Abstract

The frequency comb from a prism-based Cr:forsterite laser has been frequency stabilized using intra cavity prism insertion and pump power modulation. Absolute frequency measurements of a CW fiber laser stabilized to the P(13) transition of acetylene demonstrate a fractional instability of 2×1011 at a 1s gate time, limited by a commercial Global Positioning System (GPS)-disciplined rubidium oscillator. Additionally, absolute frequency measurements made simultaneously using a second frequency comb indicate relative instabilities of 3×1012 for both combs for a 1s gate time. Estimations of the carrier-envelope offset frequency linewidth based on relative intensity noise and the response dynamics of the carrier-envelope offset to pump power changes confirm the observed linewidths.

© 2009 Optical Society of America

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2009 (2)

2008 (4)

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, U. Griebner, V. Petrov, and F. Rotermund, “Mode-locked self-starting Cr:forsterite laser using a single-walled carbon nanotube saturable absorber,” Opt. Lett. 33, 2449-2451 (2008).
[CrossRef]

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef]

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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]

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

2007 (3)

S. T. 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]

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian fceo phase excursions,” Appl. Phys. B 86, 219-227 (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]

2006 (2)

2005 (2)

2004 (2)

2003 (6)

2002 (3)

F. W. Helbing, G. Steinmayer, U. Keller, R. S. Windeler, J. Stenger, and H. R. Telle, “Carrier-envelope offset dynamics of mode-locked lasers,” Opt. Lett. 27, 194-196 (2002).
[CrossRef]

Z. Wei, Y. Kaboyashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74, S171-S176 (2002).
[CrossRef]

T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[CrossRef]

2001 (1)

2000 (2)

A. Robertson, H. Fuchs, U. Ernst, R. Wallenstein, V. Scheuer, and T. Tschudi, “Prismless femtosecond Cr:forsterite laser,” J. Opt. Soc. Am. B 17, 668-671 (2000).
[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]

1993 (2)

1992 (2)

1991 (1)

1988 (1)

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagishi, H. Anzai, and Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040-1042 (1988).
[CrossRef]

1986 (1)

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

1966 (1)

J. A. Barnes and D. W. Allan, “A statistical model of flicker noise,” Proc. IEEE 54, 176-178 (1966).
[CrossRef]

Alfano, R. R.

Allan, D. W.

J. A. Barnes and D. W. Allan, “A statistical model of flicker noise,” Proc. IEEE 54, 176-178 (1966).
[CrossRef]

wJ. A. Barnes and D. W. Allan, “Variances based on data with dead time between the measurements,” in Proceedings of the 19th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting (National Bureau of Standards, 1987).

Amezcua-Correa, R.

Angelow, G.

Anzai, H.

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagishi, H. Anzai, and Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040-1042 (1988).
[CrossRef]

Baker, K. A.

Barnes, J. A.

J. A. Barnes and D. W. Allan, “A statistical model of flicker noise,” Proc. IEEE 54, 176-178 (1966).
[CrossRef]

wJ. A. Barnes and D. W. Allan, “Variances based on data with dead time between the measurements,” in Proceedings of the 19th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting (National Bureau of Standards, 1987).

Bartels, A.

Benabid, F.

Benedick, A. J.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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]

Bergquist, J. C.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef]

Bi, Z. Y.

L. S. Ma, Z. Y. 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]

Brusch, A.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef]

Carrig, T. J.

Cho, W. B.

Choi, S. Y.

Chou, C. W.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef]

Chudoba, C.

Corwin, K. L.

K. Knabe, S. Wu, J. Lim, K. A. Tillman, P. S. Light, F. Couny, N. Wheeler, R. Thapa, A. M. Jones, J. W. Nicholson, B. R. Washburn, F. Benabid, and K. L. Corwin, “10 kHz accuracy of an optical frequency reference based on C122H2-filled large-core kagome photonic crystal fibers,” Opt. Express 17, 16017-16026 (2009).
[CrossRef]

J. K. Lim, K. Knabe, K. A. Tillman, W. Neely, Y. S. Wang, R. Amezcua-Correa, F. Couny, P. S. Light, F. Benabid, J. C. Knight, K. L. Corwin, J. W. Nicholson, and B. R. Washburn, “A phase-stabilized carbon nanotube fiber laser frequency comb,” Opt. Express 17, 14115-14120 (2009).
[CrossRef]

