Abstract

The generation of frequency combs in the mid-infrared (MIR) spectral range by quantum cascade lasers (QCLs) has the potential for revolutionizing dual-comb multi-heterodyne spectroscopy in the molecular fingerprint region. However, in contrast to frequency combs based on passively mode-locked ultrafast lasers, their operation relies on a completely different mechanism resulting from a four-wave mixing process occurring in the semiconductor gain medium that locks the modes together. As a result, these lasers do not emit pulses and no direct self-referencing of a QCL comb spectrum has been achieved so far. Here, we present a detailed frequency noise characterization of a MIR QCL frequency comb operating at a wavelength of 8 µm with a mode spacing of ∼7.4 GHz. Using a beat measurement with a narrow-linewidth single-mode QCL in combination with a dedicated electrical scheme, we measured the frequency noise properties of an optical mode of the QCL comb, and indirectly of its offset frequency for the first time, without detecting it by the standard approach of nonlinear interferometry applied to ultrafast mode-locked lasers. In addition, we also separately measured the noise of the comb mode spacing extracted electrically from the QCL. We observed a strong anti-correlation between the frequency fluctuations of the offset frequency and mode spacing, leading to optical modes with a linewidth slightly below 1 MHz in the free-running QCL comb (at 1-s integration time), which is narrower than the individual contributions of the offset frequency and mode spacing that are at least 2 MHz each.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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  27. S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82(12), 123116 (2011).
    [Crossref]
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    [Crossref]

2019 (5)

N. Opačak and B. Schwarz, “Theory of Frequency-Modulated Combs in Lasers with Spatial Hole Burning, Dispersion, and Kerr Nonlinearity,” Phys. Rev. Lett. 123(24), 243902 (2019).
[Crossref]

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

A. Shehzad, P. Brochard, R. Matthey, T. Südmeyer, and S. Schilt, “10 kHz linewidth mid-infrared quantum cascade laser by stabilization to an optical delay line,” Opt. Lett. 44(14), 3470–3473 (2019).
[Crossref]

J. Hillbrand, A. M. Andrews, H. Detz, G. Strasser, and B. Schwarz, “Coherent injection locking of quantum cascade laser frequency combs,” Nat. Photonics 13(2), 101–104 (2019).
[Crossref]

2018 (3)

P. Brochard, V. J. Wittwer, S. Bilicki, B. Resan, K. J. Weingarten, S. Schilt, and T. Südmeyer, “Frequency Noise Characterization of a 25-GHz Diode-Pumped Mode-Locked Laser With Indirect Carrier-Envelope Offset Noise Assessment,” IEEE Photonics J. 10(1), 1–10 (2018).
[Crossref]

M. Piccardo, D. Kazakov, N. A. Rubin, P. Chevalier, Y. Wang, F. Xie, K. Lascola, A. Belyanin, and F. Capasso, “Time-dependent population inversion gratings in laser frequency combs,” Optica 5(4), 475–478 (2018).
[Crossref]

M. Singleton, P. Jouy, M. Beck, and J. Faist, “Evidence of linear chirp in mid-infrared quantum cascade lasers,” Optica 5(8), 948–953 (2018).
[Crossref]

2016 (3)

2015 (2)

P. Brochard, S. Schilt, V. J. Wittwer, and T. Südmeyer, “Characterizing the carrier-envelope offset in an optical frequency comb without traditional f-to-2f interferometry,” Opt. Lett. 40(23), 5522–5525 (2015).
[Crossref]

S. Schilt, L. Tombez, C. Tardy, A. Bismuto, S. Blaser, R. Maulini, R. Terazzi, M. Rochat, and T. Südmeyer, “An experimental study of noise in mid-infrared quantum cascade lasers of different designs,” Appl. Phys. B 119(1), 189–201 (2015).
[Crossref]

2013 (1)

L. Tombez, F. Cappelli, S. Schilt, G. Di Domenico, S. Bartalini, and D. Hofstetter, “Wavelength tuning and thermal dynamics of continuous-wave mid-infrared distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 103(3), 031111 (2013).
[Crossref]

2012 (3)

2011 (1)

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82(12), 123116 (2011).
[Crossref]

2010 (1)

2007 (3)

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

A. Schlatter, S. C. Zeller, R. Paschotta, and U. Keller, “Simultaneous measurement of the phase noise on all optical modes of a mode-locked laser,” Appl. Phys. B 88(3), 385–391 (2007).
[Crossref]

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89(4), 535–538 (2007).
[Crossref]

2006 (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 82(2), 265–273 (2006).
[Crossref]

2002 (2)

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

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B: Lasers Opt. 74(1), 1–6 (2002).
[Crossref]

2000 (2)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

1999 (1)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[Crossref]

Alfieri, C. G. E.

