Abstract

Long-term mutual coherence is a key factor that affects the signal-to-noise ratio and resolution of a dual-comb interferometer. To realize a phase-stable dual-comb interferometer configuration, tightly phase-locked loop systems or digital error correction methods with external optical reference are commonly used. This paper presents a self-referencing digital error correction method based on the short-term spectral characteristics of interferograms to reduce the cost and complexity of the phase-stable dual-comb interferometer configuration. In our experiment, fully mutual coherence of a dual-comb interferometer is reconstructed and 1 Hz theoretical linewidth in 1 s acquisition time is achieved by digitally compensating for time jitter, center frequency jitter, and carrier-envelope-phase jitter, offering an effective technique for advanced dual-comb applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

2018 (7)

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
[Crossref]

M. Yan, L. Zhang, Q. Hao, X. Shen, X. Qian, H. Chen, X. Ren, and H. Zeng, “Surface-Enhanced Dual-Comb Coherent Raman Spectroscopy with Nanoporous Gold Films,” Laser Photonics Rev. 12(9), 1800096 (2018).
[Crossref]

Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018).
[Crossref]

H. Mikami, J. Harmon, H. Kobayashi, S. Hamad, Y. Wang, O. Iwata, K. Suzuki, T. Ito, Y. Aisaka, N. Kutsuna, K. Nagasawa, H. Watarai, Y. Ozeki, and K. Goda, “Ultrafast confocal fluorescence microscopy beyond the fluorescence lifetime limit,” Optica 5(2), 117–126 (2018).
[Crossref]

Z. Zhu, G. Xu, K. Ni, Q. Zhou, and G. Wu, “Synthetic-wavelength-based dual-comb interferometry for fast and precise absolute distance measurement,” Opt. Express 26(5), 5747–5757 (2018).
[Crossref]

E. Hase, T. Minamikawa, T. Mizuno, S. Miyamoto, R. Ichikawa, Y.-D. Hsieh, K. Shibuya, K. Sato, Y. Nakajima, A. Asahara, K. Minoshima, Y. Mizutani, T. Iwata, H. Yamamoto, and T. Yasui, “Scan-less confocal phase imaging based on dual-comb microscopy,” Optica 5(5), 634–643 (2018).
[Crossref]

Z. Zhu, K. Ni, Q. Zhou, and G. Wu, “Digital correction method for realizing a phase-stable dual-comb interferometer,” Opt. Express 26(13), 16813–16823 (2018).
[Crossref]

2017 (4)

2016 (2)

D. Burghoff, Y. Yang, and Q. Hu, “Computational multiheterodyne spectroscopy,” Sci. Adv. 2(11), e1601227 (2016).
[Crossref]

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

2015 (2)

H. Shi, Y. Song, F. Liang, L. Xu, M. Hu, and C. Wang, “Effect of timing jitter on time-of-flight distance measurements using dual femtosecond lasers,” Opt. Express 23(11), 14057–14069 (2015).
[Crossref]

O. Sho, I. Kana, I. Hajime, H. Kazumoto, O. Atsushi, S. Hiroyuki, and H. Feng-Lei, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9 µm,” Appl. Phys. Express 8(8), 082402 (2015).
[Crossref]

2014 (1)

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picque, and T. W. Hansch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5(1), 3375 (2014).
[Crossref]

2013 (1)

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502(7471), 355–358 (2013).
[Crossref]

2012 (2)

2010 (4)

N. R. Newbury, I. Coddington, and W. Swann, “Sensitivity of coherent dual-comb spectroscopy,” Opt. Express 18(8), 7929–7945 (2010).
[Crossref]

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]

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent dual-comb spectroscopy at high signal-to-noise ratio,” Phys. Rev. A 82(4), 043817 (2010).
[Crossref]

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
[Crossref]

2009 (1)

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

2008 (2)

2007 (1)

2006 (2)

M. Brehm, A. Schliesser, and F. Keilmann, “Spectroscopic near-field microscopy using frequency combs in the mid-infrared,” Opt. Express 14(23), 11222–11233 (2006).
[Crossref]

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B: Lasers Opt. 82(2), 265–273 (2006).
[Crossref]

2005 (1)

2004 (1)

2003 (1)

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

2002 (2)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref]

S. Schiller, “Spectrometry with frequency combs,” Opt. Lett. 27(9), 766–768 (2002).
[Crossref]

2001 (1)

L.-S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, “Sub-10-femtosecond active synchronization of two passively mode-locked Ti:sapphire oscillators,” Phys. Rev. A 64(2), 021802 (2001).
[Crossref]

Aisaka, Y.

