Abstract

We demonstrate repetition-rate downsampling of optical frequency combs by way of pulse gating. This results in a frequency comb with reduced repetition rate and increased pulse energy, which enables efficient spectral broadening and f-2f interferometry. To explore the technique, we downsample a 250 MHz repetition-rate comb to 25 MHz and detect the carrier–envelope offset frequency of the downsampled pulse train. We investigate the effects of pulse gating on the noise properties of the pulse train and the limitations of the technique by characterizing the phase-noise spectrum of the downsampled comb and deliberately imposing timing jitter on the pulse gate. We show that, up to an expected reduction modulo the new repetition rate, downsampling neither shifts nor introduces noise to the carrier–envelope offset frequency of the comb above the level of several microhertz. Additionally, we discuss the effect of downsampling on the spectrum of intensity fluctuations of the optical pulse train. Finally, we discuss some practical considerations relevant for the application of the technique to frequency combs with repetition rates in the 10 GHz range and higher.

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  23. M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quantum Electron. 15, 103–113 (2009).
    [Crossref]
  24. J. M. Dudley, G. G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
    [Crossref]
  25. H.-A. Bachor and P. J. Manson, “Practical implications of quantum noise,” J. Mod. Opt. 37, 1727–1740 (1990).
    [Crossref]
  26. F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30, 1775–1785 (2013).
    [Crossref]
  27. D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. Conf. Ser. 723, 12035 (2016).
    [Crossref]
  28. A. M. Heidt, “Efficient adaptive step size method for the simulation of supercontinuum generation in optical fibers,” J. Lightwave Technol. 27, 3984–3991 (2009).
    [Crossref]
  29. J. Hult, “A fourth-order Runge-Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25, 3770–3775 (2007).
    [Crossref]
  30. G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2007).
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  32. R. Driad, J. Rosenzweig, R. E. Makon, R. Losch, V. Hurm, H. Walcher, and M. Schlechtweg, “InP DHBT-based IC technology for 100-Gb/s Ethernet,” IEEE Trans. Electron. Devices 58, 2604–2609 (2011).
    [Crossref]

2018 (1)

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

2017 (2)

V. Brasch, E. Lucas, J. D. Jost, M. Geiselmann, and T. J. Kippenberg, “Self-referenced photonic chip soliton Kerr frequency comb,” Light Sci. Appl. 6, e16202 (2017).
[Crossref]

K. Beha, D. C. Cole, P. Del’Haye, A. Coillet, S. A. Diddams, and S. B. Papp, “Electronic synthesis of light,” Optica 4, 406–411 (2017).
[Crossref]

2016 (2)

D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. Conf. Ser. 723, 12035 (2016).
[Crossref]

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

2015 (1)

2014 (1)

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

2013 (2)

2011 (1)

R. Driad, J. Rosenzweig, R. E. Makon, R. Losch, V. Hurm, H. Walcher, and M. Schlechtweg, “InP DHBT-based IC technology for 100-Gb/s Ethernet,” IEEE Trans. Electron. Devices 58, 2604–2609 (2011).
[Crossref]

2010 (3)

D. Mandridis, I. Ozdur, F. Quinlan, M. Akbulut, J. J. Plant, P. W. Juodawlkis, and P. J. Delfyett, “Low-noise, low repetition rate, semiconductor-based mode-locked laser source suitable for high bandwidth photonic analog–digital conversion,” Appl. Opt. 49, 2850–2857 (2010).
[Crossref]

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, S. Aozasa, A. Mori, H. Nakano, A. Takada, and M. Koga, “Octave-spanning frequency comb generated by 250  fs pulse train emitted from 25  GHz externally phase-modulated laser diode for carrier-envelope-offset-locking,” Electron. Lett. 46, 1343–1344 (2010).
[Crossref]

S. A. Diddams, “The evolving optical frequency comb [Invited],” J. Opt. Soc. Am. B 27, B51–B62 (2010).
[Crossref]

2009 (3)

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref]

A. M. Heidt, “Efficient adaptive step size method for the simulation of supercontinuum generation in optical fibers,” J. Lightwave Technol. 27, 3984–3991 (2009).
[Crossref]

