Abstract

Terahertz frequency metrology by radio frequency downconversion using femtosecond optical sampling relies on the harmonic factor retrieval between the terahertz frequency and the optical sampling rate. At typical femtosecond laser repetition rates, this imposes an ambiguity for frequency metrology. We report on a dual-comb sampling system for the unambiguous frequency measurement of terahertz quantum cascade lasers with hertz-level precision. Two Ti:sapphire oscillators with 10 GHz repetition rate are used for the electro-optic sampling of terahertz radiation at 2.5 THz emitted by actively mode-locked terahertz quantum cascade lasers with 9.7 GHz and 19.6 GHz repetition rates. By coherent downconversion, the emitted terahertz waveforms are measured in the radio frequency domain. The terahertz frequency comb is stabilized by employing a phase-locked loop on a radio frequency beat-note signal. A second infrared sampling comb is used to measure the absolute frequencies of the terahertz radiation. This method, which is based on the detuning of the sampling repetition rates, allows the direct retrieval of the quantum cascade laser’s absolute frequency in real time without using additional optical frequency references for calibration. In order to demonstrate the feasibility of the stabilization and readout technique, a high-resolution spectroscopy measurement on gaseous methanol is presented.

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2016 (1)

2015 (1)

2014 (1)

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

2013 (1)

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

2012 (2)

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

2011 (2)

J. C. Pearson, B. J. Drouin, S. Yu, and H. Gupta, “Microwave spectroscopy of methanol between 2.48 and 2.77 THz,” J. Opt. Soc. Am. B 28, 2549–2577 (2011).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

2010 (2)

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18, 20799–20816 (2010).
[Crossref]

2009 (1)

2008 (1)

2004 (1)

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[Crossref]

2003 (1)

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, “A new method to determine the absolute mode number of a mode-locked femtosecond-laser comb used for absolute optical frequency measurements,” IEEE J. Sel. Top. Quantum. Electron. 9, 1066–1071 (2003).
[Crossref]

1998 (1)

H. Pickett, R. Poynter, E. Cohen, M. Delitsky, J. Pearson, and H. Müller, “Submillimeter, millimeter, and microwave spectral line catalog,” J. Quant. Spectrosc. Radiat. Transfer 60, 883–890 (1998).
[Crossref]

Alton, J.

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[Crossref]

Barbieri, S.

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18, 20799–20816 (2010).
[Crossref]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[Crossref]

Bartalini, S.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
[Crossref]

Bartels, A.

Bartolini, P.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

Beere, H.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18, 20799–20816 (2010).
[Crossref]

Beere, H. E.

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[Crossref]

Cahyadi, H.

Cancio, P.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

Cohen, E.

H. Pickett, R. Poynter, E. Cohen, M. Delitsky, J. Pearson, and H. Müller, “Submillimeter, millimeter, and microwave spectral line catalog,” J. Quant. Spectrosc. Radiat. Transfer 60, 883–890 (1998).
[Crossref]

Colombelli, R.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

Consolino, L.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
[Crossref]

Davies, A. G.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18, 20799–20816 (2010).
[Crossref]

De Natale, P.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
[Crossref]

De Pas, M.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

Dekorsy, T.

Delitsky, M.

H. Pickett, R. Poynter, E. Cohen, M. Delitsky, J. Pearson, and H. Müller, “Submillimeter, millimeter, and microwave spectral line catalog,” J. Quant. Spectrosc. Radiat. Transfer 60, 883–890 (1998).
[Crossref]

Diddams, S. A.

Ding, L.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

Drouin, B. J.

Filloux, P.

Fowler, J.

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[Crossref]

Gebs, R.

Gellie, P.

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18, 20799–20816 (2010).
[Crossref]

Gupta, H.

Hayashi, K.

Heinecke, D.

Heinecke, D. C.

Hsieh, Y.-D.

Ichikawa, R.

Inaba, H.

Inguscio, M.

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
[Crossref]

Iwata, T.

Jagtap, V.

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

Janke, C.

Khanna, S. P.

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18, 20799–20816 (2010).
[Crossref]

Klatt, G.

Kliebisch, O.

Lampin, J.-F.

Linfield, E. H.

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18, 20799–20816 (2010).
[Crossref]

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[Crossref]

Ma, L.-S.

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, “A new method to determine the absolute mode number of a mode-locked femtosecond-laser comb used for absolute optical frequency measurements,” IEEE J. Sel. Top. Quantum. Electron. 9, 1066–1071 (2003).
[Crossref]

Maineult, W.

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

Manquest, C.

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18, 20799–20816 (2010).
[Crossref]

Minoshima, K.

Mizutani, Y.

Moruzzi, G.

