Abstract

We demonstrate a self-referencing locking method for an optical frequency comb that leads to an offset-free frequency comb. It works with a standard f2f interferometer and phase-locks the carrier–envelope offset frequency to the repetition frequency. This technique uses neither an acousto-optic modulator nor difference frequency generation. No synthesizer signals are needed aside from a reference signal to stabilize the repetition rate. We test the performance by comparing it with an independent comb system; it does not result in any performance degradation when compared with the conventional phase-locking method. The offset-free comb realized by this technique may become a powerful and universal tool for use in frequency-comb-related research.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

K. Nakamura, S. Okubo, M. Schramm, K. Kashiwagi, and H. Inaba, “Offset-free all-fiber frequency comb with an acousto-optic modulator and two f-2f interferometers,” Appl. Phys. Express 10, 072501 (2017).
[Crossref]

2016 (1)

2015 (4)

2012 (1)

2011 (1)

2010 (2)

2009 (1)

2007 (1)

P. H. Bucksbaum, “The future of attosecond spectroscopy,” Science 317, 766–769 (2007).
[Crossref]

2006 (3)

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B 39, R203–R262 (2006).
[Crossref]

J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
[Crossref]

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[Crossref]

2005 (1)

2004 (1)

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

2002 (2)

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
[Crossref]

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
[Crossref]

2001 (1)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[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]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

1999 (3)

J. Reichert, R. Holzwarth, T. Udem, and T. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. 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, 327–332 (1999).
[Crossref]

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Accurate measurement of large optical frequency differences with a mode-locked laser,” Opt. Lett. 24, 881–883 (1999).
[Crossref]

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Anderson, A.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics 4, 462–465 (2010).
[Crossref]

Assion, A.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics 4, 462–465 (2010).
[Crossref]

Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Balcou, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Baltuska, A.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Baltuška, A.

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
[Crossref]

Bammer, F.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Bauer, D.

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B 39, R203–R262 (2006).
[Crossref]

Becker, W.

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B 39, R203–R262 (2006).
[Crossref]

Binhammer, T.

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Brida, D.

Bucksbaum, P. H.

P. H. Bucksbaum, “The future of attosecond spectroscopy,” Science 317, 766–769 (2007).
[Crossref]

Corkum, P. B.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
[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, 635–639 (2000).
[Crossref]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

Diddams, S. A.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[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]

Drescher, M.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Dunlop, A.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. 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, 327–332 (1999).
[Crossref]

Fehrenbacher, D.

Fermann, M.

Frei, H.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics 4, 462–465 (2010).
[Crossref]

Fuji, T.

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
[Crossref]

Goulielmakis, E.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Grebing, C.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics 4, 462–465 (2010).
[Crossref]

Hall, J. L.

J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
[Crossref]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[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]

Hänsch, T.

J. Reichert, R. Holzwarth, T. Udem, and T. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Hänsch, T. W.

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[Crossref]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Accurate measurement of large optical frequency differences with a mode-locked laser,” Opt. Lett. 24, 881–883 (1999).
[Crossref]

Harth, A.

Heinzmann, U.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Holzwarth, R.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

J. Reichert, R. Holzwarth, T. Udem, and T. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Accurate measurement of large optical frequency differences with a mode-locked laser,” Opt. Lett. 24, 881–883 (1999).
[Crossref]

Hong, F.-L.

Hong, K.-H.

Hosaka, K.

Huber, R.

Inaba, H.

Itatani, J.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
[Crossref]

Ito, I.

Ivanov, M. Y.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
[Crossref]

Iwakuni, K.

Jiang, J.

Jones, D. J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[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]

Kälberer, T.

Kashiwagi, K.

K. Nakamura, S. Okubo, M. Schramm, K. Kashiwagi, and H. Inaba, “Offset-free all-fiber frequency comb with an acousto-optic modulator and two f-2f interferometers,” Appl. Phys. Express 10, 072501 (2017).
[Crossref]

Katsuyama, T.

Kawato, S.

Keller, U.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. 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, 327–332 (1999).
[Crossref]

Kienberger, R.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Kleineberg, U.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Kobayashi, T.

Kobayashi, Y.

Kohno, T.

Koke, S.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics 4, 462–465 (2010).
[Crossref]

Krauss, G.

Krausz, F.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
[Crossref]

Kuse, N.

Lee, C.-C.