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quantum Electron. 15, 103–113 (2009).
[Crossref]

2007 (2)

J. Hult, “A fourth-order Runge-Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25, 3770–3775 (2007).
[Crossref]

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

2006 (2)

J. Rauschenberger, T. Fuji, M. Hentschel, A.-J. Verhoef, T. Udem, C. Gohle, T. W. Hansch, and F. Krausz, “Carrier-envelope phase-stabilized amplifier system,” Laser Phys. Lett. 3, 37–42 (2006).
[Crossref]

J. M. Dudley, G. G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

2005 (1)

2003 (2)

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[Crossref]

S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
[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, 635–639 (2000).
[Crossref]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

1998 (1)

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223 (1998).
[Crossref]

1990 (1)

H.-A. Bachor and P. J. Manson, “Practical implications of quantum noise,” J. Mod. Opt. 37, 1727–1740 (1990).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2007).

Akbulut, M.

Aozasa, S.

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, S. Aozasa, A. Mori, H. Nakano, A. Takada, and M. Koga, “Octave-spanning frequency comb generated by 250  fs pulse train emitted from 25  GHz externally phase-modulated laser diode for carrier-envelope-offset-locking,” Electron. Lett. 46, 1343–1344 (2010).
[Crossref]

Apolonski, A.

Arcizet, O.

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

Bachor, H.-A.

H.-A. Bachor and P. J. Manson, “Practical implications of quantum noise,” J. Mod. Opt. 37, 1727–1740 (1990).
[Crossref]

Backus, S.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223 (1998).
[Crossref]

Baltuska, A.

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[Crossref]

Bartels, A.

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref]

Beha, K.

K. Beha, D. C. Cole, P. Del’Haye, A. Coillet, S. A. Diddams, and S. B. Papp, “Electronic synthesis of light,” Optica 4, 406–411 (2017).
[Crossref]

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

Beha, K. M.

D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. Conf. Ser. 723, 12035 (2016).
[Crossref]

Berroth, M.

D. Ferenci, M. Grozing, M. Berroth, R. Makon, R. Driad, and J. Rosenzweig, “A 25  GHz analog demultiplexer with a novel track and hold circuit for a 50  GS/s A/D-conversion system in InP DHBT technology,” in Microwave Symposium Digest (2012), pp. 1–3.

Bluestone, A.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

Bowers, J. E.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

Brasch, V.

V. Brasch, E. Lucas, J. D. Jost, M. Geiselmann, and T. J. Kippenberg, “Self-referenced photonic chip soliton Kerr frequency comb,” Light Sci. Appl. 6, e16202 (2017).
[Crossref]

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. Pfeiffer, and T. J. Kippenberg, “Counting the cycles of light using a self-referenced optical microresonator,” Optica 2, 706–711 (2015).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Briles, T. C.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

T. E. Drake, T. C. Briles, Q. Li, D. Westly, B. Robert Ilic, J. R. Stone, K. Srinivasan, S. A. Diddams, and S. B. Papp, “An octave-bandwidth Kerr optical frequency comb on a silicon chip,” in Conference on Lasers Electro-Optics, OSA Technical Digest (2016), paper STu3Q.4.

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. A. Westly, B. R. Ilic, S. A. Diddams, and S. B. Papp, “Kerr-microresonator solitons for accurate carrier-envelope-frequency stabilization,” arXiv:1711.06251 (2017).

Carlson, D. R.

E. S. Lamb, D. R. Carlson, D. D. Hickstein, J. R. Stone, S. A. Diddams, and S. B. Papp, “Optical-frequency measurements with a Kerr-microcomb and photonic-chip supercontinuum,” arXiv:1710.02872 (2017).

Chang, L.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

Coen, S.

J. M. Dudley, G. G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

Coillet, A.

K. Beha, D. C. Cole, P. Del’Haye, A. Coillet, S. A. Diddams, and S. B. Papp, “Electronic synthesis of light,” Optica 4, 406–411 (2017).
[Crossref]

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

Cole, D. C.

