Abstract

We derive an analytical approximation for the measured pulse width error in spectral shearing methods, such as spectral phase interferometry for direct electric-field reconstruction (SPIDER), caused by an anomalous delay between the two sheared pulse components. This analysis suggests that, as pulses approach the single-cycle limit, the resulting requirements on the calibration and stability of this delay become significant, requiring precision orders of magnitude higher than the scale of a wavelength. This is demonstrated by numerical simulations of SPIDER pulse reconstruction using actual data from a sub-two-cycle laser. We briefly propose methods to minimize the effects of this sensitivity in SPIDER and review variants of spectral shearing that attempt to avoid this difficulty.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
    [CrossRef]
  2. E. Matsubara, K. Yamane, T. Sekikawa, and M. Yamashita, “Generation of 2.6fs optical pulses using induced-phase modulation in a gas-filled hollow fiber,” J. Opt. Soc. Am. B 24, 985-989 (2007).
    [CrossRef]
  3. P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381-387 (2007).
    [CrossRef]
  4. I. A. Walmsley and V. Wong, “Characterization of the electric field of ultrashort optical pulses,” J. Opt. Soc. Am. B 13, 2453-2563 (1996).
    [CrossRef]
  5. J. Nicholson, J. Jasapara, W. Rudolph, F. Omenetto, and A. Taylor, “Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements,” Opt. Lett. 24, 1774-1776 (1999).
    [CrossRef]
  6. D. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571-579 (1993).
    [CrossRef]
  7. J. Chung and A. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” J. Spec. Top. Quantum Electron. 7, 656-666 (2001).
    [CrossRef]
  8. C. Iaconis and I. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort pulses,” IEEE J. Quantum Electron. 35, 501-509 (1999).
    [CrossRef]
  9. I. A. Walmsley, “Characterization of ultrashort optical pulses in the few-cycle regime using spectral phase interferometry for direct electric-field reconstruction,” in Few-Cycle Laser Pulse Generation and its Applications, F.Kärtner, ed. (Springer, 2004), pp. 265-291.
  10. E. H. Armstrong, “A method of reducing disturbances in radio signaling by a system of frequency modulation,” Proc. IRE 24, 689-740 (1936).
    [CrossRef]
  11. L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67-S75 (2000).
    [CrossRef]
  12. S. Jensen and M. Anderson, “Measuring ultrashort optical pulses in the presence of noise: an empirical study of the performance of spectral phase interferometry for direct electric field reconstruction,” Appl. Opt. 43, 883-893 (2004).
    [CrossRef] [PubMed]
  13. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997).
  14. K. Yamane, Z. Zhang, K. Oka, R. Morita, and M. Yamashita, “Optical pulse compression to 3.4fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258-2260 (2003).
    [CrossRef] [PubMed]
  15. H. M. Crespo, J. R. Birge, E. L. Falcão Filho, M. Y. Sander, A. Benedick, and F. X. Kärtner, “Non-intrusive phase-stabilization of sub-two-cycle pulses from a prismless octave-spanning Ti:sapphire laser,” Opt. Lett., doc. ID 90799 (posted 14 March 2008, in press).
  16. C. Dorrer, “Influence of the calibration of the detector on spectral interferometry,” J. Opt. Soc. Am. B 16, 1160-1168 (1999).
    [CrossRef]
  17. C. Dorrer, “Implementation of spectral phase interferometry for direct electric-field reconstruction with a simultaneously recorded reference interferogram,” Opt. Lett. 24, 1532-1534 (1999).
    [CrossRef]
  18. T. Shuman, I. A. Walmsley, L. Waxer, M. Anderson, C. Iaconis, and J. Bromage, “Real-time spider: ultrashort pulse characterization at 20Hz,” Opt. Express 5, 134-143 (1999).
    [CrossRef] [PubMed]
  19. B. von Vacano, T. Buckup, and M. Motzkus, “Shaper-assisted collinear spider: fast and simple broadband pulse compression in nonlinear microscopy,” J. Opt. Soc. Am. B 24, 1091-1100 (2007).
    [CrossRef]
  20. J. R. Birge, H. M. Crespo, M. Sander, and F. X. Kärtner, “Non-instrusive sub-two-cycle carrier-envelope stabilized pulses using engineered chirped mirrors,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2008).
  21. J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31, 2063-2065 (2006).
    [CrossRef] [PubMed]
  22. C. Dorrer, P. Londero, and I. A. Walmsley, “Homodyne detection in spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 26, 1510-1512 (2001).
    [CrossRef]
  23. P. Baum, S. Lockbrunner, and E. Riedle, “Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses,” Opt. Lett. 29, 210-212 (2004).
    [CrossRef] [PubMed]
  24. E. Kosik, A. Radunksy, I. Walmsley, and C. Dorrer, “Interferometric technique for measuring broadband ultrashort pulses at the sampling limit,” Opt. Lett. 30, 326-328 (2005).
    [CrossRef] [PubMed]
  25. A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31, 1914-1916 (2006).
    [CrossRef] [PubMed]
  26. J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry (2DSI) for ultrashort pulse characterization,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2006).
  27. J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization and optimization,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.Miller, and A.Weiner, eds. (Springer, 2006), pp. 160-162.
  28. M. Y. Sander, H. M. Crespo, J. R. Birge, and F. X. Kärtner, “Modeling of octave-spanning sub-two-cycle titanium:sapphire lasers: simulation and experiment,” in Proceedings of the Conference on Ultrafast Phenomena, Stresa, Italy, June 2008.
  29. S.-P. Gorza, P. Wasylczyk, and I. A. Walmsley, “Spectral shearing interferometry with spatially chirped replicas for measuring ultrashort pulses,” Opt. Express 15, 15168-15174 (2007).
    [CrossRef] [PubMed]

