Abstract

We investigate how suppressed modes in frequency combs are modified upon frequency doubling and self-phase modulation. We find, both experimentally and by using a simplified model, that these side-modes are amplified relative to the principal comb modes. Whereas frequency doubling increases their relative strength by 6 dB, the growth due to self-phase modulation can be much stronger and generally increases with nonlinear propagation length. Upper limits for this effect are derived in this work. This behavior has implications for high-precision calibration of spectrographs with frequency combs used for example in astronomy. For this application, Fabry-Pérot filter cavities are used to increase the mode spacing to exceed the resolution of the spectrograph. Frequency conversion and/or spectral broadening after non-perfect filtering reamplify the suppressed modes, which can lead to calibration errors.

© 2013 OSA

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2012 (8)

H.-W. Chen, G. Chang, S. Xu, Z. Yang, and F. X. Kärtner, “3 GHz, fundamentally mode-locked, femtosecond Yb-fiber laser,” Opt. Lett. 37, 3522–3524 (2012).
[Crossref] [PubMed]

T. Wilken, G. Lo Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. Gonzalez Hernandez, R. Rebolo, T. W. Haensch, Th. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485, 611–614 (2012).
[Crossref] [PubMed]

M. T. Murphy, C. R. Locke, P. S. Light, A. N. Luiten, and J. S. Lawrence, “Laser frequency comb techniques for precise astronomical spectroscopy,” Mon. Not. R. Astron. Soc. 422, 761–771 (2012).
[Crossref]

D. F. Phillips, A. G. Glenday, C.-H. Li, C. Cramer, G. Furesz, G. Chang, A. J. Benedick, L.-J. Chen, F. X. Kärtner, S. Korzennik, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “Calibration of an astrophysical spectrograph below 1 m/s using a laser frequency comb,” Opt. Express 20, 13711–13726 (2012).
[Crossref] [PubMed]

G. G. Ycas, F. Quinlan, S. A. Diddams, S. Osterman, S. Mahadevan, S. Redman, R. Terrien, L. Ramsey, C. F. Bender, B. Botzer, and S. Sigurdsson, “Demonstration of on-sky calibration of astronomical spectra using a 25 GHz near-IR laser frequency comb,” Opt. Express 20, 6631–6643 (2012).
[Crossref] [PubMed]

G. Chang, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, R. L. Walsworth, and F. X. Kärtner, “Optimization of filtering schemes for broadband astro-combs,” Opt. Express 20, 24987–25013 (2012).
[Crossref] [PubMed]

H.-P. Doerr, T. Steinmetz, R. Holzwarth, T. Kentischer, and W. Schmidt, “Laser frequency comb system for absolute calibration of the VTT echelle spectrograph,” Solar Phys. 280, 663–670 (2012).
[Crossref]

H.-P. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, Th. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012).
[Crossref]

2011 (1)

2010 (5)

2009 (3)

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5, 276–280 (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. W. Hänsch, and Th. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96, 251–256 (2009).
[Crossref]

2008 (4)

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and Th. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (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]

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D 48, 57–66 (2008).
[Crossref]

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

2007 (2)

M. T. Murphy, Th. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. W. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

J. J. McFerran, L. Nenadovic, W. C. Swann, J. B. Schlager, and N. R. Newbury, “A passively mode-locked fiber laser at 1.54 μm with a fundamental repetition frequency reaching 2 GHz,” Opt. Express 15, 13155–13166 (2007).
[Crossref] [PubMed]

2002 (1)

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

1998 (1)

Z. F. Fan, P. J. S. Heim, and M. Dagenais, “Highly coherent RF signal generation by heterodyne optical phase locking of external cavity semiconductor lasers,” IEEE Photonics Technol. Lett. 10, 719–721 (1998).
[Crossref]

1995 (2)

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. W. Hänsch, “A compact grating-stabilized diode-laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

M. Mayor and D. Queloz, “A Jupiter-mass companion to a solar-type star,” Nature 378, 355–359 (1995).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics(Academic, 1989).

Araujo-Hauck, C.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and Th. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96, 251–256 (2009).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and Th. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, Th. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. W. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Avila, G.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Bartels, A.

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref] [PubMed]

Bender, C. F.

Benedick, A. J.

Birge, J. R.

Bonifacio, P.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Botzer, B.

Bouchy, F.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Braje, D. A.

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D 48, 57–66 (2008).
[Crossref]

Brenn, A.

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5, 276–280 (2009).
[Crossref]

Chang, G.