R. Thapa, K. Knabe, M. Faheem, A. Naweed, O. L. Weaver, and K. L. Corwin, “Saturated absorption spectroscopy of acetylene gas inside large-core photonic bandgap fiber,” Opt. Lett. 31, 2489-2491 (2006).
[CrossRef]

K. L. Corwin, I. Thomann, T. Dennis, R. W. Fox, W. Swann, E. A. Curtis, C. W. Oates, G. Wilpers, A. Bartels, S. L. Gilbert, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “Absolute-frequency measurements with a stabilized near-infrared optical frequency comb from a Cr:forsterite laser,” Opt. Lett. 29, 397-399 (2004).
[CrossRef]

I. Thomann, A. Bartels, K. L. Corwin, N. R. Newbury, L. Hollberg, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “420 MHz Cr:forsterite femtosecond ring laser and continuum generation in the 1-2 μm range,” Opt. Lett. 28, 1368-1370(2003).
[CrossRef]

N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. 28, 944-946 (2003).
[CrossRef]

Couny, F.

Cundiff, S. T.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Intensity-related dynamics of femtosecond frequency combs,” Opt. Lett. 28, 851-853 (2003).
[CrossRef]

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[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]

Curtis, E. A.

Dawkins, S. T.

S. T. 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]

Dennis, T.

Diddams, S. A.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef]

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

K. Kim, B. R. Washburn, G. Wilpers, C. W. Oates, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. E. Yan, “Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser,” Opt. Lett. 30, 932-934 (2005).
[CrossRef]

K. L. Corwin, I. Thomann, T. Dennis, R. W. Fox, W. Swann, E. A. Curtis, C. W. Oates, G. Wilpers, A. Bartels, S. L. Gilbert, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “Absolute-frequency measurements with a stabilized near-infrared optical frequency comb from a Cr:forsterite laser,” Opt. Lett. 29, 397-399 (2004).
[CrossRef]

L. S. Ma, Z. Y. 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]

I. Thomann, A. Bartels, K. L. Corwin, N. R. Newbury, L. Hollberg, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “420 MHz Cr:forsterite femtosecond ring laser and continuum generation in the 1-2 μm range,” Opt. Lett. 28, 1368-1370(2003).
[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]

DiMarcello, F.

Dong, L.

I. Hartl, A. Ruehl, R. Thapa, H. A. McKay, B. K. Thomas, L. Fu, L. Dong, and M. E. Fermann, “Rapidly scanning Fourier transform spectrometer based on a GHz repetition rate Yb-fiber laser pair,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009).

Drullinger, R. E.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef]

Ernst, U.

Faheem, M.

Fendel, P.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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]

Fermann, M. E.

I. Hartl, A. Ruehl, R. Thapa, H. A. McKay, B. K. Thomas, L. Fu, L. Dong, and M. E. Fermann, “Rapidly scanning Fourier transform spectrometer based on a GHz repetition rate Yb-fiber laser pair,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009).

Fleming, J.

Fortier, T. M.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef]

Fox, R. W.

Fu, L.

I. Hartl, A. Ruehl, R. Thapa, H. A. McKay, B. K. Thomas, L. Fu, L. Dong, and M. E. Fermann, “Rapidly scanning Fourier transform spectrometer based on a GHz repetition rate Yb-fiber laser pair,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009).

Fuchs, H.

Fujimoto, J. G.

Gayen, S. K.

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagishi, H. Anzai, and Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040-1042 (1988).
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C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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).
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Griebner, U.

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).
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T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
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I. Hartl, A. Ruehl, R. Thapa, H. A. McKay, B. K. Thomas, L. Fu, L. Dong, and M. E. Fermann, “Rapidly scanning Fourier transform spectrometer based on a GHz repetition rate Yb-fiber laser pair,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009).

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K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Intensity-related dynamics of femtosecond frequency combs,” Opt. Lett. 28, 851-853 (2003).
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K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
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T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
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T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
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Itano, W. M.

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Jones, A. M.

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]

Jones, R. J.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
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K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Intensity-related dynamics of femtosecond frequency combs,” Opt. Lett. 28, 851-853 (2003).
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Jorgensen, C.

Kaboyashi, Y.

Z. Wei, Y. Kaboyashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74, S171-S176 (2002).
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Kartner, F. X.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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).
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C. Chudoba, J. G. Fujimoto, E. P. Ippen, H. A. Haus, U. Morgner, F. X. Kartner, V. Scheuer, G. Angelow, and T. Tschudi, “All-solid-state Cr:forsterite laser generating 14 fs pulses at 1.3 μm,” Opt. Lett. 26, 292-294 (2001).
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Lee, S.

