Abstract

We present a dual-comb spectrometer based on two passively mode-locked waveguide lasers integrated in a single Er-doped ZBLAN chip. This original design yields two free-running frequency combs having a high level of mutual stability. We developed in parallel a self-correction algorithm that compensates residual relative fluctuations and yields mode-resolved spectra without the help of any reference laser or control system. Fluctuations are extracted directly from the interferograms using the concept of ambiguity function, which leads to a significant simplification of the instrument that will greatly ease its widespread adoption and commercial deployment. Comparison with a correction algorithm relying on a single-frequency laser indicates discrepancies of only 50 attoseconds on optical timings. The capacities of this instrument are finally demonstrated with the acquisition of a high-resolution molecular spectrum covering 20 nm. This new chip-based multi-laser platform is ideal for the development of high-repetition-rate, compact and fieldable comb spectrometers in the near- and mid-infrared.

© 2017 Optical Society of America

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2016 (12)

P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
[Crossref]

I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414–426 (2016).
[Crossref]

T. Ideguchi, T. Nakamura, Y. Kobayashi, and K. Goda, “Kerr-lens mode-locked bidirectional dual-comb ring laser for broadband dual-comb spectroscopy,” Optica 3(7), 748–753 (2016).
[Crossref]

S. Mehravar, R. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a free-running bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 231104 (2016).
[Crossref]

X. Zhao, G. Hu, B. Zhao, C. Li, Y. Pan, Y. Liu, T. Yasui, and Z. Zheng, “Picometer-resolution dual-comb spectroscopy with a free-running fiber laser,” Opt. Express 24(19), 21833–21845 (2016).
[Crossref] [PubMed]

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, “On-chip, self-detected terahertz dual-comb source,” Appl. Phys. Lett. 108(17), 171104 (2016).
[Crossref]

D. Burghoff, Y. Yang, and Q. Hu, “Computational multiheterodyne spectroscopy,” Sci. Adv. 2(11), 1601227 (2016).
[Crossref]

C. Khurmi, N. B. Hébert, W. Q. Zhang, S. V. Afshar, G. Chen, J. Genest, T. M. Monro, and D. G. Lancaster, “Ultrafast pulse generation in a mode-locked erbium chip waveguide laser,” Opt. Express 24(24), 27177–27183 (2016).
[Crossref] [PubMed]

S. M. Link, A. Klenner, and U. Keller, “Dual-comb modelocked lasers: semiconductor saturable absorber mirror decouples noise stabilization,” Opt. Express 24(3), 1889–1902 (2016).
[Crossref] [PubMed]

D. G. Lancaster, Y. Li, Y. Duan, S. Gross, M. W. Withford, and T. M. Monro, “Er3+ active Yb3+ Ce3+ co-doped fluorozirconate guided-wave chip lasers,” IEEE Photonics Technol. Lett. 28(21), 2315–2318 (2016).
[Crossref]

G.-W. Truong, E. M. Waxman, K. C. Cossel, E. Baumann, A. Klose, F. R. Giorgetta, W. C. Swann, N. R. Newbury, and I. Coddington, “Accurate frequency referencing for fieldable dual-comb spectroscopy,” Opt. Express 24(26), 30495–30504 (2016).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
[Crossref] [PubMed]

2015 (6)

2014 (2)

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
[Crossref] [PubMed]

D. Choudhury, J. R. Macdonald, and A. K. Kar, “Ultrafast laser inscription: perspectives on future integrated applications,” Laser Photonics Rev. 8(6), 827–846 (2014).
[Crossref]

2013 (4)

2012 (2)

K. C. Cossel, D. N. Gresh, L. C. Sinclair, T. Coffey, L. V. Skripnikov, A. N. Petrov, N. S. Mosyagin, A. V. Titov, R. W. Field, E. R. Meyer, E. A. Cornell, and J. Ye, “Broadband velocity modulation spectroscopy of HfF+: Towards a measurement of the electron electric dipole moment,” Chem. Phys. Lett. 546, 1–11 (2012).
[Crossref]

J. Roy, J.-D. Deschênes, S. Potvin, and J. Genest, “Continuous real-time correction and averaging for frequency comb interferometry,” Opt. Express 20(20), 21932–21939 (2012).
[Crossref] [PubMed]

2011 (2)

E. Baumann, F. Giorgetta, W. Swann, A. Zolot, I. Coddington, and N. Newbury, “Spectroscopy of the methane ν3 band with an accurate midinfrared coherent dual-comb spectrometer,” Phys. Rev. A 84(6), 062513 (2011).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref] [PubMed]

2010 (2)