D. F. Phillips, A. G. Glenday, C.-H. Li, C. Cramer, G. Furesz, G. Chang, A. J. Benedick, L.-J. Chen, F. X. Kärtner, S. Korzennik, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “Calibration of an astrophysical spectrograph below 1 m/s using a laser frequency comb,” Opt. Express 20, 13711–13726 (2012).
[Crossref] [PubMed]

H.-W. Chen, G. Chang, S. Xu, Z. Yang, and F. X. Kärtner, “3 GHz, fundamentally mode-locked, femtosecond Yb-fiber laser,” Opt. Lett. 37, 3522–3524 (2012).
[Crossref] [PubMed]

G. Chang, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, R. L. Walsworth, and F. X. Kärtner, “Optimization of filtering schemes for broadband astro-combs,” Opt. Express 20, 24987–25013 (2012).
[Crossref] [PubMed]

A. J. Benedick, G. Chang, J. R. Birge, L.-J. Chen, A. G. Glenday, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, S. Korzennik, G. Furesz, R. L. Walsworth, and F. X. Kärtner, “Visible wavelength astro-comb,” Opt. Express 18, 19175–19184 (2010).
[Crossref] [PubMed]

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Chang, L.-J. Chen, C. Cramer, P. Fendel, G. Furesz, F. X. Kärtner, S. Korzennik, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “In-situ determination of astro-comb calibrator lines to better than 10 cm s−1,” Opt. Express 18, 13239–13249 (2010).
[Crossref] [PubMed]

G. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kaertner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express 18, 12736–12747 (2010).
[Crossref] [PubMed]

Chen, H.-W.

Chen, L.-J.

Cramer, C.

Cristiani, S.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Curto, G. L.

T. Wilken, R. Probst, T. W. Hänsch, Th. Udem, T. Steinmetz, R. Holzwarth, A. Manescau, G. L. Curto, L. Pasquini, S. Stark, H. Hundertmark, and P. St. J. Russell, “Suppressed mode recovery in nonlinear fibers of a Fabry-Perot-filtered frequency comb,” in “CLEO:2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011), p. CWQ2.

D’Odorico, S.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and Th. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, Th. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. W. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

D’Odorico, V.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Dagenais, M.

Z. F. Fan, P. J. S. Heim, and M. Dagenais, “Highly coherent RF signal generation by heterodyne optical phase locking of external cavity semiconductor lasers,” IEEE Photonics Technol. Lett. 10, 719–721 (1998).
[Crossref]

Dekker, H.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

M. T. Murphy, Th. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. W. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Delabre, B.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Dessauges, M.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Diddams, S. A.

G. G. Ycas, F. Quinlan, S. A. Diddams, S. Osterman, S. Mahadevan, S. Redman, R. Terrien, L. Ramsey, C. F. Bender, B. Botzer, and S. Sigurdsson, “Demonstration of on-sky calibration of astronomical spectra using a 25 GHz near-IR laser frequency comb,” Opt. Express 20, 6631–6643 (2012).
[Crossref] [PubMed]

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-spaced optical frequency comb spanning >400 nm for near-infrared astronomical spectrograph calibration,” Rev. Sci. Instrum. 81, 063105 (2010).
[Crossref] [PubMed]

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref] [PubMed]

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D 48, 57–66 (2008).
[Crossref]

Doerr, H.-P.

H.-P. Doerr, T. Steinmetz, R. Holzwarth, T. Kentischer, and W. Schmidt, “Laser frequency comb system for absolute calibration of the VTT echelle spectrograph,” Solar Phys. 280, 663–670 (2012).
[Crossref]

H.-P. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, Th. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012).
[Crossref]

Esslinger, T.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. W. Hänsch, “A compact grating-stabilized diode-laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Fan, Z. F.

Z. F. Fan, P. J. S. Heim, and M. Dagenais, “Highly coherent RF signal generation by heterodyne optical phase locking of external cavity semiconductor lasers,” IEEE Photonics Technol. Lett. 10, 719–721 (1998).
[Crossref]

Fendel, P.

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Chang, L.-J. Chen, C. Cramer, P. Fendel, G. Furesz, F. X. Kärtner, S. Korzennik, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “In-situ determination of astro-comb calibrator lines to better than 10 cm s−1,” Opt. Express 18, 13239–13249 (2010).
[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]

Fischer, M.

M. T. Murphy, Th. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. W. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++(Cambridge University, 2002).

Fortier, T.

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D 48, 57–66 (2008).
[Crossref]

Franz, M.