Asahara, A.

Atsushi, O.

O. Sho, I. Kana, I. Hajime, H. Kazumoto, O. Atsushi, S. Hiroyuki, and H. Feng-Lei, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9 µm,” Appl. Phys. Express 8(8), 082402 (2015).
[Crossref]

Bartels, A.

J. Ye, S. T. Cundiff, F. X. Kärtner, E. P. Ippen, A. Bartels, A. L. Gaeta, R. S. Windeler, G. Steinmeyer, U. Keller, and T. Kobayashi, “Femtosecond Optical Frequency Comb: Principle, Operation, and Applications,” (2005).

Baumann, E.

Bergeron, H.

Bernhardt, B.

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502(7471), 355–358 (2013).
[Crossref]

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
[Crossref]

Bohn, B. J.

Brehm, M.

Burghoff, D.

D. Burghoff, Y. Yang, and Q. Hu, “Computational multiheterodyne spectroscopy,” Sci. Adv. 2(11), e1601227 (2016).
[Crossref]

Chen, G. Y.

Chen, H.

M. Yan, L. Zhang, Q. Hao, X. Shen, X. Qian, H. Chen, X. Ren, and H. Zeng, “Surface-Enhanced Dual-Comb Coherent Raman Spectroscopy with Nanoporous Gold Films,” Laser Photonics Rev. 12(9), 1800096 (2018).
[Crossref]

Chen, Z.

Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018).
[Crossref]

Coddington, I.

G. Ycas, F. R. Giorgetta, K. C. Cossel, E. M. Waxman, E. Baumann, N. R. Newbury, and I. Coddington, “Mid-infrared dual-comb spectroscopy of volatile organic compounds across long open-air paths,” Optica 6(2), 165–168 (2019).
[Crossref]

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

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent dual-comb spectroscopy at high signal-to-noise ratio,” Phys. Rev. A 82(4), 043817 (2010).
[Crossref]

N. R. Newbury, I. Coddington, and W. Swann, “Sensitivity of coherent dual-comb spectroscopy,” Opt. Express 18(8), 7929–7945 (2010).
[Crossref]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

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]

Cossel, K. C.

Cundiff, S. T.

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

J. Ye, S. T. Cundiff, F. X. Kärtner, E. P. Ippen, A. Bartels, A. L. Gaeta, R. S. Windeler, G. Steinmeyer, U. Keller, and T. Kobayashi, “Femtosecond Optical Frequency Comb: Principle, Operation, and Applications,” (2005).

Deschênes, J.-D.

Feng-Lei, H.

O. Sho, I. Kana, I. Hajime, H. Kazumoto, O. Atsushi, S. Hiroyuki, and H. Feng-Lei, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9 µm,” Appl. Phys. Express 8(8), 082402 (2015).
[Crossref]

Freude, W.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
[Crossref]

Gaeta, A. L.

J. Ye, S. T. Cundiff, F. X. Kärtner, E. P. Ippen, A. Bartels, A. L. Gaeta, R. S. Windeler, G. Steinmeyer, U. Keller, and T. Kobayashi, “Femtosecond Optical Frequency Comb: Principle, Operation, and Applications,” (2005).

Ganin, D.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
[Crossref]

Genest, J.

Giaccari, P.

Giorgetta, F. R.

Goda, K.

Gohle, C.

Guelachvili, G.

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picque, and T. W. Hansch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5(1), 3375 (2014).
[Crossref]

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502(7471), 355–358 (2013).
[Crossref]

T. Ideguchi, A. Poisson, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Adaptive dual-comb spectroscopy in the green region,” Opt. Lett. 37(23), 4847–4849 (2012).
[Crossref]

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
[Crossref]

Hajime, I.

O. Sho, I. Kana, I. Hajime, H. Kazumoto, O. Atsushi, S. Hiroyuki, and H. Feng-Lei, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9 µm,” Appl. Phys. Express 8(8), 082402 (2015).
[Crossref]

Hamad, S.

Hansch, T. W.

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picque, and T. W. Hansch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5(1), 3375 (2014).
[Crossref]

Hänsch, T. W.