J.-D. Deschênes, P. Giaccari, and J. Genest, “Optical referencing technique with CW lasers as intermediate oscillators for continuous full delay range frequency comb interferometry,” Opt. Express 18(22), 23358–23370 (2010).
[Crossref] [PubMed]

S. Beecher, R. Thomson, N. Psaila, Z. Sun, T. Hasan, A. Rozhin, A. Ferrari, and A. Kar, “320 fs pulse generation from an ultrafast laser inscribed waveguide laser mode-locked by a nanotube saturable absorber,” Appl. Phys. Lett. 97(11), 111114 (2010).
[Crossref]

2008 (3)

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (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(7187), 610–612 (2008).
[Crossref] [PubMed]

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol. Opt. Phy. 55, 1–60 (2008).
[Crossref]

2007 (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref]

2005 (2)

W. C. Swann and S. L. Gilbert, “Line centers, pressure shift, and pressure broadening of 1530–1560 nm hydrogen cyanide wavelength calibration lines,” J. Opt. Soc. Am. B 22(8), 1749–1756 (2005).
[Crossref]

A. Marian, M. C. Stowe, D. Felinto, and J. Ye, “Direct frequency comb measurements of absolute optical frequencies and population transfer dynamics,” Phys. Rev. Lett. 95(2), 023001 (2005).
[Crossref] [PubMed]

2004 (1)

K. Nagamatsu, S. Nagaoka, M. Higashihata, N. Vasa, Z. Meng, S. Buddhudu, T. Okada, Y. Kubota, N. Nishimura, and T. Teshima, “Influence of Yb3+ and Ce3+ codoping on fluorescence characteristics of Er3+-doped fluoride glass under 980 nm excitation,” Opt. Mater. 27(2), 337–342 (2004).
[Crossref]

2003 (2)

H. H. Funke, B. L. Grissom, C. E. McGrew, and M. W. Raynor, “Techniques for the measurement of trace moisture in high-purity electronic specialty gases,” Rev. Sci. Instrum. 74(9), 3909–3933 (2003).
[Crossref]

J. B. Schlager, B. E. Callicoatt, R. P. Mirin, N. A. Sanford, D. J. Jones, and J. Ye, “Passively mode-locked glass waveguide laser with 14-fs timing jitter,” Opt. Lett. 28(23), 2411–2413 (2003).
[Crossref] [PubMed]

2002 (1)

O. Berntsson, L.-G. Danielsson, B. Lagerholm, and S. Folestad, “Quantitative in-line monitoring of powder blending by near infrared reflection spectroscopy,” Powder Technol. 123(2), 185–193 (2002).
[Crossref]

2001 (1)

2000 (2)

E. Thoen, E. Koontz, D. Jones, D. Barbier, F. Kartner, E. Ippen, and L. Kolodziejski, “Erbium-ytterbium waveguide laser mode-locked with a semiconductor saturable absorber mirror,” IEEE Photonics Technol. Lett. 12(2), 149–151 (2000).
[Crossref]

R. Holzwarth, T. Udem, T. W. Hänsch, J. Knight, W. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref] [PubMed]

1996 (1)

1991 (1)

R. Smart, D. Hanna, A. Tropper, S. Davey, S. Carter, and D. Szebesta, “CW room temperature upconversion lasing at blue, green and red wavelengths in infrared-pumped Pr3+-doped fluoride fibre,” Electron. Lett. 27(14), 1307–1309 (1991).
[Crossref]

1981 (1)

R. Fork, B. Greene, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38(9), 671–672 (1981).
[Crossref]

Afshar, S. V.

Anstie, J.

G.-W. Truong, J. Anstie, E. May, T. Stace, and A. Luiten, “Accurate lineshape spectroscopy and the boltzmann constant,” Nat. Commun. 6, 8345 (2015).
[Crossref] [PubMed]

Anstie, J. D.

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref]

Barbier, D.

E. Thoen, E. Koontz, D. Jones, D. Barbier, F. Kartner, E. Ippen, and L. Kolodziejski, “Erbium-ytterbium waveguide laser mode-locked with a semiconductor saturable absorber mirror,” IEEE Photonics Technol. Lett. 12(2), 149–151 (2000).
[Crossref]

Baumann, E.

G.-W. Truong, E. M. Waxman, K. C. Cossel, E. Baumann, A. Klose, F. R. Giorgetta, W. C. Swann, N. R. Newbury, and I. Coddington, “Accurate frequency referencing for fieldable dual-comb spectroscopy,” Opt. Express 24(26), 30495–30504 (2016).
[Crossref]

E. Baumann, F. Giorgetta, W. Swann, A. Zolot, I. Coddington, and N. Newbury, “Spectroscopy of the methane ν3 band with an accurate midinfrared coherent dual-comb spectrometer,” Phys. Rev. A 84(6), 062513 (2011).
[Crossref]

Beck, M.