H.-P. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, Th. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012).
[Crossref]

Furesz, G.

Glenday, A. G.

Gonzalez Hernandez, J. I.

T. Wilken, G. Lo Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. Gonzalez Hernandez, R. Rebolo, T. W. Haensch, Th. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485, 611–614 (2012).
[Crossref] [PubMed]

Grazian, A.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Haehnelt, M.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Haensch, T. W.

T. Wilken, G. Lo Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. Gonzalez Hernandez, R. Rebolo, T. W. Haensch, Th. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485, 611–614 (2012).
[Crossref] [PubMed]

Hänsch, T. W.

H.-P. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, Th. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012).
[Crossref]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, Th. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19, 15690–15695 (2011).
[Crossref] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and Th. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. 405, L16–L20 (2010).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and Th. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96, 251–256 (2009).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and Th. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, Th. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. W. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. W. Hänsch, “A compact grating-stabilized diode-laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

T. Wilken, R. Probst, T. W. Hänsch, Th. Udem, T. Steinmetz, R. Holzwarth, A. Manescau, G. L. Curto, L. Pasquini, S. Stark, H. Hundertmark, and P. St. J. Russell, “Suppressed mode recovery in nonlinear fibers of a Fabry-Perot-filtered frequency comb,” in “CLEO:2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011), p. CWQ2.

Heim, P. J. S.

Z. F. Fan, P. J. S. Heim, and M. Dagenais, “Highly coherent RF signal generation by heterodyne optical phase locking of external cavity semiconductor lasers,” IEEE Photonics Technol. Lett. 10, 719–721 (1998).
[Crossref]

Heinecke, D.

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref] [PubMed]

Hemmerich, A.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. W. Hänsch, “A compact grating-stabilized diode-laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Holzwarth, R.

T. Wilken, G. Lo Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. Gonzalez Hernandez, R. Rebolo, T. W. Haensch, Th. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485, 611–614 (2012).
[Crossref] [PubMed]

H.-P. Doerr, T. Steinmetz, R. Holzwarth, T. Kentischer, and W. Schmidt, “Laser frequency comb system for absolute calibration of the VTT echelle spectrograph,” Solar Phys. 280, 663–670 (2012).
[Crossref]

H.-P. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, Th. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012).
[Crossref]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, Th. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19, 15690–15695 (2011).
[Crossref] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and Th. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. 405, L16–L20 (2010).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and Th. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96, 251–256 (2009).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and Th. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, Th. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. W. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

T. Wilken, R. Probst, T. W. Hänsch, Th. Udem, T. Steinmetz, R. Holzwarth, A. Manescau, G. L. Curto, L. Pasquini, S. Stark, H. Hundertmark, and P. St. J. Russell, “Suppressed mode recovery in nonlinear fibers of a Fabry-Perot-filtered frequency comb,” in “CLEO:2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011), p. CWQ2.

Hundertmark, H.

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, Th. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19, 15690–15695 (2011).
[Crossref] [PubMed]

T. Wilken, R. Probst, T. W. Hänsch, Th. Udem, T. Steinmetz, R. Holzwarth, A. Manescau, G. L. Curto, L. Pasquini, S. Stark, H. Hundertmark, and P. St. J. Russell, “Suppressed mode recovery in nonlinear fibers of a Fabry-Perot-filtered frequency comb,” in “CLEO:2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011), p. CWQ2.

Kaertner, F. X.

Kang, M. S.

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5, 276–280 (2009).
[Crossref]

Kärtner, F. X.

D. F. Phillips, A. G. Glenday, C.-H. Li, C. Cramer, G. Furesz, G. Chang, A. J. Benedick, L.-J. Chen, F. X. Kärtner, S. Korzennik, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “Calibration of an astrophysical spectrograph below 1 m/s using a laser frequency comb,” Opt. Express 20, 13711–13726 (2012).
[Crossref] [PubMed]

H.-W. Chen, G. Chang, S. Xu, Z. Yang, and F. X. Kärtner, “3 GHz, fundamentally mode-locked, femtosecond Yb-fiber laser,” Opt. Lett. 37, 3522–3524 (2012).
[Crossref] [PubMed]

G. Chang, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, R. L. Walsworth, and F. X. Kärtner, “Optimization of filtering schemes for broadband astro-combs,” Opt. Express 20, 24987–25013 (2012).
[Crossref] [PubMed]

A. J. Benedick, G. Chang, J. R. Birge, L.-J. Chen, A. G. Glenday, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, S. Korzennik, G. Furesz, R. L. Walsworth, and F. X. Kärtner, “Visible wavelength astro-comb,” Opt. Express 18, 19175–19184 (2010).
[Crossref] [PubMed]

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Chang, L.-J. Chen, C. Cramer, P. Fendel, G. Furesz, F. X. Kärtner, S. Korzennik, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “In-situ determination of astro-comb calibrator lines to better than 10 cm s−1,” Opt. Express 18, 13239–13249 (2010).
[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]

Kentischer, T.