K. Beha, D. C. Cole, P. Del’Haye, A. Coillet, S. A. Diddams, and S. B. Papp, “Electronic synthesis of light,” Optica 4, 406–411 (2017).
[Crossref]

D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. Conf. Ser. 723, 12035 (2016).
[Crossref]

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

Cundiff, S. T.

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

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, 635–639 (2000).
[Crossref]

Del’Haye, P.

K. Beha, D. C. Cole, P. Del’Haye, A. Coillet, S. A. Diddams, and S. B. Papp, “Electronic synthesis of light,” Optica 4, 406–411 (2017).
[Crossref]

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

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

Delfyett, P. J.

Diddams, S. A.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

K. Beha, D. C. Cole, P. Del’Haye, A. Coillet, S. A. Diddams, and S. B. Papp, “Electronic synthesis of light,” Optica 4, 406–411 (2017).
[Crossref]

D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. Conf. Ser. 723, 12035 (2016).
[Crossref]

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30, 1775–1785 (2013).
[Crossref]

S. A. Diddams, “The evolving optical frequency comb [Invited],” J. Opt. Soc. Am. B 27, B51–B62 (2010).
[Crossref]

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref]

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, 635–639 (2000).
[Crossref]

T. E. Drake, T. C. Briles, Q. Li, D. Westly, B. Robert Ilic, J. R. Stone, K. Srinivasan, S. A. Diddams, and S. B. Papp, “An octave-bandwidth Kerr optical frequency comb on a silicon chip,” in Conference on Lasers Electro-Optics, OSA Technical Digest (2016), paper STu3Q.4.

E. S. Lamb, D. R. Carlson, D. D. Hickstein, J. R. Stone, S. A. Diddams, and S. B. Papp, “Optical-frequency measurements with a Kerr-microcomb and photonic-chip supercontinuum,” arXiv:1710.02872 (2017).

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. A. Westly, B. R. Ilic, S. A. Diddams, and S. B. Papp, “Kerr-microresonator solitons for accurate carrier-envelope-frequency stabilization,” arXiv:1711.06251 (2017).

Drake, T.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

Drake, T. E.

T. E. Drake, T. C. Briles, Q. Li, D. Westly, B. Robert Ilic, J. R. Stone, K. Srinivasan, S. A. Diddams, and S. B. Papp, “An octave-bandwidth Kerr optical frequency comb on a silicon chip,” in Conference on Lasers Electro-Optics, OSA Technical Digest (2016), paper STu3Q.4.

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. A. Westly, B. R. Ilic, S. A. Diddams, and S. B. Papp, “Kerr-microresonator solitons for accurate carrier-envelope-frequency stabilization,” arXiv:1711.06251 (2017).

Driad, R.

R. Driad, J. Rosenzweig, R. E. Makon, R. Losch, V. Hurm, H. Walcher, and M. Schlechtweg, “InP DHBT-based IC technology for 100-Gb/s Ethernet,” IEEE Trans. Electron. Devices 58, 2604–2609 (2011).
[Crossref]

D. Ferenci, M. Grozing, M. Berroth, R. Makon, R. Driad, and J. Rosenzweig, “A 25  GHz analog demultiplexer with a novel track and hold circuit for a 50  GS/s A/D-conversion system in InP DHBT technology,” in Microwave Symposium Digest (2012), pp. 1–3.

Dudley, J. M.

J. M. Dudley, G. G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

Durfee, C. G.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223 (1998).
[Crossref]

Ferenci, D.

D. Ferenci, M. Grozing, M. Berroth, R. Makon, R. Driad, and J. Rosenzweig, “A 25  GHz analog demultiplexer with a novel track and hold circuit for a 50  GS/s A/D-conversion system in InP DHBT technology,” in Microwave Symposium Digest (2012), pp. 1–3.

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

Fortier, T.

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

Fortier, T. M.

Fredrick, C.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. A. Westly, B. R. Ilic, S. A. Diddams, and S. B. Papp, “Kerr-microresonator solitons for accurate carrier-envelope-frequency stabilization,” arXiv:1711.06251 (2017).

Fuji, T.