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, “On-chip, self-detected terahertz dual-comb source,” Appl. Phys. Lett. 108(17), 171104 (2016).
[Crossref]

G. Villares, J. Wolf, D. Kazakov, M. J. Süess, A. Hugi, M. Beck, and J. Faist, “On-chip dual-comb based on quantum cascade laser frequency combs,” Appl. Phys. Lett. 107(25), 251104 (2015).
[Crossref]

Beecher, S.

S. Beecher, R. Thomson, N. Psaila, Z. Sun, T. Hasan, A. Rozhin, A. Ferrari, and A. Kar, “320 fs pulse generation from an ultrafast laser inscribed waveguide laser mode-locked by a nanotube saturable absorber,” Appl. Phys. Lett. 97(11), 111114 (2010).
[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]

Berntsson, O.

O. Berntsson, L.-G. Danielsson, B. Lagerholm, and S. Folestad, “Quantitative in-line monitoring of powder blending by near infrared reflection spectroscopy,” Powder Technol. 123(2), 185–193 (2002).
[Crossref]

Bjork, B. J.

A. Foltynowicz, P. Masłowski, A. J. Fleisher, B. J. Bjork, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide,” Appl. Phys. B 110(2), 163–175 (2013).
[Crossref]

Bosco, L.

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Del’Haye, P.

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M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol. Opt. Phy. 55, 1–60 (2008).
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Faist, J.

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, “On-chip, self-detected terahertz dual-comb source,” Appl. Phys. Lett. 108(17), 171104 (2016).
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G. Villares, J. Wolf, D. Kazakov, M. J. Süess, A. Hugi, M. Beck, and J. Faist, “On-chip dual-comb based on quantum cascade laser frequency combs,” Appl. Phys. Lett. 107(25), 251104 (2015).
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P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
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S. Beecher, R. Thomson, N. Psaila, Z. Sun, T. Hasan, A. Rozhin, A. Ferrari, and A. Kar, “320 fs pulse generation from an ultrafast laser inscribed waveguide laser mode-locked by a nanotube saturable absorber,” Appl. Phys. Lett. 97(11), 111114 (2010).
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K. C. Cossel, D. N. Gresh, L. C. Sinclair, T. Coffey, L. V. Skripnikov, A. N. Petrov, N. S. Mosyagin, A. V. Titov, R. W. Field, E. R. Meyer, E. A. Cornell, and J. Ye, “Broadband velocity modulation spectroscopy of HfF+: Towards a measurement of the electron electric dipole moment,” Chem. Phys. Lett. 546, 1–11 (2012).
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A. Foltynowicz, P. Masłowski, A. J. Fleisher, B. J. Bjork, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide,” Appl. Phys. B 110(2), 163–175 (2013).
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O. Berntsson, L.-G. Danielsson, B. Lagerholm, and S. Folestad, “Quantitative in-line monitoring of powder blending by near infrared reflection spectroscopy,” Powder Technol. 123(2), 185–193 (2002).
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P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
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A. Foltynowicz, P. Masłowski, A. J. Fleisher, B. J. Bjork, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide,” Appl. Phys. B 110(2), 163–175 (2013).
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Gerginov, V.

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol. Opt. Phy. 55, 1–60 (2008).
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Gilbert, S. L.

Giorgetta, F.

E. Baumann, F. Giorgetta, W. Swann, A. Zolot, I. Coddington, and N. Newbury, “Spectroscopy of the methane ν3 band with an accurate midinfrared coherent dual-comb spectrometer,” Phys. Rev. A 84(6), 062513 (2011).
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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).
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Golling, M.

Gong, Z.

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K. C. Cossel, D. N. Gresh, L. C. Sinclair, T. Coffey, L. V. Skripnikov, A. N. Petrov, N. S. Mosyagin, A. V. Titov, R. W. Field, E. R. Meyer, E. A. Cornell, and J. Ye, “Broadband velocity modulation spectroscopy of HfF+: Towards a measurement of the electron electric dipole moment,” Chem. Phys. Lett. 546, 1–11 (2012).
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H. H. Funke, B. L. Grissom, C. E. McGrew, and M. W. Raynor, “Techniques for the measurement of trace moisture in high-purity electronic specialty gases,” Rev. Sci. Instrum. 74(9), 3909–3933 (2003).
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Guelachvili, G.

