Abstract

An experimental verification of energy conservation in a parametric oscillator is reported with an optical frequency precision of approximately 200 kHz (< 10-6 nm). This high precision is made possible by simultaneously measuring the frequency offsets of the pump, signal and idler frequency combs in a singly-resonant femtosecond optical parametric oscillator system without any phase control.

© 2007 Optical Society of America

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References

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  1. R. H. Kingston, “Parametric amplification and oscillation at optical frequencies,” Proc. Institute of Radio Engineers 50,472 (1962).
  2. N. M. Kroll, “Parametric amplification in spatially extended media and the application to the design of tunable oscillators at optical frequencies,” Phys. Rev. 127,1207–1211 (1962).
    [CrossRef]
  3. S. A. Akhmanov and R. V. Khokhlov, “Concerning one possibility of amplification of light waves,” Sov. Phys. JETP 16,252 (1963).
  4. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127,1918–1939 (1962).
    [CrossRef]
  5. R. A. Baumgartner and R. K. Byer , “Optical Parametric Amplification,” IEEE J. Quantum. Electron. QE-15,432–444 (1979).
    [CrossRef]
  6. T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Common. 127,69–72 (1996).
    [CrossRef]
  7. R. Wynands, O. Coste, C. Rembe, and D. Meschede, “How accurate is optical second-harmonic generation” pt. Lett. 20,1095 –1097 (1995).
  8. 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] [PubMed]
  9. 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 sub-harmonic,” Proceedings of the 13th Annual Meeting of IEEE Lasers and Electro-Optics Society, 13-16 November 2000, Vol 1, pp.298.
  10. Y. R. Shen, The principles of nonlinear optics (Wiley InterScience, New York, 1984), pp.188.
  11. Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka , “Optical phase locking among femtosecond subharmonic pulses,” Opt. Lett. 28,1377–1379 (2003).
    [CrossRef] [PubMed]
  12. A. Baltuska, 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] [PubMed]
  13. Y. Kobayashi and K. Torizuka, “Measurement of the optical phase relation among subharmonic pulses in a femtosecond optical parametric oscillator,” Opt. Lett. 25,856–858 (2000).
    [CrossRef]
  14. Y. Kobayashi and K. Torizuka, “Carrier-phase control among subharmonic pulses in a femtosecond optical parametric oscillator,” Opt. Lett. 26,1295–1297 (2001).
    [CrossRef]
  15. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm” Opt. Lett. 25,25–27 (2000).
    [CrossRef]
  16. L. Xu. C. Spielmann, A. Poppe, T. Brabec, and F. Krausz, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21,2008–2010 (1996).
    [CrossRef] [PubMed]
  17. D. C. Edelstein, E. S. Wachman, and C. L. Tang, “Broadly tunable high repetition rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 54,1728–1730 (1989).
    [CrossRef]
  18. M. Zimmermann, C. Gohle, R. Holzwarth, T. Udem, and T. W. Hänsch, “Optical clockwork with an offset-free difference-frequency comb: accuracy of sum- and difference-frequency generation,” Opt. Lett. 29,310–312 (2004).
    [CrossRef] [PubMed]
  19. T. Hirooka, S. Ono, K. Hagiudaand, and M. Nakazawa, “Stimulated Brillouin scattering in dispersion-decreasing fiber with ultrahigh-speed femtosecond soliton pulse compression,” Opt. Lett. 30,364–366 (2005).
    [CrossRef] [PubMed]
  20. K. S. Abedin, “Observation of strong stimulated Brillouin scattering in single-mode As2Se3 chalcogenide fiber,” Opt. Express 13,10266–10271 (2005).
    [CrossRef] [PubMed]
  21. W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down12 conversion with a broadband pump,” Phys. Rev. A 56,1627–1634 (1997).
    [CrossRef]
  22. T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72,545–591 (2000).
    [CrossRef]

2005 (2)

2004 (1)

2003 (1)

2002 (1)

A. Baltuska, 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] [PubMed]

2001 (1)

2000 (5)

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72,545–591 (2000).
[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm” Opt. Lett. 25,25–27 (2000).
[CrossRef]

Y. Kobayashi and K. Torizuka, “Measurement of the optical phase relation among subharmonic pulses in a femtosecond optical parametric oscillator,” Opt. Lett. 25,856–858 (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] [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 sub-harmonic,” Proceedings of the 13th Annual Meeting of IEEE Lasers and Electro-Optics Society, 13-16 November 2000, Vol 1, pp.298.

