Abstract

Carrier-envelope phase stabilization of a 200MHz octave-spanning Ti:sapphire laser without external broadening is demonstrated. The individual comb lines spaced by 200MHz can conveniently be resolved using commercial wavemeters. The accumulated in-loop carrier-envelope phase error (integrated from 2.5 mHz to 10 MHz) using a broadband analog mixer as phase detector is 0.117 rad, equivalent to 50 attosecond carrier-envelope phase jitter at 800 nm.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
  2. R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, �??Optical Frequency Synthesizer for Precision Spectroscopy,�?? Phys. Rev. Lett. 85, 2264-2267 (2000).
    [CrossRef] [PubMed]
  3. In this paper, the term �??octave-spanning laser�?? refers to a femtosecond mode-locked laser whose carrier-envelope frequency can be measured using f -to-2 f self-referencing without external spectral broadening.
  4. U. Morgner, R. Ell, G. Metzler, T. R. Schibli, F. X. Kärtner, J. G. Fujimoto, H. A. Haus, and E. P. Ippen, �??Nonlinear Optics with Phase-Controlled Pulses in the Sub-Two-Cycle Regime,�?? Phys. Rev. Lett. 86, 5462-5465 (2001).
    [CrossRef] [PubMed]
  5. R. Ell, U. Morgner, F. X. Kärtner, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, M. J. Lederer, A. Boiko, and B. Luther-Davies, �??Generation of 5-fs pulses and octave-spanning spectra directly from a Ti:sapphire laser,�?? Opt. Lett. 26, 373-375 (2001).
    [CrossRef]
  6. T. M. Fortier, D. J. Jones, and S. T. Cundiff, �??Phase stabilization of an octave-spanning Ti:sapphire laser,�?? Opt. Lett. 28, 2198-2200 (2003).
    [CrossRef] [PubMed]
  7. L. Matos, D. Kleppner, O. Kuzucu, T. R. Schibli, J. Kim, E. P. Ippen, and F. X. Kaertner, �??Direct frequency comb generation from an octave-spanning, prismless Ti:sapphire laser,�?? Opt. Lett. 29, 1683-1685 (2004).
    [CrossRef] [PubMed]
  8. 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]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. O. D. Mücke, T. Tritschler, M.Wegener, U. Morgner, F. X. Kärtner, G. Khitrova, and H. M. Gibbs, �??Carrier-wave Rabi flopping: role of the carrier-envelope phase,�?? Opt. Lett. 29, 2160-2162 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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  17. W. S. Graves, M. Farkhondeh, F. X. Kaertner, R. Milner, C. Tschalaer, J. B. van der Laan, F.Wang, A. Zolfaghari, T. Zwart, W. M. Fawley, and D. E. Moncton, �??X-ray laser seeding for short pulses and narrow bandwidth,�?? Proc. of the 2003 Part. Accel. Conf. 2, 959-961 (2003), <a href= "http://intl.ieeexplore.ieee.org/iel5/9054/28710/01289566.pdf"> http://intl.ieeexplore.ieee.org/iel5/9054/28710/01289566.pdf </a>
    [CrossRef]
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    [CrossRef]
  19. T. M. Ramond, S. A. Diddams, L. Hollberg, and A. Bartels, �??Phase-coherent link from optical to microwave frequencies by means of the broadband continuum from a 1-GHz Ti:sapphire femtosecond oscillator,�?? Opt. Lett. 27, 1842-1844 (2002).
    [CrossRef]
  20. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, �??Determining the carrier-envelope offset frequency of 5-fs pulses with extreme nonlinear optics in ZnO,�?? Opt. Lett. 27, 2127-2129 (2002).
    [CrossRef]
  21. T. Tritschler, K. D. Hof, M.W. Klein, and M. Wegener, �??Variation of the carrier-envelope phase of few-cycle laser pulses owing to the Gouy phase: a solid-state-based measurement,�?? Opt. Lett. 30, 753-755 (2005).
    [CrossRef] [PubMed]
  22. T. Fuji, J. Rauschenberger, A. Apolonski, V. S. Yakovlev, G. Tempea, T. Udem, C. Gohle, T.W. Hänsch, W. Lehnert, M. Scherer, and F. Krausz, �??Monolithic carrier-envelope phase-stabilization scheme,�?? Opt. Lett. 30, 332-334 (2005).
    [CrossRef] [PubMed]
  23. B. R.Washburn, S. A. Diddams, N. R. Newbury, J.W. Nicholson, M. F. Yan, and C. G. Jørgensen, �??Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,�?? Opt. Lett. 29, 250-252 (2004).
    [CrossRef] [PubMed]
  24. T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inaba, A. Onae, H. Matsumoto, I. Hartl, and M. E. Fermann, �??Frequency metrology with a turnkey all-fiber system,�?? Opt. Lett. 29, 2467-2469 (2004).
    [CrossRef] [PubMed]
  25. P. Kubina, P. Adel, F. Adler, G. Grosche, T.W. H¨ansch, R. Holzwarth, A. Leitenstorfer, B. Lipphardt, and H. Schnatz, �??Long term comparison of two fiber based frequency comb systems,�?? Opt. Express 13, 904-909 (2005), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-904.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-904.</a>
    [CrossRef] [PubMed]
  26. S. T. Cundiff, J. Ye, and J. L. Hall, �??Optical frequency synthesis based on mode-locked lasers,�?? Rev. Sci. Instrum. 72, 3749-3771 (2001).
    [CrossRef]
  27. J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, �??Ultraprecise Measurement of Optical Frequency Ratios,�?? Phys. Rev. Lett. 88, 073601 (2002).

