Abstract

It has previously been reported that a peak at the spectral position of the second harmonic of an excitation laser can be generated in an inversion-symmetric medium in the regime of extreme nonlinear optics and that this peak may be exploited to measure the carrier-envelope phase of the excitation pulse. Here we revisit this phenomenon with regard to reverse engineering the carrier-envelope phase and demonstrate that the thin-film thickness and the incident field can have a drastic influence on pulse propagation, and so the reverse engineering would likely fail.

© 2006 Optical Society of America

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References

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  1. G. L. Lamb, Jr., Rev. Mod. Phys. 43, 99 (1971).
    [CrossRef]
  2. S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967).
    [CrossRef]
  3. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1995).
  4. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).
  5. I. I. Rabi, Phys. Rev. 51, 652 (1937).
    [CrossRef]
  6. I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, Phys. Rev. 53, 318 (1938).
    [CrossRef]
  7. S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
    [CrossRef] [PubMed]
  8. S. Hughes, Phys. Rev. Lett. 81, 3363 (1998).
    [CrossRef]
  9. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 87, 057401 (2001).
    [CrossRef] [PubMed]
  10. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 89, 127401 (2002).
    [CrossRef] [PubMed]
  11. T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 90, 217404 (2003).
    [CrossRef] [PubMed]
  12. See, e.g., M. Mehendale, S. A. Mitchell, J.-P. Likforman, D. M. Villeneuve, and P. B. Corkum, Opt. Lett. 25, 1672 (2000).
  13. See, e.g., 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).
    [PubMed]
  14. R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
    [CrossRef] [PubMed]
  15. See, e.g., K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, J. Appl. Phys. 87, 7820 (2000).
  16. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  17. This pulse area corresponds to (is created with) a peak incident electric field of 35GV/m in vacuum.

2003 (1)

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

2002 (1)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

2001 (1)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

2000 (3)

See, e.g., 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).
[PubMed]

See, e.g., K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, J. Appl. Phys. 87, 7820 (2000).

See, e.g., M. Mehendale, S. A. Mitchell, J.-P. Likforman, D. M. Villeneuve, and P. B. Corkum, Opt. Lett. 25, 1672 (2000).

1998 (1)

S. Hughes, Phys. Rev. Lett. 81, 3363 (1998).
[CrossRef]

1995 (1)

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
[CrossRef] [PubMed]

1994 (1)

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[CrossRef] [PubMed]

1971 (1)

G. L. Lamb, Jr., Rev. Mod. Phys. 43, 99 (1971).
[CrossRef]

1967 (1)

S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967).
[CrossRef]

1938 (1)

I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, Phys. Rev. 53, 318 (1938).
[CrossRef]

1937 (1)

I. I. Rabi, Phys. Rev. 51, 652 (1937).
[CrossRef]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1995).

Aoyama, M.

See, e.g., K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, J. Appl. Phys. 87, 7820 (2000).

Arnold, J. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
[CrossRef] [PubMed]

Corkum, P. B.

Cundiff, S. T.

See, e.g., 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).
[PubMed]

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[CrossRef] [PubMed]

Diddams, S. A.

See, e.g., 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).
[PubMed]

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1995).

Feldmann, J.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[CrossRef] [PubMed]

Göbel, E. O.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[CrossRef] [PubMed]

Gogny, D. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
[CrossRef] [PubMed]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Hahn, E. L.

S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967).
[CrossRef]

Hall, J. L.

See, e.g., 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).
[PubMed]

Haug, H.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).

Horie, M.

See, e.g., K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, J. Appl. Phys. 87, 7820 (2000).

Hughes, S.

S. Hughes, Phys. Rev. Lett. 81, 3363 (1998).
[CrossRef]

Igasaki, Y.

See, e.g., K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, J. Appl. Phys. 87, 7820 (2000).

Ino, Ch.

See, e.g., K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, J. Appl. Phys. 87, 7820 (2000).

Jones, D. J.

See, e.g., 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).
[PubMed]

Kärtner, F. X.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

Knorr, A.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[CrossRef] [PubMed]

Koch, S. W.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[CrossRef] [PubMed]

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).

Kusch, P.

I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, Phys. Rev. 53, 318 (1938).
[CrossRef]

Lamb, G. L.

G. L. Lamb, Jr., Rev. Mod. Phys. 43, 99 (1971).
[CrossRef]

Likforman, J.-P.

McCall, S. L.

S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967).
[CrossRef]

Mehendale, M.

Millman, S.

I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, Phys. Rev. 53, 318 (1938).
[CrossRef]

Mitchell, S. A.

Morgner, U.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

Mücke, O. D.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

Nickel, H.

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[CrossRef] [PubMed]

Postava, K.

See, e.g., K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, J. Appl. Phys. 87, 7820 (2000).

Rabi, I. I.

I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, Phys. Rev. 53, 318 (1938).
[CrossRef]

I. I. Rabi, Phys. Rev. 51, 652 (1937).
[CrossRef]

Ranka, J. K.

See, e.g., 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).
[PubMed]

Stentz, A.

See, e.g., 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).
[PubMed]

Sueki, H.

See, e.g., K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, J. Appl. Phys. 87, 7820 (2000).

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Tritschler, T.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

Villeneuve, D. M.

Wegener, M.

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

Windeler, R. S.

See, e.g., 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).
[PubMed]

Yamaguchi, T.

See, e.g., K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, J. Appl. Phys. 87, 7820 (2000).

Zacharias, J. R.

I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, Phys. Rev. 53, 318 (1938).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

See, e.g., K. Postava, H. Sueki, M. Aoyama, T. Yamaguchi, Ch. Ino, Y. Igasaki, and M. Horie, J. Appl. Phys. 87, 7820 (2000).

Opt. Lett. (1)

Phys. Rev. (2)

I. I. Rabi, Phys. Rev. 51, 652 (1937).
[CrossRef]

I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, Phys. Rev. 53, 318 (1938).
[CrossRef]

Phys. Rev. A (1)

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (6)

S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967).
[CrossRef]

S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Phys. Rev. Lett. 73, 1178 (1994).
[CrossRef] [PubMed]

S. Hughes, Phys. Rev. Lett. 81, 3363 (1998).
[CrossRef]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 87, 057401 (2001).
[CrossRef] [PubMed]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 89, 127401 (2002).
[CrossRef] [PubMed]

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, Phys. Rev. Lett. 90, 217404 (2003).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

G. L. Lamb, Jr., Rev. Mod. Phys. 43, 99 (1971).
[CrossRef]

Science (1)

See, e.g., 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).
[PubMed]

Other (4)

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1995).

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

This pulse area corresponds to (is created with) a peak incident electric field of 35GV/m in vacuum.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the light–matter geometry. An ultrashort several-cycle optical pulse comes in from the left and excites a nonlinear thin film of thickness t, where the film and substrate have optical dielectric constants, ϵ f and ϵ s , respectively.

Fig. 2
Fig. 2

Contour plot of the transmitted THG in disguise of SHG near the resonance energy of the TLA ensemble ( 3.3 eV ) . Panels (a)–(f) depict various film thicknesses of the nonlinear medium for two different substrate optical constants and a fixed input intensity from a 5 fs pulse with a central energy at 1.6 eV . The phase shown is the CEP π 2 .

Fig. 3
Fig. 3

Contour plots (a)–(d) show the transmitted nonlinear field near the energy gap for different input intensities and two different substrate optical constants; the thickness of the nonlinear film is fixed at 100 nm .

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