Lee, Y. S.

Leitenstorfer, A.

Liehl, A.

Miloševic, D. B.

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B 39, R203–R262 (2006).
[Crossref]

Minoshima, K.

Mohr, C.

Morgner, U.

Muller, H. G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Nakajima, Y.

Nakamura, K.

K. Nakamura, S. Okubo, M. Schramm, K. Kashiwagi, and H. Inaba, “Offset-free all-fiber frequency comb with an acousto-optic modulator and two f-2f interferometers,” Appl. Phys. Express 10, 072501 (2017).
[Crossref]

Nakamura, T.

Nam, C. H.

Okubo, S.

K. Nakamura, S. Okubo, M. Schramm, K. Kashiwagi, and H. Inaba, “Offset-free all-fiber frequency comb with an acousto-optic modulator and two f-2f interferometers,” Appl. Phys. Express 10, 072501 (2017).
[Crossref]

K. Iwakuni, S. Okubo, O. Tadanaga, H. Inaba, A. Onae, F.-L. Hong, and H. Sasada, “Generation of a frequency comb spanning more than 3.6 octaves from ultraviolet to mid infrared,” Opt. Lett. 41, 3980–3983 (2016).
[Crossref]

S. Okubo, A. Onae, K. Hosaka, H. Sera, H. Inaba, and F.-L. Hong, “Novel phase-locking schemes for the carrier envelope offset frequency of an optical frequency comb,” Appl. Phys. Express 8, 112402 (2015).
[Crossref]

Onae, A.

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Paulus, G. G.

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B 39, R203–R262 (2006).
[Crossref]

Quéré, F.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
[Crossref]

Ranka, J. K.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[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]

Rausch, S.

Reichert, J.

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Accurate measurement of large optical frequency differences with a mode-locked laser,” Opt. Lett. 24, 881–883 (1999).
[Crossref]

J. Reichert, R. Holzwarth, T. Udem, and T. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Riek, C.

Sasada, H.

Schibli, T. R.

Schramm, M.

K. Nakamura, S. Okubo, M. Schramm, K. Kashiwagi, and H. Inaba, “Offset-free all-fiber frequency comb with an acousto-optic modulator and two f-2f interferometers,” Appl. Phys. Express 10, 072501 (2017).
[Crossref]

Schulz, E.

Scrinzi, A.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Seletskiy, D. V.

Sell, A.

Sera, H.

S. Okubo, A. Onae, K. Hosaka, H. Sera, H. Inaba, and F.-L. Hong, “Novel phase-locking schemes for the carrier envelope offset frequency of an optical frequency comb,” Appl. Phys. Express 8, 112402 (2015).
[Crossref]

Siegel, M.

Steinmeyer, G.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics 4, 462–465 (2010).
[Crossref]

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. 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, 327–332 (1999).
[Crossref]

Stenger, J.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. 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, 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, 635–639 (2000).
[Crossref]

Sulzer, P.

Sung, J. H.

Sutter, D.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. 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, 327–332 (1999).
[Crossref]

Tadanaga, O.

Telle, H.

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. 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, 327–332 (1999).
[Crossref]

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Udem, T.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

J. Reichert, R. Holzwarth, T. Udem, and T. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Accurate measurement of large optical frequency differences with a mode-locked laser,” Opt. Lett. 24, 881–883 (1999).
[Crossref]

T. Udem, “Phasenkohärente optische Frequenzmessungen am Wasserstoffatom: Bestimmung der Rydberg-Konstanten und der 1S-Lamb-Verschiebung,” Ph.D. thesis (Ludwig-Maximilians University Munich, 1997). Written in German.

Uiberacker, M.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Westerwalbesloh, T.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[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, 635–639 (2000).
[Crossref]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

Yakovlev, V.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Yasuda, M.

Ye, J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

Yu, T. J.

