Abstract

Dual-comb spectroscopy is an emerging new spectroscopic tool that exploits the frequency resolution, frequency accuracy, broad bandwidth, and brightness of frequency combs for ultrahigh-resolution, high-sensitivity broadband spectroscopy. By using two coherent frequency combs, dual-comb spectroscopy allows a sample’s spectral response to be measured on a comb tooth-by-tooth basis rapidly and without the size constraints or instrument response limitations of conventional spectrometers. This review describes dual-comb spectroscopy and summarizes the current state of the art. As frequency comb technology progresses, dual-comb spectroscopy will continue to mature and could surpass conventional broadband spectroscopy for a wide range of laboratory and field applications.

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2016 (3)

G. Millot, S. Pitois, M. Yan, T. Hovhannisyan, A. Bendahmane, T. W. Hänsch, and N. Picqué, “Frequency-agile dual-comb spectroscopy,” Nat. Photonics 10, 27–30 (2016).
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P. Masłowski, 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, 021802 (2016).
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M. A. R. Reber, Y. Chen, and T. K. Allison, “Cavity-enhanced ultrafast spectroscopy: ultrafast meets ultrasensitive,” Optica 3, 311–317 (2016).

2015 (21)

S. M. Link, A. Klenner, M. Mangold, C. A. Zaugg, M. Golling, B. W. Tilma, and U. Keller, “Dual-comb modelocked laser,” Opt. Express 23, 5521–5531 (2015).
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T. Yasui, Y. Iyonaga, Y.-D. Hsieh, Y. Sakaguchi, F. Hindle, S. Yokoyama, T. Araki, and M. Hashimoto, “Super-resolution discrete Fourier transform spectroscopy beyond time-window size limitation using precisely periodic pulsed radiation,” Optica 2, 460–467 (2015).
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S. Duval, M. Bernier, V. Fortin, J. Genest, M. Piché, and R. Vallée, “Femtosecond fiber lasers reach the mid-infrared,” Optica 2, 623–626 (2015).
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P. Martín-Mateos, B. Jerez, and P. Acedo, “Dual electro-optic optical frequency combs for multiheterodyne molecular dispersion spectroscopy,” Opt. Express 23, 21149–21158 (2015).
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T. Hu, S. D. Jackson, and D. D. Hudson, “Ultrafast pulses from a mid-infrared fiber laser,” Opt. Lett. 40, 4226–4228 (2015).
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K. F. Lee, C. Mohr, J. Jiang, P. G. Schunemann, K. L. Vodopyanov, and M. E. Fermann, “Midinfrared frequency comb from self-stable degenerate GaAs optical parametric oscillator,” Opt. Express 23, 26596–26603 (2015).
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F. C. Cruz, D. L. Maser, T. Johnson, G. Ycas, A. Klose, F. R. Giorgetta, I. Coddington, and S. A. Diddams, “Mid-infrared optical frequency combs based on difference frequency generation for molecular spectroscopy,” Opt. Express 23, 26814–26824 (2015).
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V. Durán, S. Tainta, and V. Torres-Company, “Ultrafast electrooptic dual-comb interferometry,” Opt. Express 23, 30557–30569 (2015).
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S. Okubo, Y.-D. Hsieh, H. Inaba, A. Onae, M. Hashimoto, and T. Yasui, “Near-infrared broadband dual-frequency-comb spectroscopy with a resolution beyond the Fourier limit determined by the observation time window,” Opt. Express 23, 33184–33193 (2015).
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A. Khodabakhsh, A. C. Johansson, and A. Foltynowicz, “Noise-immune cavity-enhanced optical frequency comb spectroscopy: a sensitive technique for high-resolution broadband molecular detection,” Appl. Phys. B 119, 87–96 (2015).
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T. Yasui, R. Ichikawa, Y.-D. Hsieh, K. Hayashi, H. Cahyadi, F. Hindle, Y. Sakaguchi, T. Iwata, Y. Mizutani, H. Yamamoto, K. Minoshima, and H. Inaba, “Adaptive sampling dual terahertz comb spectroscopy using dual free-running femtosecond lasers,” Sci. Rep. 5, 10786 (2015).
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L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited article: A compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
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K. Lee, J. Lee, Y.-S. Jang, S. Han, H. Jang, Y.-J. Kim, and S.-W. Kim, “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep. 5, 15726 (2015).
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I. A. Finneran, J. T. Good, D. B. Holland, P. B. Carroll, M. A. Allodi, and G. A. Blake, “Decade-spanning high-precision terahertz frequency comb,” Phys. Rev. Lett. 114, 163902 (2015).
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Y. Jin, S. M. Cristescu, F. J. M. Harren, and J. Mandon, “Femtosecond optical parametric oscillators toward real-time dual-comb spectroscopy,” Appl. Phys. B 119, 65–74 (2015).
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J. T. Good, D. B. Holland, I. A. Finneran, P. B. Carroll, M. J. Kelley, and G. A. Blake, “A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer,” Rev. Sci. Instrum. 86, 103107 (2015).
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S. Okubo, K. Iwakuni, H. Inaba, K. Hosaka, A. Onae, H. Sasada, and F.-L. Hong, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9  μm,” Appl. Phys. Express 8, 082402 (2015).
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F. Zhu, A. Bicer, R. Askar, J. Bounds, A. A. Kolomenskii, V. Kelessides, M. Amani, and H. A. Schuessler, “Mid-infrared dual frequency comb spectroscopy based on fiber lasers for the detection of methane in ambient air,” Laser Phys. Lett. 12, 095701 (2015).
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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, 251104 (2015).
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F. R. Giorgetta, G. B. Rieker, E. Baumann, W. C. Swann, L. C. Sinclair, J. Kofler, I. Coddington, and N. R. Newbury, “Broadband phase spectroscopy over turbulent air paths,” Phys. Rev. Lett. 115, 103901 (2015).
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P. Martin-Mateos, M. Ruiz-Llata, J. Posada-Roman, and P. Acedo, “Dual-comb architecture for fast spectroscopic measurements and spectral characterization,” IEEE Photon. Technol. Lett. 27, 1309–1312 (2015).
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2014 (15)