Li, C. H.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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).
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Light, P. S.

Lim, J.

Lim, J. K.

Lorini, L.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
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S. T. 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).
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L. S. Ma, Z. Y. 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).
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K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Intensity-related dynamics of femtosecond frequency combs,” Opt. Lett. 28, 851-853 (2003).
[CrossRef]

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
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McFerran, J. J.

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian fceo phase excursions,” Appl. Phys. B 86, 219-227 (2007).
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S. T. 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).
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I. Hartl, A. Ruehl, R. Thapa, H. A. McKay, B. K. Thomas, L. Fu, L. Dong, and M. E. Fermann, “Rapidly scanning Fourier transform spectrometer based on a GHz repetition rate Yb-fiber laser pair,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009).

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Monberg, E.

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Nathel, H.

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Neely, W.

Newbury, N. R.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
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J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian fceo phase excursions,” Appl. Phys. B 86, 219-227 (2007).
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B. R. Washburn, W. C. Swann, and N. R. Newbury, “Response dynamics of the frequency comb output from a femtosecond fiber laser,” Opt. Express 13, 10622-10633 (2005).
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K. Kim, B. R. Washburn, G. Wilpers, C. W. Oates, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. E. Yan, “Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser,” Opt. Lett. 30, 932-934 (2005).
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N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. 28, 944-946 (2003).
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K. Knabe, S. Wu, J. Lim, K. A. Tillman, P. S. Light, F. Couny, N. Wheeler, R. Thapa, A. M. Jones, J. W. Nicholson, B. R. Washburn, F. Benabid, and K. L. Corwin, “10 kHz accuracy of an optical frequency reference based on C122H2-filled large-core kagome photonic crystal fibers,” Opt. Express 17, 16017-16026 (2009).
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J. K. Lim, K. Knabe, K. A. Tillman, W. Neely, Y. S. Wang, R. Amezcua-Correa, F. Couny, P. S. Light, F. Benabid, J. C. Knight, K. L. Corwin, J. W. Nicholson, and B. R. Washburn, “A phase-stabilized carbon nanotube fiber laser frequency comb,” Opt. Express 17, 14115-14120 (2009).
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K. Kim, B. R. Washburn, G. Wilpers, C. W. Oates, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. E. Yan, “Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser,” Opt. Lett. 30, 932-934 (2005).
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K. L. Corwin, I. Thomann, T. Dennis, R. W. Fox, W. Swann, E. A. Curtis, C. W. Oates, G. Wilpers, A. Bartels, S. L. Gilbert, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “Absolute-frequency measurements with a stabilized near-infrared optical frequency comb from a Cr:forsterite laser,” Opt. Lett. 29, 397-399 (2004).
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I. Thomann, A. Bartels, K. L. Corwin, N. R. Newbury, L. Hollberg, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “420 MHz Cr:forsterite femtosecond ring laser and continuum generation in the 1-2 μm range,” Opt. Lett. 28, 1368-1370(2003).
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J. W. Nicholson, M. F. Yan, P. Wisk, J. Fleming, F. DiMarcello, E. Monberg, A. Yablon, C. Jorgensen, and T. Veng, “All-fiber, octave-spanning supercontinuum,” Opt. Lett. 28, 643-645 (2003).
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Oates, C.

L. S. Ma, Z. Y. 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).
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Oates, C. W.

Oskay, W. H.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
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Petricevic, V.

Petrich, G. S.

Petrov, V.

Phillips, D. F.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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).
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Pollock, C. R.

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).
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Robertsson, L.

L. S. Ma, Z. Y. 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).
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T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
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Ruehl, A.

I. Hartl, A. Ruehl, R. Thapa, H. A. McKay, B. K. Thomas, L. Fu, L. Dong, and M. E. Fermann, “Rapidly scanning Fourier transform spectrometer based on a GHz repetition rate Yb-fiber laser pair,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009).

Sasselov, D.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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).
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Schibli, T. R.

Schmidt, P. O.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
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Sennaroglu, A.

Stalnaker, J. E.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
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Steinmayer, G.

Stenger, J.

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).
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Swann, W.