J. Rauschenberger, T. Fuji, M. Hentschel, A.-J. Verhoef, T. Udem, C. Gohle, T. W. Hansch, and F. Krausz, “Carrier-envelope phase-stabilized amplifier system,” Laser Phys. Lett. 3, 37–42 (2006).
[Crossref]

C. Gohle, J. Rauschenberger, T. Fuji, T. Udem, A. Apolonski, F. Krausz, and T. W. Hansch, “Carrier envelope phase noise in stabilized amplifier systems,” Opt. Lett. 30, 2487–2489 (2005).
[Crossref]

Geiselmann, M.

V. Brasch, E. Lucas, J. D. Jost, M. Geiselmann, and T. J. Kippenberg, “Self-referenced photonic chip soliton Kerr frequency comb,” Light Sci. Appl. 6, e16202 (2017).
[Crossref]

Genty, G. G.

J. M. Dudley, G. G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

Gohle, C.

J. Rauschenberger, T. Fuji, M. Hentschel, A.-J. Verhoef, T. Udem, C. Gohle, T. W. Hansch, and F. Krausz, “Carrier-envelope phase-stabilized amplifier system,” Laser Phys. Lett. 3, 37–42 (2006).
[Crossref]

C. Gohle, J. Rauschenberger, T. Fuji, T. Udem, A. Apolonski, F. Krausz, and T. W. Hansch, “Carrier envelope phase noise in stabilized amplifier systems,” Opt. Lett. 30, 2487–2489 (2005).
[Crossref]

Gorodetsky, M. L.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Goulielmakis, E.

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[Crossref]

Grozing, M.

D. Ferenci, M. Grozing, M. Berroth, R. Makon, R. Driad, and J. Rosenzweig, “A 25  GHz analog demultiplexer with a novel track and hold circuit for a 50  GS/s A/D-conversion system in InP DHBT technology,” in Microwave Symposium Digest (2012), pp. 1–3.

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, 635–639 (2000).
[Crossref]

Hansch, T. W.

J. Rauschenberger, T. Fuji, M. Hentschel, A.-J. Verhoef, T. Udem, C. Gohle, T. W. Hansch, and F. Krausz, “Carrier-envelope phase-stabilized amplifier system,” Laser Phys. Lett. 3, 37–42 (2006).
[Crossref]

C. Gohle, J. Rauschenberger, T. Fuji, T. Udem, A. Apolonski, F. Krausz, and T. W. Hansch, “Carrier envelope phase noise in stabilized amplifier systems,” Opt. Lett. 30, 2487–2489 (2005).
[Crossref]

Hänsch, T. W.

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[Crossref]

Harvey, J. D.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

Heidt, A. M.

Heinecke, D.

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref]

Hentschel, M.

J. Rauschenberger, T. Fuji, M. Hentschel, A.-J. Verhoef, T. Udem, C. Gohle, T. W. Hansch, and F. Krausz, “Carrier-envelope phase-stabilized amplifier system,” Laser Phys. Lett. 3, 37–42 (2006).
[Crossref]

Herr, T.

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. Pfeiffer, and T. J. Kippenberg, “Counting the cycles of light using a self-referenced optical microresonator,” Optica 2, 706–711 (2015).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Hickstein, D. D.

E. S. Lamb, D. R. Carlson, D. D. Hickstein, J. R. Stone, S. A. Diddams, and S. B. Papp, “Optical-frequency measurements with a Kerr-microcomb and photonic-chip supercontinuum,” arXiv:1710.02872 (2017).

Hirano, M.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quantum Electron. 15, 103–113 (2009).
[Crossref]

Holzwarth, R.

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

Hoon Lee, S.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

Hult, J.

Hurm, V.

R. Driad, J. Rosenzweig, R. E. Makon, R. Losch, V. Hurm, H. Walcher, and M. Schlechtweg, “InP DHBT-based IC technology for 100-Gb/s Ethernet,” IEEE Trans. Electron. Devices 58, 2604–2609 (2011).
[Crossref]

Ilic, B. R.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. A. Westly, B. R. Ilic, S. A. Diddams, and S. B. Papp, “Kerr-microresonator solitons for accurate carrier-envelope-frequency stabilization,” arXiv:1711.06251 (2017).

Ishizawa, A.

