Abstract

For characterization of Fourier-synthesized optical waveforms of femtosecond multicolor phase-coherent pulses, we report relative-phase measurements among Fourier components from optically phase-locked two-color mode-locked lasers. The interference of two simultaneous second-order frequency-mixing processes in a common nonlinear crystal was utilized. The relative phases among three-color components with a frequency ratio of 2ω:3ω:4ω were measured by observing the interference fringes of two simultaneous frequency-mixing outputs. The inner field structure of the synthesized waveforms can be determined except for the ambiguity of its temporal shift with respect to the synthesized envelope, which corresponds to the carrier-envelope phase slip of one of the source lasers.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. W. Hänsch, Opt. Commun. 80, 71 (1990).
    [CrossRef]
  2. K. Shimoda, Jpn. J. Appl. Phys. 34, 3566 (1995).
    [CrossRef]
  3. M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
    [CrossRef] [PubMed]
  4. R. K. Shelton, L.-S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, Science 293, 1286 (2001).
    [CrossRef] [PubMed]
  5. D. Yoshitomi, Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, Opt. Lett. 30, 1408 (2005).
    [CrossRef] [PubMed]
  6. A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. A. Diddams, Opt. Lett. 29, 403 (2004).
    [CrossRef] [PubMed]
  7. Y. Kobayashi, D. Yoshitomi, M. Kakehata, H. Takada, and K. Torizuka, Opt. Lett. 30, 2496 (2005).
    [CrossRef] [PubMed]
  8. J. Kim, T. R. Schibli, L. Matos, H. Byun, and F. X. Kärtner, in Joint Conference on Ultrafast Optics V and Applications of High Field and Short Wavelength Sources XI (Springer, 2005), paper M3-5.
    [PubMed]
  9. Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, Appl. Phys. Lett. 83, 839 (2003).
    [CrossRef]
  10. B. J. S. Gale, J. H. Sun, and D. T. Reid, Opt. Express 16, 1616 (2008).
    [CrossRef] [PubMed]
  11. E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
    [CrossRef] [PubMed]
  12. Y. Kobayashi, D. Yoshitomi, K. Iwata, H. Takada, and K. Torizuka, Opt. Express 15, 9748 (2007).
    [CrossRef] [PubMed]
  13. S. N. Goda, M. Y. Shverdin, D. R. Walker, and S. E. Harris, Opt. Lett. 30, 1222 (2005).
    [CrossRef] [PubMed]
  14. D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
    [CrossRef]
  15. C. Iaconis and I. A. Walmsley, Opt. Lett. 23, 792 (1998).
    [CrossRef]
  16. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
    [CrossRef] [PubMed]
  17. R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Phys. Rev. Lett. 85, 2264 (2000).
    [CrossRef] [PubMed]

2008 (1)

2007 (1)

2005 (4)

2004 (2)

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. A. Diddams, Opt. Lett. 29, 403 (2004).
[CrossRef] [PubMed]

2003 (1)

Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, Appl. Phys. Lett. 83, 839 (2003).
[CrossRef]

2001 (1)

R. K. Shelton, L.-S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, Science 293, 1286 (2001).
[CrossRef] [PubMed]

2000 (2)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Phys. Rev. Lett. 85, 2264 (2000).
[CrossRef] [PubMed]

1998 (1)

1995 (1)

K. Shimoda, Jpn. J. Appl. Phys. 34, 3566 (1995).
[CrossRef]

1993 (1)

D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

1990 (1)

T. W. Hänsch, Opt. Commun. 80, 71 (1990).
[CrossRef]

Baltuska, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Bartels, A.

Byun, H.

J. Kim, T. R. Schibli, L. Matos, H. Byun, and F. X. Kärtner, in Joint Conference on Ultrafast Optics V and Applications of High Field and Short Wavelength Sources XI (Springer, 2005), paper M3-5.
[PubMed]

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Diddams, S. A.

A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. A. Diddams, Opt. Lett. 29, 403 (2004).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Drescher, M.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Gale, B. J. S.

Goda, S. N.

Goulielmakis, E.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Hall, J. L.

R. K. Shelton, L.-S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, Science 293, 1286 (2001).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Phys. Rev. Lett. 85, 2264 (2000).
[CrossRef] [PubMed]

T. W. Hänsch, Opt. Commun. 80, 71 (1990).
[CrossRef]

Harris, S. E.

S. N. Goda, M. Y. Shverdin, D. R. Walker, and S. E. Harris, Opt. Lett. 30, 1222 (2005).
[CrossRef] [PubMed]

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef] [PubMed]

Heinzmann, U.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Hollberg, L.

Holzwarth, R.

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Phys. Rev. Lett. 85, 2264 (2000).
[CrossRef] [PubMed]

Iaconis, C.

Iwata, K.

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Kakehata, M.

Kane, D. J.

D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Kapteyn, H. C.

R. K. Shelton, L.-S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, Science 293, 1286 (2001).
[CrossRef] [PubMed]

Kärtner, F. X.

J. Kim, T. R. Schibli, L. Matos, H. Byun, and F. X. Kärtner, in Joint Conference on Ultrafast Optics V and Applications of High Field and Short Wavelength Sources XI (Springer, 2005), paper M3-5.
[PubMed]

Kienberger, R.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Kim, J.