Swann, W. C.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef]

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian fceo phase excursions,” Appl. Phys. B 86, 219-227 (2007).
[CrossRef]

B. R. Washburn, W. C. Swann, and N. R. Newbury, “Response dynamics of the frequency comb output from a femtosecond fiber laser,” Opt. Express 13, 10622-10633 (2005).
[CrossRef]

Szentgyorgyi, A.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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]

Tandon, S. N.

Telle, H. R.

Thapa, R.

Thomann, I.

Thomas, B. K.

I. Hartl, A. Ruehl, R. Thapa, H. A. McKay, B. K. Thomas, L. Fu, L. Dong, and M. E. Fermann, “Rapidly scanning Fourier transform spectrometer based on a GHz repetition rate Yb-fiber laser pair,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009).

Tillman, K. A.

Torizuka, K.

Z. Wei, Y. Kaboyashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74, S171-S176 (2002).
[CrossRef]

Tschudi, T.

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[CrossRef]

Veng, T.

von der Linde, D.

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

Wallenstein, R.

Walsworth, R. L.

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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).
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Wang, Y. S.

Washburn, B. R.

Weaver, O. L.

Wei, Z.

Z. Wei, Y. Kaboyashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74, S171-S176 (2002).
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Wheeler, N.

Wilpers, G.

Windeler, R. S.

L. S. Ma, Z. Y. 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]

N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. 28, 944-946 (2003).
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F. W. Helbing, G. Steinmayer, U. Keller, R. S. Windeler, J. Stenger, and H. R. Telle, “Carrier-envelope offset dynamics of mode-locked lasers,” Opt. Lett. 27, 194-196 (2002).
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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]

Wineland, D. J.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef]

Wise, F.

Wisk, P.

Wu, S.

Yablon, A.

Yamagishi, K.

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagishi, H. Anzai, and Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040-1042 (1988).
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Yamaguchi, Y.

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagishi, H. Anzai, and Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040-1042 (1988).
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Yan, M. E.

Yan, M. F.

Yanovsky, V.

Ye, J.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Intensity-related dynamics of femtosecond frequency combs,” Opt. Lett. 28, 851-853 (2003).
[CrossRef]

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

Yim, J. H.

Zucco, M.

L. S. Ma, Z. Y. 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]

Appl. Phys. B (3)

Z. Wei, Y. Kaboyashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74, S171-S176 (2002).
[CrossRef]

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

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian fceo phase excursions,” Appl. Phys. B 86, 219-227 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

V. Petricevic, S. K. Gayen, R. R. Alfano, K. Yamagishi, H. Anzai, and Y. Yamaguchi, “Laser action in chromium-doped forsterite,” Appl. Phys. Lett. 52, 1040-1042 (1988).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

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

S. T. 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]

J. Opt. Soc. Am. B (1)

Nature (2)

T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature 416, 233-237 (2002).
[CrossRef]

C. H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kartner, 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]

Opt. Express (4)

Opt. Lett. (18)

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Intensity-related dynamics of femtosecond frequency combs,” Opt. Lett. 28, 851-853 (2003).
[CrossRef]

N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. 28, 944-946 (2003).
[CrossRef]

J. W. Nicholson, M. F. Yan, P. Wisk, J. Fleming, F. DiMarcello, E. Monberg, A. Yablon, C. Jorgensen, and T. Veng, “All-fiber, octave-spanning supercontinuum,” Opt. Lett. 28, 643-645 (2003).
[CrossRef]

F. Couny, P. S. Light, and F. Benabid, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett. 31, 3574-3576 (2006).
[CrossRef]

R. Thapa, K. Knabe, M. Faheem, A. Naweed, O. L. Weaver, and K. L. Corwin, “Saturated absorption spectroscopy of acetylene gas inside large-core photonic bandgap fiber,” Opt. Lett. 31, 2489-2491 (2006).
[CrossRef]

A. Seas, V. Petricevic, and R. R. Alfano, “Continuous-wave mode-locked operation of a chromium-doped forsterite laser,” Opt. Lett. 16, 1668-1670 (1991).
[CrossRef]

A. Seas, V. Petricevic, and R. R. Alfano, “Generation of sub-100 fs pulses from a CW mode-locked chromium-doped forsterite laser,” Opt. Lett. 17, 937-939 (1992).
[CrossRef]

A. Sennaroglu, T. J. Carrig, and C. R. Pollock, “Femtosecond pulse generation by using an additive-pulse mode-locked chromium-doped forsterite laser operated at 77 K,” Opt. Lett. 17, 1216-1218 (1992).
[CrossRef]