N. Picqué and T. W. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13(3), 146–157 (2019).
[Crossref]

Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018).
[Crossref]

M. Yan, P.-L. Luo, K. Iwakuni, G. Millot, T. W. Hänsch, and N. Picqué, “Mid-infrared dual-comb spectroscopy with electro-optic modulators,” Light: Sci. Appl. 6(10), e17076 (2017).
[Crossref]

K. J. Mohler, B. J. Bohn, M. Yan, G. Mélen, T. W. Hänsch, and N. Picqué, “Dual-comb coherent Raman spectroscopy with lasers of 1-GHz pulse repetition frequency,” Opt. Lett. 42(2), 318–321 (2017).
[Crossref]

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502(7471), 355–358 (2013).
[Crossref]

T. Ideguchi, A. Poisson, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Adaptive dual-comb spectroscopy in the green region,” Opt. Lett. 37(23), 4847–4849 (2012).
[Crossref]

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
[Crossref]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref]

Hao, Q.

M. Yan, L. Zhang, Q. Hao, X. Shen, X. Qian, H. Chen, X. Ren, and H. Zeng, “Surface-Enhanced Dual-Comb Coherent Raman Spectroscopy with Nanoporous Gold Films,” Laser Photonics Rev. 12(9), 1800096 (2018).
[Crossref]

Harmon, J.

Hase, E.

Hébert, N. B.

Hiroyuki, S.

O. Sho, I. Kana, I. Hajime, H. Kazumoto, O. Atsushi, S. Hiroyuki, and H. Feng-Lei, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9 µm,” Appl. Phys. Express 8(8), 082402 (2015).
[Crossref]

Holzner, S.

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502(7471), 355–358 (2013).
[Crossref]

Holzwarth, R.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
[Crossref]

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M. Yan, P.-L. Luo, K. Iwakuni, G. Millot, T. W. Hänsch, and N. Picqué, “Mid-infrared dual-comb spectroscopy with electro-optic modulators,” Light: Sci. Appl. 6(10), e17076 (2017).
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Keller, U.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B: Lasers Opt. 82(2), 265–273 (2006).
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Kippenberg, T. J.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
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Kobayashi, T.

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B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
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P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
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P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
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P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
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Lancaster, D. G.

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Liang, F.

Luo, P.-L.

M. Yan, P.-L. Luo, K. Iwakuni, G. Millot, T. W. Hänsch, and N. Picqué, “Mid-infrared dual-comb spectroscopy with electro-optic modulators,” Light: Sci. Appl. 6(10), e17076 (2017).
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L.-S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, “Sub-10-femtosecond active synchronization of two passively mode-locked Ti:sapphire oscillators,” Phys. Rev. A 64(2), 021802 (2001).
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P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
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Mikami, H.

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M. Yan, P.-L. Luo, K. Iwakuni, G. Millot, T. W. Hänsch, and N. Picqué, “Mid-infrared dual-comb spectroscopy with electro-optic modulators,” Light: Sci. Appl. 6(10), e17076 (2017).
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L.-S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, “Sub-10-femtosecond active synchronization of two passively mode-locked Ti:sapphire oscillators,” Phys. Rev. A 64(2), 021802 (2001).
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I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (2008).
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N. R. Newbury and W. C. Swann, “Low-noise fiber-laser frequency combs (Invited),” J. Opt. Soc. Am. B 24(8), 1756–1770 (2007).
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Z. Zhu, K. Ni, Q. Zhou, and G. Wu, “Digital correction method for realizing a phase-stable dual-comb interferometer,” Opt. Express 26(13), 16813–16823 (2018).
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Z. Zhu, G. Xu, K. Ni, Q. Zhou, and G. Wu, “Synthetic-wavelength-based dual-comb interferometry for fast and precise absolute distance measurement,” Opt. Express 26(5), 5747–5757 (2018).
[Crossref]

H. Yu, K. Ni, Q. Zhou, X. Li, and G. Wu, “A simulation method for dual-comb spectroscopy with jitter noise,” in Real-time Photonic Measurements, Data Management, and Processing III, (International Society for Optics and Photonics, 2018), 108220Q.