Andrews, A. M.

J. Hillbrand, A. M. Andrews, H. Detz, G. Strasser, and B. Schwarz, “Coherent injection locking of quantum cascade laser frequency combs,” Nat. Photonics 13(2), 101–104 (2019).
[Crossref]

Apolonski, A.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

Bartalini, S.

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

L. Tombez, F. Cappelli, S. Schilt, G. Di Domenico, S. Bartalini, and D. Hofstetter, “Wavelength tuning and thermal dynamics of continuous-wave mid-infrared distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 103(3), 031111 (2013).
[Crossref]

Beck, M.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

M. Singleton, P. Jouy, M. Beck, and J. Faist, “Evidence of linear chirp in mid-infrared quantum cascade lasers,” Optica 5(8), 948–953 (2018).
[Crossref]

Belyanin, A.

Bilicki, S.

P. Brochard, V. J. Wittwer, S. Bilicki, B. Resan, K. J. Weingarten, S. Schilt, and T. Südmeyer, “Frequency Noise Characterization of a 25-GHz Diode-Pumped Mode-Locked Laser With Indirect Carrier-Envelope Offset Noise Assessment,” IEEE Photonics J. 10(1), 1–10 (2018).
[Crossref]

Bismuto, A.

S. Schilt, L. Tombez, C. Tardy, A. Bismuto, S. Blaser, R. Maulini, R. Terazzi, M. Rochat, and T. Südmeyer, “An experimental study of noise in mid-infrared quantum cascade lasers of different designs,” Appl. Phys. B 119(1), 189–201 (2015).
[Crossref]

Blaser, S.

S. Schilt, L. Tombez, C. Tardy, A. Bismuto, S. Blaser, R. Maulini, R. Terazzi, M. Rochat, and T. Südmeyer, “An experimental study of noise in mid-infrared quantum cascade lasers of different designs,” Appl. Phys. B 119(1), 189–201 (2015).
[Crossref]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref]

Borri, S.

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

Brochard, P.

Bucalovic, N.

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo loops of a fully stabilized Er: fiber optical frequency comb,” J. Opt. Soc. Am. B 29(10), 2944–2957 (2012).
[Crossref]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82(12), 123116 (2011).
[Crossref]

Campa, A.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

Campo, G.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

Cancio, P.

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

Cancio Pastor, P.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

Capasso, F.

Cappelli, F.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

L. Tombez, F. Cappelli, S. Schilt, G. Di Domenico, S. Bartalini, and D. Hofstetter, “Wavelength tuning and thermal dynamics of continuous-wave mid-infrared distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 103(3), 031111 (2013).
[Crossref]

Chevalier, P.

Coddington, I.

Consolino, L.

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

Davies, A. G.

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

De Natale, P.

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

Detz, H.

J. Hillbrand, A. M. Andrews, H. Detz, G. Strasser, and B. Schwarz, “Coherent injection locking of quantum cascade laser frequency combs,” Nat. Photonics 13(2), 101–104 (2019).
[Crossref]

Devenoges, L.

Di Domenico, G.

L. Tombez, F. Cappelli, S. Schilt, G. Di Domenico, S. Bartalini, and D. Hofstetter, “Wavelength tuning and thermal dynamics of continuous-wave mid-infrared distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 103(3), 031111 (2013).
[Crossref]

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo loops of a fully stabilized Er: fiber optical frequency comb,” J. Opt. Soc. Am. B 29(10), 2944–2957 (2012).
[Crossref]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82(12), 123116 (2011).
[Crossref]

G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49(25), 4801–4807 (2010).
[Crossref]

Di Francesco, J.

Diddams, S. A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

Dolgovskiy, V.

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo loops of a fully stabilized Er: fiber optical frequency comb,” J. Opt. Soc. Am. B 29(10), 2944–2957 (2012).
[Crossref]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82(12), 123116 (2011).
[Crossref]

Dunlop, A. E.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[Crossref]

Eramo, R.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

Faist, J.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

M. Singleton, P. Jouy, M. Beck, and J. Faist, “Evidence of linear chirp in mid-infrared quantum cascade lasers,” Optica 5(8), 948–953 (2018).
[Crossref]

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref]

Galli, I.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

Garrasi, K.