A. Sennaroglu, C. R. Pollock, and H. Nathel, “Generation of 48 fs pulses and measurement of crystal Dispersion by using a regeneratively initiated self-mode-locked chromium-doped forsterite laser,” Opt. Lett. 18, 826-828 (1993).
[CrossRef]

Y. Pang, V. Yanovsky, F. Wise, and B. I. Minkov, “Self-mode-locked Cr-forsterite laser,” Opt. Lett. 18, 1168-1170 (1993).
[CrossRef]

C. Chudoba, J. G. Fujimoto, E. P. Ippen, H. A. Haus, U. Morgner, F. X. Kartner, V. Scheuer, G. Angelow, and T. Tschudi, “All-solid-state Cr:forsterite laser generating 14 fs pulses at 1.3 μm,” Opt. Lett. 26, 292-294 (2001).
[CrossRef]

I. Thomann, A. Bartels, K. L. Corwin, N. R. Newbury, L. Hollberg, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “420 MHz Cr:forsterite femtosecond ring laser and continuum generation in the 1-2 μm range,” Opt. Lett. 28, 1368-1370(2003).
[CrossRef]

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

F. W. Helbing, G. Steinmayer, U. Keller, R. S. Windeler, J. Stenger, and H. R. Telle, “Carrier-envelope offset dynamics of mode-locked lasers,” Opt. Lett. 27, 194-196 (2002).
[CrossRef]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28, 947-949 (2003).
[CrossRef]

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, U. Griebner, V. Petrov, and F. Rotermund, “Mode-locked self-starting Cr:forsterite laser using a single-walled carbon nanotube saturable absorber,” Opt. Lett. 33, 2449-2451 (2008).
[CrossRef]

K. Kim, B. R. Washburn, G. Wilpers, C. W. Oates, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. E. Yan, “Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser,” Opt. Lett. 30, 932-934 (2005).
[CrossRef]

K. L. Corwin, I. Thomann, T. Dennis, R. W. Fox, W. Swann, E. A. Curtis, C. W. Oates, G. Wilpers, A. Bartels, S. L. Gilbert, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “Absolute-frequency measurements with a stabilized near-infrared optical frequency comb from a Cr:forsterite laser,” Opt. Lett. 29, 397-399 (2004).
[CrossRef]

Proc. IEEE (1)

J. A. Barnes and D. W. Allan, “A statistical model of flicker noise,” Proc. IEEE 54, 176-178 (1966).
[CrossRef]

Science (3)

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]

L. S. Ma, Z. Y. 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]

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef]

Other (3)

I. Hartl, A. Ruehl, R. Thapa, H. A. McKay, B. K. Thomas, L. Fu, L. Dong, and M. E. Fermann, “Rapidly scanning Fourier transform spectrometer based on a GHz repetition rate Yb-fiber laser pair,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009).

wJ. A. Barnes and D. W. Allan, “Variances based on data with dead time between the measurements,” in Proceedings of the 19th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting (National Bureau of Standards, 1987).

P. T. Systems, Operators Manual (2006), www.ptsyst.com/GPS10RB-B.pdf.

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Figures (12)

Fig. 1
Fig. 1

Cavity configuration for the prism-based Cr:forsterite laser ( F 1 , 100 mm focusing lens; M 1 and M 2 , cavity mirrors; ROC, radius of curvature; M 3 , cavity folding mirror; P 1 and P 2 , SF6 dispersion prisms; HR, high reflector; O/C, output coupler) including the two servo-controlled elements for both f rep and f 0 stabilization. The inset shows an example power spectrum with λ center = 1249 nm and Δ λ 40 nm .

Fig. 2
Fig. 2

Sample supercontinuum spectrum, which is a concatenation of two measurements. Black curve: recorded using an optical spectrum analyzer ( λ max = 1700 nm ) with a 1 nm resolution. Gray curve: recorded using an extended InGaAs photodetector and monochromator (wavelength sensitivity 1400 2350 nm , with a 2 nm resolution).

Fig. 3
Fig. 3

Schematic of the self-referencing f-to- 2 f interferometer used for f 0 detection, f rep detection, and heterodyne signal ( f beat ) detection. (HNLF, highly nonlinear fiber; SC, supercontinuum; DM, dichroic mirrors; λ / 2 and λ / 4 , half- and quarter-wave plates; PPLN, periodically poled lithium niobate; BPF, 1030 nm bandpass filter; PBS, polarization beam splitter; LP, linear polarizer.