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
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R. Smart, D. Hanna, A. Tropper, S. Davey, S. Carter, and D. Szebesta, “CW room temperature upconversion lasing at blue, green and red wavelengths in infrared-pumped Pr3+-doped fluoride fibre,” Electron. Lett. 27(14), 1307–1309 (1991).
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T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
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Hasan, T.

S. Beecher, R. Thomson, N. Psaila, Z. Sun, T. Hasan, A. Rozhin, A. Ferrari, and A. Kar, “320 fs pulse generation from an ultrafast laser inscribed waveguide laser mode-locked by a nanotube saturable absorber,” Appl. Phys. Lett. 97(11), 111114 (2010).
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Higashihata, M.

K. Nagamatsu, S. Nagaoka, M. Higashihata, N. Vasa, Z. Meng, S. Buddhudu, T. Okada, Y. Kubota, N. Nishimura, and T. Teshima, “Influence of Yb3+ and Ce3+ codoping on fluorescence characteristics of Er3+-doped fluoride glass under 980 nm excitation,” Opt. Mater. 27(2), 337–342 (2004).
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Holzwarth, R.

T. J. Kippenberg, R. Holzwarth, and S. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref]

R. Holzwarth, T. Udem, T. W. Hänsch, J. Knight, W. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
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X. Zhao, G. Hu, B. Zhao, C. Li, Y. Pan, Y. Liu, T. Yasui, and Z. Zheng, “Picometer-resolution dual-comb spectroscopy with a free-running fiber laser,” Opt. Express 24(19), 21833–21845 (2016).
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Z. Gong, X. Zhao, G. Hu, J. Liu, and Z. Zheng, “Polarization multiplexed, dual-frequency ultrashort pulse generation by a birefringent mode-locked fiber laser,” in CLEO: 2014, (Optical Society of America, 2014), pp. JTh2A–20.

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D. Burghoff, Y. Yang, and Q. Hu, “Computational multiheterodyne spectroscopy,” Sci. Adv. 2(11), 1601227 (2016).
[Crossref]

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G. Villares, J. Wolf, D. Kazakov, M. J. Süess, A. Hugi, M. Beck, and J. Faist, “On-chip dual-comb based on quantum cascade laser frequency combs,” Appl. Phys. Lett. 107(25), 251104 (2015).
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T. Ideguchi, T. Nakamura, Y. Kobayashi, and K. Goda, “Kerr-lens mode-locked bidirectional dual-comb ring laser for broadband dual-comb spectroscopy,” Optica 3(7), 748–753 (2016).
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T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
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E. Thoen, E. Koontz, D. Jones, D. Barbier, F. Kartner, E. Ippen, and L. Kolodziejski, “Erbium-ytterbium waveguide laser mode-locked with a semiconductor saturable absorber mirror,” IEEE Photonics Technol. Lett. 12(2), 149–151 (2000).
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Ippen, E. P.

Jackson, S. D.

Jiang, J.

P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
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Johansson, A. C.

P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
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Jones, D.

E. Thoen, E. Koontz, D. Jones, D. Barbier, F. Kartner, E. Ippen, and L. Kolodziejski, “Erbium-ytterbium waveguide laser mode-locked with a semiconductor saturable absorber mirror,” IEEE Photonics Technol. Lett. 12(2), 149–151 (2000).
[Crossref]

Jones, D. J.

Kar, A.

S. Beecher, R. Thomson, N. Psaila, Z. Sun, T. Hasan, A. Rozhin, A. Ferrari, and A. Kar, “320 fs pulse generation from an ultrafast laser inscribed waveguide laser mode-locked by a nanotube saturable absorber,” Appl. Phys. Lett. 97(11), 111114 (2010).
[Crossref]

Kar, A. K.

D. Choudhury, J. R. Macdonald, and A. K. Kar, “Ultrafast laser inscription: perspectives on future integrated applications,” Laser Photonics Rev. 8(6), 827–846 (2014).
[Crossref]

Kartner, F.

E. Thoen, E. Koontz, D. Jones, D. Barbier, F. Kartner, E. Ippen, and L. Kolodziejski, “Erbium-ytterbium waveguide laser mode-locked with a semiconductor saturable absorber mirror,” IEEE Photonics Technol. Lett. 12(2), 149–151 (2000).
[Crossref]

Kärtner, F. X.

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

Kazakov, D.

G. Villares, J. Wolf, D. Kazakov, M. J. Süess, A. Hugi, M. Beck, and J. Faist, “On-chip dual-comb based on quantum cascade laser frequency combs,” Appl. Phys. Lett. 107(25), 251104 (2015).
[Crossref]

Keller, U.

Khodabakhsh, A.

P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
[Crossref]

Khurmi, C.

Kieu, K.