G. Moruzzi, M. Winnewisser, I. Mukhopadhyay, and F. Strumia, Microwave, Infrared, and Laser Transitions of Methanol Atlas of Assigned Lines from 0 to 1258  cm–1 (Taylor & Francis, 1995).

Mukhopadhyay, I.

G. Moruzzi, M. Winnewisser, I. Mukhopadhyay, and F. Strumia, Microwave, Infrared, and Laser Transitions of Methanol Atlas of Assigned Lines from 0 to 1258  cm–1 (Taylor & Francis, 1995).

Müller, H.

H. Pickett, R. Poynter, E. Cohen, M. Delitsky, J. Pearson, and H. Müller, “Submillimeter, millimeter, and microwave spectral line catalog,” J. Quant. Spectrosc. Radiat. Transfer 60, 883–890 (1998).
[Crossref]

Pearson, J.

H. Pickett, R. Poynter, E. Cohen, M. Delitsky, J. Pearson, and H. Müller, “Submillimeter, millimeter, and microwave spectral line catalog,” J. Quant. Spectrosc. Radiat. Transfer 60, 883–890 (1998).
[Crossref]

Pearson, J. C.

Picard, S.

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, “A new method to determine the absolute mode number of a mode-locked femtosecond-laser comb used for absolute optical frequency measurements,” IEEE J. Sel. Top. Quantum. Electron. 9, 1066–1071 (2003).
[Crossref]

Pickett, H.

H. Pickett, R. Poynter, E. Cohen, M. Delitsky, J. Pearson, and H. Müller, “Submillimeter, millimeter, and microwave spectral line catalog,” J. Quant. Spectrosc. Radiat. Transfer 60, 883–890 (1998).
[Crossref]

Poynter, R.

H. Pickett, R. Poynter, E. Cohen, M. Delitsky, J. Pearson, and H. Müller, “Submillimeter, millimeter, and microwave spectral line catalog,” J. Quant. Spectrosc. Radiat. Transfer 60, 883–890 (1998).
[Crossref]

Ravaro, M.

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

Riley, W. J.

W. J. Riley, Handbook of Frequency Stability Analysis (National Institute of Standards and Technology, 2008).

Ritchie, D.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18, 20799–20816 (2010).
[Crossref]

Ritchie, D. A.

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[Crossref]

Robertsson, L.

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, “A new method to determine the absolute mode number of a mode-locked femtosecond-laser comb used for absolute optical frequency measurements,” IEEE J. Sel. Top. Quantum. Electron. 9, 1066–1071 (2003).
[Crossref]

Sagnes, I.

Santarelli, G.

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

Sirtori, C.

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

P. Gellie, S. Barbieri, J.-F. Lampin, P. Filloux, C. Manquest, C. Sirtori, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, H. Beere, and D. Ritchie, “Injection-locking of terahertz quantum cascade lasers up to 35GHz using RF amplitude modulation,” Opt. Express 18, 20799–20816 (2010).
[Crossref]

Strumia, F.

G. Moruzzi, M. Winnewisser, I. Mukhopadhyay, and F. Strumia, Microwave, Infrared, and Laser Transitions of Methanol Atlas of Assigned Lines from 0 to 1258  cm–1 (Taylor & Francis, 1995).

Taschin, A.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
[Crossref]

Torre, R.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

Tredicucci, A.

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
[Crossref]

Vitiello, M. S.

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
[Crossref]

Windeler, R. S.

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, “A new method to determine the absolute mode number of a mode-locked femtosecond-laser comb used for absolute optical frequency measurements,” IEEE J. Sel. Top. Quantum. Electron. 9, 1066–1071 (2003).
[Crossref]

Winnewisser, M.

G. Moruzzi, M. Winnewisser, I. Mukhopadhyay, and F. Strumia, Microwave, Infrared, and Laser Transitions of Methanol Atlas of Assigned Lines from 0 to 1258  cm–1 (Taylor & Francis, 1995).

Yamamoto, H.

Yasui, T.

Yu, S.

Zucco, M.

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, “A new method to determine the absolute mode number of a mode-locked femtosecond-laser comb used for absolute optical frequency measurements,” IEEE J. Sel. Top. Quantum. Electron. 9, 1066–1071 (2003).
[Crossref]

Appl. Phys. Lett. (1)

S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade lasers operating up to 70 K in continuous wave,” Appl. Phys. Lett. 85, 1674–1676 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum. Electron. (1)

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, “A new method to determine the absolute mode number of a mode-locked femtosecond-laser comb used for absolute optical frequency measurements,” IEEE J. Sel. Top. Quantum. Electron. 9, 1066–1071 (2003).
[Crossref]

J. Infrared Millimeter Waves (1)

M. Ravaro, V. Jagtap, C. Manquest, P. Gellie, G. Santarelli, C. Sirtori, S. P. Khanna, E. H. Linfield, and S. Barbieri, “Spectral properties of THz quantum-cascade lasers: frequency noise, phase-locking and absolute frequency measurement,” J. Infrared Millimeter Waves 34, 342–356 (2013).
[Crossref]