2007 (4)

2006 (2)

2005 (1)

2004 (2)

2003 (2)

K. Yamane, Z. Zhang, K. Oka, R. Morita, and M. Yamashita, “Optical pulse compression to 3.4fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258-2260 (2003).
[CrossRef] [PubMed]

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
[CrossRef]

2001 (2)

J. Chung and A. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” J. Spec. Top. Quantum Electron. 7, 656-666 (2001).
[CrossRef]

C. Dorrer, P. Londero, and I. A. Walmsley, “Homodyne detection in spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 26, 1510-1512 (2001).
[CrossRef]

2000 (1)

L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

1999 (5)

1996 (1)

1993 (1)

D. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571-579 (1993).
[CrossRef]

1936 (1)

E. H. Armstrong, “A method of reducing disturbances in radio signaling by a system of frequency modulation,” Proc. IRE 24, 689-740 (1936).
[CrossRef]

Anderson, M.

Angelow, G.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
[CrossRef]

Armstrong, E. H.

E. H. Armstrong, “A method of reducing disturbances in radio signaling by a system of frequency modulation,” Proc. IRE 24, 689-740 (1936).
[CrossRef]

Baum, P.

Benedick, A.

H. M. Crespo, J. R. Birge, E. L. Falcão Filho, M. Y. Sander, A. Benedick, and F. X. Kärtner, “Non-intrusive phase-stabilization of sub-two-cycle pulses from a prismless octave-spanning Ti:sapphire laser,” Opt. Lett., doc. ID 90799 (posted 14 March 2008, in press).

Birge, J. R.

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31, 2063-2065 (2006).
[CrossRef] [PubMed]

J. R. Birge, H. M. Crespo, M. Sander, and F. X. Kärtner, “Non-instrusive sub-two-cycle carrier-envelope stabilized pulses using engineered chirped mirrors,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2008).

H. M. Crespo, J. R. Birge, E. L. Falcão Filho, M. Y. Sander, A. Benedick, and F. X. Kärtner, “Non-intrusive phase-stabilization of sub-two-cycle pulses from a prismless octave-spanning Ti:sapphire laser,” Opt. Lett., doc. ID 90799 (posted 14 March 2008, in press).