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

Giusfredi, G.

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

Gohle, C.

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89(4), 535–538 (2007).
[Crossref]

Golling, M.

Hakobyan, S.

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

Hänsch, T. W.

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89(4), 535–538 (2007).
[Crossref]

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

Hillbrand, J.

J. Hillbrand, A. M. Andrews, H. Detz, G. Strasser, and B. Schwarz, “Coherent injection locking of quantum cascade laser frequency combs,” Nat. Photonics 13(2), 101–104 (2019).
[Crossref]

Hinkov, B.

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

Hofstetter, D.

L. Tombez, F. Cappelli, S. Schilt, G. Di Domenico, S. Bartalini, and D. Hofstetter, “Wavelength tuning and thermal dynamics of continuous-wave mid-infrared distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 103(3), 031111 (2013).
[Crossref]

L. Tombez, S. Schilt, J. Di Francesco, P. Thomann, and D. Hofstetter, “Temperature dependence of the frequency noise in a mid-IR DFB quantum cascade laser from cryogenic to room temperature,” Opt. Express 20(7), 6851–6859 (2012).
[Crossref]

Holzwarth, R.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

Hugi, A.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref]

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

Jornod, N.

Jouy, P.

Kazakov, D.

Keller, U.

P. Brochard, N. Jornod, S. Schilt, V. J. Wittwer, S. Hakobyan, D. Waldburger, S. M. Link, C. G. E. Alfieri, M. Golling, L. Devenoges, J. Morel, U. Keller, and T. Südmeyer, “First investigation of the noise and modulation properties of the carrier-envelope offset in a modelocked semiconductor laser,” Opt. Lett. 41(14), 3165–3168 (2016).
[Crossref]

A. Schlatter, S. C. Zeller, R. Paschotta, and U. Keller, “Simultaneous measurement of the phase noise on all optical modes of a mode-locked laser,” Appl. Phys. B 88(3), 385–391 (2007).
[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 82(2), 265–273 (2006).
[Crossref]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[Crossref]

Krausz, F.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

Lascola, K.

Li, L.

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

Linfield, E. H.

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

Link, S. M.

Lipphardt, B.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B: Lasers Opt. 74(1), 1–6 (2002).
[Crossref]

Liu, H. C.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref]

Matthey, R.

Maulini, R.

S. Schilt, L. Tombez, C. Tardy, A. Bismuto, S. Blaser, R. Maulini, R. Terazzi, M. Rochat, and T. Südmeyer, “An experimental study of noise in mid-infrared quantum cascade lasers of different designs,” Appl. Phys. B 119(1), 189–201 (2015).
[Crossref]

Mazzotti, D.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

Mezzapesa, F. P.

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

Morel, J.

Nafa, M.

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

Newbury, N.

Newbury, N. R.

Opacak, N.

N. Opačak and B. Schwarz, “Theory of Frequency-Modulated Combs in Lasers with Spatial Hole Burning, Dispersion, and Kerr Nonlinearity,” Phys. Rev. Lett. 123(24), 243902 (2019).
[Crossref]

Paschotta, R.

A. Schlatter, S. C. Zeller, R. Paschotta, and U. Keller, “Simultaneous measurement of the phase noise on all optical modes of a mode-locked laser,” Appl. Phys. B 88(3), 385–391 (2007).
[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 82(2), 265–273 (2006).
[Crossref]

Piccardo, M.

Poppe, A.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

Resan, B.

P. Brochard, V. J. Wittwer, S. Bilicki, B. Resan, K. J. Weingarten, S. Schilt, and T. Südmeyer, “Frequency Noise Characterization of a 25-GHz Diode-Pumped Mode-Locked Laser With Indirect Carrier-Envelope Offset Noise Assessment,” IEEE Photonics J. 10(1), 1–10 (2018).
[Crossref]

Rochat, M.

S. Schilt, L. Tombez, C. Tardy, A. Bismuto, S. Blaser, R. Maulini, R. Terazzi, M. Rochat, and T. Südmeyer, “An experimental study of noise in mid-infrared quantum cascade lasers of different designs,” Appl. Phys. B 119(1), 189–201 (2015).
[Crossref]

Rösch, M.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

Rubin, N. A.

Scalari, G.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

Schiller, S.

Schilt, S.