1997 (1)

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down12 conversion with a broadband pump,” Phys. Rev. A 56,1627–1634 (1997).
[CrossRef]

1996 (2)

L. Xu. C. Spielmann, A. Poppe, T. Brabec, and F. Krausz, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21,2008–2010 (1996).
[CrossRef] [PubMed]

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Common. 127,69–72 (1996).
[CrossRef]

1995 (1)

R. Wynands, O. Coste, C. Rembe, and D. Meschede, “How accurate is optical second-harmonic generation” pt. Lett. 20,1095 –1097 (1995).

1989 (1)

D. C. Edelstein, E. S. Wachman, and C. L. Tang, “Broadly tunable high repetition rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 54,1728–1730 (1989).
[CrossRef]

1979 (1)

R. A. Baumgartner and R. K. Byer , “Optical Parametric Amplification,” IEEE J. Quantum. Electron. QE-15,432–444 (1979).
[CrossRef]

1963 (1)

S. A. Akhmanov and R. V. Khokhlov, “Concerning one possibility of amplification of light waves,” Sov. Phys. JETP 16,252 (1963).

1962 (3)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127,1918–1939 (1962).
[CrossRef]

R. H. Kingston, “Parametric amplification and oscillation at optical frequencies,” Proc. Institute of Radio Engineers 50,472 (1962).

N. M. Kroll, “Parametric amplification in spatially extended media and the application to the design of tunable oscillators at optical frequencies,” Phys. Rev. 127,1207–1211 (1962).
[CrossRef]

Abedin, K. S.

Akhmanov, S. A.

S. A. Akhmanov and R. V. Khokhlov, “Concerning one possibility of amplification of light waves,” Sov. Phys. JETP 16,252 (1963).

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127,1918–1939 (1962).
[CrossRef]

Baltuska, A.

A. Baltuska, 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] [PubMed]

Baumgartner, R. A.

R. A. Baumgartner and R. K. Byer , “Optical Parametric Amplification,” IEEE J. Quantum. Electron. QE-15,432–444 (1979).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127,1918–1939 (1962).
[CrossRef]

Brabec, T.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72,545–591 (2000).
[CrossRef]

L. Xu. C. Spielmann, A. Poppe, T. Brabec, and F. Krausz, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21,2008–2010 (1996).
[CrossRef] [PubMed]

Byer, R. K.

R. A. Baumgartner and R. K. Byer , “Optical Parametric Amplification,” IEEE J. Quantum. Electron. QE-15,432–444 (1979).
[CrossRef]

Coste, O.

R. Wynands, O. Coste, C. Rembe, and D. Meschede, “How accurate is optical second-harmonic generation” pt. Lett. 20,1095 –1097 (1995).

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] [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 288,635–639 (2000).
[CrossRef] [PubMed]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127,1918–1939 (1962).
[CrossRef]

Edelstein, D. C.

D. C. Edelstein, E. S. Wachman, and C. L. Tang, “Broadly tunable high repetition rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 54,1728–1730 (1989).
[CrossRef]

Fuji, T.

A. Baltuska, 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] [PubMed]

Gohle, C.

Grice, W. P.

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down12 conversion with a broadband pump,” Phys. Rev. A 56,1627–1634 (1997).
[CrossRef]

Hagiudaand, K.

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] [PubMed]

Hänsch, T. W.

Hirooka, T.

Holzwarth, R.

Ikegami, T.

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Common. 127,69–72 (1996).
[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 288,635–639 (2000).
[CrossRef] [PubMed]

Kakehata, M.

Khokhlov, R. V.

S. A. Akhmanov and R. V. Khokhlov, “Concerning one possibility of amplification of light waves,” Sov. Phys. JETP 16,252 (1963).