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization and optimization,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.Miller, and A.Weiner, eds. (Springer, 2006), pp. 160-162.

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry (2DSI) for ultrashort pulse characterization,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2006).

M. Y. Sander, H. M. Crespo, J. R. Birge, and F. X. Kärtner, “Modeling of octave-spanning sub-two-cycle titanium:sapphire lasers: simulation and experiment,” in Proceedings of the Conference on Ultrafast Phenomena, Stresa, Italy, June 2008.

Bromage, J.

Buckup, T.

Chung, J.

J. Chung and A. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” J. Spec. Top. Quantum Electron. 7, 656-666 (2001).
[CrossRef]

Corkum, P. B.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381-387 (2007).
[CrossRef]

Crespo, H. M.

J. R. Birge, H. M. Crespo, M. Sander, and F. X. Kärtner, “Non-instrusive sub-two-cycle carrier-envelope stabilized pulses using engineered chirped mirrors,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2008).

H. M. Crespo, J. R. Birge, E. L. Falcão Filho, M. Y. Sander, A. Benedick, and F. X. Kärtner, “Non-intrusive phase-stabilization of sub-two-cycle pulses from a prismless octave-spanning Ti:sapphire laser,” Opt. Lett., doc. ID 90799 (posted 14 March 2008, in press).

M. Y. Sander, H. M. Crespo, J. R. Birge, and F. X. Kärtner, “Modeling of octave-spanning sub-two-cycle titanium:sapphire lasers: simulation and experiment,” in Proceedings of the Conference on Ultrafast Phenomena, Stresa, Italy, June 2008.

Dorrer, C.

Ell, R.

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31, 2063-2065 (2006).
[CrossRef] [PubMed]

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization and optimization,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.Miller, and A.Weiner, eds. (Springer, 2006), pp. 160-162.

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry (2DSI) for ultrashort pulse characterization,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2006).

Falcão Filho, E. L.

H. M. Crespo, J. R. Birge, E. L. Falcão Filho, M. Y. Sander, A. Benedick, and F. X. Kärtner, “Non-intrusive phase-stabilization of sub-two-cycle pulses from a prismless octave-spanning Ti:sapphire laser,” Opt. Lett., doc. ID 90799 (posted 14 March 2008, in press).

Fujimoto, J. G.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
[CrossRef]

Gallmann, L.

L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

Gorza, S.-P.

Iaconis, C.

C. Iaconis and I. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort pulses,” IEEE J. Quantum Electron. 35, 501-509 (1999).
[CrossRef]

T. Shuman, I. A. Walmsley, L. Waxer, M. Anderson, C. Iaconis, and J. Bromage, “Real-time spider: ultrashort pulse characterization at 20Hz,” Opt. Express 5, 134-143 (1999).
[CrossRef] [PubMed]

Ippen, E. P.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
[CrossRef]

Jasapara, J.

Jensen, S.

Kane, D.

D. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571-579 (1993).
[CrossRef]

Kärtner, F. X.

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31, 2063-2065 (2006).
[CrossRef] [PubMed]

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
[CrossRef]

J. R. Birge, H. M. Crespo, M. Sander, and F. X. Kärtner, “Non-instrusive sub-two-cycle carrier-envelope stabilized pulses using engineered chirped mirrors,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2008).

H. M. Crespo, J. R. Birge, E. L. Falcão Filho, M. Y. Sander, A. Benedick, and F. X. Kärtner, “Non-intrusive phase-stabilization of sub-two-cycle pulses from a prismless octave-spanning Ti:sapphire laser,” Opt. Lett., doc. ID 90799 (posted 14 March 2008, in press).

M. Y. Sander, H. M. Crespo, J. R. Birge, and F. X. Kärtner, “Modeling of octave-spanning sub-two-cycle titanium:sapphire lasers: simulation and experiment,” in Proceedings of the Conference on Ultrafast Phenomena, Stresa, Italy, June 2008.