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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M. Cassinerio, A. Gambetta, N. Coluccelli, P. Laporta, and G. Galzerano, “Absolute dual-comb spectroscopy at 1.55  μm by free-running Er:fiber lasers,” Appl. Phys. Lett. 104, 231102 (2014).
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Y. Wang, M. G. Soskind, W. Wang, and G. Wysocki, “High-resolution multi-heterodyne spectroscopy based on Fabry-Perot quantum cascade lasers,” Appl. Phys. Lett. 104, 031114 (2014).
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G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
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Y.-D. Hsieh, Y. Iyonaga, Y. Sakaguchi, S. Yokoyama, H. Inaba, K. Minoshima, F. Hindle, T. Araki, and T. Yasui, “Spectrally interleaved, comb-mode-resolved spectroscopy using swept dual terahertz combs,” Sci. Rep. 4, 3816 (2014).

A. Hipke, S. A. Meek, T. Ideguchi, T. W. Hänsch, and N. Picqué, “Broadband Doppler-limited two-photon and stepwise excitation spectroscopy with laser frequency combs,” Phys. Rev. A 90, 011805 (2014).
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L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, I. Coddington, and N. R. Newbury, “Optical phase noise from atmospheric fluctuations and its impact on optical time-frequency transfer,” Phys. Rev. A 89, 023805 (2014).
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A. J. Fleisher, B. J. Bjork, T. Q. Bui, K. C. Cossel, M. Okumura, and J. Ye, “Mid-infrared time-resolved frequency comb spectroscopy of transient free radicals,” J. Phys. Chem. Lett. 5, 2241–2246 (2014).
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J. Lee, K. Lee, Y.-S. Jang, H. Jang, S. Han, S.-H. Lee, K.-I. Kang, C.-W. Lim, Y.-J. Kim, and S.-W. Kim, “Testing of a femtosecond pulse laser in outer space,” Sci. Rep. 4, 5134 (2014).

