Abstract

To realize a broadband, large-line-spacing astro-comb, suitable for wavelength calibration of astrophysical spectrographs, from a narrowband, femtosecond laser frequency comb (“source-comb”), one must integrate the source-comb with three additional components: (1) one or more filter cavities to multiply the source-comb’s repetition rate and thus line spacing; (2) power amplifiers to boost the power of pulses from the filtered comb; and (3) highly nonlinear optical fiber to spectrally broaden the filtered and amplified narrowband frequency comb. In this paper we analyze the interplay of Fabry-Perot (FP) filter cavities with power amplifiers and nonlinear broadening fiber in the design of astro-combs optimized for radial-velocity (RV) calibration accuracy. We present analytic and numeric models and use them to evaluate a variety of FP filtering schemes (labeled as identical, co-prime, fraction-prime, and conjugate cavities), coupled to chirped-pulse amplification (CPA). We find that even a small nonlinear phase can reduce suppression of filtered comb lines, and increase RV error for spectrograph calibration. In general, filtering with two cavities prior to the CPA fiber amplifier outperforms an amplifier placed between the two cavities. In particular, filtering with conjugate cavities is able to provide <1 cm/s RV calibration error with >300 nm wavelength coverage. Such superior performance will facilitate the search for and characterization of Earth-like exoplanets, which requires <10 cm/s RV calibration error.

© 2012 OSA

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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]
  2. 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,” Nature 452(7187), 610–612 (2008).
    [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]
  4. 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]
  5. G. Q. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kärtner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express 18(12), 12736–12747 (2010).
    [CrossRef] [PubMed]
  6. T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
    [CrossRef]
  7. C.-H. Li, A. G. Glenday, A. J. Benedick, G. Q. 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?1,” Opt. Express 18(12), 13239–13249 (2010).
    [CrossRef] [PubMed]
  8. 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(6), 063105 (2010).
    [CrossRef] [PubMed]
  9. A. J. Benedick, G. Q. 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(18), 19175–19184 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
    [CrossRef] [PubMed]
  13. 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(6), 6631–6643 (2012).
    [CrossRef] [PubMed]
  14. L.-J. Chen, G. Q. Chang, C. H. Li, A. J. Benedick, D. F. Philips, R. L. Walsworth, and F. X. Kärtner, “Broadband dispersion-free optical cavities based on zero group delay dispersion mirror sets,” Opt. Express 18(22), 23204–23211 (2010).
    [CrossRef] [PubMed]
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  17. 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]
  18. C.-H. Li, G. Q. Chang, A. G. Glenday, N. Langellier, A. Zibrov, D. F. Phillips, F. X. Kärtner, A. Szentgyorgyi, and R. L. Walsworth, “Conjugate Fabry-Perot cavity pair for improved astro-comb accuracy,” Opt. Lett. 37(15), 3090–3092 (2012).
    [CrossRef] [PubMed]
  19. 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(17), 3522–3524 (2012).
    [CrossRef] [PubMed]

2012 (4)

2011 (2)

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, T. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19(17), 15690–15695 (2011).
[CrossRef] [PubMed]

G. Schettino, E. Oliva, M. Inguscio, C. Baffa, E. Giani, A. Tozzi, and P. C. Pastor, “Optical frequency comb as a general-purpose and wide-band calibration source for astronomical high resolution infrared spectrographs,” Exp. Astron. 31(1), 69–81 (2011).
[CrossRef]

2010 (6)

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[CrossRef]

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(6), 063105 (2010).
[CrossRef] [PubMed]

G. Q. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kärtner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express 18(12), 12736–12747 (2010).
[CrossRef] [PubMed]

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Q. 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?1,” Opt. Express 18(12), 13239–13249 (2010).
[CrossRef] [PubMed]

A. J. Benedick, G. Q. 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(18), 19175–19184 (2010).
[CrossRef] [PubMed]

L.-J. Chen, G. Q. Chang, C. H. Li, A. J. Benedick, D. F. Philips, R. L. Walsworth, and F. X. Kärtner, “Broadband dispersion-free optical cavities based on zero group delay dispersion mirror sets,” Opt. Express 18(22), 23204–23211 (2010).
[CrossRef] [PubMed]

2009 (2)

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,” 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]

Araujo-Hauck, C.

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]

Baffa, C.

G. Schettino, E. Oliva, M. Inguscio, C. Baffa, E. Giani, A. Tozzi, and P. C. Pastor, “Optical frequency comb as a general-purpose and wide-band calibration source for astronomical high resolution infrared spectrographs,” Exp. Astron. 31(1), 69–81 (2011).
[CrossRef]

Bender, C. F.

Benedick, A. J.

Birge, J. R.

Botzer, B.