Kingston, R. H.

R. H. Kingston, “Parametric amplification and oscillation at optical frequencies,” Proc. Institute of Radio Engineers 50,472 (1962).

Kobayashi, T.

A. Baltuska, 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] [PubMed]

Kobayashi, Y.

Krausz, F.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72,545–591 (2000).
[CrossRef]

L. Xu. C. Spielmann, A. Poppe, T. Brabec, and F. Krausz, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21,2008–2010 (1996).
[CrossRef] [PubMed]

Kroll, N. M.

N. M. Kroll, “Parametric amplification in spatially extended media and the application to the design of tunable oscillators at optical frequencies,” Phys. Rev. 127,1207–1211 (1962).
[CrossRef]

Meschede, D.

R. Wynands, O. Coste, C. Rembe, and D. Meschede, “How accurate is optical second-harmonic generation” pt. Lett. 20,1095 –1097 (1995).

Nakazawa, M.

Ohshima, S.

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Common. 127,69–72 (1996).
[CrossRef]

Ono, S.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127,1918–1939 (1962).
[CrossRef]

Poppe, A.

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 sub-harmonic,” Proceedings of the 13th Annual Meeting of IEEE Lasers and Electro-Optics Society, 13-16 November 2000, Vol 1, pp.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 288,635–639 (2000).
[CrossRef] [PubMed]

Ranka, J. K.

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 sub-harmonic,” Proceedings of the 13th Annual Meeting of IEEE Lasers and Electro-Optics Society, 13-16 November 2000, Vol 1, pp.298.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm” Opt. Lett. 25,25–27 (2000).
[CrossRef]

Rembe, C.

R. Wynands, O. Coste, C. Rembe, and D. Meschede, “How accurate is optical second-harmonic generation” pt. Lett. 20,1095 –1097 (1995).

Sakuma, E.

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Common. 127,69–72 (1996).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The principles of nonlinear optics (Wiley InterScience, New York, 1984), pp.188.

Slyusarev, S.

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Common. 127,69–72 (1996).
[CrossRef]

Spielmann, L. Xu. C.

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] [PubMed]

Stentz, A. J.

Takada, H.

Tang, C. L.

D. C. Edelstein, E. S. Wachman, and C. L. Tang, “Broadly tunable high repetition rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 54,1728–1730 (1989).
[CrossRef]

Torizuka, K.

Udem, T.

Wachman, E. S.

D. C. Edelstein, E. S. Wachman, and C. L. Tang, “Broadly tunable high repetition rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 54,1728–1730 (1989).
[CrossRef]

Walmsley, I. A.

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down12 conversion with a broadband pump,” Phys. Rev. A 56,1627–1634 (1997).
[CrossRef]

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 sub-harmonic,” Proceedings of the 13th Annual Meeting of IEEE Lasers and Electro-Optics Society, 13-16 November 2000, Vol 1, pp.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 288,635–639 (2000).
[CrossRef] [PubMed]

Windeler, R. S.

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 sub-harmonic,” Proceedings of the 13th Annual Meeting of IEEE Lasers and Electro-Optics Society, 13-16 November 2000, Vol 1, pp.298.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm” Opt. Lett. 25,25–27 (2000).
[CrossRef]

Wynands, R.

R. Wynands, O. Coste, C. Rembe, and D. Meschede, “How accurate is optical second-harmonic generation” pt. Lett. 20,1095 –1097 (1995).

Zimmermann, M.

