10 kHz resolution bandwidth) in the spectrum of the mixed and divided signal of the offset frequency at the carrier frequency of 20 MHz.

Fig. 5
Fig. 5

(a) Counting record of the offset frequency and the repetition rate for the unlocked system with 1 s gate period. The vertical coordinate axis shows the changes in frequencies. (b) Counting record of the offset frequency and the repetition rate for the locked system with 1 s gate period. c) Calculated Allan deviation for both frequencies. As a guide to the eye, the green line marks a τ 1 2 dependency. The offset frequency data are corrected for the division factor and represent the stability of the actual offset frequency.

Fig. 6
Fig. 6

(a) Offset frequency phase noise and integrated phase noise. (b) Amplitude noise of the pump laser and the 10 GHz laser and corresponding noise floors. The measured integrated relative intensity noise for the pump laser and the 10 GHz laser is 0.047% and 0.054%, respectively.

Fig. 7
Fig. 7

Microwave power at 10 GHz versus photocurrent for two different photodetectors. Both photodetectors were terminated with 50 Ω resistors.

Equations (3)

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σ f R ( 1 s ) = δ f R f R = 1.9 10 3 Hz 10 10 9 Hz = 1.9 10 13
σ f 0 ( 1 s ) = δ f 0 f 0 = 6 10 3 Hz 2.7 10 9 Hz = 2.2 10 12 .
f 0 ( t ) = Δ Φ C E ( t ) 2 π f R ,

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