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(1), 57–66 (2008).
[CrossRef]

Chang, G.

Chang, G. Q.

Chen, H.-W.

Chen, L.-J.

Cramer, C.

Curto, G. L.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

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.

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(6), 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(6), 063105 (2010).
[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]

Fendel, P.

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Q. 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?1,” Opt. Express 18(12), 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,” 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]

Furesz, G.

Giani, E.

G. Schettino, E. Oliva, M. Inguscio, C. Baffa, E. Giani, A. Tozzi, and P. C. Pastor, “Optical frequency comb as a general-purpose and wide-band calibration source for astronomical high resolution infrared spectrographs,” Exp. Astron. 31(1), 69–81 (2011).
[CrossRef]

Glenday, A. G.

González Hernández, J. I.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

Hänsch, T. W.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, T. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19(17), 15690–15695 (2011).
[CrossRef] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[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]

Holzwarth, R.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, T. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19(17), 15690–15695 (2011).
[CrossRef] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[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]

Hundertmark, H.

Inguscio, M.

G. Schettino, E. Oliva, M. Inguscio, C. Baffa, E. Giani, A. Tozzi, and P. C. Pastor, “Optical frequency comb as a general-purpose and wide-band calibration source for astronomical high resolution infrared spectrographs,” Exp. Astron. 31(1), 69–81 (2011).
[CrossRef]

Kärtner, F. X.

C.-H. Li, G. Q. Chang, A. G. Glenday, N. Langellier, A. Zibrov, D. F. Phillips, F. X. Kärtner, A. Szentgyorgyi, and R. L. Walsworth, “Conjugate Fabry-Perot cavity pair for improved astro-comb accuracy,” Opt. Lett. 37(15), 3090–3092 (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(17), 3522–3524 (2012).
[CrossRef] [PubMed]

G. Q. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kärtner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express 18(12), 12736–12747 (2010).
[CrossRef] [PubMed]

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Q. 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?1,” Opt. Express 18(12), 13239–13249 (2010).
[CrossRef] [PubMed]

L.-J. Chen, G. Q. Chang, C. H. Li, A. J. Benedick, D. F. Philips, R. L. Walsworth, and F. X. Kärtner, “Broadband dispersion-free optical cavities based on zero group delay dispersion mirror sets,” Opt. Express 18(22), 23204–23211 (2010).
[CrossRef] [PubMed]

A. J. Benedick, G. Q. 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(18), 19175–19184 (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,” 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.

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]

Korzennik, S.

Langellier, N.

Li, C. H.

Li, C.-H.

Limpert, J.

Lo Curto, G.

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[CrossRef]

Lovis, C.

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[CrossRef]

Mahadevan, S.

Manescau, A.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[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]

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]

Oliva, E.

G. Schettino, E. Oliva, M. Inguscio, C. Baffa, E. Giani, A. Tozzi, and P. C. Pastor, “Optical frequency comb as a general-purpose and wide-band calibration source for astronomical high resolution infrared spectrographs,” Exp. Astron. 31(1), 69–81 (2011).
[CrossRef]

Osterman, S.

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(6), 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(6), 063105 (2010).
[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]

Pasquini, L.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[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]

Pastor, P. C.

G. Schettino, E. Oliva, M. Inguscio, C. Baffa, E. Giani, A. Tozzi, and P. C. Pastor, “Optical frequency comb as a general-purpose and wide-band calibration source for astronomical high resolution infrared spectrographs,” Exp. Astron. 31(1), 69–81 (2011).
[CrossRef]

Philips, D. F.

Phillips, D. F.

Probst, R. A.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, T. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19(17), 15690–15695 (2011).
[CrossRef] [PubMed]

Quinlan, F.

Rammler, S.

Ramsey, L.

Rebolo, R.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

Redman, S.

Russell, P. St. J.

Sasselov, D.

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Q. 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?1,” Opt. Express 18(12), 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,” Nature 452(7187), 610–612 (2008).
[CrossRef] [PubMed]

Schettino, G.

G. Schettino, E. Oliva, M. Inguscio, C. Baffa, E. Giani, A. Tozzi, and P. C. Pastor, “Optical frequency comb as a general-purpose and wide-band calibration source for astronomical high resolution infrared spectrographs,” Exp. Astron. 31(1), 69–81 (2011).
[CrossRef]

Schimpf, D. N.

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]

Seise, E.

Sigurdsson, S.

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]

Stark, S. P.

Steinmetz, T.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, T. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19(17), 15690–15695 (2011).
[CrossRef] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[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.

Terrien, R.

Tozzi, A.