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, A. Takada, T. Sogawa, and M. Koga, “Phase-noise characteristics of a 25-GHz-spaced optical frequency comb based on a phase- and intensity-modulated laser,” Opt. Express 21, 29186–29194 (2013).
[Crossref]

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, S. Aozasa, A. Mori, H. Nakano, A. Takada, and M. Koga, “Octave-spanning frequency comb generated by 250  fs pulse train emitted from 25  GHz externally phase-modulated laser diode for carrier-envelope-offset-locking,” Electron. Lett. 46, 1343–1344 (2010).
[Crossref]

Jiang, H.

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, 635–639 (2000).
[Crossref]

Jost, J. D.

V. Brasch, E. Lucas, J. D. Jost, M. Geiselmann, and T. J. Kippenberg, “Self-referenced photonic chip soliton Kerr frequency comb,” Light Sci. Appl. 6, e16202 (2017).
[Crossref]

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. Pfeiffer, and T. J. Kippenberg, “Counting the cycles of light using a self-referenced optical microresonator,” Optica 2, 706–711 (2015).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Juodawlkis, P. W.

Kapteyn, H. C.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223 (1998).
[Crossref]

Kienberger, R.

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[Crossref]

Kippenberg, T. J.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

V. Brasch, E. Lucas, J. D. Jost, M. Geiselmann, and T. J. Kippenberg, “Self-referenced photonic chip soliton Kerr frequency comb,” Light Sci. Appl. 6, e16202 (2017).
[Crossref]

J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. Pfeiffer, and T. J. Kippenberg, “Counting the cycles of light using a self-referenced optical microresonator,” Optica 2, 706–711 (2015).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

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

Koga, M.

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, A. Takada, T. Sogawa, and M. Koga, “Phase-noise characteristics of a 25-GHz-spaced optical frequency comb based on a phase- and intensity-modulated laser,” Opt. Express 21, 29186–29194 (2013).
[Crossref]

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, S. Aozasa, A. Mori, H. Nakano, A. Takada, and M. Koga, “Octave-spanning frequency comb generated by 250  fs pulse train emitted from 25  GHz externally phase-modulated laser diode for carrier-envelope-offset-locking,” Electron. Lett. 46, 1343–1344 (2010).
[Crossref]

Komljenovic, T.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

Kondratiev, N. M.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Krausz, F.

J. Rauschenberger, T. Fuji, M. Hentschel, A.-J. Verhoef, T. Udem, C. Gohle, T. W. Hansch, and F. Krausz, “Carrier-envelope phase-stabilized amplifier system,” Laser Phys. Lett. 3, 37–42 (2006).
[Crossref]

C. Gohle, J. Rauschenberger, T. Fuji, T. Udem, A. Apolonski, F. Krausz, and T. W. Hansch, “Carrier envelope phase noise in stabilized amplifier systems,” Opt. Lett. 30, 2487–2489 (2005).
[Crossref]

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972–989 (2003).
[Crossref]

Kruglov, V. I.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

Lamb, E. S.

E. S. Lamb, D. R. Carlson, D. D. Hickstein, J. R. Stone, S. A. Diddams, and S. B. Papp, “Optical-frequency measurements with a Kerr-microcomb and photonic-chip supercontinuum,” arXiv:1710.02872 (2017).

Lecaplain, C.

Lee, H.

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

Li, Q.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

T. E. Drake, T. C. Briles, Q. Li, D. Westly, B. Robert Ilic, J. R. Stone, K. Srinivasan, S. A. Diddams, and S. B. Papp, “An octave-bandwidth Kerr optical frequency comb on a silicon chip,” in Conference on Lasers Electro-Optics, OSA Technical Digest (2016), paper STu3Q.4.

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. A. Westly, B. R. Ilic, S. A. Diddams, and S. B. Papp, “Kerr-microresonator solitons for accurate carrier-envelope-frequency stabilization,” arXiv:1711.06251 (2017).

Losch, R.

R. Driad, J. Rosenzweig, R. E. Makon, R. Losch, V. Hurm, H. Walcher, and M. Schlechtweg, “InP DHBT-based IC technology for 100-Gb/s Ethernet,” IEEE Trans. Electron. Devices 58, 2604–2609 (2011).
[Crossref]

Lucas, E.