A. Shehzad, P. Brochard, R. Matthey, T. Südmeyer, and S. Schilt, “10 kHz linewidth mid-infrared quantum cascade laser by stabilization to an optical delay line,” Opt. Lett. 44(14), 3470–3473 (2019).
[Crossref]

P. Brochard, V. J. Wittwer, S. Bilicki, B. Resan, K. J. Weingarten, S. Schilt, and T. Südmeyer, “Frequency Noise Characterization of a 25-GHz Diode-Pumped Mode-Locked Laser With Indirect Carrier-Envelope Offset Noise Assessment,” IEEE Photonics J. 10(1), 1–10 (2018).
[Crossref]

P. Brochard, N. Jornod, S. Schilt, V. J. Wittwer, S. Hakobyan, D. Waldburger, S. M. Link, C. G. E. Alfieri, M. Golling, L. Devenoges, J. Morel, U. Keller, and T. Südmeyer, “First investigation of the noise and modulation properties of the carrier-envelope offset in a modelocked semiconductor laser,” Opt. Lett. 41(14), 3165–3168 (2016).
[Crossref]

P. Brochard, S. Schilt, V. J. Wittwer, and T. Südmeyer, “Characterizing the carrier-envelope offset in an optical frequency comb without traditional f-to-2f interferometry,” Opt. Lett. 40(23), 5522–5525 (2015).
[Crossref]

S. Schilt, L. Tombez, C. Tardy, A. Bismuto, S. Blaser, R. Maulini, R. Terazzi, M. Rochat, and T. Südmeyer, “An experimental study of noise in mid-infrared quantum cascade lasers of different designs,” Appl. Phys. B 119(1), 189–201 (2015).
[Crossref]

L. Tombez, F. Cappelli, S. Schilt, G. Di Domenico, S. Bartalini, and D. Hofstetter, “Wavelength tuning and thermal dynamics of continuous-wave mid-infrared distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 103(3), 031111 (2013).
[Crossref]

L. Tombez, S. Schilt, J. Di Francesco, P. Thomann, and D. Hofstetter, “Temperature dependence of the frequency noise in a mid-IR DFB quantum cascade laser from cryogenic to room temperature,” Opt. Express 20(7), 6851–6859 (2012).
[Crossref]

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo loops of a fully stabilized Er: fiber optical frequency comb,” J. Opt. Soc. Am. B 29(10), 2944–2957 (2012).
[Crossref]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82(12), 123116 (2011).
[Crossref]

G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49(25), 4801–4807 (2010).
[Crossref]

Schlatter, A.

A. Schlatter, S. C. Zeller, R. Paschotta, and U. Keller, “Simultaneous measurement of the phase noise on all optical modes of a mode-locked laser,” Appl. Phys. B 88(3), 385–391 (2007).
[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 82(2), 265–273 (2006).
[Crossref]

Schori, C.

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo loops of a fully stabilized Er: fiber optical frequency comb,” J. Opt. Soc. Am. B 29(10), 2944–2957 (2012).
[Crossref]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82(12), 123116 (2011).
[Crossref]

Schwarz, B.

J. Hillbrand, A. M. Andrews, H. Detz, G. Strasser, and B. Schwarz, “Coherent injection locking of quantum cascade laser frequency combs,” Nat. Photonics 13(2), 101–104 (2019).
[Crossref]

N. Opačak and B. Schwarz, “Theory of Frequency-Modulated Combs in Lasers with Spatial Hole Burning, Dispersion, and Kerr Nonlinearity,” Phys. Rev. Lett. 123(24), 243902 (2019).
[Crossref]

Shehzad, A.

Siciliani de Cumis, M.

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

Singleton, M.

Spielmann, C.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

Stein, B.

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89(4), 535–538 (2007).
[Crossref]

Steinmeyer, G.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[Crossref]

Stenger, J.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B: Lasers Opt. 74(1), 1–6 (2002).
[Crossref]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[Crossref]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

Strasser, G.

J. Hillbrand, A. M. Andrews, H. Detz, G. Strasser, and B. Schwarz, “Coherent injection locking of quantum cascade laser frequency combs,” Nat. Photonics 13(2), 101–104 (2019).
[Crossref]

Südmeyer, T.

Sutter, D. H.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[Crossref]

Swann, W.

Swann, W. C.

Tardy, C.

S. Schilt, L. Tombez, C. Tardy, A. Bismuto, S. Blaser, R. Maulini, R. Terazzi, M. Rochat, and T. Südmeyer, “An experimental study of noise in mid-infrared quantum cascade lasers of different designs,” Appl. Phys. B 119(1), 189–201 (2015).
[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 82(2), 265–273 (2006).
[Crossref]

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B: Lasers Opt. 74(1), 1–6 (2002).
[Crossref]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[Crossref]

Tempea, G.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

Terazzi, R.