H.-P. Doerr, T. Steinmetz, R. Holzwarth, T. Kentischer, and W. Schmidt, “Laser frequency comb system for absolute calibration of the VTT echelle spectrograph,” Solar Phys. 280, 663–670 (2012).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and Th. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

Kentischer, T. J.

H.-P. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, Th. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012).
[Crossref]

Kirchner, M. S.

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D 48, 57–66 (2008).
[Crossref]

König, W.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. W. Hänsch, “A compact grating-stabilized diode-laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Korzennik, S.

Lawrence, J. S.

M. T. Murphy, C. R. Locke, P. S. Light, A. N. Luiten, and J. S. Lawrence, “Laser frequency comb techniques for precise astronomical spectroscopy,” Mon. Not. R. Astron. Soc. 422, 761–771 (2012).
[Crossref]

Levshakov, S.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Li, C.-H.

D. F. Phillips, A. G. Glenday, C.-H. Li, C. Cramer, G. Furesz, G. Chang, A. J. Benedick, L.-J. Chen, F. X. Kärtner, S. Korzennik, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “Calibration of an astrophysical spectrograph below 1 m/s using a laser frequency comb,” Opt. Express 20, 13711–13726 (2012).
[Crossref] [PubMed]

G. Chang, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, R. L. Walsworth, and F. X. Kärtner, “Optimization of filtering schemes for broadband astro-combs,” Opt. Express 20, 24987–25013 (2012).
[Crossref] [PubMed]

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Chang, L.-J. Chen, C. Cramer, P. Fendel, G. Furesz, F. X. Kärtner, S. Korzennik, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “In-situ determination of astro-comb calibrator lines to better than 10 cm s−1,” Opt. Express 18, 13239–13249 (2010).
[Crossref] [PubMed]

A. J. Benedick, G. Chang, J. R. Birge, L.-J. Chen, A. G. Glenday, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, S. Korzennik, G. Furesz, R. L. Walsworth, and F. X. Kärtner, “Visible wavelength astro-comb,” Opt. Express 18, 19175–19184 (2010).
[Crossref] [PubMed]

G. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kaertner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express 18, 12736–12747 (2010).
[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]

Light, P. S.

M. T. Murphy, C. R. Locke, P. S. Light, A. N. Luiten, and J. S. Lawrence, “Laser frequency comb techniques for precise astronomical spectroscopy,” Mon. Not. R. Astron. Soc. 422, 761–771 (2012).
[Crossref]

Liske, J.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Lo Curto, G.

T. Wilken, G. Lo Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. Gonzalez Hernandez, R. Rebolo, T. W. Haensch, Th. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485, 611–614 (2012).
[Crossref] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and Th. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. 405, L16–L20 (2010).
[Crossref]

Locke, C. R.

M. T. Murphy, C. R. Locke, P. S. Light, A. N. Luiten, and J. S. Lawrence, “Laser frequency comb techniques for precise astronomical spectroscopy,” Mon. Not. R. Astron. Soc. 422, 761–771 (2012).
[Crossref]

Lovis, C.

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T. Wilken, R. Probst, T. W. Hänsch, Th. Udem, T. Steinmetz, R. Holzwarth, A. Manescau, G. L. Curto, L. Pasquini, S. Stark, H. Hundertmark, and P. St. J. Russell, “Suppressed mode recovery in nonlinear fibers of a Fabry-Perot-filtered frequency comb,” in “CLEO:2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011), p. CWQ2.

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H.-P. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, Th. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012).
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T. Wilken, G. Lo Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. Gonzalez Hernandez, R. Rebolo, T. W. Haensch, Th. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485, 611–614 (2012).
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Schlager, J. B.