V. Brasch, E. Lucas, J. D. Jost, M. Geiselmann, and T. J. Kippenberg, “Self-referenced photonic chip soliton Kerr frequency comb,” Light Sci. Appl. 6, e16202 (2017).
[Crossref]

Makon, R.

D. Ferenci, M. Grozing, M. Berroth, R. Makon, R. Driad, and J. Rosenzweig, “A 25  GHz analog demultiplexer with a novel track and hold circuit for a 50  GS/s A/D-conversion system in InP DHBT technology,” in Microwave Symposium Digest (2012), pp. 1–3.

Makon, R. E.

R. Driad, J. Rosenzweig, R. E. Makon, R. Losch, V. Hurm, H. Walcher, and M. Schlechtweg, “InP DHBT-based IC technology for 100-Gb/s Ethernet,” IEEE Trans. Electron. Devices 58, 2604–2609 (2011).
[Crossref]

Mandridis, D.

Manson, P. J.

H.-A. Bachor and P. J. Manson, “Practical implications of quantum noise,” J. Mod. Opt. 37, 1727–1740 (1990).
[Crossref]

Mizutori, A.

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, A. Takada, T. Sogawa, and M. Koga, “Phase-noise characteristics of a 25-GHz-spaced optical frequency comb based on a phase- and intensity-modulated laser,” Opt. Express 21, 29186–29194 (2013).
[Crossref]

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, S. Aozasa, A. Mori, H. Nakano, A. Takada, and M. Koga, “Octave-spanning frequency comb generated by 250  fs pulse train emitted from 25  GHz externally phase-modulated laser diode for carrier-envelope-offset-locking,” Electron. Lett. 46, 1343–1344 (2010).
[Crossref]

Mori, A.

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, S. Aozasa, A. Mori, H. Nakano, A. Takada, and M. Koga, “Octave-spanning frequency comb generated by 250  fs pulse train emitted from 25  GHz externally phase-modulated laser diode for carrier-envelope-offset-locking,” Electron. Lett. 46, 1343–1344 (2010).
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Murnane, M. M.

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T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. A. Westly, B. R. Ilic, S. A. Diddams, and S. B. Papp, “Kerr-microresonator solitons for accurate carrier-envelope-frequency stabilization,” arXiv:1711.06251 (2017).

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Spencer, D. T.

D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. Hoon Lee, D. Yoon Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).

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T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. A. Westly, B. R. Ilic, S. A. Diddams, and S. B. Papp, “Kerr-microresonator solitons for accurate carrier-envelope-frequency stabilization,” arXiv:1711.06251 (2017).

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P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
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Appl. Opt. (1)

Electron. Lett. (1)

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, S. Aozasa, A. Mori, H. Nakano, A. Takada, and M. Koga, “Octave-spanning frequency comb generated by 250  fs pulse train emitted from 25  GHz externally phase-modulated laser diode for carrier-envelope-offset-locking,” Electron. Lett. 46, 1343–1344 (2010).
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IEEE Trans. Electron. Devices (1)

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Laser Phys. Lett. (1)

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Figures (4)