Ozawa, A.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
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Paschotta, R.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B: Lasers Opt. 82(2), 265–273 (2006).
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P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
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T. Ideguchi, A. Poisson, G. Guelachvili, N. Picque, and T. W. Hansch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5(1), 3375 (2014).
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Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018).
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M. Yan, P.-L. Luo, K. Iwakuni, G. Millot, T. W. Hänsch, and N. Picqué, “Mid-infrared dual-comb spectroscopy with electro-optic modulators,” Light: Sci. Appl. 6(10), e17076 (2017).
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K. J. Mohler, B. J. Bohn, M. Yan, G. Mélen, T. W. Hänsch, and N. Picqué, “Dual-comb coherent Raman spectroscopy with lasers of 1-GHz pulse repetition frequency,” Opt. Lett. 42(2), 318–321 (2017).
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T. Ideguchi, A. Poisson, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Adaptive dual-comb spectroscopy in the green region,” Opt. Lett. 37(23), 4847–4849 (2012).
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B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
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T. Ideguchi, A. Poisson, G. Guelachvili, N. Picque, and T. W. Hansch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5(1), 3375 (2014).
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T. Ideguchi, A. Poisson, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Adaptive dual-comb spectroscopy in the green region,” Opt. Lett. 37(23), 4847–4849 (2012).
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P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
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Ren, X.

M. Yan, L. Zhang, Q. Hao, X. Shen, X. Qian, H. Chen, X. Ren, and H. Zeng, “Surface-Enhanced Dual-Comb Coherent Raman Spectroscopy with Nanoporous Gold Films,” Laser Photonics Rev. 12(9), 1800096 (2018).
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R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B: Lasers Opt. 82(2), 265–273 (2006).
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Shelton, R. K.

L.-S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, “Sub-10-femtosecond active synchronization of two passively mode-locked Ti:sapphire oscillators,” Phys. Rev. A 64(2), 021802 (2001).
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Shen, X.

M. Yan, L. Zhang, Q. Hao, X. Shen, X. Qian, H. Chen, X. Ren, and H. Zeng, “Surface-Enhanced Dual-Comb Coherent Raman Spectroscopy with Nanoporous Gold Films,” Laser Photonics Rev. 12(9), 1800096 (2018).
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Sho, O.

O. Sho, I. Kana, I. Hajime, H. Kazumoto, O. Atsushi, S. Hiroyuki, and H. Feng-Lei, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9 µm,” Appl. Phys. Express 8(8), 082402 (2015).
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Song, Y.

Steinmeyer, G.

J. Ye, S. T. Cundiff, F. X. Kärtner, E. P. Ippen, A. Bartels, A. L. Gaeta, R. S. Windeler, G. Steinmeyer, U. Keller, and T. Kobayashi, “Femtosecond Optical Frequency Comb: Principle, Operation, and Applications,” (2005).

Suzuki, K.

Swann, W.

Swann, W. C.

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent dual-comb spectroscopy at high signal-to-noise ratio,” Phys. Rev. A 82(4), 043817 (2010).
[Crossref]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
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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]

N. R. Newbury and W. C. Swann, “Low-noise fiber-laser frequency combs (Invited),” J. Opt. Soc. Am. B 24(8), 1756–1770 (2007).
[Crossref]

Telle, H. R.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B: Lasers Opt. 82(2), 265–273 (2006).
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P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
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B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
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T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
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P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
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J. Ye, S. T. Cundiff, F. X. Kärtner, E. P. Ippen, A. Bartels, A. L. Gaeta, R. S. Windeler, G. Steinmeyer, U. Keller, and T. Kobayashi, “Femtosecond Optical Frequency Comb: Principle, Operation, and Applications,” (2005).

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P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
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Wu, G.

Z. Zhu, K. Ni, Q. Zhou, and G. Wu, “Digital correction method for realizing a phase-stable dual-comb interferometer,” Opt. Express 26(13), 16813–16823 (2018).
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Z. Zhu, G. Xu, K. Ni, Q. Zhou, and G. Wu, “Synthetic-wavelength-based dual-comb interferometry for fast and precise absolute distance measurement,” Opt. Express 26(5), 5747–5757 (2018).
[Crossref]

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Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018).
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M. Yan, L. Zhang, Q. Hao, X. Shen, X. Qian, H. Chen, X. Ren, and H. Zeng, “Surface-Enhanced Dual-Comb Coherent Raman Spectroscopy with Nanoporous Gold Films,” Laser Photonics Rev. 12(9), 1800096 (2018).
[Crossref]

M. Yan, P.-L. Luo, K. Iwakuni, G. Millot, T. W. Hänsch, and N. Picqué, “Mid-infrared dual-comb spectroscopy with electro-optic modulators,” Light: Sci. Appl. 6(10), e17076 (2017).
[Crossref]

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[Crossref]

J. Ye, S. T. Cundiff, F. X. Kärtner, E. P. Ippen, A. Bartels, A. L. Gaeta, R. S. Windeler, G. Steinmeyer, U. Keller, and T. Kobayashi, “Femtosecond Optical Frequency Comb: Principle, Operation, and Applications,” (2005).