S. Mehravar, R. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a free-running bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 231104 (2016).
[Crossref]

Kippenberg, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref]

Kippenberg, T. J.

T. J. Kippenberg, R. Holzwarth, and S. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref] [PubMed]

Klenner, A.

Klose, A.

Knight, J.

R. Holzwarth, T. Udem, T. W. Hänsch, J. Knight, W. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref] [PubMed]

Kobayashi, Y.

Kolodziejski, L.

E. Thoen, E. Koontz, D. Jones, D. Barbier, F. Kartner, E. Ippen, and L. Kolodziejski, “Erbium-ytterbium waveguide laser mode-locked with a semiconductor saturable absorber mirror,” IEEE Photonics Technol. Lett. 12(2), 149–151 (2000).
[Crossref]

Koontz, E.

E. Thoen, E. Koontz, D. Jones, D. Barbier, F. Kartner, E. Ippen, and L. Kolodziejski, “Erbium-ytterbium waveguide laser mode-locked with a semiconductor saturable absorber mirror,” IEEE Photonics Technol. Lett. 12(2), 149–151 (2000).
[Crossref]

Kowalevicz, A. M.

Kowzan, G.

P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
[Crossref]

Kubota, Y.

K. Nagamatsu, S. Nagaoka, M. Higashihata, N. Vasa, Z. Meng, S. Buddhudu, T. Okada, Y. Kubota, N. Nishimura, and T. Teshima, “Influence of Yb3+ and Ce3+ codoping on fluorescence characteristics of Er3+-doped fluoride glass under 980 nm excitation,” Opt. Mater. 27(2), 337–342 (2004).
[Crossref]

Lagerholm, B.

O. Berntsson, L.-G. Danielsson, B. Lagerholm, and S. Folestad, “Quantitative in-line monitoring of powder blending by near infrared reflection spectroscopy,” Powder Technol. 123(2), 185–193 (2002).
[Crossref]

Lancaster, D. G.

Lee, K. F.

P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
[Crossref]

Li, C.

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, Y.

D. G. Lancaster, Y. Li, Y. Duan, S. Gross, M. W. Withford, and T. M. Monro, “Er3+ active Yb3+ Ce3+ co-doped fluorozirconate guided-wave chip lasers,” IEEE Photonics Technol. Lett. 28(21), 2315–2318 (2016).
[Crossref]

Liang, H.

Link, S. M.

Liu, J.

Z. Gong, X. Zhao, G. Hu, J. Liu, and Z. Zheng, “Polarization multiplexed, dual-frequency ultrashort pulse generation by a birefringent mode-locked fiber laser,” in CLEO: 2014, (Optical Society of America, 2014), pp. JTh2A–20.

Liu, Y.

Luiten, A.

G.-W. Truong, J. Anstie, E. May, T. Stace, and A. Luiten, “Accurate lineshape spectroscopy and the boltzmann constant,” Nat. Commun. 6, 8345 (2015).
[Crossref] [PubMed]

Luiten, A. N.

Macdonald, J. R.

D. Choudhury, J. R. Macdonald, and A. K. Kar, “Ultrafast laser inscription: perspectives on future integrated applications,” Laser Photonics Rev. 8(6), 827–846 (2014).
[Crossref]

Mangold, M.

Marian, A.

A. Marian, M. C. Stowe, D. Felinto, and J. Ye, “Direct frequency comb measurements of absolute optical frequencies and population transfer dynamics,” Phys. Rev. Lett. 95(2), 023001 (2005).
[Crossref] [PubMed]

Maslowski, P.

P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
[Crossref]

A. Foltynowicz, P. Masłowski, A. J. Fleisher, B. J. Bjork, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide,” Appl. Phys. B 110(2), 163–175 (2013).
[Crossref]

May, E.

G.-W. Truong, J. Anstie, E. May, T. Stace, and A. Luiten, “Accurate lineshape spectroscopy and the boltzmann constant,” Nat. Commun. 6, 8345 (2015).
[Crossref] [PubMed]

McGrew, C. E.

H. H. Funke, B. L. Grissom, C. E. McGrew, and M. W. Raynor, “Techniques for the measurement of trace moisture in high-purity electronic specialty gases,” Rev. Sci. Instrum. 74(9), 3909–3933 (2003).
[Crossref]

Mehravar, S.