L. C. Sinclair, I. Coddington, W. C. Swann, G. B. Rieker, A. Hati, K. Iwakuni, and N. R. Newbury, “Operation of an optically coherent frequency comb outside the metrology lab,” Opt. Express 22, 6996–7006 (2014).
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S. Boudreau and J. Genest, “Range-resolved vibrometry using a frequency comb in the OSCAT configuration,” Opt. Express 22, 8101–8113 (2014).
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D. A. Long, A. J. Fleisher, K. O. Douglass, S. E. Maxwell, K. Bielska, J. T. Hodges, and D. F. Plusquellic, “Multiheterodyne spectroscopy with optical frequency combs generated from a continuous-wave laser,” Opt. Lett. 39, 2688–2690 (2014).
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Y. Jin, S. M. Cristescu, F. J. M. Harren, and J. Mandon, “Two-crystal mid-infrared optical parametric oscillator for absorption and dispersion dual-comb spectroscopy,” Opt. Lett. 39, 3270–3273 (2014).
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I. Znakovskaya, E. Fill, N. Forget, P. Tournois, M. Seidel, O. Pronin, F. Krausz, and A. Apolonski, “Dual frequency comb spectroscopy with a single laser,” Opt. Lett. 39, 5471–5474 (2014).
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G. B. Rieker, F. R. Giorgetta, W. C. Swann, J. Kofler, A. M. Zolot, L. C. Sinclair, E. Baumann, C. Cromer, G. Petron, C. Sweeney, P. P. Tans, I. Coddington, and N. R. Newbury, “Frequency-comb-based remote sensing of greenhouse gases over kilometer air paths,” Optica 1, 290–298 (2014).
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2013 (11)

S. Potvin, S. Boudreau, J.-D. Deschênes, and J. Genest, “Fully referenced single-comb interferometry using optical sampling by laser-cavity tuning,” Appl. Opt. 52, 248–255 (2013).
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S. Boudreau, S. Levasseur, C. Perilla, S. Roy, and J. Genest, “Chemical detection with hyperspectral lidar using dual frequency combs,” Opt. Express 21, 7411–7418 (2013).
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N. Kuse, A. Ozawa, and Y. Kobayashi, “Static FBG strain sensor with high resolution and large dynamic range by dual-comb spectroscopy,” Opt. Express 21, 11141–11149 (2013).
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Z. Zhang, X. Fang, T. Gardiner, and D. T. Reid, “High-power asynchronous midinfrared optical parametric oscillator frequency combs,” Opt. Lett. 38, 2077–2079 (2013).
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Z. Zhang, T. Gardiner, and D. T. Reid, “Mid-infrared dual-comb spectroscopy with an optical parametric oscillator,” Opt. Lett. 38, 3148–3150 (2013).
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S. Potvin and J. Genest, “Dual-comb spectroscopy using frequency-doubled combs around 775  nm,” Opt. Express 21, 30707–30715 (2013).
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A. Klee, J. Davila-Rodriguez, C. Williams, and P. J. Delfyett, “Characterization of semiconductor-based optical frequency comb sources using generalized multiheterodyne detection,” IEEE J. Sel. Top. Quantum Electron. 19, 1100711 (2013).
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M. Zeitouny, P. Balling, P. Křen, P. Mašika, R. C. Horsten, S. T. Persijn, H. P. Urbach, and N. Bhattacharya, “Multi-correlation Fourier transform spectroscopy with the resolved modes of a frequency comb laser,” Ann. Phys. 525, 437–442 (2013).
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A. M. Zolot, F. R. Giorgetta, E. Baumann, W. C. Swann, I. Coddington, and N. R. Newbury, “Broad-band frequency references in the near-infrared: accurate dual comb spectroscopy of methane and acetylene,” J. Quant. Spectrosc. Radiat. Transf. 118, 26–39 (2013).
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T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502, 355–358 (2013).
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F. Zhu, T. Mohamed, J. Strohaber, A. A. Kolomenskii, T. Udem, and H. A. Schuessler, “Real-time dual frequency comb spectroscopy in the near infrared,” Appl. Phys. Lett. 102, 121116 (2013).
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2012 (15)