J. Kim, T. R. Schibli, L. Matos, H. Byun, and F. X. Kärtner, in Joint Conference on Ultrafast Optics V and Applications of High Field and Short Wavelength Sources XI (Springer, 2005), paper M3-5.
[PubMed]

Kleineberg, U.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Knight, J. C.

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Phys. Rev. Lett. 85, 2264 (2000).
[CrossRef] [PubMed]

Kobayashi, Y.

Krausz, F.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Ma, L.-S.

R. K. Shelton, L.-S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, Science 293, 1286 (2001).
[CrossRef] [PubMed]

Matos, L.

J. Kim, T. R. Schibli, L. Matos, H. Byun, and F. X. Kärtner, in Joint Conference on Ultrafast Optics V and Applications of High Field and Short Wavelength Sources XI (Springer, 2005), paper M3-5.
[PubMed]

Murnane, M. M.

R. K. Shelton, L.-S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, Science 293, 1286 (2001).
[CrossRef] [PubMed]

Newbury, N. R.

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Reid, D. T.

Russell, P. St. J.

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Phys. Rev. Lett. 85, 2264 (2000).
[CrossRef] [PubMed]

Schibli, T. R.

J. Kim, T. R. Schibli, L. Matos, H. Byun, and F. X. Kärtner, in Joint Conference on Ultrafast Optics V and Applications of High Field and Short Wavelength Sources XI (Springer, 2005), paper M3-5.
[PubMed]

Scrinzi, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Shelton, R. K.

R. K. Shelton, L.-S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, Science 293, 1286 (2001).
[CrossRef] [PubMed]

Shimoda, K.

K. Shimoda, Jpn. J. Appl. Phys. 34, 3566 (1995).
[CrossRef]

Shverdin, M. Y.

S. N. Goda, M. Y. Shverdin, D. R. Walker, and S. E. Harris, Opt. Lett. 30, 1222 (2005).
[CrossRef] [PubMed]

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[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, Science 288, 635 (2000).
[CrossRef] [PubMed]

Sun, J. H.

Takada, H.

Thomann, I.

Torizuka, K.

Trebino, R.

D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Udem, Th.

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Phys. Rev. Lett. 85, 2264 (2000).
[CrossRef] [PubMed]

Uiberacker, M.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Wadsworth, W. J.

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Phys. Rev. Lett. 85, 2264 (2000).
[CrossRef] [PubMed]

Walker, D. R.

S. N. Goda, M. Y. Shverdin, D. R. Walker, and S. E. Harris, Opt. Lett. 30, 1222 (2005).
[CrossRef] [PubMed]

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef] [PubMed]

Walmsley, I. A.

Westerwalbesloh, Th.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Yakovlev, V.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Yavuz, D. D.

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef] [PubMed]

Ye, J.

R. K. Shelton, L.-S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, Science 293, 1286 (2001).
[CrossRef] [PubMed]

Yin, G. Y.

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef] [PubMed]

Yoshitomi, D.

Appl. Phys. Lett. (1)

Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, Appl. Phys. Lett. 83, 839 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. J. Kane and R. Trebino, IEEE J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Shimoda, Jpn. J. Appl. Phys. 34, 3566 (1995).
[CrossRef]

Opt. Commun. (1)

T. W. Hänsch, Opt. Commun. 80, 71 (1990).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. Lett. (2)

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, Phys. Rev. Lett. 85, 2264 (2000).
[CrossRef] [PubMed]

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef] [PubMed]

Science (3)

R. K. Shelton, L.-S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, Science 293, 1286 (2001).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Science 305, 1267 (2004).
[CrossRef] [PubMed]

Other (1)

J. Kim, T. R. Schibli, L. Matos, H. Byun, and F. X. Kärtner, in Joint Conference on Ultrafast Optics V and Applications of High Field and Short Wavelength Sources XI (Springer, 2005), paper M3-5.
[PubMed]

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 (5)

Fig. 1
Fig. 1

Schematic of the relative-phase measurements.

Fig. 2
Fig. 2

Calculated phase shifts of SHG and SFG with two thicknesses, when the phase-matching angle is 27°. The dashed curve shows the differences. The shaded areas represent the calculated intensity profiles.

Fig. 3
Fig. 3

Schematic layout of the experimental setup. PMT, photomultiplier tube; APD, avalanche photodiode; DCP, delay compensation plate; OAP, off-axis parabolic mirror.

Fig. 4
Fig. 4

(a) RF spectrum of out-of-loop beat signals in Measurement I (resolution 100 kHz ). (b) In-loop and out-of-loop phase noise spectra and rms integration.

Fig. 5
Fig. 5

Measured interference fringes (a) between SHG of 3 ω and SFG of 2 ω + 4 ω and (b) between 4 ω and SHG of 2 ω . The delay path lengths of (a) 3 ω and (b) 4 ω were changed. (c) Reconstructed field structure and (d) intensity profile of the synthesized waveform with the actual amplitudes (blue, solid curve) and the assumed equal amplitudes (red, dotted curve) of Fourier components, when the two delays are tuned at the arrowed position in (a) and (b).

Equations (2)

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

E ( t ) = n = 2 , 3 , 4 A n ( t ) exp [ i ( n ω t + φ n ) ] + c.c. ,
E ( t ) = n = 2 , 3 , 4 A n ( t ) exp [ i { n ω ( t + τ ) + α n } ] + c.c ..

Metrics