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

J. Quant. Spectrosc. Radiat. Transfer (1)

H. Pickett, R. Poynter, E. Cohen, M. Delitsky, J. Pearson, and H. Müller, “Submillimeter, millimeter, and microwave spectral line catalog,” J. Quant. Spectrosc. Radiat. Transfer 60, 883–890 (1998).
[Crossref]

Nat. Photonics (3)

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5, 306–313 (2011).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. X (1)

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 021006 (2014).
[Crossref]

Other (2)

G. Moruzzi, M. Winnewisser, I. Mukhopadhyay, and F. Strumia, Microwave, Infrared, and Laser Transitions of Methanol Atlas of Assigned Lines from 0 to 1258  cm–1 (Taylor & Francis, 1995).

W. J. Riley, Handbook of Frequency Stability Analysis (National Institute of Standards and Technology, 2008).

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Figures (7)

Fig. 1.
Fig. 1. (a) Schematic overview of the dual-comb sampling setup. The two femtosecond lasers have the same wavelength but are depicted in red and orange for visual clarity. The terahertz beam path is indicated in gray. The dashed black line marks the common 10 MHz reference clock shared among all synthesizers. The dashed light blue path matches the stabilization feedback loop, which is shown in more detail in Fig. 1(b). A full description is given in the text. ZnTe, 2 mm thick ZnTe crystal; QWP, quarter-wave plate; PBSC, polarizing beam-splitter cube; BP, electronic bandpass filter; (b) detailed view of the signal conditioning of the first photodiode for frequency stabilization and in-loop characterization. After the longitudinal beat-mode spectrum is amplified, and a single mode is filtered, the signal is split into a feedback loop branch and an in-loop characterization branch [not shown in Fig. 1(a)].
Fig. 2.
Fig. 2. (a) Longitudinal beat-mode spectrum sampled by the master femtosecond laser. The dashed red line indicates the selected beat mode for frequency stabilization and characterization. (b) Detailed spectrum of the phase-locked loop monitor signal and the 400 kHz filtered counting signal. Both spectra have been acquired using 3 kHz resolution bandwidth. (c) SNR of the locked beat signal versus resolution bandwidth of the spectrum analyzer; (d) plot of the frequency deviation from the desired beat-mode frequency fbset over time. The dashed lines indicate the 5·MAD filter criterion for outlier removal. (e) Logarithmic στ plot of the overlapping Allan deviation.
Fig. 3.
Fig. 3. Electronic spectrum of the simultaneously measured beat-mode signals as sampled by the master laser (a) at 10 kHz resolution bandwidth and the slave laser (b) at 3 kHz, which stem from the same longitudinal mode of the QCL.
Fig. 4.
Fig. 4. Schematic of the extended setup for absorption spectroscopy. The part labeled frequency metrology is identical to Fig. 1. TPX, polymethylpentene; TIA, transimpedance amplifier.
Fig. 5.
Fig. 5. FTIR spectrum of the QCL with 19.6 GHz longitudinal mode spacing at 21 K temperature and 1.4 A drive current. The QCL mode, which is tuned to a methanol absorption line, is indicated by the black arrow.
Fig. 6.
Fig. 6. Absorption spectra of methanol for the observed E2 transition at (a) 0.4 mbar and (b) 0.85 mbar nominal pressure, respectively. The fitted Voigt profile is shown in red.
Fig. 7.
Fig. 7. Plot of the pressure-induced line center shift observed in this work in comparison to other works on this particular E2 transition.

Tables (2)

Tables Icon

Table 1. Set of Parameters for Determining the Absolute Frequency from the Beat Signals Shown in Fig. 1

Tables Icon

Table 2. Measured Absorption Line Is an E2 Transition with Rotational Quantum Number J=26J=25, Projection Quantum Number K=8K=7, and Torsion Quantum Number vt=0vt=0

Equations (8)

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

ES(t)=EQCL(t)·IIIfR,fs(t),
=exp(i·2πνQCL·t)fR,fs×m=qpEmexp(i[2πmfR,QCL+ϕm])×k=exp(i·2πkfR,fs)+cc.
fb=νQCLn·fR,fs,n=int(νQCLfR,fs),
Δf˜=fR,QCLr·fR,fs,r=int(fR,QCLfR,fs),
ES(t)=exp(i·2πfb·t)fR,fs×m=qpEmexp(i[2πmΔf˜·t+ϕm])×IIIfR,fs(t)+cc.
n=ΔfbΔfR,fs.
δn=1ΔfR,fsδ(Δfb)=n×δ(Δfb)Δfb.
MADmedian|y(i)median[y(i)]|KMAD.