R. Grilli, G. Méjean, C. Abd Alrahman, I. Ventrillard, S. Kassi, and D. Romanini, “Cavity-enhanced multiplexed comb spectroscopy down to the photon shot noise,” Phys. Rev. A 85, 051804 (2012).
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I. Coddington, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing fast arbitrary CW waveforms with 1500  THz/s instantaneous chirps,” IEEE J. Sel. Top. Quantum Electron. 18, 228–238 (2012).
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D. W. Chandler and K. E. Strecker, “Dual-etalon frequency-comb cavity ringdown spectrometer,” J. Chem. Phys. 136, 154201 (2012).
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A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6, 440–449 (2012).
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F. Keilmann and S. Amarie, “Mid-infrared frequency comb spanning an octave based on an Er fiber laser and difference-frequency generation,” J. Infrared Millim. Terahertz Waves 33, 479–484 (2012).
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Z. Zhang, C. Gu, J. Sun, C. Wang, T. Gardiner, and D. T. Reid, “Asynchronous midinfrared ultrafast optical parametric oscillator for dual-comb spectroscopy,” Opt. Lett. 37, 187–189 (2012).
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V. Michaud-Belleau, J. Roy, S. Potvin, J.-R. Carrier, L.-S. Verret, M. Charlebois, J. Genest, and C. N. Allen, “Whispering gallery mode sensing with a dual frequency comb probe,” Opt. Express 20, 3066–3075 (2012).
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A. M. Zolot, F. R. Giorgetta, E. Baumann, J. W. Nicholson, W. C. Swann, I. Coddington, and N. R. Newbury, “Direct-comb molecular spectroscopy with accurate, resolved comb teeth over 43  THz,” Opt. Lett. 37, 638–640 (2012).
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N. Leindecker, A. Marandi, R. L. Byer, K. L. Vodopyanov, J. Jiang, I. Hartl, M. Fermann, and P. G. Schunemann, “Octave-spanning ultrafast OPO with 2.6–6.1  μm instantaneous bandwidth pumped by femtosecond Tm-fiber laser,” Opt. Express 20, 7046–7053 (2012).
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S. Boudreau and J. Genest, “Referenced passive spectroscopy using dual frequency combs,” Opt. Express 20, 7375–7387 (2012).
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C. R. Phillips, J. Jiang, C. Mohr, A. C. Lin, C. Langrock, M. Snure, D. Bliss, M. Zhu, I. Hartl, J. S. Harris, M. E. Fermann, and M. M. Fejer, “Widely tunable midinfrared difference frequency generation in orientation-patterned GaAs pumped with a femtosecond Tm-fiber system,” Opt. Lett. 37, 2928–2930 (2012).
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L. Nugent-Glandorf, T. Neely, F. Adler, A. J. Fleisher, K. C. Cossel, B. Bjork, T. Dinneen, J. Ye, and S. A. Diddams, “Mid-infrared virtually imaged phased array spectrometer for rapid and broadband trace gas detection,” Opt. Lett. 37, 3285–3287 (2012).
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J. Roy, J.-D. Deschênes, S. Potvin, and J. Genest, “Continuous real-time correction and averaging for frequency comb interferometry,” Opt. Express 20, 21932–21939 (2012).
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T. Ideguchi, B. Bernhardt, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Raman-induced Kerr-effect dual-comb spectroscopy,” Opt. Lett. 37, 4498–4500 (2012).
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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, 4847–4849 (2012).
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2011 (5)

N. Leindecker, A. Marandi, R. L. Byer, and K. L. Vodopyanov, “Broadband degenerate OPO for mid-infrared frequency comb generation,” Opt. Express 19, 6296–6302 (2011).
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T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
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N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5, 186–188 (2011).
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E. Baumann, F. R. Giorgetta, W. C. Swann, A. M. Zolot, I. Coddington, and N. R. Newbury, “Spectroscopy of the methane ν3 band with an accurate midinfrared coherent dual-comb spectrometer,” Phys. Rev. A 84, 062513 (2011).
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G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron. 17, 159–168 (2011).
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2010 (16)