S. Schilt, L. Tombez, C. Tardy, A. Bismuto, S. Blaser, R. Maulini, R. Terazzi, M. Rochat, and T. Südmeyer, “An experimental study of noise in mid-infrared quantum cascade lasers of different designs,” Appl. Phys. B 119(1), 189–201 (2015).
[Crossref]

Thomann, P.

Tombez, L.

S. Schilt, L. Tombez, C. Tardy, A. Bismuto, S. Blaser, R. Maulini, R. Terazzi, M. Rochat, and T. Südmeyer, “An experimental study of noise in mid-infrared quantum cascade lasers of different designs,” Appl. Phys. B 119(1), 189–201 (2015).
[Crossref]

L. Tombez, F. Cappelli, S. Schilt, G. Di Domenico, S. Bartalini, and D. Hofstetter, “Wavelength tuning and thermal dynamics of continuous-wave mid-infrared distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 103(3), 031111 (2013).
[Crossref]

L. Tombez, S. Schilt, J. Di Francesco, P. Thomann, and D. Hofstetter, “Temperature dependence of the frequency noise in a mid-IR DFB quantum cascade laser from cryogenic to room temperature,” Opt. Express 20(7), 6851–6859 (2012).
[Crossref]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82(12), 123116 (2011).
[Crossref]

Udem, T.

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89(4), 535–538 (2007).
[Crossref]

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

Villares, G.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref]

Vitiello, M. S.

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

Waldburger, D.

Walker, D. R.

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89(4), 535–538 (2007).
[Crossref]

Wang, Y.

Weingarten, K. J.

P. Brochard, V. J. Wittwer, S. Bilicki, B. Resan, K. J. Weingarten, S. Schilt, and T. Südmeyer, “Frequency Noise Characterization of a 25-GHz Diode-Pumped Mode-Locked Laser With Indirect Carrier-Envelope Offset Noise Assessment,” IEEE Photonics J. 10(1), 1–10 (2018).
[Crossref]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

Wittwer, V. J.

Xie, F.

Zaffalon, M.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82(12), 123116 (2011).
[Crossref]

Zeller, S. C.

A. Schlatter, S. C. Zeller, R. Paschotta, and U. Keller, “Simultaneous measurement of the phase noise on all optical modes of a mode-locked laser,” Appl. Phys. B 88(3), 385–391 (2007).
[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 82(2), 265–273 (2006).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (5)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[Crossref]

A. Schlatter, S. C. Zeller, R. Paschotta, and U. Keller, “Simultaneous measurement of the phase noise on all optical modes of a mode-locked laser,” Appl. Phys. B 88(3), 385–391 (2007).
[Crossref]

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89(4), 535–538 (2007).
[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 82(2), 265–273 (2006).
[Crossref]

S. Schilt, L. Tombez, C. Tardy, A. Bismuto, S. Blaser, R. Maulini, R. Terazzi, M. Rochat, and T. Südmeyer, “An experimental study of noise in mid-infrared quantum cascade lasers of different designs,” Appl. Phys. B 119(1), 189–201 (2015).
[Crossref]

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

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B: Lasers Opt. 74(1), 1–6 (2002).
[Crossref]

Appl. Phys. Lett. (1)

L. Tombez, F. Cappelli, S. Schilt, G. Di Domenico, S. Bartalini, and D. Hofstetter, “Wavelength tuning and thermal dynamics of continuous-wave mid-infrared distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 103(3), 031111 (2013).
[Crossref]

IEEE Photonics J. (1)

P. Brochard, V. J. Wittwer, S. Bilicki, B. Resan, K. J. Weingarten, S. Schilt, and T. Südmeyer, “Frequency Noise Characterization of a 25-GHz Diode-Pumped Mode-Locked Laser With Indirect Carrier-Envelope Offset Noise Assessment,” IEEE Photonics J. 10(1), 1–10 (2018).
[Crossref]

J. Opt. Soc. Am. B (2)

Laser Photonics Rev. (1)

F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, “Frequency stability characterization of a quantum cascade laser frequency comb,” Laser Photonics Rev. 10(4), 623–630 (2016).
[Crossref]

Nat. Commun. (1)