Yu, H.

H. Yu, K. Ni, Q. Zhou, X. Li, and G. Wu, “A simulation method for dual-comb spectroscopy with jitter noise,” in Real-time Photonic Measurements, Data Management, and Processing III, (International Society for Optics and Photonics, 2018), 108220Q.

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R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B: Lasers Opt. 82(2), 265–273 (2006).
[Crossref]

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M. Yan, L. Zhang, Q. Hao, X. Shen, X. Qian, H. Chen, X. Ren, and H. Zeng, “Surface-Enhanced Dual-Comb Coherent Raman Spectroscopy with Nanoporous Gold Films,” Laser Photonics Rev. 12(9), 1800096 (2018).
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M. Yan, L. Zhang, Q. Hao, X. Shen, X. Qian, H. Chen, X. Ren, and H. Zeng, “Surface-Enhanced Dual-Comb Coherent Raman Spectroscopy with Nanoporous Gold Films,” Laser Photonics Rev. 12(9), 1800096 (2018).
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Z. Zhu, K. Ni, Q. Zhou, and G. Wu, “Digital correction method for realizing a phase-stable dual-comb interferometer,” Opt. Express 26(13), 16813–16823 (2018).
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Z. Zhu, G. Xu, K. Ni, Q. Zhou, and G. Wu, “Synthetic-wavelength-based dual-comb interferometry for fast and precise absolute distance measurement,” Opt. Express 26(5), 5747–5757 (2018).
[Crossref]

H. Yu, K. Ni, Q. Zhou, X. Li, and G. Wu, “A simulation method for dual-comb spectroscopy with jitter noise,” in Real-time Photonic Measurements, Data Management, and Processing III, (International Society for Optics and Photonics, 2018), 108220Q.

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Appl. Phys. B: Lasers Opt. (1)

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B: Lasers Opt. 82(2), 265–273 (2006).
[Crossref]

Appl. Phys. Express (1)

O. Sho, I. Kana, I. Hajime, H. Kazumoto, O. Atsushi, S. Hiroyuki, and H. Feng-Lei, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9 µm,” Appl. Phys. Express 8(8), 082402 (2015).
[Crossref]

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

Laser Photonics Rev. (1)

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M. Yan, P.-L. Luo, K. Iwakuni, G. Millot, T. W. Hänsch, and N. Picqué, “Mid-infrared dual-comb spectroscopy with electro-optic modulators,” Light: Sci. Appl. 6(10), e17076 (2017).
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Nat. Photonics (3)

N. Picqué and T. W. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13(3), 146–157 (2019).
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Nature (2)

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502(7471), 355–358 (2013).
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Opt. Express (10)

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Optica (4)

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Figures (8)

Fig. 1.
Fig. 1. Experimental setup. Red solid lines represent optical fiber paths, while black dashed lines are electrical wires. OFC: optical frequency comb; PD: photodetector; BPF: optical band-pass filter; PLL: phase-locked loop; LPF: electronic low-pass filter; ADC: analog-to-digital converter.
Fig. 2.
Fig. 2. Principle of DCI: (a), (b) Time domain aspect: asynchronous optical sampling. Two OFCs (red and blue) are mixed to generate optical pulse cross-correlation function (black) at a stretched scale. (c), (d) Frequency domain aspect: multi-heterodyne interference. Optical frequency longitudinal modes of dual OFCs (blue and green) beat reciprocally to generate RF frequency components (purple) according to a mode-to-mode heterodyne interference.
Fig. 3.
Fig. 3. Time domain IGMs. (a) Complete simulated IGMs. (b) 100× magnified view of simulated IGMs. (c) 500000× magnified view of simulated IGMs, showing an apodized IGM. (d) Complete experimental IGMs. (e) 100× magnified view of experimental IGMs. (f) 500000× magnified view of experimental IGMs, having larger pulse width due to the leakage effect of the optical band-pass filter.
Fig. 4.
Fig. 4. Comparison between artificially added jitter noise and calculated jitter noise by short-time Fourier transform. (a) Red curve, artificially added time jitter, blue curve, calculated time jitter. (b) Red curve, artificially added center frequency jitter, blue curve, calculated center frequency jitter. (c) Red curve, artificially added carrier envelope phase jitter, blue curve, calculated carrier envelope phase jitter. (d) Difference between artificially added time jitter and calculated time jitter. (e) Difference between artificially added center frequency jitter and calculated center frequency jitter. (f) Difference between artificially added carrier envelope phase jitter and calculated carrier envelop phase jitter.
Fig. 5.
Fig. 5. Effects of digital error correction steps on simulated IGMs and corresponding spectra. Each apodized IGM is periodically superimposed according to referencing repetition period. (a) Raw simulated IGMs. (b) Time jitter corrected IGMs. (c) Center frequency corrected IGMs. (d) Fully phase-aligned IGMs. (e)–(f) Corresponding normalized spectra of apodized IGMs displayed in (a)–(d).
Fig. 6.
Fig. 6. Effects of digital error correction steps on experimental IGMs and corresponding spectra. Each apodized IGM is periodically superimposed according to the referencing repetition period. (a) Raw sampled IGMs. (b) Time jitter corrected IGMs. (c) Center frequency corrected IGMs. (d) Fully phase-aligned IGMs. (e)–(f) Corresponding normalized spectra of apodized IGMs displayed in (a)–(d).
Fig. 7.
Fig. 7. Different forms of jitter noise in raw IGMs and fully phase-aligned IGMs. (a) Time jitter of raw IGMs. (b) Time jitter of fully corrected IGMs. (c) Center frequency jitter of raw IGMs. (d) Center frequency jitter of fully corrected IGMs. (e) Carrier envelope phase jitter of raw IGMs. (f) Carrier envelope phase jitter of fully corrected IGMs.
Fig. 8.
Fig. 8. RF spectrum of 1 s sampled IGMs (red, offset by 1.1) and fully phase-aligned IGMs with resolved frequency components (blue). (a) Complete spectrum of raw IGMs and fully corrected IGMs. (b) A 1000× magnified view showing dozens of frequency components near center frequency. (c) A 300000× magnified view showing single-frequency component near center frequency, realizing 1 Hz theoretical linewidth.