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H.-P. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, Th. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012).
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H.-P. Doerr, T. Steinmetz, R. Holzwarth, T. Kentischer, and W. Schmidt, “Laser frequency comb system for absolute calibration of the VTT echelle spectrograph,” Solar Phys. 280, 663–670 (2012).
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H.-P. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, Th. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012).
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T. Wilken, G. Lo Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. Gonzalez Hernandez, R. Rebolo, T. W. Haensch, Th. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485, 611–614 (2012).
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T. Wilken, R. Probst, T. W. Hänsch, Th. Udem, T. Steinmetz, R. Holzwarth, A. Manescau, G. L. Curto, L. Pasquini, S. Stark, H. Hundertmark, and P. St. J. Russell, “Suppressed mode recovery in nonlinear fibers of a Fabry-Perot-filtered frequency comb,” in “CLEO:2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011), p. CWQ2.

Udry, S.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Vanzella, E.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++(Cambridge University, 2002).

Viel, M.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Vuletic, V.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. W. Hänsch, “A compact grating-stabilized diode-laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Walsworth, R. L.

G. Chang, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, R. L. Walsworth, and F. X. Kärtner, “Optimization of filtering schemes for broadband astro-combs,” Opt. Express 20, 24987–25013 (2012).
[Crossref] [PubMed]

D. F. Phillips, A. G. Glenday, C.-H. Li, C. Cramer, G. Furesz, G. Chang, A. J. Benedick, L.-J. Chen, F. X. Kärtner, S. Korzennik, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “Calibration of an astrophysical spectrograph below 1 m/s using a laser frequency comb,” Opt. Express 20, 13711–13726 (2012).
[Crossref] [PubMed]

A. J. Benedick, G. Chang, J. R. Birge, L.-J. Chen, A. G. Glenday, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, S. Korzennik, G. Furesz, R. L. Walsworth, and F. X. Kärtner, “Visible wavelength astro-comb,” Opt. Express 18, 19175–19184 (2010).
[Crossref] [PubMed]

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Chang, L.-J. Chen, C. Cramer, P. Fendel, G. Furesz, F. X. Kärtner, S. Korzennik, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “In-situ determination of astro-comb calibrator lines to better than 10 cm s−1,” Opt. Express 18, 13239–13249 (2010).
[Crossref] [PubMed]

G. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kaertner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express 18, 12736–12747 (2010).
[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]

Weidemüller, M.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. W. Hänsch, “A compact grating-stabilized diode-laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Wiklind, T.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Wilken, T.

T. Wilken, G. Lo Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. Gonzalez Hernandez, R. Rebolo, T. W. Haensch, Th. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485, 611–614 (2012).
[Crossref] [PubMed]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, Th. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19, 15690–15695 (2011).
[Crossref] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and Th. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. 405, L16–L20 (2010).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and Th. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96, 251–256 (2009).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and Th. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

T. Wilken, R. Probst, T. W. Hänsch, Th. Udem, T. Steinmetz, R. Holzwarth, A. Manescau, G. L. Curto, L. Pasquini, S. Stark, H. Hundertmark, and P. St. J. Russell, “Suppressed mode recovery in nonlinear fibers of a Fabry-Perot-filtered frequency comb,” in “CLEO:2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011), p. CWQ2.

Xu, S.

Yang, Z.

Ycas, G.

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-spaced optical frequency comb spanning >400 nm for near-infrared astronomical spectrograph calibration,” Rev. Sci. Instrum. 81, 063105 (2010).
[Crossref] [PubMed]

Ycas, G. G.

Zimmermann, C.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. W. Hänsch, “A compact grating-stabilized diode-laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Zucker, S.

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

Appl. Phys. B (1)

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and Th. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96, 251–256 (2009).
[Crossref]

Eur. Phys. J. D (1)

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D 48, 57–66 (2008).
[Crossref]

IEEE Photonics Technol. Lett. (1)

Z. F. Fan, P. J. S. Heim, and M. Dagenais, “Highly coherent RF signal generation by heterodyne optical phase locking of external cavity semiconductor lasers,” IEEE Photonics Technol. Lett. 10, 719–721 (1998).
[Crossref]

Mon. Not. R. Astron. Soc. (4)

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and Th. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. 405, L16–L20 (2010).
[Crossref]

J. Liske, A. Grazian, E. Vanzella, M. Dessauges, M. Viel, L. Pasquini, M. Haehnelt, S. Cristiani, F. Pepe, G. Avila, P. Bonifacio, F. Bouchy, H. Dekker, B. Delabre, S. D’Odorico, V. D’Odorico, S. Levshakov, C. Lovis, M. Mayor, P. Molaro, L. Moscardini, M. T. Murphy, D. Queloz, P. Shaver, S. Udry, T. Wiklind, and S. Zucker, “Cosmic dynamics in the era of extremely large telescopes,” Mon. Not. R. Astron. Soc. 386, 1192–1218 (2008).
[Crossref]