Nature

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, �??Attosecond control of electronic processes by intense light fields,�?? Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

R. Ell, U. Morgner, F. X. Kärtner, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, M. J. Lederer, A. Boiko, and B. Luther-Davies, �??Generation of 5-fs pulses and octave-spanning spectra directly from a Ti:sapphire laser,�?? Opt. Lett. 26, 373-375 (2001).
[CrossRef]

T. M. Fortier, D. J. Jones, and S. T. Cundiff, �??Phase stabilization of an octave-spanning Ti:sapphire laser,�?? Opt. Lett. 28, 2198-2200 (2003).
[CrossRef] [PubMed]

L. Matos, D. Kleppner, O. Kuzucu, T. R. Schibli, J. Kim, E. P. Ippen, and F. X. Kaertner, �??Direct frequency comb generation from an octave-spanning, prismless Ti:sapphire laser,�?? Opt. Lett. 29, 1683-1685 (2004).
[CrossRef] [PubMed]

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]

O. D. Mücke, O. Kuzucu, F. N. C. Wong, E. P. Ippen, F. X. K¨artner, S. M. Foreman, D. J. Jones, L.-S. Ma, J. L. Hall, and J. Ye, �??Experimental implementation of optical clockwork without carrier-envelope phase control,�?? Opt. Lett. 29, 2806-2808 (2004).
[CrossRef] [PubMed]

S. M. Foreman, A. Marian, J. Ye, E. A. Petrukhin, M. A. Gubin, O. D. Mücke, F. N. C. Wong, E. P. Ippen, and F. X. Kärtner, �??Demonstration of a HeNe/CH4-based optical molecular clock,�?? Opt. Lett. 30, 570-572 (2005).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M.Wegener, U. Morgner, F. X. Kärtner, G. Khitrova, and H. M. Gibbs, �??Carrier-wave Rabi flopping: role of the carrier-envelope phase,�?? Opt. Lett. 29, 2160-2162 (2004).
[CrossRef] [PubMed]

A. Bartels and H. Kurz, �??Generation of a broadband continuum by a Ti:sapphire femtosecond oscillator with a 1-GHz repetition rate,�?? Opt. Lett. 27, 1839-1841 (2002).
[CrossRef]

T. M. Ramond, S. A. Diddams, L. Hollberg, and A. Bartels, �??Phase-coherent link from optical to microwave frequencies by means of the broadband continuum from a 1-GHz Ti:sapphire femtosecond oscillator,�?? Opt. Lett. 27, 1842-1844 (2002).
[CrossRef]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, �??Determining the carrier-envelope offset frequency of 5-fs pulses with extreme nonlinear optics in ZnO,�?? Opt. Lett. 27, 2127-2129 (2002).
[CrossRef]

T. Tritschler, K. D. Hof, M.W. Klein, and M. Wegener, �??Variation of the carrier-envelope phase of few-cycle laser pulses owing to the Gouy phase: a solid-state-based measurement,�?? Opt. Lett. 30, 753-755 (2005).
[CrossRef] [PubMed]

T. Fuji, J. Rauschenberger, A. Apolonski, V. S. Yakovlev, G. Tempea, T. Udem, C. Gohle, T.W. Hänsch, W. Lehnert, M. Scherer, and F. Krausz, �??Monolithic carrier-envelope phase-stabilization scheme,�?? Opt. Lett. 30, 332-334 (2005).
[CrossRef] [PubMed]