Fig. 1.
Fig. 1. (a) Schematic for downsampling a 250 MHz Er:fiber comb and detecting the offset frequency of the resulting 25 MHz pulse train. PC–polarization controller, DCF–dispersion-compensating fiber, EDFA–erbium-doped fiber amplifier, HNLF–highly nonlinear fiber, PPLN–periodically poled lithium niobate, BPF–(optical) band-pass filter. (b) Input (bottom, orange) and downsampled (top, blue) pulse trains from a 1 GHz photodetector, with the electronic gate superimposed on the input pulse train (black). (c) Octave-spanning supercontinuum generated after downsampling (top, blue), second-harmonic generated for f 0 detection (purple), and for comparison, the supercontinuum generated by the same apparatus without downsampling (orange). (d) Detected repetition rate and f 0 beat at 100 kHz resolution bandwidth; signal-to-noise ratio of f 0 is 30 dB. (e) Counted frequency of the detected free-running offset beat. Data are taken for 2000    s at 10 ms gate time. The offset frequency of the 250 MHz commercial comb was adjusted between measurements shown in (d) and (e) to simplify electronic processing.
Fig. 2.
Fig. 2. (a) Measured repetition-rate phase noise of spectral components of the supercontinuum, selected by a 990 ± 5    nm band-pass filter (dotted-dashed orange), 1650 nm long-pass filter (dotted yellow), and the entire downsampled 25 MHz frequency comb measured immediately before the EDFA (solid blue); the 250 MHz comb (large-dashed gray, shifted by 20 log ( 1 / 10 ) = 20    dB ). Also shown is the phase noise of the electronic gate generator (top, solid black). (b) Amplitude of the downsampled pulse-train modulation due to 250 ps jitter at 5 MHz rate. The position of a data point on the x axis indicates its mean position within the gate, shown in dashed black. Measurement uncertainties arise due to a latency between the optical trigger and the start of the electronic gating signal that varies on the order of 50 ps. (c) Deviation of the carrier–envelope offset frequency of the downsampled comb from the 250 MHz comb’s offset frequency as a function of the alignment of optical pulses within the gate.
Fig. 3.
Fig. 3. Fluctuations at 50 MHz Fourier frequency in the detected photocurrent as a function of the time-averaged photocurrent in three cases: CW laser at the shot-noise limit (lowest, yellow), 10 GHz pulse train (middle, red), and 2.5 GHz downsampled pulse train (highest, blue). Dots show measured data, and curves show fits to the data. The fit for the shot-noise-limited laser has a single free parameter, which is a scaling factor of order 1 due to frequency dependence of the photodetector’s transimpedance gain. The fits for the pulse trains have a scaling factor in common, and have as an additional parameter the amplitude of the technical noise on the pulse train. This is 153.9    dBc / Hz for the 10 GHz pulse train and increases by a factor of 1.7 2 to 149.3    dBc / Hz for the 2.5 GHz downsampled pulse train. Inset: Optimized fits (dashed red) to the experimental data for the downsampled 2.5 GHz pulse train using only shot-noise or linear technical noise scaling, demonstrating that both noise processes are important for explaining the data.
Fig. 4.
Fig. 4. Investigation of incomplete pulse extinction and amplification. (a) A burst consisting of a fully transmitted 1 nJ, 100 fs pulse and 100 fs partially transmitted adjacent pulses with energies of 0.18 nJ and 0.45 nJ. Blue indicates initial sech 2 pulses, and orange indicates the intensity after propagation through 30 cm HNLF. Note that the x axis has been broken. (b) Top panel: optical spectra corresponding to the pulses shown in orange in (a), showing the composite spectrum of the three pulses (top, blue) and the spectra of the 1 nJ central pulse (second, orange), the 0.45 nJ adjacent pulse (third, green), and the 0.18 nJ adjacent pulse (bottom, purple). Bottom panel: calculated spectral coherence averaged over 2000 simulations for the case of shot-noise only (top, black) and for the case of fluctuating amplitudes of the first and last pulses as described in the text, after simulated amplification in a linear-regime optical amplifier (second, teal), and a saturated optical amplifier (bottom, maroon). For the case of linear-regime operation, high spectral coherence is preserved in the extreme ends of the supercontinuum, even as it is lost in the center, in contrast with the complete loss of coherence after amplification in saturation.

Equations (5)

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a ( t ) = [ n A ( t n / f r ) e i n ϕ ] [ m Rect ( t m / f g t g ) ] ,
F { a } ( f ) 4 π f r n m 1 m F { A } ( f 0 + n f r ) × sin ( π m t g f g ) δ ( f f 0 n f r m f g ) ,
σ PEF 2 = 0 f r 2 d f S PEF ( f ) .
σ PEF 2 = 0 f r / 2 d f S o = 0 f r / 2 N d f S ,
| g 12 ( 1 ) ( λ ) | = | E 1 * ( λ ) E 2 ( λ ) | E 1 ( λ ) | 2 | E 2 ( λ ) | 2 | = | E 1 * ( λ ) E 2 ( λ ) | E ( λ ) | 2 | .

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