Yudin, G. L.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
[Crossref]

Appl. Phys. B (1)

H. Telle, G. Steinmeyer, A. Dunlop, J. Stenger, D. 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, 327–332 (1999).
[Crossref]

Appl. Phys. Express (2)

K. Nakamura, S. Okubo, M. Schramm, K. Kashiwagi, and H. Inaba, “Offset-free all-fiber frequency comb with an acousto-optic modulator and two f-2f interferometers,” Appl. Phys. Express 10, 072501 (2017).
[Crossref]

S. Okubo, A. Onae, K. Hosaka, H. Sera, H. Inaba, and F.-L. Hong, “Novel phase-locking schemes for the carrier envelope offset frequency of an optical frequency comb,” Appl. Phys. Express 8, 112402 (2015).
[Crossref]

J. Phys. B (1)

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B 39, R203–R262 (2006).
[Crossref]

Nat. Photonics (1)

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics 4, 462–465 (2010).
[Crossref]

Nature (1)

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Opt. Commun. (1)

J. Reichert, R. Holzwarth, T. Udem, and T. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Optica (1)

Phys. Rev. Lett. (3)

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
[Crossref]

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
[Crossref]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

Rev. Mod. Phys. (2)

J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
[Crossref]

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[Crossref]

Science (3)

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]

P. H. Bucksbaum, “The future of attosecond spectroscopy,” Science 317, 766–769 (2007).
[Crossref]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Other (1)

T. Udem, “Phasenkohärente optische Frequenzmessungen am Wasserstoffatom: Bestimmung der Rydberg-Konstanten und der 1S-Lamb-Verschiebung,” Ph.D. thesis (Ludwig-Maximilians University Munich, 1997). Written in German.

Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1.

Generating an offset-free comb. (a) The power of the signal at frep at the output V+(t) of the f2f interferometer is reduced with a balanced detector. This allows the signals at frepfceo and frep+fceo to be phase-locked to each other, resulting in frepfceo=frep+fceo, i.e., fceo=0. (b) f2f interferometer for balanced detection and the electronics for the dual-beat phase-lock. The polarizations are such that the usual f2f interferometer output is obtained at V+(t) while a pure signal at frep is present at V(t). HWP, half-wave plate; PPLN, periodically poled lithium niobate; PBS, polarizing beam splitter; OBPF, optical bandpass filter; BPF, RF bandpass filter; DBM, double balanced mixer; PID, proportional-integral-differential control. (c) RF spectrum observed with the f2f interferometer. The signal power at frep is reduced from 11  dBm (unbalanced, gray) to 42  dBm (balanced, red) by adjusting the variable attenuator.

Fig. 2.
Fig. 2.

(a) In-loop beat spectrum of the dual-beat phase-lock at frep. (b) In-loop beat spectrum of the conventional fceo phase-lock. (c) Allan deviation of the frequency difference between the in-loop beat and frep signals for the dual-beat phase-lock (red, solid circles), and Allan deviation of the in-loop beat frequency of the conventional phase-locked fceo (blue, open circles).

Fig. 3.
Fig. 3.

Validation of offset-free comb by comb–comb comparison. (a) Schematic of the experimental setup; PLL, phase-locked loop. (b) Frequency relation of the two combs and the reference laser at 1535 nm (195 THz). The two combs have identical repetition rates and are offset by 29.9 MHz. (c) Out-of-loop beat frequency counted with a 1 s gate time. (d) Relative Allan deviation of the out-of-loop beat frequency at 1020 nm (294 THz) for the dual-beat phase-lock (red, solid circles) and the conventional phase-locking scheme (blue, open circles).

Fig. 4.
Fig. 4.

Contour plot of the bi-polar in-lock error signal Verr,stabilized/V0 given in Eq. (7). The zeros of this function (solid and dashed curves) represent locking points for the zero-offset dual-beat phase-lock loop. Here, 2ϕ is the phase difference between the frepfceo and frep+fceo signals, and x is the amplitude of the residual frep divided by the amplitude of the other two signals. Solid and dashed curves represent locking points with opposite control circuit polarities. Similar to a mixer-generated phase error signal, the error signal repeats with a periodicity 2π for |x|>0.5. In contrast, the error signal has locking points every multiple of π for |x|<0.5 (gray zone).

Equations (7)

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νn=nfrep+fceo.
νCW=nfrep.
E(t)=mEmcos[2π(mfrep+fceo)t+ϕ],
VBD(t)=B{xcos(2πfrept)+cos[2π(frepfceo)tϕ]+cos[2π(frep+fceo)t+ϕ]}
Verr(t)=V02xcos(2πfceot+ϕ)+cos(4πfceot+2ϕ)x2+2.
VBD,stabilized(t)=B(2cosϕ+x)cos(2πfrept)
Verr,stabilized(t)=V02xcosϕ+cos2ϕx2+2.