M. T. Murphy, Th. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. W. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

M. T. Murphy, C. R. Locke, P. S. Light, A. N. Luiten, and J. S. Lawrence, “Laser frequency comb techniques for precise astronomical spectroscopy,” Mon. Not. R. Astron. Soc. 422, 761–771 (2012).
[Crossref]

Nat. Phys. (1)

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5, 276–280 (2009).
[Crossref]

Nature (4)

T. Wilken, G. Lo Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. Gonzalez Hernandez, R. Rebolo, T. W. Haensch, Th. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485, 611–614 (2012).
[Crossref] [PubMed]

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref] [PubMed]

M. Mayor and D. Queloz, “A Jupiter-mass companion to a solar-type star,” Nature 378, 355–359 (1995).
[Crossref]

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]

Opt. Commun. (1)

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. W. Hänsch, “A compact grating-stabilized diode-laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Opt. Express (8)

G. Chang, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, R. L. Walsworth, and F. X. Kärtner, “Optimization of filtering schemes for broadband astro-combs,” Opt. Express 20, 24987–25013 (2012).
[Crossref] [PubMed]

A. J. Benedick, G. Chang, J. R. Birge, L.-J. Chen, A. G. Glenday, C.-H. Li, D. F. Phillips, A. Szentgyorgyi, S. Korzennik, G. Furesz, R. L. Walsworth, and F. X. Kärtner, “Visible wavelength astro-comb,” Opt. Express 18, 19175–19184 (2010).
[Crossref] [PubMed]

J. J. McFerran, L. Nenadovic, W. C. Swann, J. B. Schlager, and N. R. Newbury, “A passively mode-locked fiber laser at 1.54 μm with a fundamental repetition frequency reaching 2 GHz,” Opt. Express 15, 13155–13166 (2007).
[Crossref] [PubMed]

D. F. Phillips, A. G. Glenday, C.-H. Li, C. Cramer, G. Furesz, G. Chang, A. J. Benedick, L.-J. Chen, F. X. Kärtner, S. Korzennik, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “Calibration of an astrophysical spectrograph below 1 m/s using a laser frequency comb,” Opt. Express 20, 13711–13726 (2012).
[Crossref] [PubMed]

G. G. Ycas, F. Quinlan, S. A. Diddams, S. Osterman, S. Mahadevan, S. Redman, R. Terrien, L. Ramsey, C. F. Bender, B. Botzer, and S. Sigurdsson, “Demonstration of on-sky calibration of astronomical spectra using a 25 GHz near-IR laser frequency comb,” Opt. Express 20, 6631–6643 (2012).
[Crossref] [PubMed]

G. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kaertner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express 18, 12736–12747 (2010).
[Crossref] [PubMed]

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Chang, L.-J. Chen, C. Cramer, P. Fendel, G. Furesz, F. X. Kärtner, S. Korzennik, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “In-situ determination of astro-comb calibrator lines to better than 10 cm s−1,” Opt. Express 18, 13239–13249 (2010).
[Crossref] [PubMed]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, Th. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19, 15690–15695 (2011).
[Crossref] [PubMed]

Opt. Lett. (1)

Proc. SPIE (1)

H.-P. Doerr, T. J. Kentischer, T. Steinmetz, R. A. Probst, M. Franz, R. Holzwarth, Th. Udem, T. W. Hänsch, and W. Schmidt, “Performance of a laser frequency comb calibration system with a high-resolution solar echelle spectrograph,” Proc. SPIE 8450, 84501G (2012).
[Crossref]

Rev. Sci. Instrum. (1)

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-spaced optical frequency comb spanning >400 nm for near-infrared astronomical spectrograph calibration,” Rev. Sci. Instrum. 81, 063105 (2010).
[Crossref] [PubMed]

Science (2)

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and Th. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref] [PubMed]

Solar Phys. (1)

H.-P. Doerr, T. Steinmetz, R. Holzwarth, T. Kentischer, and W. Schmidt, “Laser frequency comb system for absolute calibration of the VTT echelle spectrograph,” Solar Phys. 280, 663–670 (2012).
[Crossref]

Other (4)

G. P. Agrawal, Nonlinear Fiber Optics(Academic, 1989).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++(Cambridge University, 2002).