L. Consolino, M. Nafa, F. Cappelli, K. Garrasi, F. P. Mezzapesa, L. Li, A. G. Davies, E. H. Linfield, M. S. Vitiello, P. De Natale, and S. Bartalini, “Fully phase-stabilized quantum cascade laser frequency comb,” Nat. Commun. 10(1), 2938 (2019).
[Crossref]

Nat. Photonics (2)

J. Hillbrand, A. M. Andrews, H. Detz, G. Strasser, and B. Schwarz, “Coherent injection locking of quantum cascade laser frequency combs,” Nat. Photonics 13(2), 101–104 (2019).
[Crossref]

F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, “Retrieval of phase relation and emission profile of quantum cascade laser frequency combs,” Nat. Photonics 13(8), 562–568 (2019).
[Crossref]

Nature (1)

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Optica (3)

Phys. Rev. Lett. (2)

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

N. Opačak and B. Schwarz, “Theory of Frequency-Modulated Combs in Lasers with Spatial Hole Burning, Dispersion, and Kerr Nonlinearity,” Phys. Rev. Lett. 123(24), 243902 (2019).
[Crossref]

Rev. Sci. Instrum. (1)

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82(12), 123116 (2011).
[Crossref]

Science (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Scheme of the experimental setup implemented to measure the frequency noise of the unknown free-running offset f0 of the QCL comb. The frequency noise of f0 is indirectly measured by separately detecting the mode spacing fFSR by RF extraction (lower branch of the scheme) and the heterodyne beat between one optical line of the QCL comb and a narrow-linewidth DFB-QCL at 1256.7 cm−1. The beat signal is filtered, up-converted and frequency-divided by a large number N = 5,112 using a frequency pre-scaler (÷6) and a direct digital synthesizer (DDS, upper branch of the scheme). The two signals are then combined (mixed) to remove the noise contribution of fFSR, such that the resulting signal fout is representative of the noise of f0 only. BS: beamsplitter; PD: photodetector: PID: proportional-integral-derivative servo controller; TBM: triple-balanced mixer; SSB: single sideband mixer; DDS: direct digital synthesizer; ESA: electrical spectrum analyzer; PNA: phase noise analyzer. A representative intermode beat note electrically extracted from the QCL comb with a bias-T is shown on the lower left part of the figure, after amplification. The signal is centered at 7.37 GHz.
Fig. 2.
Fig. 2. Frequency noise power spectral density (FN-PSD) separately measured for an optical mode νN (pink), for the mode spacing up-scaled to the optical frequency (N·fFSR, blue) and indirectly assessed for the offset signal f0 (green). The typical frequency noise spectrum of the reference DFB-QCL locked to the delay line and used to characterize the QCL comb is also displayed (grey, from [18]), as well as the contribution of the current noise of the QCL driver to the comb frequency noise (light brown, obtained by recording the current noise on a resistive load and converting it into an equivalent frequency noise using the measured transfer function discussed in Section 3, here for the optical line νN). The measurement noise floor at high frequency is indicated by the dash-dotted line and the β-separation line [20] used to estimate the linewidths by the dashed line.
Fig. 3.
Fig. 3. Frequency dependence of the sum of the complex coherences ΓΔ between the frequency variations of f0 and fFSR in the free-running QCL comb. The plot is restricted to 100 kHz, as the noise spectra of f0 and N·fFSR are limited by the experimental noise floor at higher frequencies.
Fig. 4.
Fig. 4. Transfer function in amplitude (a) and phase (b) of N·fFSR (blue), f0 (green) and νN (optical line, pink) measured for a modulation of the QCL current applied through its driver.
Fig. 5.
Fig. 5. (a) Experimental scheme used to stabilize the mode spacing of the QCL comb to an external frequency reference at 7.37 GHz by feedback to the QCL current. DBM: double balanced mixer; PID: proportional-integral-derivative servo controller; ESA: electrical spectrum analyzer; PNA: phase noise analyzer. (b) Phase noise PSD of the QCL mode spacing in free-running mode (blue) and phase-locked to an external reference (red). The phase noise of the frequency reference is also displayed in grey.
Fig. 6.
Fig. 6. Frequency noise PSD of an optical comb line (upper traces) and of the mode spacing (lower curves) measured for the free-running QCL and when the mode spacing is phase-locked to an external RF reference. The noise bump occurring in the latter case at ∼40 kHz corresponds to the servo bump of the stabilization loop.

Equations (1)

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Γ Δ = ( S f b S f 0 S N f FSR ) / S f 0 S N f FSR .

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