G. Schettino, E. Oliva, M. Inguscio, C. Baffa, E. Giani, A. Tozzi, and P. C. Pastor, “Optical frequency comb as a general-purpose and wide-band calibration source for astronomical high resolution infrared spectrographs,” Exp. Astron. 31(1), 69–81 (2011).
[CrossRef]

Tünnermann, A.

Udem, T.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, T. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19(17), 15690–15695 (2011).
[CrossRef] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[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, G. Q. Chang, A. G. Glenday, N. Langellier, A. Zibrov, D. F. Phillips, F. X. Kärtner, A. Szentgyorgyi, and R. L. Walsworth, “Conjugate Fabry-Perot cavity pair for improved astro-comb accuracy,” Opt. Lett. 37(15), 3090–3092 (2012).
[CrossRef] [PubMed]

L.-J. Chen, G. Q. Chang, C. H. Li, A. J. Benedick, D. F. Philips, R. L. Walsworth, and F. X. Kärtner, “Broadband dispersion-free optical cavities based on zero group delay dispersion mirror sets,” Opt. Express 18(22), 23204–23211 (2010).
[CrossRef] [PubMed]

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Q. 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?1,” Opt. Express 18(12), 13239–13249 (2010).
[CrossRef] [PubMed]

G. Q. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kärtner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express 18(12), 12736–12747 (2010).
[CrossRef] [PubMed]

A. J. Benedick, G. Q. 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(18), 19175–19184 (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,” Nature 452(7187), 610–612 (2008).
[CrossRef] [PubMed]

Wilken, T.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, T. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19(17), 15690–15695 (2011).
[CrossRef] [PubMed]

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[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]

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(6), 063105 (2010).
[CrossRef] [PubMed]

Ycas, G. G.

Zibrov, A.

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]

Exp. Astron. (1)

G. Schettino, E. Oliva, M. Inguscio, C. Baffa, E. Giani, A. Tozzi, and P. C. Pastor, “Optical frequency comb as a general-purpose and wide-band calibration source for astronomical high resolution infrared spectrographs,” Exp. Astron. 31(1), 69–81 (2011).
[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]

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

T. Wilken, C. Lovis, A. Manescau, T. Steinmetz, L. Pasquini, G. Lo Curto, T. W. Hänsch, R. Holzwarth, and T. Udem, “High-precision calibration of spectrographs,” Mon. Not. R. Astron. Soc. Lett. 405(1), L16–L20 (2010).
[CrossRef]

Nature (2)

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,” Nature 452(7187), 610–612 (2008).
[CrossRef] [PubMed]

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet obersavtions calibrated at the centimeter-per-second level,” Nature 485(7400), 611–614 (2012).
[CrossRef] [PubMed]

Opt. Express (8)

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]

D. N. Schimpf, E. Seise, J. Limpert, and A. Tünnermann, “Self-phase modulation compensated by positive dispersion in chirped-pulse systems,” Opt. Express 17(7), 4997–5007 (2009).
[CrossRef] [PubMed]

G. Q. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kärtner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express 18(12), 12736–12747 (2010).
[CrossRef] [PubMed]

C.-H. Li, A. G. Glenday, A. J. Benedick, G. Q. 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?1,” Opt. Express 18(12), 13239–13249 (2010).
[CrossRef] [PubMed]

A. J. Benedick, G. Q. 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(18), 19175–19184 (2010).
[CrossRef] [PubMed]

L.-J. Chen, G. Q. Chang, C. H. Li, A. J. Benedick, D. F. Philips, R. L. Walsworth, and F. X. Kärtner, “Broadband dispersion-free optical cavities based on zero group delay dispersion mirror sets,” Opt. Express 18(22), 23204–23211 (2010).
[CrossRef] [PubMed]

S. P. Stark, T. Steinmetz, R. A. Probst, H. Hundertmark, T. Wilken, T. W. Hänsch, T. Udem, P. St. J. Russell, and R. Holzwarth, “14 GHz visible supercontinuum generation: calibration sources for astronomical spectrographs,” Opt. Express 19(17), 15690–15695 (2011).
[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(6), 6631–6643 (2012).
[CrossRef] [PubMed]

Opt. Lett. (2)

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(6), 063105 (2010).
[CrossRef] [PubMed]

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 (1)

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

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Figures (13)

Fig. 1
Fig. 1

Schematics of two alternate broadband astro-comb designs: (a) a broadband source-comb is filtered by a broadband FP filter cavity; and (b) a narrowband source-comb is filtered by narrowband FP filter cavities, amplified, and then spectrally broadened in a nonlinear fiber.