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry (2DSI) for ultrashort pulse characterization,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2006).

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization and optimization,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.Miller, and A.Weiner, eds. (Springer, 2006), pp. 160-162.

Keller, U.

L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

Kim, J.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
[CrossRef]

Kosik, E.

Krausz, F.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381-387 (2007).
[CrossRef]

Kuzucu, O.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
[CrossRef]

Lockbrunner, S.

Londero, P.

Matsubara, E.

Matuschek, N.

L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

Morita, R.

Motzkus, M.

Nicholson, J.

Oka, K.

Omenetto, F.

Radunksy, A.

Riedle, E.

Rudolph, W.

Sander, M.

J. R. Birge, H. M. Crespo, M. Sander, and F. X. Kärtner, “Non-instrusive sub-two-cycle carrier-envelope stabilized pulses using engineered chirped mirrors,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2008).

Sander, M. Y.

H. M. Crespo, J. R. Birge, E. L. Falcão Filho, M. Y. Sander, A. Benedick, and F. X. Kärtner, “Non-intrusive phase-stabilization of sub-two-cycle pulses from a prismless octave-spanning Ti:sapphire laser,” Opt. Lett., doc. ID 90799 (posted 14 March 2008, in press).

M. Y. Sander, H. M. Crespo, J. R. Birge, and F. X. Kärtner, “Modeling of octave-spanning sub-two-cycle titanium:sapphire lasers: simulation and experiment,” in Proceedings of the Conference on Ultrafast Phenomena, Stresa, Italy, June 2008.

Scheuer, V.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
[CrossRef]

Schibli, T. R.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
[CrossRef]

Sekikawa, T.

Shuman, T.

Steinmeyer, G.

A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31, 1914-1916 (2006).
[CrossRef] [PubMed]

L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

Stibenz, G.

Sutter, D.

L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

Taylor, A.

Trebino, R.

D. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571-579 (1993).
[CrossRef]

von Vacano, B.

Walmsley, I.

E. Kosik, A. Radunksy, I. Walmsley, and C. Dorrer, “Interferometric technique for measuring broadband ultrashort pulses at the sampling limit,” Opt. Lett. 30, 326-328 (2005).
[CrossRef] [PubMed]

C. Iaconis and I. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort pulses,” IEEE J. Quantum Electron. 35, 501-509 (1999).
[CrossRef]

Walmsley, I. A.

Wasylczyk, P.

Waxer, L.

Weiner, A.

J. Chung and A. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” J. Spec. Top. Quantum Electron. 7, 656-666 (2001).
[CrossRef]

Wong, V.

Wyatt, A. S.

Yamane, K.

Yamashita, M.

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997).

Zhang, Z.

Appl. Opt. (1)

Appl. Phys. B (1)

L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571-579 (1993).
[CrossRef]

C. Iaconis and I. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort pulses,” IEEE J. Quantum Electron. 35, 501-509 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Towards single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9, 990-1001 (2003).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Spec. Top. Quantum Electron. (1)

J. Chung and A. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” J. Spec. Top. Quantum Electron. 7, 656-666 (2001).
[CrossRef]

Nat. Phys. (1)

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381-387 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (8)

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31, 2063-2065 (2006).
[CrossRef] [PubMed]

C. Dorrer, P. Londero, and I. A. Walmsley, “Homodyne detection in spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 26, 1510-1512 (2001).
[CrossRef]

P. Baum, S. Lockbrunner, and E. Riedle, “Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses,” Opt. Lett. 29, 210-212 (2004).
[CrossRef] [PubMed]

E. Kosik, A. Radunksy, I. Walmsley, and C. Dorrer, “Interferometric technique for measuring broadband ultrashort pulses at the sampling limit,” Opt. Lett. 30, 326-328 (2005).
[CrossRef] [PubMed]

A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31, 1914-1916 (2006).
[CrossRef] [PubMed]