Appl. Phys. Lett. (1)

D. C. Edelstein, E. S. Wachman, and C. L. Tang, “Broadly tunable high repetition rate femtosecond optical parametric oscillator,” Appl. Phys. Lett. 54,1728–1730 (1989).
[CrossRef]

IEEE J. Quantum. Electron. (1)

R. A. Baumgartner and R. K. Byer , “Optical Parametric Amplification,” IEEE J. Quantum. Electron. QE-15,432–444 (1979).
[CrossRef]

Opt. Common. (1)

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Common. 127,69–72 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (7)

Phys. Rev. (2)

N. M. Kroll, “Parametric amplification in spatially extended media and the application to the design of tunable oscillators at optical frequencies,” Phys. Rev. 127,1207–1211 (1962).
[CrossRef]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127,1918–1939 (1962).
[CrossRef]

Phys. Rev. A (1)

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down12 conversion with a broadband pump,” Phys. Rev. A 56,1627–1634 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

A. Baltuska, 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] [PubMed]

Proc. Institute of Radio Engineers (1)

R. H. Kingston, “Parametric amplification and oscillation at optical frequencies,” Proc. Institute of Radio Engineers 50,472 (1962).

pt. Lett. (1)

R. Wynands, O. Coste, C. Rembe, and D. Meschede, “How accurate is optical second-harmonic generation” pt. Lett. 20,1095 –1097 (1995).

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72,545–591 (2000).
[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 288,635–639 (2000).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

S. A. Akhmanov and R. V. Khokhlov, “Concerning one possibility of amplification of light waves,” Sov. Phys. JETP 16,252 (1963).

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 sub-harmonic,” Proceedings of the 13th Annual Meeting of IEEE Lasers and Electro-Optics Society, 13-16 November 2000, Vol 1, pp.298.

Y. R. Shen, The principles of nonlinear optics (Wiley InterScience, New York, 1984), pp.188.

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Figures (4)

Fig.1.
Fig.1.

(a). Illustration of the change in the carrier-envelope phase between successive pulses (pump, signal or idler), and the relationship between the roundtrip carrier envelope phase-slip, Δϕ, and the carrier-envelope phase-slip frequency, Ω CEP . (b). The carrier-envelope phase-slip frequencies of the pump, signal and idler pulses equal their comb-offset frequencies. The modes of these pulses (black lines) are illustrated relative to an idealized frequency scale with zero DC-offset and a scale spacing equal to the laser inter-mode frequency separation, Δω (grey lines). The pump offset frequency equals the sum of the offset frequencies of the signal and idler pulses. (c). Measurement of the pump, signal and idler carrier-envelope phase-slip frequencies is made using the pump super-continuum (grey lines) which itself has a DC-offset equal to Ω CEP p Beating the pump super-continuum against its own second-harmonic, the signal second-harmonic and the pump-idler sum-frequency light results in detectable beat frequencies at Ω CEP p , 2Ω CEP s −Ω CEP p and Ω CEP i respectively.

Fig. 2.
Fig. 2.

Schematic of the experimental system. GTI, Gires-Tournois interferometer mirror; OC, output coupler; PBS, polarising beam-splitter; IF, interference filter; APD, avalanche photodiode; CM ,cold mirror (highly reflecting at 520nm and highly transmitting at 1040nm); KTP, potassium titanyl phosphate nonlinear crystal; P, BK7 glass prism.

Fig. 3.
Fig. 3.

RF spectrum analyser screen showing frequency sidebands generated by interference between the super-continuum reference spectrum and: (1) red frequency-doubled signal pulses (33.55MHz), (2) yellow pump + idler sum-frequency mixing light (41.4MHz) and, (3) frequency-doubled pump super-continuum light (49.15MHz). The resolution bandwidth of the measurements was 100kHz. When the negative sideband of the red beat is used (-33.55MHz) the data illustrate that Ω red beat −Ω pump beat = −2Ω yellow beat .

Fig. 4.
Fig. 4.

Difference between the pump beat linear frequency (Ω pump beat /2π)and the signal SHG beat linear frequency (Ω red beat /2π) shown as a function of the yellow beat linear frequency(Ω yellow beat /2π). The slope is -1.995 +;/− 0.004 and the intercept is −0.1 +/− 0.4 MHz.

Equations (6)

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

ϕ p = ϕ s + ϕ i π / 2
Ω p CEP = Ω s CEP + Ω i CEP
ω p = Ω p CEP + j Δ ω
ω s = Ω s CEP + k Δ ω
ω i = Ω i CEP + l Δ ω
Ω p CEP = ΔΩ + Ω s CEP + Ω i CEP

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