Abstract

We propose and analyze a new approach to generate a broadband astro-comb by spectral broadening of a narrowband astro-comb inside a highly nonlinear optical fiber. Numerical modeling shows that cascaded four-wave-mixing dramatically degrades the input comb’s side-mode suppression and causes side-mode amplitude asymmetry. These two detrimental effects can systematically shift the center-of-gravity of astro-comb spectral lines as measured by an astrophysical spectrograph with resolution ≈100,000; and thus lead to wavelength calibration inaccuracy and instability. Our simulations indicate that this performance penalty, as a result of nonlinear spectral broadening, can be compensated by using a filtering cavity configured for double-pass. As an explicit example, we present a design based on an Yb-fiber source comb (with 1 GHz repetition rate) that is filtered by double-passing through a low finesse cavity (finesse = 208), and subsequent spectrally broadened in a 2-cm, SF6-glass photonic crystal fiber. Spanning more than 300 nm with 16 GHz line spacing, the resulting astro-comb is predicted to provide 1 cm/s (~10 kHz) radial velocity calibration accuracy for an astrophysical spectrograph. Such extreme performance will be necessary for the search for and characterization of Earth-like extra-solar planets, and in direct measurements of the change of the rate of cosmological expansion.

© 2010 OSA

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References

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  1. M. T. Murphy, T. 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(2), 839–847 (2007).
    [Crossref]
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    [Crossref] [PubMed]
  3. 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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  6. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 251–256 (2009).
    [Crossref]
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    [Crossref] [PubMed]
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2009 (3)

2008 (3)

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (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(1), 57–66 (2008).
[Crossref]

2007 (1)

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

2004 (1)

2003 (1)

2002 (2)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O Hedekvist, “Fiber-based optical parametric amplifiers and their Applications,” IEEE Sel. Top Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

A. L. Gaeta, “Nonlinear propagation and continuum generation in microstructured optical fibers,” Opt. Lett. 27(11), 924–926 (2002).
[Crossref]

Andrekson, P. A.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O Hedekvist, “Fiber-based optical parametric amplifiers and their Applications,” IEEE Sel. Top Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Araujo-Hauck, C.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Benedick, A. J.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

Braje, D. A.

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34(7), 872–874 (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(1), 57–66 (2008).
[Crossref]

Chang, G. Q.

Coen, S.

D’Odorico, S.

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Dekker, H.

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Diddams, S. A.

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34(7), 872–874 (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(1), 57–66 (2008).
[Crossref]

D'Odorico, S.

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Dudley, J. M.

Fendel, P.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

Fischer, M.

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

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(1), 57–66 (2008).
[Crossref]

Fortier, T. M.

Gaeta, A. L.

Glenday, A. G.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

Hänsch, T. W.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 251–256 (2009).
[Crossref]

H. Hundertmark, S. Rammler, T. Wilken, R. Holzwarth, T. W. Hänsch, and P. St. J. Russell, “Octave-spanning supercontinuum generated in SF6-glass PCF by a 1060 nm mode-locked fibre laser delivering 20 pJ per pulse,” Opt. Express 17(3), 1919–1924 (2009).
[Crossref] [PubMed]

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O Hedekvist, “Fiber-based optical parametric amplifiers and their Applications,” IEEE Sel. Top Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Hedekvist, P. O

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O Hedekvist, “Fiber-based optical parametric amplifiers and their Applications,” IEEE Sel. Top Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Hollberg, L.

Holzwarth, R.

H. Hundertmark, S. Rammler, T. Wilken, R. Holzwarth, T. W. Hänsch, and P. St. J. Russell, “Octave-spanning supercontinuum generated in SF6-glass PCF by a 1060 nm mode-locked fibre laser delivering 20 pJ per pulse,” Opt. Express 17(3), 1919–1924 (2009).
[Crossref] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Hundertmark, H.

Kärtner, F. X.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

Kentischer, T.

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Kirchner, M. S.

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34(7), 872–874 (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(1), 57–66 (2008).
[Crossref]

Li, C.-H.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

Li, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O Hedekvist, “Fiber-based optical parametric amplifiers and their Applications,” IEEE Sel. Top Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Manescau, A.

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Murphy, M. T.

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Norris, T. B.

Osterman, 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(1), 57–66 (2008).
[Crossref]

Pasquini, L.

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Phillips, D. F.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

Rammler, S.

Russell, P. St. J.

Sasselov, D.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

Schmidt, W.

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Sizmann, A.

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Steinmetz, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Szentgyorgyi, A.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

Udem, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Walsworth, R. L.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1),” Nature 452(7187), 610–612 (2008).
[Crossref] [PubMed]

Weiner, A. M.

Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O Hedekvist, “Fiber-based optical parametric amplifiers and their Applications,” IEEE Sel. Top Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Wilken, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 251–256 (2009).
[Crossref]

H. Hundertmark, S. Rammler, T. Wilken, R. Holzwarth, T. W. Hänsch, and P. St. J. Russell, “Octave-spanning supercontinuum generated in SF6-glass PCF by a 1060 nm mode-locked fibre laser delivering 20 pJ per pulse,” Opt. Express 17(3), 1919–1924 (2009).
[Crossref] [PubMed]

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Winful, H. G.