S. Mehravar, R. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a free-running bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 231104 (2016).
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K. Nagamatsu, S. Nagaoka, M. Higashihata, N. Vasa, Z. Meng, S. Buddhudu, T. Okada, Y. Kubota, N. Nishimura, and T. Teshima, “Influence of Yb3+ and Ce3+ codoping on fluorescence characteristics of Er3+-doped fluoride glass under 980 nm excitation,” Opt. Mater. 27(2), 337–342 (2004).
[Crossref]

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K. C. Cossel, D. N. Gresh, L. C. Sinclair, T. Coffey, L. V. Skripnikov, A. N. Petrov, N. S. Mosyagin, A. V. Titov, R. W. Field, E. R. Meyer, E. A. Cornell, and J. Ye, “Broadband velocity modulation spectroscopy of HfF+: Towards a measurement of the electron electric dipole moment,” Chem. Phys. Lett. 546, 1–11 (2012).
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P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
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K. C. Cossel, D. N. Gresh, L. C. Sinclair, T. Coffey, L. V. Skripnikov, A. N. Petrov, N. S. Mosyagin, A. V. Titov, R. W. Field, E. R. Meyer, E. A. Cornell, and J. Ye, “Broadband velocity modulation spectroscopy of HfF+: Towards a measurement of the electron electric dipole moment,” Chem. Phys. Lett. 546, 1–11 (2012).
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K. Nagamatsu, S. Nagaoka, M. Higashihata, N. Vasa, Z. Meng, S. Buddhudu, T. Okada, Y. Kubota, N. Nishimura, and T. Teshima, “Influence of Yb3+ and Ce3+ codoping on fluorescence characteristics of Er3+-doped fluoride glass under 980 nm excitation,” Opt. Mater. 27(2), 337–342 (2004).
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K. Nagamatsu, S. Nagaoka, M. Higashihata, N. Vasa, Z. Meng, S. Buddhudu, T. Okada, Y. Kubota, N. Nishimura, and T. Teshima, “Influence of Yb3+ and Ce3+ codoping on fluorescence characteristics of Er3+-doped fluoride glass under 980 nm excitation,” Opt. Mater. 27(2), 337–342 (2004).
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Newbury, N.

I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414–426 (2016).
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E. Baumann, F. Giorgetta, W. Swann, A. Zolot, I. Coddington, and N. Newbury, “Spectroscopy of the methane ν3 band with an accurate midinfrared coherent dual-comb spectrometer,” Phys. Rev. A 84(6), 062513 (2011).
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Newbury, N. R.

Nishimura, N.

K. Nagamatsu, S. Nagaoka, M. Higashihata, N. Vasa, Z. Meng, S. Buddhudu, T. Okada, Y. Kubota, N. Nishimura, and T. Teshima, “Influence of Yb3+ and Ce3+ codoping on fluorescence characteristics of Er3+-doped fluoride glass under 980 nm excitation,” Opt. Mater. 27(2), 337–342 (2004).
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Norwood, R.

S. Mehravar, R. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a free-running bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 231104 (2016).
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K. Nagamatsu, S. Nagaoka, M. Higashihata, N. Vasa, Z. Meng, S. Buddhudu, T. Okada, Y. Kubota, N. Nishimura, and T. Teshima, “Influence of Yb3+ and Ce3+ codoping on fluorescence characteristics of Er3+-doped fluoride glass under 980 nm excitation,” Opt. Mater. 27(2), 337–342 (2004).
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Pan, Y.

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M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol. Opt. Phy. 55, 1–60 (2008).
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K. C. Cossel, D. N. Gresh, L. C. Sinclair, T. Coffey, L. V. Skripnikov, A. N. Petrov, N. S. Mosyagin, A. V. Titov, R. W. Field, E. R. Meyer, E. A. Cornell, and J. Ye, “Broadband velocity modulation spectroscopy of HfF+: Towards a measurement of the electron electric dipole moment,” Chem. Phys. Lett. 546, 1–11 (2012).
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Peyghambarian, N.

S. Mehravar, R. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a free-running bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 231104 (2016).
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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).
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Rozhin, A.

S. Beecher, R. Thomson, N. Psaila, Z. Sun, T. Hasan, A. Rozhin, A. Ferrari, and A. Kar, “320 fs pulse generation from an ultrafast laser inscribed waveguide laser mode-locked by a nanotube saturable absorber,” Appl. Phys. Lett. 97(11), 111114 (2010).
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R. Holzwarth, T. Udem, T. W. Hänsch, J. Knight, W. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
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P. Maslowski, K. F. Lee, A. C. Johansson, A. Khodabakhsh, G. Kowzan, L. Rutkowski, A. A. Mills, C. Mohr, J. Jiang, M. E. Fermann, and A. Foltynowicz, “Surpassing the path-limited resolution of fourier-transform spectrometry with frequency combs,” Phys. Rev. A 93(2), 021802 (2016).
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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).
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M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, “On-chip, self-detected terahertz dual-comb source,” Appl. Phys. Lett. 108(17), 171104 (2016).
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Stowe, M. C.