R. Gebs, P. Klopp, G. Klatt, T. Dekorsy, U. Griebner, and A. Bartels, “Time-domain terahertz spectroscopy based on asynchronous optical sampling with femtosecond semiconductor disk laser,” Electron. Lett. 46, 75–76 (2010).
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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, 55–57 (2010).
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B. Bernhardt, E. Sorokin, P. Jacquet, R. Thon, T. Becker, I. T. Sorokina, N. Picqué, and T. W. Hänsch, “Mid-infrared dual-comb spectroscopy with 2.4  μm Cr2+:ZnSe femtosecond lasers,” Appl. Phys. B 100, 3–8 (2010).
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I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent dual-comb spectroscopy at high signal-to-noise ratio,” Phys. Rev. A 82, 043817 (2010).
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F. R. Giorgetta, I. Coddington, E. Baumann, W. C. Swann, and N. R. Newbury, “Fast high-resolution spectroscopy of dynamic continuous-wave laser sources,” Nat. Photonics 4, 853–857 (2010).
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F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
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Z. Li, H. Pan, H. Chen, A. Beling, and J. C. Campbell, “High-saturation-current modified uni-traveling-carrier photodiode with Cliff layer,” IEEE J. Quantum Electron. 46, 626–632 (2010).
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T. Hochrein, R. Wilk, M. Mei, R. Holzwarth, N. Krumbholz, and M. Koch, “Optical sampling by laser cavity tuning,” Opt. Express 18, 1613–1617 (2010).
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R. Gebs, G. Klatt, C. Janke, T. Dekorsy, and A. Bartels, “High-speed asynchronous optical sampling with sub-50  fs time resolution,” Opt. Express 18, 5974–5983 (2010).
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N. R. Newbury, I. Coddington, and W. C. Swann, “Sensitivity of coherent dual-comb spectroscopy,” Opt. Express 18, 7929–7945 (2010).
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I. Coddington, W. C. Swann, and N. R. Newbury, “Time-domain spectroscopy of molecular free-induction decay in the infrared,” Opt. Lett. 35, 1395–1397 (2010).
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T. Yasui, M. Nose, A. Ihara, K. Kawamoto, S. Yokoyama, H. Inaba, K. Minoshima, and T. Araki, “Fiber-based, hybrid terahertz spectrometer using dual fiber combs,” Opt. Lett. 35, 1689–1691 (2010).
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M. Godbout, J.-D. Deschênes, and J. Genest, “Spectrally resolved laser ranging with frequency combs,” Opt. Express 18, 15981–15989 (2010).
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F. Adler, P. Masłowski, A. Foltynowicz, K. C. Cossel, T. C. Briles, I. Hartl, and J. Ye, “Mid-infrared Fourier transform spectroscopy with a broadband frequency comb,” Opt. Express 18, 21861–21872 (2010).
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J.-D. Deschênes, P. Giaccarri, and J. Genest, “Optical referencing technique with CW lasers as intermediate oscillators for continuous full delay range frequency comb interferometry,” Opt. Express 18, 23358–23370 (2010).
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S. A. Diddams, “The evolving optical frequency comb [Invited],” J. Opt. Soc. Am. B 27, B51–B62 (2010).
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A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78, 035107 (2007).
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C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, “Frequency comb Vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
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T. Kraetschmer, J. W. Walewski, and S. T. Sanders, “Continuous-wave frequency comb Fourier transform source based on a high-dispersion cavity,” Opt. Lett. 31, 3179–3181 (2006).
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M. Brehm, A. Schliesser, and F. Keilmann, “Spectroscopic near-field microscopy using frequency combs in the mid-infrared,” Opt. Express 14, 11222–11233 (2006).
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T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88, 241104 (2006).
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2005 (2)

T. Yasui, E. Saneyoshi, and T. Araki, “Asynchronous optical sampling terahertz time-domain spectroscopy for ultrahigh spectral resolution and rapid data acquisition,” Appl. Phys. Lett. 87, 061101 (2005).
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A. Schliesser, M. Brehm, F. Keilmann, and D. van der Weide, “Frequency-comb infrared spectrometer for rapid, remote chemical sensing,” Opt. Express 13, 9029–9038 (2005).
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2001 (1)

S.-J. Lee, B. Widiyatmoko, M. Kourogi, and M. Ohtsu, “Ultrahigh scanning speed optical coherence tomography using optical frequency comb generators,” Jpn. J. Appl. Phys. 40, L878–L880 (2001).
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Figures (6)

Fig. 1.
Fig. 1.