Fig. 2
Fig. 2

Nonlinear fiber-optic spectral broadening of a narrowband astro-comb degrades side-mode suppression and causes side-mode amplitude asymmetry, which translate into wavelength calibration error. (a) Narrowband astro-comb generated by filtering a source-comb with one or more narrowband FP cavities. Red, solid lines denote the desired astro-comb lines. Side modes, unwanted, partially suppressed source-comb lines, exist due to the finite suppression of the FP filtering; (b) Broadband astro-comb after nonlinear spectral broadening inside an optical fiber. Cascade four-wave-mixing degrades side-mode suppression and causes side-mode amplitude asymmetry; (c) When used for calibrating astrophysical spectrographs, the broadband astro-comb in (b) generates systematic calibration error. See the text for a detailed discussion.

Fig. 3
Fig. 3

Pulse repetition-rate multiplication by a FP filtering cavity begins with (a) a train of identical pulses. (b) After the FP cavity, a temporally modulated, high repetition rate pulse train is produced. In this example, Trs = 8Tra, i.e., M = 8, and the finesse of the FP filter cavity F = 100. A0(t), A1(t)… AM-1(t) denote the amplitudes of M pulses within one modulation period.

Fig. 4
Fig. 4

Schematic representation of analytic model of astro-comb spectral filtering and power amplification. (a) Two sequential arrangements for mode-filtering and power amplification with the second Fabry-Perot Cavity (FPC 2) either before or after the fiber amplifier. (b) Modeling of source-comb, FPC, and amplifier in frequency or time domain. CPA: chirped-pulse amplification; SPM: self-phase modulation.

Fig. 5
Fig. 5

(a) Transmission of 4 types of FP cavity combinations in the absence of the CPA fiber amplifier: single cavity (purple-circles), identical cavities (green-triangles), co-prime cavities (blue-squares), and fraction-prime cavities (red-diamonds). All the cavities are constructed from two identical mirrors with 98.8% power reflectivity. (Dispersion from mirror coatings and cavity air are neglected.) (b) RV error corresponding to the 4 FP filtering methods. Also shown in (b) is the envelope of the source-comb optical spectrum (green-dashed curve) with a full-width-half-maximum of 200 times the astro-comb spacing.

Fig. 6
Fig. 6

(a)-(c) Relative power of the first three side modes as a function of normalized frequency for filtering schemes 1-3; Inset on (c) shows a close-up view of the 1st side modes at the spectrum’s central region. (d) RV error as a function of normalized frequency for filtering schemes 1-3. (Nonlinear phase for these calculations: Beff = 0.6.)

Fig. 7
Fig. 7

Relative power of the 9th and 27th side modes as a function of normalized frequency for filtering schemes (a) 4 and (b) 5. (c) RV error as a function of normalized frequency for filtering schemes 4 and 5. (Nonlinear phase for these calculations: Beff = 0.6.)

Fig. 8
Fig. 8

(a)-(b) Relative power of the 1st, 8th, 2nd, and 16th side modes as a function of normalized frequency for filtering scheme 6 and 7; (c) RV error as a function of normalized frequency for filtering schemes 6 and 7. Nonlinear phase Beff = 0.6. SMs: side modes. Insets of (b) show a close-up of the side modes in the spectrum’s central region.

Fig. 9
Fig. 9

Schematic of a broadband astro-comb, consisting of three key components: (1) a mode-locked femtosecond laser as the narrowband source-comb, (2) two filtering cavities followed by a fiber amplifier to obtain the amplified, narrowband astro-comb, and (3) highly nonlinear fiber for spectral broadening to achieve the broadband astro-comb.

Fig. 10
Fig. 10

(a) Relative power of the first three side modes in the broadband astro-comb using filtering scheme 3 (two identical FP cavities followed by a CPA amplifier). (b) RV error as a function of wavelength (blue curve) and the astro-comb spectrum (green curve).

Fig. 11
Fig. 11

(a) Relative power of the 9th and 27th side modes in the broadband astro-comb using filtering scheme 5 (two co-prime cavities followed by a CPA amplifier). (b) RV error as a function of wavelength (blue curve) and the astro-comb spectrum (green curve).

Fig. 12
Fig. 12

(a) Relative power of the 1st, 2nd, 8th, and 16th side modes in the broadband astro-comb using filtering scheme 7 (two fraction-prime cavities followed by a CPA amplifier). (b) RV error as a function of wavelength (blue curve) and the astro-comb spectrum (green curve). Insets of (a) show an expanded view of the side modes at the spectral region corresponding to the left peak of the astro-comb spectrum (green curve in (b)).

Fig. 13
Fig. 13

(a) Relative power of the first three side modes in the broadband astro-comb using conjugate FP cavities for filtering (two conjugate FP cavities followed by a CPA amplifier); inset: astro-comb spectrum. (b) RV error as a function of wavelength for three filtering schemes: identical cavities (green-dashed), fraction-prime cavities (blue), and conjugate cavities (red).