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol. Opt. Phy. 55, 1–60 (2008).
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M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
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S. Beecher, R. Thomson, N. Psaila, Z. Sun, T. Hasan, A. Rozhin, A. Ferrari, and A. Kar, “320 fs pulse generation from an ultrafast laser inscribed waveguide laser mode-locked by a nanotube saturable absorber,” Appl. Phys. Lett. 97(11), 111114 (2010).
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I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414–426 (2016).
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E. Baumann, F. Giorgetta, W. Swann, A. Zolot, I. Coddington, and N. Newbury, “Spectroscopy of the methane ν3 band with an accurate midinfrared coherent dual-comb spectrometer,” Phys. Rev. A 84(6), 062513 (2011).
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Szebesta, D.

R. Smart, D. Hanna, A. Tropper, S. Davey, S. Carter, and D. Szebesta, “CW room temperature upconversion lasing at blue, green and red wavelengths in infrared-pumped Pr3+-doped fluoride fibre,” Electron. Lett. 27(14), 1307–1309 (1991).
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K. Nagamatsu, S. Nagaoka, M. Higashihata, N. Vasa, Z. Meng, S. Buddhudu, T. Okada, Y. Kubota, N. Nishimura, and T. Teshima, “Influence of Yb3+ and Ce3+ codoping on fluorescence characteristics of Er3+-doped fluoride glass under 980 nm excitation,” Opt. Mater. 27(2), 337–342 (2004).
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S. Beecher, R. Thomson, N. Psaila, Z. Sun, T. Hasan, A. Rozhin, A. Ferrari, and A. Kar, “320 fs pulse generation from an ultrafast laser inscribed waveguide laser mode-locked by a nanotube saturable absorber,” Appl. Phys. Lett. 97(11), 111114 (2010).
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M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol. Opt. Phy. 55, 1–60 (2008).
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R. Smart, D. Hanna, A. Tropper, S. Davey, S. Carter, and D. Szebesta, “CW room temperature upconversion lasing at blue, green and red wavelengths in infrared-pumped Pr3+-doped fluoride fibre,” Electron. Lett. 27(14), 1307–1309 (1991).
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R. Holzwarth, T. Udem, T. W. Hänsch, J. Knight, W. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
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M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
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K. Nagamatsu, S. Nagaoka, M. Higashihata, N. Vasa, Z. Meng, S. Buddhudu, T. Okada, Y. Kubota, N. Nishimura, and T. Teshima, “Influence of Yb3+ and Ce3+ codoping on fluorescence characteristics of Er3+-doped fluoride glass under 980 nm excitation,” Opt. Mater. 27(2), 337–342 (2004).
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M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, “On-chip, self-detected terahertz dual-comb source,” Appl. Phys. Lett. 108(17), 171104 (2016).
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R. Holzwarth, T. Udem, T. W. Hänsch, J. Knight, W. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
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P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
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E. Baumann, F. Giorgetta, W. Swann, A. Zolot, I. Coddington, and N. Newbury, “Spectroscopy of the methane ν3 band with an accurate midinfrared coherent dual-comb spectrometer,” Phys. Rev. A 84(6), 062513 (2011).
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Adv. At. Mol. Opt. Phy. (1)

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol. Opt. Phy. 55, 1–60 (2008).
[Crossref]

Appl. Phys. B (1)

A. Foltynowicz, P. Masłowski, A. J. Fleisher, B. J. Bjork, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide,” Appl. Phys. B 110(2), 163–175 (2013).
[Crossref]

Appl. Phys. Lett. (5)

S. Mehravar, R. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a free-running bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 231104 (2016).
[Crossref]

R. Fork, B. Greene, and C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking,” Appl. Phys. Lett. 38(9), 671–672 (1981).
[Crossref]

G. Villares, J. Wolf, D. Kazakov, M. J. Süess, A. Hugi, M. Beck, and J. Faist, “On-chip dual-comb based on quantum cascade laser frequency combs,” Appl. Phys. Lett. 107(25), 251104 (2015).
[Crossref]

M. Rösch, G. Scalari, G. Villares, L. Bosco, M. Beck, and J. Faist, “On-chip, self-detected terahertz dual-comb source,” Appl. Phys. Lett. 108(17), 171104 (2016).
[Crossref]

S. Beecher, R. Thomson, N. Psaila, Z. Sun, T. Hasan, A. Rozhin, A. Ferrari, and A. Kar, “320 fs pulse generation from an ultrafast laser inscribed waveguide laser mode-locked by a nanotube saturable absorber,” Appl. Phys. Lett. 97(11), 111114 (2010).
[Crossref]