J. Schneider, “The extrasolar planets encyclopaedia,” http://exoplanet.eu/catalog.php .

T. Wilken, R. Probst, T. W. Hänsch, Th. Udem, T. Steinmetz, R. Holzwarth, A. Manescau, G. L. Curto, L. Pasquini, S. Stark, H. Hundertmark, and P. St. J. Russell, “Suppressed mode recovery in nonlinear fibers of a Fabry-Perot-filtered frequency comb,” in “CLEO:2011 - Laser Applications to Photonic Applications,” (Optical Society of America, 2011), p. CWQ2.

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Figures (12)

Fig. 1
Fig. 1

(a) Frequency domain: A Fabry-Pérot cavity is used as a spectral filter. Its free spectral range is an integer multiple (here m = 4) of the initial mode spacing ωr = 2π/Tr. (b) The finite finesse of the cavity leads to unwanted side-modes to each principal mode. (c) In the time domain the pulse stored inside the cavity gets replenished by the next pulse from the initial pulse train only every mth round trip. The finite finesse leads to an exponential decay of the pulse energy between these events with a normalized electric field reduction h. The resulting amplitude modulation causes the side bands to appear.

Fig. 2
Fig. 2

Spectral envelope of the principal modes (black line) and interleaved side-modes (red line), for a filter ratio of m = 2 and an initial suppression of 74 dB. The optical pulses are initially transform limited with 100 fs FWHM pulse duration and Gaussian shape. (a) Before nonlinear propagation. (b) After nonlinear propagation over a distance of 44 times the nonlinear length.

Fig. 3
Fig. 3

Side-mode suppression versus optical frequency after propagation over 44 times the nonlinear length for different values of the initial side-mode suppression. The initial suppression is written at each curve, and the filter ratio is m = 2. The optical pulses have a 100 fs FWHM pulse duration with a Gaussian envelope and no initial chirp.

Fig. 4
Fig. 4

(a) Evolution of the RMS-bandwidth as a function of the propagation length z for Gaussian pulses with 100 fs FWHM pulse duration, 74 dB initial side-mode suppression and different initial chirps C. Red dashed line: Approximation given by Eq. (5). (b) Evolution of the average side-mode suppression (independent of chirp and pulse duration) and the lowest side-mode suppression within the −20 dB-bandwidth for initially unchirped pulses.

Fig. 5
Fig. 5

(a) RMS-bandwidth versus propagation length for different initial suppressions. For initial suppressions ≥54 dB the curves are virtually identical. The dashed line is the linear approximation given by Eq. (5). (b) Average side-mode suppression versus propagation length for different initial suppressions. Here, the dashed lines represent the approximation for high side-mode suppression given by Eq. (6). In all cases, the pulses are assumed to have a 100 fs FWHM duration, Gaussian shape, and no initial chirp.

Fig. 6
Fig. 6

Evolution of (a) the RMS-bandwidth and (b) the average side-mode suppression during nonlinear propagation for initially unchirped 100 fs-pulses in different dispersion regimes. The curve for normal dispersion assumes +25 fs2 per initial LNL. In the case of anomalous dispersion solitons of various orders are formed depending on the amount of dispersion. The pulses are launched with a Gaussian shape except for the first order soliton, which starts out as a sech2 pulse.

Fig. 7
Fig. 7

Average side-mode suppression versus spectral bandwidth, with and without self-steepening and self-phase modulation (SPM). All other parameters are the same as in Fig. 2. (a) Comparison of pure self-steepening with pure SPM. (b) Comparison of a mixture of self-steepening and SPM with pure SPM. In all cases, the curve that includes self-steepening is below the one for pure SPM. This means, that for a given amount of spectral broadening, self-steepening amplifies the side-modes less than SPM.

Fig. 8
Fig. 8

Basic experimental setup of which several variations have been used in the experiments described here. Comb: 250 MHz mode-locked ytterbium-doped fiber frequency comb; Nd:YAG: Neodymium-doped continuous-wave laser; ECDL: External-cavity diode laser; Yb-amp: Ytterbium-doped fiber power amplifier; GPC: Combined grating and prism compressor; SHG: Second-harmonic generation stage; HWP: Half-wave plate; PCF: Tapered photonic crystal fiber.

Fig. 9
Fig. 9

Mode suppression at 1064 (532) nm with two filter cavities of 2.25 GHz and 18 GHz FSR: Beat measurement before SHG (red circles), theoretically expected values before SHG (hollow circles) and beat measurement after SHG (blue triangles). Inset: Larger section of the comb structure with principal modes and side-modes. The red square shows the modes under investigation. Bottom: Difference of side-mode suppression before and after SHG. The dashed line marks the 6 dB-level.

