Abstract

We have generated femtosecond subharmonic pulses by using an optical parametric oscillator. The optical frequencies of the idler and the signal are one third and two thirds, respectively, of the optical frequency of the pump pulse. The carrier phase of the signal pulse relative to that of the pump pulse was locked by electronic feedback. The carrier-envelope phase slip frequency of the signal pulse relative to that of the pump was locked to F/6, where F is defined as the repetition frequency.

© 2001 Optical Society of America

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References

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  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, 635 (2000).
    [CrossRef] [PubMed]
  2. A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
    [CrossRef] [PubMed]
  3. T. W. Hänsch, “A proposed subfemtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Commun. 80, 71 (1990).
    [CrossRef]
  4. K. Shimoda, “Theory and application of optical subharmonic oscillator,” Jpn. J. Appl. Phys. 34, 3566 (1995).
    [CrossRef]
  5. S. Slyusarev, T. Ikegami, and S. Ohshima, “Phase-coherent optical frequency division by 3 of 532-nm laser light with a continuous-wave optical parametric oscillator,” Opt. Lett. 24, 1856 (1999).
    [CrossRef]
  6. D.-H. Lee, M. E. Klein, J.-P. Meyn, P. Gross, R. Wallenstein, and K.-J. Boller, “Self-injection-locking of a CW-OPO by intracavity frequency-doubling the idler wave,” Opt. Express 5, 114 (1999); http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  7. Y. Kobayashi and K. Torizuka, “Measurement of the optical phase relation among subharmonic pulses in a femtosecond optical parametric oscillator,” Opt. Lett. 25, 856 (2000).
    [CrossRef]
  8. B. R. Washburn, S. E. Ralph, J. K. Ranka, and R. S. Windeler, “Controlling the phase of a femtosecond optical parametric oscillator via coherent mixing of the pump-generated supercontinuum and an OPO subharmonic,” in Proceedings of Lasers and Electro-Optics Society Annual Meeting (LEOS2000) (Lasers and Electro-Optics Society, Piscataway, N.J., 2000), p. 298.
  9. Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984), p. 118.

2000 (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 (2000).
[CrossRef] [PubMed]

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Y. Kobayashi and K. Torizuka, “Measurement of the optical phase relation among subharmonic pulses in a femtosecond optical parametric oscillator,” Opt. Lett. 25, 856 (2000).
[CrossRef]

1999 (2)

1995 (1)

K. Shimoda, “Theory and application of optical subharmonic oscillator,” Jpn. J. Appl. Phys. 34, 3566 (1995).
[CrossRef]

1990 (1)

T. W. Hänsch, “A proposed subfemtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Commun. 80, 71 (1990).
[CrossRef]

Apolonski, A.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Boller, K.-J.

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 (2000).
[CrossRef] [PubMed]

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, 635 (2000).
[CrossRef] [PubMed]

Gross, P.

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 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

T. W. Hänsch, “A proposed subfemtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Commun. 80, 71 (1990).
[CrossRef]

Holzwarth, R.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Ikegami, T.

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 (2000).
[CrossRef] [PubMed]

Klein, M. E.

Kobayashi, Y.

Krausz, F.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Lee, D.-H.

Meyn, J.-P.

Ohshima, S.

Poppe, A.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Ralph, S. E.

B. R. Washburn, S. E. Ralph, J. K. Ranka, and R. S. Windeler, “Controlling the phase of a femtosecond optical parametric oscillator via coherent mixing of the pump-generated supercontinuum and an OPO subharmonic,” in Proceedings of Lasers and Electro-Optics Society Annual Meeting (LEOS2000) (Lasers and Electro-Optics Society, Piscataway, N.J., 2000), p. 298.

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, 635 (2000).
[CrossRef] [PubMed]

B. R. Washburn, S. E. Ralph, J. K. Ranka, and R. S. Windeler, “Controlling the phase of a femtosecond optical parametric oscillator via coherent mixing of the pump-generated supercontinuum and an OPO subharmonic,” in Proceedings of Lasers and Electro-Optics Society Annual Meeting (LEOS2000) (Lasers and Electro-Optics Society, Piscataway, N.J., 2000), p. 298.

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984), p. 118.

Shimoda, K.

K. Shimoda, “Theory and application of optical subharmonic oscillator,” Jpn. J. Appl. Phys. 34, 3566 (1995).
[CrossRef]

Slyusarev, S.

Spielmann, Ch.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

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 (2000).
[CrossRef] [PubMed]

Tempea, G.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Torizuka, K.

Udem, Th.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Wallenstein, R.

Washburn, B. R.

B. R. Washburn, S. E. Ralph, J. K. Ranka, and R. S. Windeler, “Controlling the phase of a femtosecond optical parametric oscillator via coherent mixing of the pump-generated supercontinuum and an OPO subharmonic,” in Proceedings of Lasers and Electro-Optics Society Annual Meeting (LEOS2000) (Lasers and Electro-Optics Society, Piscataway, N.J., 2000), p. 298.

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 (2000).
[CrossRef] [PubMed]

B. R. Washburn, S. E. Ralph, J. K. Ranka, and R. S. Windeler, “Controlling the phase of a femtosecond optical parametric oscillator via coherent mixing of the pump-generated supercontinuum and an OPO subharmonic,” in Proceedings of Lasers and Electro-Optics Society Annual Meeting (LEOS2000) (Lasers and Electro-Optics Society, Piscataway, N.J., 2000), p. 298.

Jpn. J. Appl. Phys. (1)

K. Shimoda, “Theory and application of optical subharmonic oscillator,” Jpn. J. Appl. Phys. 34, 3566 (1995).
[CrossRef]

Opt. Commun. (1)

T. W. Hänsch, “A proposed subfemtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Commun. 80, 71 (1990).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

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, 635 (2000).
[CrossRef] [PubMed]

Other (2)

B. R. Washburn, S. E. Ralph, J. K. Ranka, and R. S. Windeler, “Controlling the phase of a femtosecond optical parametric oscillator via coherent mixing of the pump-generated supercontinuum and an OPO subharmonic,” in Proceedings of Lasers and Electro-Optics Society Annual Meeting (LEOS2000) (Lasers and Electro-Optics Society, Piscataway, N.J., 2000), p. 298.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984), p. 118.

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Figures (4)

Fig. 1
Fig. 1

Time–frequency correspondence and relation between Δθ and δ. In the time domain the synthesized electric fields maintain the subfemtosecond pulse train when Δθp:Δθs:Δθi=3:2:1, although the ratio of the pulse peak to the train envelope shifts corresponding to Δθp. In the frequency domain, the elements of the frequency comb of subharmonic pulse trains are spaced by F.

Fig. 2
Fig. 2

Experimental setup for locking the carrier phase among subharmonic pulses. Solid lines, optical paths; dashed lines, electrical paths. PM, photomultiplier; PD, photodiode; LPF, low-pass filter; BPF, bandpass filter; λ/2, half-wave plate; HM, half-mirror; SH, second harmonic; OC, output coupler; verdi, frequency-doubled Nd:YVO4 laser.

Fig. 3
Fig. 3

rf power spectrum of the combined frequency-doubled signal and sum frequency between the pump and the idler without phase locking. The superimposed trace with 10  scans shows the fluctuation of the beat frequency. Inset, averaged beat signals. The beat notes disappear when traces are averaged over 100  scans.

Fig. 4
Fig. 4

Carrier-phase slip frequency of the signal compared with that of the pump with feedback. The traces are averaged over 100  scans. The beat frequency is locked to F/6=12 MHz. The spectrum width of the beat note is 500 kHz.

Equations (1)

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f=6 Δl/λsF,

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