Tables (1)

Tables Icon

Table 1 Seven Filtering Schemes Compared in this Paper. FPC: Fabry-Perot Cavity; CPA: Chirped-pulse Amplification

Equations (82)

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ν COG ν astrocomb + f rs [ k=1 m k(k f rs )( P k u P k l )]/[ P 0 +(k f rs ) k=1 m ( P k u + P k l )] ,
ΔRV=c ν COG ν astrocomb ν astrocomb c f rs ν astrocomb [ k=1 m j(k f rs )( P k u P k l ) ]/[ P 0 +(k f rs ) k=1 m ( P k u + P k l ) ],
A ˜ s (ω)= A ˜ 0 (ω) l= + δ(ωl ω rs ) .
E out E in = (1R) e jϕ/2 1R× e jϕ .
t FP = E out E in e jϕ/2 = 1R 1R× e jϕ = 1R 12Rcosϕ+ R 2 e jφ .
A i str (t)= 1 i2π| ϕ str | exp(j t 2 2 ϕ str ) A ˜ i ( t ϕ str ).
A ˜ i amp (ω)=exp( gL 2 ) A ˜ i (ω)exp(j ϕ str 2 ω 2 )exp(j B i s i (ω)),
A ˜ amp (ω)=[ A ˜ 0 amp (ω)+ A ˜ 1 amp (ω) e jω T ra +...+ A ˜ M1 amp (ω) e jω(M1) T ra ] l= + δ(ωl ω rs ) ,
A ˜ 1 (ω)={ m=0 M1 R m exp[ jωm T ra +j R 2m B 1,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) ,
A ˜ 2 (ω)= 1R 1 e jω T ra R { m=0 M1 R m exp[ jωm T ra +j R 2m B 1,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) .
A ˜ 3 (ω)={ m=0 M1 ρ m R m exp[ jωm T ra +j ρ m 2 R 2m B 3,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) ,
A ˜ 4 (ω)= 1R 1 e jω T rs / M 2 R { m=0 M 1 1 R m exp[ jωm T ra +j R 2m B 4,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) .
A ˜ 5 (ω)={ m=0 M1 R p(m) exp[ jωm T ra +j R 2p(m) B 5,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) ,
A ˜ 6 (ω)= 1R 1 e jω T rs N/M R { m=0 M1 R m exp[ jωm T ra +j R 2m B 6,0 s 0 (ω) ] } A ˜ 0 s (ω) l= + δ(ωl ω rs ) .
A ˜ 7 (ω)={ m=0 M1 η(m)exp[ jωm T ra +jη(m) B 7,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) ,
max( R 2m ) B 1,0 =max( ρ m 2 R 2m ) B 3,0 =max( R 2m ) B 4,0 / M 2 2 =max( R 2p(m) ) B 5,0 =max( R 2m ) B 6,0 =max(η(m)) B 7,0 B eff ,
A z +( n=2 β n i n1 n! n T n )A=iγ( 1+ i ω 0 T )( A(z,T) + R(t') | A(z,Tt') | 2 dt' ),
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 ),
t FP1 t FP2 = (1R) 2 /[12Rcos(2πq/M)+ R 2 ]= | t FP1 | 2 .
A ˜ a (ω)= A ˜ s (ω) t FP = A ˜ 0 (ω) 1R 1 e jω/ f ra R l= + δ(ωl ω rs ) = A ˜ 0 (ω) 1R 1 e jω T ra R l= + δ(ωl ω rs ) ,
A ˜ a (ω)= A ˜ 0 (ω) 1R 1 R M 1 e jωM T ra R M 1 e jω T ra R l= + δ(ωl ω rs ) .
1 e jωM T ra R M 1 e jω T ra R = n=0 M1 R n e jnω T ra ,