B. R.Washburn, S. A. Diddams, N. R. Newbury, J.W. Nicholson, M. F. Yan, and C. G. Jørgensen, �??Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,�?? Opt. Lett. 29, 250-252 (2004).
[CrossRef] [PubMed]

T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inaba, A. Onae, H. Matsumoto, I. Hartl, and M. E. Fermann, �??Frequency metrology with a turnkey all-fiber system,�?? Opt. Lett. 29, 2467-2469 (2004).
[CrossRef] [PubMed]

Part. Accel. Conf. 2, 2003

W. S. Graves, M. Farkhondeh, F. X. Kaertner, R. Milner, C. Tschalaer, J. B. van der Laan, F.Wang, A. Zolfaghari, T. Zwart, W. M. Fawley, and D. E. Moncton, �??X-ray laser seeding for short pulses and narrow bandwidth,�?? Proc. of the 2003 Part. Accel. Conf. 2, 959-961 (2003), <a href= "http://intl.ieeexplore.ieee.org/iel5/9054/28710/01289566.pdf"> http://intl.ieeexplore.ieee.org/iel5/9054/28710/01289566.pdf </a>
[CrossRef]

Phys. Rev. Lett.

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, �??Ultraprecise Measurement of Optical Frequency Ratios,�?? Phys. Rev. Lett. 88, 073601 (2002).

G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, �??Measurement of the Phase of Few-Cycle Laser Pulses,�?? Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, �??Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,�?? Phys. Rev. Lett. 92, 147403 (2004).
[CrossRef] [PubMed]

R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, �??Optical Frequency Synthesizer for Precision Spectroscopy,�?? Phys. Rev. Lett. 85, 2264-2267 (2000).
[CrossRef] [PubMed]

U. Morgner, R. Ell, G. Metzler, T. R. Schibli, F. X. Kärtner, J. G. Fujimoto, H. A. Haus, and E. P. Ippen, �??Nonlinear Optics with Phase-Controlled Pulses in the Sub-Two-Cycle Regime,�?? Phys. Rev. Lett. 86, 5462-5465 (2001).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

S. T. Cundiff, J. Ye, and J. L. Hall, �??Optical frequency synthesis based on mode-locked lasers,�?? Rev. Sci. Instrum. 72, 3749-3771 (2001).
[CrossRef]

Science

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]

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, �??United Time-Frequency Spectroscopy for Dynamics and Global Structure,�?? Science 306, 2063-2068 (2004).
[CrossRef] [PubMed]

Other

In this paper, the term �??octave-spanning laser�?? refers to a femtosecond mode-locked laser whose carrier-envelope frequency can be measured using f -to-2 f self-referencing without external spectral broadening.

A. Bartels, in Femtosecond Optical Frequency Comb Technology: Principle, Operation, and Application, edited by J. Ye and S. T. Cundiff (Springer, 2005), pp. 79.

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Figures (4)

Fig. 1.
Fig. 1.

Carrier-envelope phase stabilized 200MHz octave-spanning Ti:sapphire laser. The femtosecond laser itself (located inside the grey area) has a compact 20 cm×30 cm foot-print. AOM, acousto-optical modulator; S, silver end mirror; OC, output coupling mirror; PBS, polarizing beam splitter cube; PMT, photomultiplier tube; PD, digital phase detector; LF, loop filter; VSA, vector signal analyzer. The carrier-envelope frequency is phase locked to 36 MHz.

Fig. 2.
Fig. 2.

Output spectrum of the Ti:sapphire laser on a linear (black curve) and on a logarithmic scale (red curve). The reflectivity of the ZnSe/MgF2 output coupler (blue curve) is shown for comparison. The wavelengths 570 and 1140 nm used for f -to-2f self-referencing are indicated by two dashed lines. The Fourier limit of the pulse spectrum is 3.6 fs.

Fig. 3.
Fig. 3.

Radio-frequency power spectrum of fundamental and frequency-doubled light transmitted through a 10 nm wide interference filter centered at 570 nm, resolution bandwidth (RBW) is 100 kHz. The peak at the carrier-envelope frequency f ϕ exhibits a signal-to-noise ratio of ~35 dB, sufficient for direct and routine carrier-envelope phase stabilization.

Fig. 4.
Fig. 4.

Power spectral density (PSD) of the carrier-envelope phase fluctuations Sf (blue and red curves) and integrated carrier-envelope phase error Δ ϕ (green and orange curves) measured with a digital phase detector and mixer, respectively.

Equations (1)

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Δ ϕ = [ 2 10 MHz f S ϕ ( f ) d f ] 1 2 ,

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