Chem. Phys. Lett. (1)

K. C. Cossel, D. N. Gresh, L. C. Sinclair, T. Coffey, L. V. Skripnikov, A. N. Petrov, N. S. Mosyagin, A. V. Titov, R. W. Field, E. R. Meyer, E. A. Cornell, and J. Ye, “Broadband velocity modulation spectroscopy of HfF+: Towards a measurement of the electron electric dipole moment,” Chem. Phys. Lett. 546, 1–11 (2012).
[Crossref]

Electron. Lett. (1)

R. Smart, D. Hanna, A. Tropper, S. Davey, S. Carter, and D. Szebesta, “CW room temperature upconversion lasing at blue, green and red wavelengths in infrared-pumped Pr3+-doped fluoride fibre,” Electron. Lett. 27(14), 1307–1309 (1991).
[Crossref]

IEEE Photonics Technol. Lett. (2)

E. Thoen, E. Koontz, D. Jones, D. Barbier, F. Kartner, E. Ippen, and L. Kolodziejski, “Erbium-ytterbium waveguide laser mode-locked with a semiconductor saturable absorber mirror,” IEEE Photonics Technol. Lett. 12(2), 149–151 (2000).
[Crossref]

D. G. Lancaster, Y. Li, Y. Duan, S. Gross, M. W. Withford, and T. M. Monro, “Er3+ active Yb3+ Ce3+ co-doped fluorozirconate guided-wave chip lasers,” IEEE Photonics Technol. Lett. 28(21), 2315–2318 (2016).
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J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

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Figures (7)

Fig. 1
Fig. 1 Schematic of the dual-comb spectrometer. Two parallel waveguides laser-inscribed in an Er-doped ZBLAN glass chip are used to generate a pair of frequency comb lasers, which are mode-locked with a common SAM. The fibre-coupled outputs are used to perform dual-comb spectroscopy. PC: polarization controller, D1 and D2: detectors.
Fig. 2
Fig. 2 (a) Spectrum of each frequency comb. They span 9 nm around 1555 nm and show excellent spectral overlap. The resolution of the optical spectrum analyzer is set to 0.2 nm (0.03 nm for the inset). (b) Averaged IGM obtained with a self-corrected sequence of IGMs.
Fig. 3
Fig. 3 Beat note between two comb modes, one from each comb, for different observation times: 71 ms (grey) and 1/Δfr ∼ 95 μs (red, green, blue). Coloured traces are computed from three different sections of the 71 ms measurement. Their width is close to the transform limit, which indicates that the dual-comb platform is mutually stable on a 1/Δfr timescale.
Fig. 4
Fig. 4 Normalized ambiguity map generated from measured IGMs for the case k = 100. The delay axis is centered on the expected delay kfr. The coordinates (τk, δfc,k) at the point of maximum similarity are also given. Notice how the function takes large values along an oblique line, which illustrates the coupling between apparent delay and frequency offset when working with chirped IGMs.
Fig. 5
Fig. 5 Evolution of a small region of the beat spectrum computed from a 71-ms-long IGM stream as it goes through the different correction steps. Green: Raw spectrum. Red: Spectral shifting compensated after phase correction. Modes close to fc are nearly perfect at this stage. Blue: Spectral stretching compensated after resampling. The insets show the evolution of one mode, which finally becomes transform-limited. All vertical axes are normalized to the same value.
Fig. 6
Fig. 6 (a) Extracted phase excursions δϕc (t) (blue) associated with the fluctuations on the RF comb’s central frequency. Independent measurement of the same quantity (red), denoted as δ ϕ c * ( t ), measured through an intermediate CW laser. (b) Difference between δϕc (t) and δ ϕ c * ( t ). (c) Extracted phase excursions δΔϕr (t) associated with the fluctuations on the repetition rate difference. They are normalized by 2πfr to obtain time deviations from a linear delay grid.
Fig. 7
Fig. 7 Transmission spectrum of H13C14N. Each blue point corresponds to the power of a single dual-comb mode and the point spacing is 822.4 MHz. The red curve is the result of a fit composed of 24 Voigt lines. Fit residuals show weak hot-band transitions that were not taken into account in the model.

Tables (1)

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Table 1 Lorentzian half widths retrieved from the fit compared to reference widths calculated from [46] assuming a pressure of 92.84 Torr. Uncertainties are the 2σ confidence intervals.

Equations (2)

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f n ( t ) = [ f c + δ f c ( t ) ] + n [ Δ f r + δ Δ f r ( t ) ]
χ 1 , 2 ( τ , f o ) = A 1 ( t ) A 2 * ( t + τ ) exp ( 2 π i f o t ) d t

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