A ˜ a (ω)= 1R 1 R M A ˜ 0 (ω)( n=0 M1 R n e jnω T ra ) l= + δ(ωl ω rs ) = 1R 1 R M A ˜ 0 (ω)[ l= + δ(ωl ω rs )+ e jω T ra R l= + δ(ωl ω rs ) +...+ e jω(M1) T ra R M1 l= + δ(ωl ω rs ) ] = A ˜ 0 s (ω) l= + δ(ωl ω rs )+ A ˜ 1 s (ω) e jω T ra l= + δ(ωl ω rs ) +...+ A ˜ M1 s (ω) e jω(M1) T ra l= + δ(ωl ω rs )
A a s (t)= A 0 s (t) k= + δ(tk T rs )+ A 1 s (t) k= + δ(tk T rs T ra ) +...+ A M1 s (t) k= + δ(tk T rs (M1) T ra )
A ˜ m 1,amp (ω)=exp( gL 2 ) A ˜ m s (ω)exp(j ϕ str 2 ω 2 )exp(j B 1,m s 1,m (ω)),
A ˜ m 1,amp (ω)=exp( gL 2 )( 1R 1 R M ) A ˜ 0 (ω) R m exp(j ϕ str 2 ω 2 )exp(j R 2m B 1,0 s 0 (ω)).
A ˜ 1,final (ω)={ m=0 M1 R m exp[ jωm T ra +j R 2m B 1,0 s 0 (ω) ] }( 1R 1 R M ) A ˜ 0 (ω)exp( gL+j ϕ str ω 2 2 ) l= + δ(ωl ω rs ) .
A ˜ 1 (ω)={ m=0 M1 R m exp[ jωm T ra +j R 2m B 1,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) .
A ˜ 2 (ω)= A ˜ 1 (ω)× t FP = 1R 1 e jω T ra R { m=0 M1 R m exp[ jωm T ra +j R 2m B 1,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) .
A ˜ a I (ω)= A ˜ s (ω) t FP t FP = A ˜ 0 (ω) (1R) 2 (1 e jω T ra R) 2 l= + δ(ωl ω rs ) .
A ˜ a I (ω)= A ˜ 0 (ω) ( 1R 1 R M ) 2 ( 1 e jωM T ra R M 1 e jω T ra R ) 2 l= + δ(ωl ω rs ) = A ˜ 0 (ω) ( 1R 1 R M ) 2 ( n=0 M1 R n e jnω T ra ) 2 l= + δ(ωl ω rs ) .
( n=0 M1 R n e jnω T ra ) 2 l= + δ(ωl ω rs )
=( n=0 M1 R n e j2π n M ω ω rs )( n=0 M1 R n e j2π n M ω ω rs ) l= + δ(ωl ω rs )
=( m=0 M1 k=0 M1 R m+k e j2π m+k M ω ω rs ) l= + δ(ωl ω rs )
=( n=0 M1 (n+1) R n e j2π n M ω ω rs + n=0 M1 (Mn1) R M+n e j2π M+n M ω ω rs ) l= + δ(ωl ω rs )
=( n=0 M1 (n+1) R n e j2π n M ω ω rs + n=0 M1 (Mn1) R M+n e j2π n M ω ω rs ) l= + δ(ωl ω rs )
=( n=0 M1 [(n+1)+(Mn1) R M ] R n e j2π n M ω ω rs ) l= + δ(ωl ω rs ) .
A ˜ a I (ω)= ( 1R 1 R M ) 2 A ˜ 0 (ω)( n=0 M1 [(n+1)+(Mn1) R M ] R n e j2π n M ω ω rs ) l= + δ(ωl ω rs )
= ( 1R 1 R M ) 2 A ˜ 0 (ω)( n=0 M1 [(n+1)+(Mn1) R M ] R n e jnω T ra ) l= + δ(ωl ω rs )
= ( 1R 1 R M ) 2 A ˜ 0 (ω)[ [1+(M1) R M ] l= + δ(ωl ω rs )+ e jω T ra [2+(M2) R M ]R l= + δ(ωl ω rs ) + ...+ e jω(M1) T ra M R M1 l= + δ(ωl ω rs ) ]
= A ˜ 0 I (ω) l= + δ(ωl ω rs )+ A ˜ 1 I (ω) e jω T ra l= + δ(ωl ω rs ) +...+ A ˜ M1 I (ω) e jω(M1) T ra l= + δ(ωl ω rs ) ,
A ˜ m I (ω)= ρ m R m ( 1R 1 R M ) 2 A ˜ 0 (ω),
ρ m =m+1+(Mm1) R M .
A a I (t)= ( 1R 1 R M ) 2 [ A 0 I (t) k= + δ(tk T rs )+ A 1 I (t) k= + δ(tk T rs T ra ) +...+ A M1 I (t) k= + δ(tk T rs (M1) T ra ) ]
A ˜ m 3,amp (ω)=exp( gL 2 ) A ˜ m I (ω)exp(j ϕ str 2 ω 2 )exp(j B 3,m s 3,m (ω)),
A ˜ m 3,amp (ω)=exp( gL 2 ) ( 1R 1 R M ) 2 A ˜ 0 (ω) ρ m R m exp(j ϕ str 2 ω 2 )exp(j ρ m 2 R 2m B 3,0 s 0 (ω)).