J. Nicholson, J. Jasapara, W. Rudolph, F. Omenetto, and A. Taylor, “Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements,” Opt. Lett. 24, 1774-1776 (1999).
[CrossRef]

C. Dorrer, “Implementation of spectral phase interferometry for direct electric-field reconstruction with a simultaneously recorded reference interferogram,” Opt. Lett. 24, 1532-1534 (1999).
[CrossRef]

K. Yamane, Z. Zhang, K. Oka, R. Morita, and M. Yamashita, “Optical pulse compression to 3.4fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258-2260 (2003).
[CrossRef] [PubMed]

Proc. IRE (1)

E. H. Armstrong, “A method of reducing disturbances in radio signaling by a system of frequency modulation,” Proc. IRE 24, 689-740 (1936).
[CrossRef]

Other (7)

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997).

H. M. Crespo, J. R. Birge, E. L. Falcão Filho, M. Y. Sander, A. Benedick, and F. X. Kärtner, “Non-intrusive phase-stabilization of sub-two-cycle pulses from a prismless octave-spanning Ti:sapphire laser,” Opt. Lett., doc. ID 90799 (posted 14 March 2008, in press).

I. A. Walmsley, “Characterization of ultrashort optical pulses in the few-cycle regime using spectral phase interferometry for direct electric-field reconstruction,” in Few-Cycle Laser Pulse Generation and its Applications, F.Kärtner, ed. (Springer, 2004), pp. 265-291.

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry (2DSI) for ultrashort pulse characterization,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2006).

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization and optimization,” in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.Miller, and A.Weiner, eds. (Springer, 2006), pp. 160-162.

M. Y. Sander, H. M. Crespo, J. R. Birge, and F. X. Kärtner, “Modeling of octave-spanning sub-two-cycle titanium:sapphire lasers: simulation and experiment,” in Proceedings of the Conference on Ultrafast Phenomena, Stresa, Italy, June 2008.

J. R. Birge, H. M. Crespo, M. Sander, and F. X. Kärtner, “Non-instrusive sub-two-cycle carrier-envelope stabilized pulses using engineered chirped mirrors,” in Proceedings of the Conference of Lasers and Electro-Optics (CLEO) (Optical Society of America, 2008).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Conceptual schematic of SPIDER. This model intentionally abstracts away several practical details, such as the fact that, in practice, both pulse copies are upconverted by slightly different optical frequencies. However, these details are not important to an analysis of SPIDER.

Fig. 2
Fig. 2

Spectral power density and spectral phase for an actual sub-two-cycle Ti:sapphire oscillator measured with 2DSI.

Fig. 3
Fig. 3

Simulated pulse intensity as measured (solid curve) and in truth (dashed and dashed–dotted curves) for the Ti:sapphire laser whose spectra are shown in Fig. 2, assuming delay errors of 25 and 50 nm .

Fig. 4
Fig. 4

Measured pulse FWHM and rms widths of the pulse in Fig. 3 for a range of δ τ values compared with that predicted by Eq. (8) using the half-width of the spectrum as Δ ω .

Tables (1)

Tables Icon

Table 1 Summary of Simulated Ti:sapphire Measurements

Equations (9)

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

E ( ω ) = e ( ω Δ ω ) 2 + ( 1 2 ) i ϕ ω 2 .
δ ϕ ( ω ) = δ τ ω Ω .
δ ϕ = δ τ Ω .
T = T 0 1 + ( ϕ Δ ω 2 ) 2 ,
T + δ T = T 0 1 + ( δ τ Δ ω 2 Ω + ϕ Δ ω 2 ) 2 .
δ T = ( ϕ 4 Δ ω 4 + ( ϕ ) 2 ) ( δ τ Δ ω Ω ) + O [ δ τ 2 ] .
δ T Δ ω Ω δ τ .
δ T T + δ T Δ ω 2 2 Ω δ τ ,
δ τ 5 % = 0.64 Ω Δ ω 2 = 0.32 T 0 N ,

Metrics