Appl. Phys. B (1)

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 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(1), 57–66 (2008).
[Crossref]

IEEE Sel. Top Quantum Electron. (1)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O Hedekvist, “Fiber-based optical parametric amplifiers and their Applications,” IEEE Sel. Top Quantum Electron. 8(3), 506–520 (2002).
[Crossref]

Mon. Not. R. Astron. Soc. (1)

M. T. Murphy, T. 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(2), 839–847 (2007).
[Crossref]

Nature (1)

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(7187), 610–612 (2008).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Science (1)

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 T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001), 3rd ed.

F. Quinlan, G. Ycas, S. Osterman, and S. Diddams, “A 12.5 GHz-spaced optical frequency comb spanning >400 nm for near-infrared astronomical spectrograph calibration,” arXiv:1002.4354v2.

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of proposed broadband astro-comb including 3 main components; and (b) sample of frequency comb spectrum for each stage, showing a narrow slice of the full spectrum. 56 dB and 68 dB in (b) indicate suppression of the first and second side-mode as the source comb double passes a Fabry-Perot (FP) cavity constructed using two identical mirrors of 98.5% reflectivity (see main text for more details).

Fig. 2
Fig. 2

Comparison of calculated power transmission and phase of individual source-comb lines for three different FP cavities: a low-finesse cavity at single-pass, low-finesse cavity at double-pass, and high-finesse cavity at single-pass. For the simulations, we assume a 1 GHz source comb filtered by a FP cavity with 16 GHz FSR. Note that the cavity phases for the low-finesse cavity and high-finesse cavity, both operating at single-pass, are almost indistinguishable.

Fig. 3
Fig. 3

Schematic to illustrate the time-domain modulation effect of FP cavity filtering of a uniform source-comb pulse train: (a) pulse train before FP cavity filtering; (b) pulse train after FP cavity filtering. In this example, f r a = 8 f r s , i.e., M = 8. Note that the amplitudes of these two pulse trains are displayed on different amplitude scales to emphasize the effect of finite FP cavity finesse — and hence finite side-mode suppression and time-domain amplitude modulation.

Fig. 4
Fig. 4

Simulation results corresponding to single-pass filtering with a low finesse cavity showing (a) power as a function of wavelength for each astro-comb line, with spacing of 16 GHz in the frequency domain (blue), the upper 1st side-mode 1 GHz above the astro-comb line (red), and the lower 1st side-mode 1 GHz below the astro-comb line (green) at the output of the 2-cm PCF. Inset is the input narrowband spectrum. (b) Suppression of both side-modes after nonlinear spectral broadening. The dashed line indicates suppression at the PCF input. Inset shows the suppression difference between the upper and lower 1st side-modes.

Fig. 5
Fig. 5

Simulation results corresponding to single-pass filtering with a low finesse cavity of flat phase, i.e. ϕ = 0 in Eq. (1). The power per astro-comb line (blue curve) and the power in the nearly equal upper and lower 1st side-modes (red curve) are shown vs. wavelength. The difference between the two side-modes (green curve) is caused by higher-order dispersion and nonlinearity in the PCF.

Fig. 6
Fig. 6

Simulation results corresponding to double-pass filtering with a low finesse cavity. (a) Suppression of the upper 1st (blue) and 2nd (red) side-modes. Insets show the suppression difference for the 1st (blue) and 2nd (red) side-modes. (b) Broadband astro-comb spectrum (green) and limit on RV calibration accuracy (blue) determined from side-mode suppression and asymmetry.

Fig. 7
Fig. 7

Simulation results corresponding to single-pass filtering with a high finesse cavity. (a) Suppression of the upper 1st (blue) and the upper 2nd (red) side-modes. Insets show suppression difference for the 1st (blue) and 2nd (red) side-modes. (b) Broadband astro-comb line intensity vs. wavelength (green), the RV calibration accuracy (blue), and an indication of the 10 cm/s accuracy level required for long-term surveys of earth-like extra-solar planets (dashed red line).

Equations (5)

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t s = ( 1 R ) / ( 1 R × e j φ ) = 1 R 1 2 R cos φ + R 2 e j ϕ .
A z + ( n = 2 β n i n 1 n ! n T n ) A = i γ ( 1 + i ω 0 T ) ( A ( z , T ) + R ( t ' ) | A ( z , T t ' ) | 2 d t ' ) ,
R ( t ) = ( 1 f R ) δ ( t ) + f R ( τ 1 2 + τ 2 2 ) / ( τ 1 τ 2 2 ) exp ( t / τ 2 ) sin ( t / τ 1 ) ,
Δ f f r s j = 1 m j ( ρ j u ρ j l ) ,
Δ R V = c Δ f f 0 c f r s f 0 j = 1 m j ( ρ j u ρ j l )

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