A ˜ 3,final (ω)={ m=0 M1 ρ m R m exp[ jωm T ra +j ρ m 2 R 2m B 3,0 s 0 (ω) ] } ( 1R 1 R M ) 2 A ˜ 0 (ω)exp( gL+j ϕ str ω 2 2 ) l= + δ(ωl ω rs ) .
A ˜ 3 (ω)={ m=0 M1 ρ m R m exp[ jωm T ra +j ρ m 2 R 2m B 3,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) .
A ˜ 4,amp (ω)={ m=0 M 1 1 R m exp[ jωm T ra +j R 2m B 4,0 s 0 (ω) ] }( 1R 1 R M 1 ) A ˜ 0 (ω)exp( gL+j ϕ str ω 2 2 ) l= + δ(ωl ω rs ) .
A ˜ 4,final (ω)= A ˜ 4,amp (ω)× t FP2 = 1R 1 e jω T ra2 R A ˜ 4,amp (ω),with T ra2 = T rs / M 2 =1/( f rs M 2 ).
A ˜ 4,amp (ω)= 1R 1 e jω T rs / M 2 R { m=0 M 1 1 R m exp[ jωm T ra +j R 2m B 4,0 s 0 (ω) ] }( 1R 1 R M 1 ) A ˜ 0 (ω)exp( gL+j ϕ str ω 2 2 ) l= + δ(ωl ω rs ) .
A ˜ 4 (ω)= 1R 1 e jω T rs / M 2 R { m=0 M 1 1 R m exp[ jωm T ra +j R 2m B 4,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) .
A ˜ a C (ω)= A ˜ s (ω) t FP1 t FP2 = A ˜ 0 (ω) 1R (1 e jω T ra1 R) 1R (1 e jω T ra2 R) l= + δ(ωl ω rs ) ,
A ˜ a C (ω)= A ˜ 0 (ω) (1R) 2 (1 R M ) 2 1 e jωM T ra1 R M (1 e jω T ra1 R) 1 e jωM T ra2 R M (1 e jω T ra2 R) l= + δ(ωl ω rs )
= A ˜ 0 (ω) ( 1R 1 R M ) 2 ( n=0 M1 R n e jnω T ra1 )( k=0 M1 R k e jkω T ra2 ) l= + δ(ωl ω rs )
= A ˜ 0 (ω) ( 1R 1 R M ) 2 ( n=0 M1 R n e j2π n M 1 ω ω rs )( n=0 M1 R k e j2π k M 2 ω ω rs ) l= + δ(ωl ω rs )
( n=0 M1 R n e j2π n M 1 ω ω rs ) l= + δ(ωl ω rs )
=( n=0 M 1 1 R n e j2π n M 1 ω ω rs + n=0 M 1 1 R n+ M 1 e j2π n M 1 ω ω rs + n=0 M 1 1 R n+2 M 1 e j2π n M 1 ω ω rs +...+ n=0 M 1 1 R n+( M 2 1) M 1 e j2π n M 1 ω ω rs ) l= + δ(ωl ω rs )
=( n=0 M 1 1 [ R n + R n+ M 1 + R n+2 M 1 +... R n+( M 2 1) M 1 ] e j2π n M 1 ω ω rs ) l= + δ(ωl ω rs )
=( n=0 M 1 1 1 R M 2 M 1 1 R M 1 R n e j2π n M 1 ω ω rs ) l= + δ(ωl ω rs )
=( n=0 M 1 1 R n e j2π n M 1 ω ω rs ) 1 R M 1 R M 1 l= + δ(ωl ω rs )
( n=0 M1 R n e j2π n M 1 ω ω rs )( n=0 M1 R k e j2π k M 2 ω ω rs ) l= + δ(ωl ω rs )
=( n=0 M 1 1 R n e j2π n M 1 ω ω rs )( k=0 M 2 1 R k e j2π k M 2 ω ω rs ) 1 R M 1 R M 1 1 R M 1 R M 2 l= + δ(ωl ω rs )
=( n=0 M 1 1 k=0 M 2 1 R n+k e j2π( n M 1 + k M 2 ) ω ω rs ) (1 R M ) 2 (1 R M 1 )(1 R M 2 ) l= + δ(ωl ω rs )
=( m=0 M1 R p(m) e j2π m M ω ω rs ) (1 R M ) 2 (1 R M 1 )(1 R M 2 ) l= + δ(ωl ω rs )
A ˜ a C (ω)= A ˜ s (ω) t FP1 t FP2 =( m=0 M1 R p(m) e j2π m M ω ω rs ) (1R) 2 (1 R M 1 )(1 R M 2 ) A ˜ 0 (ω) l= + δ(ωl ω rs )
A ˜ a C (ω)= (1R) 2 (1 R M 1 )(1 R M 2 ) A ˜ 0 (ω)[ R p(0) l= + δ(ωl ω rs )+ e jω T ra R p(1) l= + δ(ωl ω rs ) +... + e jω(M1) T ra R p(M1) l= + δ(ωl ω rs ) ]