Equations (17)

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E 1 ( t ) = p G 1 ( υ 1 p υ c ) exp j ( 2 π υ 1 p t + ϕ 1 p ) ,
E 2 ( t ) = q G 2 ( υ 2 q υ c ) exp j ( 2 π υ 2 q t + ϕ 2 q ) ,
U c ( t ) R e { p , q A ~ 1 p A ~ 2 q exp j 2 π ( υ 1 p υ 2 q ) t } ,
f q R F = υ 1 p υ 2 q = f c e o 1 + p f r 1 f c e o 2 q f r 2   = Δ f c e o + ( p q ) f r 2 + p Δ f r = f c e o R F + p Δ f r ,
f r 2 2 < Δ f c e o + ( p q ) f r 2 + p Δ f < f r 2 2 .
φ p R F = ϕ 1 p ϕ 2 q = φ 0 R F + 2 π f p R F τ 0 R F ,
τ 0 R F = f r 1 τ 01 f r 2 τ 02 Δ f r ,
φ 0 R F = φ 01 φ 02 + 2 π ( f c e o 1 τ 01 f c e o 2 τ 02 + Δ p f r 2 τ 02 f c e o R F τ 0 R F ) .
U c ( t ) R e { p = p m i n p m a x H ( f p R F f c R F ) exp j ( 2 π f p R F t + φ p R F ) } ,
U c ( t ) N = + h ( t N T r R F + τ 0 R F )   c o s [ 2 π f c R F ( t N T r R F + τ 0 R F ) + N Δ φ c e R F + φ 0 R F ] ,
f c R F = f c e o R F + Δ f r f r 1 ( υ c f c e o 1 ) ,
T r R F = 1 / Δ f r ,
Δ φ c e R F = 2 π f c e o R F / Δ f r .
U c ( t ) N = + h ( t N T r R F + τ 0 R F + δ τ 0 R F ( N ) )   c o s [ 2 π f c R F ( N ) ( t N T r R F + τ 0 R F + δ τ 0 R F ( N ) ) + N Δ φ c e R F + φ 0 R F + δ φ 0 R F ( N ) ] .
U c o r 1 ( t N ) = U c ( t N δ τ 0 R F ( N ) ) .
U c o r 2 ( t N ) = r e a l { S c o r 1 ( t N ) e x p j 2 π [ f c R F ( N ) f c R F ( 0 ) ] t N } .
U c o r 3 ( t N ) = r e a l { S c o r 2 ( t N ) e x p j δ φ 0 R F ( N ) }   N = + h ( t N T r R F + τ 0 R F ( 0 ) )   c o s [ 2 π f c R F ( 0 ) ( t N T r R F + τ 0 R F ( 0 ) ) + φ 0 R F ( 0 ) ] .

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