Fig. 4
Fig. 4

RF electronics used for slow (denoted by 1) and fast (denoted by 2) servo control of f 0 and f rep . The slow servo bandwidth for both cases is 1 kHz , while the fast servo bandwidth is 30 kHz for f rep (limited by the PZT) and 1 MHz for f 0 . The low-pass filter has a 3 dB cutoff at 50 MHz , while the bandpass filter has a 1% bandwidth when centered at 1 GHz . All synthesizers and counters were referenced to a Rb/GPS oscillator.

Fig. 5
Fig. 5

Sample of a stabilized f 0 signal with its center frequency = 35 MHz and S/N of 50 dB . An RF spectrum analyzer with an RBW = 100 kHz was used where a Δ f 0 FWHM 1 MHz is measured.

Fig. 6
Fig. 6

In-loop Cr:forsterite time series data showing locked signals for 70 min and for a 1 s gate time. (a) Fluctuations in f rep ( Δ f rep ) about a locked frequency of 113.005798699 MHz with σ 0.8 mHz . (b) Fluctuations in f 0 ( Δ f 0 ) about the locked frequency of 35 MHz with σ 0.9 Hz .

Fig. 7
Fig. 7

Out-of-loop measurement schematic. Both the frequency comb and the frequency stabilized CW fiber laser are referenced to a Rb/GPS oscillator. The optical bandpass filter, 1, was an angle-tuned optical interference filter centered at 1533 nm with an 8 nm bandwidth and bandpass filter 2 was a RF filter with a 6 MHz bandwidth centered at 30 MHz . The inset depicts the optical frequency comb spectrum and the stabilized laser ( f x ) in the optical domain, and the resulting heterodyne signal f beat in the RF domain.

Fig. 8
Fig. 8

Out-of-loop or heterodyned time-series data ( f beat ) generated between the Cr:forsterite comb and an acetylene stabilized CW fiber laser. A 1 s gate time was used and was recorded simultaneous to the in-loop data shown in Fig. 6. The data show f beat fluctuations ( Δ f beat ) about a locked signal of 30.060646 MHz and σ = 4.253 kHz .

Fig. 9
Fig. 9

Fractional frequency instability (or triangle deviation [34]) of the frequency comb due to both in-loop signals ( Δ f rep and Δ f 0 ) and the heterodyne signal ( Δ f beat ). The instabilities of all three signals are calculated in the optical domain using f n 195 THz . The f rep signal is counterlimited for all gate times and the frequency instability of the commercial 10 MHz Rb/GPS oscillator is included for comparison. All data are recorded using a 1 s gate time and averaged to give instabilities at longer gate times.

Fig. 10
Fig. 10

The fractional frequency instability (or triangle deviation [34]) of heterodyne signals between the stabilized CW laser and the Cr:forsterite laser, f beat   Cr : f (solid squares) and the CNFL f beat   CNFL (open star). The fractional instability of the point-to-point difference between the f beat , Cr : f and f beat , CNFL (open triangles) is plotted and shows the relative instability of the two combs. These data are also presented in Ref [37]. All data are recorded using a 1 s gate time and averaged to give instabilities at longer gate times.

Fig. 11
Fig. 11

(a) RIN spectra for the pump laser (gray) and the Cr:forsterite (black) spanning from 2 Hz to 10 MHz . (b) Relative difference between the Cr:forsterite and the pump RIN, showing how the Cr:forsterite medium acts as a low-pass filter for the pump noise with f 3 dB 700 kHz . Additional contributions between 100 Hz and 10 kHz in the Cr:forsterite spectrum are also clearly visible.

Fig. 12
Fig. 12

Experimental configuration used to make d f 0 / d P measurements. The square-wave AOM drive signal steps the pump power ( d P ), while the free-running f 0 signal is counted to measure a corresponding change in f 0 ( d f 0 ) . The inset shows sample count data; the solid curve is the f 0 signal and the dotted curve is the synchronized square-wave AOM drive signal.

Equations (3)

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f n = n f rep + f 0 .
Δ f n = ( n Δ f rep ) 2 + ( Δ f 0 ) 2 .
Δ f 0 π ( ( P d f 0 d P ) 2 0 f 3 dB RIN total ( υ ) d υ ) 1 / 2 .

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