= A ˜ 0 C (ω) l= + δ(ωl ω rs )+ A ˜ 1 C (ω) e jω T ra l= + δ(ωl ω rs ) +...+ A ˜ M1 C (ω) e jω(M1) T ra l= + δ(ωl ω rs )
A ˜ m C (ω)= R p(m) (1R) 2 (1 R M 1 )(1 R M 2 ) A ˜ 0 (ω)
m=0,1...M1
A a C (t)= A 0 C (t) k= + δ(tk T rs )+ A 1 C (t) k= + δ(tk T rs T ra ) +...+ A M1 C (t) k= + δ(tk T rs (M1) T ra )
A ˜ 5,final (ω)={ m=0 M1 R p(m) exp[ jωm T ra +j R 2p(m) B 5,0 s 0 (ω) ] } (1R) 2 A ˜ 0 (ω) (1 R M 1 )(1 R M 2 ) exp( gL+j ϕ str ω 2 2 ) l= + δ(ωl ω rs ) .
A ˜ 5 (ω)={ m=0 M1 R p(m) exp[ jωm T ra +j R 2p(m) B 5,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) .
A ˜ 6 (ω)= 1R 1 e jω T rs N/M R { m=0 M1 R m exp[ jωm T ra +j R 2m B 6,0 s 0 (ω) ] } A ˜ 0 s (ω) l= + δ(ωl ω rs ) .
A ˜ a F (ω)= A ˜ s (ω) t FP1 t FP2 = A ˜ 0 (ω) 1R (1 e jω T ra1 R) 1R (1 e jω T ra2 R) l= + δ(ωl ω rs )
A ˜ a F (ω)= A ˜ 0 (ω) (1R) 2 (1 R M ) 2 1 e jωM T ra1 R M (1 e jω T ra1 R) 1 e jωM T ra2 R M (1 e jω T ra2 R) l= + δ(ωl ω rs ) = A ˜ 0 (ω) ( 1R 1 R M ) 2 ( n=0 M1 R n e jnω T ra1 )( k=0 M1 R k e jkω T ra2 ) l= + δ(ωl ω rs ) = A ˜ 0 (ω) ( 1R 1 R M ) 2 ( n=0 M1 R n e j2π n M ω ω rs )( k=0 M1 R k e j2π Nk M ω ω rs ) l= + δ(ωl ω rs ) .
( k=0 M1 R k e j2π Nk M ω ω rs ) l= + δ(ωl ω rs ) =( m=0 M1 R f(m) e j2π m M ω ω rs ) l= + δ(ωl ω rs ) .
A ˜ 0 (ω) ( 1R 1 R M ) 2 ( n=0 M1 R n e j2π n M ω ω rs )( m=0 M1 R f(m) e j2π m M ω ω rs ) l= + δ(ωl ω rs ) = A ˜ 0 (ω) ( 1R 1 R M ) 2 ( n=0 M1 m=0 M1 R n+f(m) e j2π n+m M ω ω rs ) l= + δ(ωl ω rs ) = A ˜ 0 (ω) ( 1R 1 R M ) 2 ( n=0 M1 [ i=0 n R i+f(ni) e j2π n M ω ω rs ]+ n=0 M1 [ i=n+1 M1 R i+f(M+ni) e j2π M+n M ω ω rs ] ) l= + δ(ωl ω rs ) = A ˜ 0 (ω) ( 1R 1 R M ) 2 ( n=0 M1 [ i=0 n R i+f(ni) + i=n+1 M1 R i+f(M+ni) ] e j2π n M ω ω rs ) l= + δ(ωl ω rs ) = A ˜ 0 (ω) ( 1R 1 R M ) 2 ( n=0 M1 η(n) e j2π n M ω ω rs ) l= + δ(ωl ω rs ) ,
A ˜ a F (ω)= ( 1R 1 R M ) 2 A ˜ 0 (ω)[ η(0) l= + δ(ωl ω rs )+ e jω T ra η(1) l= + δ(ωl ω rs ) +... + e jω(M1) T ra η(M1) l= + δ(ωl ω rs ) ]
A a F (t)= A 0 F (t) k= + δ(tk T rs )+ A 1 F (t) k= + δ(tk T rs T ra ) +...+ A M1 F (t) k= + δ(tk T rs (M1) T ra )
A ˜ 7,final (ω)={ m=0 M1 η(m)exp[ jωm T ra +jη(m) B 7,0 s 0 (ω) ] } ( 1R 1 R M ) 2 A ˜ 0 (ω)exp( gL+j ϕ str ω 2 2 ) l= + δ(ωl ω rs ) .
A ˜ 7 (ω)={ m=0 M1 η(m)exp[ jωm T ra +jη(m) B 7,0 s 0 (ω) ] } A ˜ 0 (ω) l= + δ(ωl ω rs ) .

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