Fig. 10
Fig. 10

Heterodyne measurement of the principal (black) and side-mode powers (colored) around 532 nm of the broadened frequency comb. The optical power for SPM was varied by changing the pump current of the Yb-fiber amplifier of the astro-comb (see Fig. 8). The corresponding shift of the center of gravity of the group of lines is shown below each plot. For large currents some of the side-modes are amplified to powers exceeding the principal mode. In this situation we also observe strong polarization dependence of the side-mode amplification as shown at the lower graph. The dashed vertical lines indicate when the half-wave plate in front of the PCF was rotated by 20°. Side-mode color code: +2 GHz, −2 GHz, + 4GHz and −4 GHz. The side-mode suppression before spectral broadening was 32 dB.

Fig. 11
Fig. 11

Heterodyne beat note measurement at 532 nm of the principal and two strongest side-modes of a frequency doubled and spectrally broadened comb. The signal of the principal mode appears at 40 MHz, while the signal of the side-modes at +2250 MHz (−2250 MHz) appear at 2290 MHz (2210 MHz). The indicated values for the side-mode suppression include corrections for the RF-electronics.

Fig. 12
Fig. 12

Suppression of the strongest side-mode measured at 3 different wavelengths at the Tenerife VTT astro-comb system. The three red squares indicate subsequent measurements without any action taken in between. The black circles are measurements with different polarization directions before the PCF.

Equations (21)

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U ( z = 0 , T ) = exp [ ( 1 + i C ) T 2 2 T 0 2 ]
U ( z , T ) = U ( 0 , T ) exp ( i ϕ N L ) , ϕ N L = | U ( 0 , T ) | 2 z L N L
S ( ω ) = | + [ U ( z , T ) + h U ( h 2 z , T ) exp ( i ω T r 2 ) ] exp [ i ( ω ω c ) T ] d T | 2
2 π Δ f R M S = 2 ln ( 2 ) T F W H M 1 2 + C 2 2 + C 2 z L N L + 2 3 3 ( z L N L ) 2
2 π Δ f R M S 1 T F W H M 2 2 ln ( 2 ) 3 3 ( 3 4 3 2 C + z L N L )
A avg = 1 + 4 3 ( z L N L ) 2
A < 10 [ 1 + 6 π 2 ln ( 2 ) ( T F W H M Δ f R M S ) 2 ]
A avg = 4 B 2 n = S n n = P n
2 π Δ f R M S = n = ( n ω r ) 2 S ( n ω r ) n = S ( n ω r ) ( n = n ω r S ( n ω r ) n = S ( n ω r ) ) 2
2 π Δ f R M S = n = ( 2 n ω r ) 2 P n n = P n
f ( T ) = exp [ ( 1 + i C ) T 2 2 T 0 2 + i 2 A ( T ) ] , A ( T ) = 2 z L N L exp ( T 2 T 0 2 )
P n = S ( 2 n ω r ) = [ U ( z , T ) + ( 1 B ) U ( ( 1 2 B ) z , T ) ] e + i 4 π n T / T r d T × [ U * ( z , T ) + ( 1 B ) U * ( ( 1 2 B ) z , T ) ] e i 4 π n T / T r d T
= [ f ( T ) + ( 1 B ) f ( T ) e i B A ( T ) ] e + i 4 π n T / T r d T × [ f * ( T ) + ( 1 B ) f * ( T ) e + i B A ( T ) ] e i 4 π n T / T r d T .
n = P n = n = f ( T ) f * ( T ) [ 1 + ( 1 B ) ( e i B A ( T ) + e + i B A ( T ) ) + ( 1 B 2 ) e i B ( A ( T ) A ( T ) ) ] e i 4 π n ( T T ) / T r d T d T
T r 2 f ( T ) f * ( T ) [ 1 + ( 1 B ) ( e i B A ( T ) + e + i B A ( T ) ) + ( 1 B 2 ) e i B ( A ( T ) A ( T ) ) ] δ ( T T ) d T d T
n = P n = 2 π T r T 0
n = S n = π 2 T r T 0 B 2 [ 1 + 4 3 ( z L N L ) 2 ]
n = ( 2 n ω r ) 2 P n 16 ( 2 π T r ) 2 f ( T ) f * ( T ) n = n 2 e i 4 π n ( T T ) / T r d T d T
2 T r f ( T ) f * ( T ) δ ( T T ) d T d T
= 2 T r f ( T ) [ d 2 d T 2 f * ( T ) ] d T
= 2 π T r T 0 [ 1 2 + C 2 2 + C 2 z L N L + 2 3 3 ( z L N L ) 2 ]

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