(a) Simple DCS concept. Two combs with repetition rates f r and f r + Δ f r are mixed and detected by a single photoreceiver. As a result of the comb structure, each pair of optical teeth yields an rf heterodyne signal at a unique rf frequency. These rf frequencies form an rf comb of spacing Δ f r . The rf teeth can be tightly packed such that > 10 5 comb teeth can be observed simultaneously. For much of the original DCS work, f r was typically 100    MHz and Δ f r was 100 Hz to 1 kHz, but these values can vary considerably across different frequency comb sources. (b) For spectroscopy, either one or both combs are passed through the sample. The resulting absorption (or phase shifts) on the comb teeth is encoded onto the corresponding amplitude (or phase) of the measured rf comb teeth.

Fig. 2.
Fig. 2.

Spectral coverage of dual-comb spectroscopy demonstrations (top band) and underlying frequency comb technologies (bottom band). The span covers over 14 octaves across the THz, IR, and optical. DCS has also been proposed in the extreme UV [77]. Section 4 discusses some of these different demonstrations. PCA, photoconductive antenna; OPO, optical parametric oscillator; DFG, difference frequency generation; QCL, quantum cascade laser; SHG, second-harmonic generation; HHG, high-harmonic generation.

Fig. 3.
Fig. 3.

(a) Two frequency combs (red and blue) are mixed to produce (b) the rf comb. Solid gray lines indicate filter functions applied in the rf and optical to avoid aliasing effects. (c) The equivalent time-domain picture showing the pulse-to-pulse walk-off between the two comb pulse trains. (d) The photoreceiver voltage output corresponds to the product of the two comb pulses, integrated over the receiver bandwidth. This output can be viewed in laboratory time, where the samples are at time intervals of 1 / f r , or in effective time, where the samples are at time intervals of Δ T (as with FTIR interferograms). In both time scales k is the sample number. The large “centerburst” corresponds to the simultaneous arrival of the two pulses. Also visible in the “tail” to the right is a weak ringing containing absorption information of the sample gas.

Fig. 4.
Fig. 4.

Three different categories of DCS demonstrations. (a) Free-running combs can yield dual-comb spectra, but with low resolution, low frequency accuracy, and low SNR, since only limited signal averaging is possible; (b) mutually coherent combs can yield comb-tooth-resolved spectra that can be averaged for high SNR; and (c) fully referenced combs yield spectra with simultaneous high resolution, absolute frequency accuracy, and high SNR. Text boxes indicate some general rules of thumb for frequency combs based on mode-locked lasers.

Fig. 5.
Fig. 5.

Signature of the full rotational band from the C-H overtone of HCN gas as measured in the dispersive dual-comb spectrometer configuration [19]. (a) The phase and amplitude signature at 100 MHz point spacing has a signal-to-noise ratio per point of 4000 with respect to unity transmission; (b) expanded view showing the spectral sampling points; (c) joint time–frequency domain signature from the short-time Fourier transform of the data that clearly shows the free-induction decay signals in the “P” and “R” branches as vertical stripes. The overall decay results from Doppler and collisional dephasing.

Fig. 6.
Fig. 6.

Spectral SNR versus bandwidth for DCS demonstrations in the near-IR (NIR; yellow triangles) and mid-IR (MIR; red triangles). In the near-IR, data points include only experiments that enforced mutual coherence through either active phase/timing feedback [25], digital phase/timing correction [24], or analog adaptive sampling [42]. The solid triangles indicate that coherent averaging was implemented. Approximate regions of operation for FTIR and tunable laser spectroscopy (TLS) are added in blue. The number of spectral elements M is the bandwidth / f r , where f r is 100    MHz for most demonstrations shown here.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Δ ν m f r 2 = f r 2 2 Δ f r ,
Δ T = Δ f r f r ( f r + Δ f r ) 1 m f r ,
SNR NEP 1 M P 1 P 2 NEP τ ,
SNR DynRange D M τ f r .

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