Abstract

We propose and implement a versatile scheme to analyze the phase structure of femtosecond pulses. It relies on second harmonic generation in combination with phase-sensitive χ(3)-current injection driven by two time-delayed portions of the emerging ω/2ω pulse pair. Most strikingly, the group velocity dispersions of both the ω and 2ω components can be unambiguously determined from a simple Fourier transformation of the resulting current interferogram. We test the concept for 45 fs pulses at 1.45 μm and directly compare it to second harmonic frequency resolved optical gating. By choosing appropriate frequency doublers and semiconductor detectors, the scheme is applicable to many wavelength regimes and to pulses as short as a few optical cycles.

© 2014 Optical Society of America

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References

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  1. D. J. Kane and R. Trebino, Opt. Lett. 18, 823 (1993).
    [CrossRef]
  2. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
    [CrossRef]
  3. C. Iaconis and I. A. Walmsley, Opt. Lett. 23, 792 (1998).
    [CrossRef]
  4. P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, Opt. Lett. 26, 932 (2001).
    [CrossRef]
  5. P. Baum, S. Lochbrunner, and E. Riedle, Opt. Lett. 29, 210 (2004).
    [CrossRef]
  6. A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
    [CrossRef]
  7. Y. Nomura, H. Shirai, and T. Fuji, Nat. Commun. 4, 2820 (2013).
    [CrossRef]
  8. R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, Phys. Rev. Lett. 76, 1703 (1996).
    [CrossRef]
  9. A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
    [CrossRef]
  10. E. Sidick, A. Dienes, and A. Knoesen, J. Opt. Soc. Am. B 12, 1713 (1995).
    [CrossRef]
  11. S. Thunich, C. Ruppert, A. W. Holleitner, and M. Betz, Opt. Lett. 36, 1791 (2011).
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    [CrossRef]
  13. Code for Retrieving a Pulse Intensity and Phase from Its FROG Trace, available from the Trebino group at http://frog.gatech.edu/code.html .
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    [CrossRef]
  15. M. Sheik-Bahae, Phys. Rev. B 60, 11257 (1999).
    [CrossRef]
  16. L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, Nat. Phys. 3, 632 (2007).
    [CrossRef]

2013 (1)

Y. Nomura, H. Shirai, and T. Fuji, Nat. Commun. 4, 2820 (2013).
[CrossRef]

2012 (1)

2011 (2)

S. Thunich, C. Ruppert, A. W. Holleitner, and M. Betz, Opt. Lett. 36, 1791 (2011).
[CrossRef]

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
[CrossRef]

2007 (1)

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, Nat. Phys. 3, 632 (2007).
[CrossRef]

2004 (1)

2001 (1)

1999 (2)

N. Laman, A. I. Shkrebtii, J. E. Sipe, and H. M. van Driel, Appl. Phys. Lett. 75, 2581 (1999).
[CrossRef]

M. Sheik-Bahae, Phys. Rev. B 60, 11257 (1999).
[CrossRef]

1998 (1)

1997 (2)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

1996 (1)

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, Phys. Rev. Lett. 76, 1703 (1996).
[CrossRef]

1995 (1)

1993 (1)

Atanasov, R.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, Phys. Rev. Lett. 76, 1703 (1996).
[CrossRef]

Azana, J.

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
[CrossRef]

Baum, P.

Betz, M.

Bristow, A. D.

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, Nat. Phys. 3, 632 (2007).
[CrossRef]

Chu, S. T.

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
[CrossRef]

Costa, L.

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, Nat. Phys. 3, 632 (2007).
[CrossRef]

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Dienes, A.

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Fuji, T.

Y. Nomura, H. Shirai, and T. Fuji, Nat. Commun. 4, 2820 (2013).
[CrossRef]

Gu, X.

Haché, A.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, Phys. Rev. Lett. 76, 1703 (1996).
[CrossRef]

Holleitner, A. W.

Hughes, J. L. P.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, Phys. Rev. Lett. 76, 1703 (1996).
[CrossRef]

Iaconis, C.

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

D. J. Kane and R. Trebino, Opt. Lett. 18, 823 (1993).
[CrossRef]

Kimmel, M.

Knoesen, A.

Kostoulas, Y.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

Krumbügel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Laman, N.

N. Laman, A. I. Shkrebtii, J. E. Sipe, and H. M. van Driel, Appl. Phys. Lett. 75, 2581 (1999).
[CrossRef]

Little, B. E.

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
[CrossRef]

Lochbrunner, S.

Lohrenz, J.

Morandotti, R.

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
[CrossRef]

Moss, D. J.

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
[CrossRef]

Nomura, Y.

Y. Nomura, H. Shirai, and T. Fuji, Nat. Commun. 4, 2820 (2013).
[CrossRef]

O’Shea, P.

Park, Y.

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
[CrossRef]

Pasquazi, A.

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
[CrossRef]

Peccianti, M.

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
[CrossRef]

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Riedle, E.

Ruppert, C.

Sheik-Bahae, M.

M. Sheik-Bahae, Phys. Rev. B 60, 11257 (1999).
[CrossRef]

Shirai, H.

Y. Nomura, H. Shirai, and T. Fuji, Nat. Commun. 4, 2820 (2013).
[CrossRef]

Shkrebtii, A. I.

N. Laman, A. I. Shkrebtii, J. E. Sipe, and H. M. van Driel, Appl. Phys. Lett. 75, 2581 (1999).
[CrossRef]

Sidick, E.

Sipe, J. E.

N. Laman, A. I. Shkrebtii, J. E. Sipe, and H. M. van Driel, Appl. Phys. Lett. 75, 2581 (1999).
[CrossRef]

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, Phys. Rev. Lett. 76, 1703 (1996).
[CrossRef]

Spasenovic, M.

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, Nat. Phys. 3, 632 (2007).
[CrossRef]

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Thunich, S.

Trebino, R.

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, Opt. Lett. 26, 932 (2001).
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

D. J. Kane and R. Trebino, Opt. Lett. 18, 823 (1993).
[CrossRef]

van Driel, H. M.

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, Nat. Phys. 3, 632 (2007).
[CrossRef]

N. Laman, A. I. Shkrebtii, J. E. Sipe, and H. M. van Driel, Appl. Phys. Lett. 75, 2581 (1999).
[CrossRef]

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, Phys. Rev. Lett. 76, 1703 (1996).
[CrossRef]

Walmsley, I. A.

Appl. Phys. Lett. (1)

N. Laman, A. I. Shkrebtii, J. E. Sipe, and H. M. van Driel, Appl. Phys. Lett. 75, 2581 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Commun. (1)

Y. Nomura, H. Shirai, and T. Fuji, Nat. Commun. 4, 2820 (2013).
[CrossRef]

Nat. Photonics (1)

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azana, and D. J. Moss, Nat. Photonics 5, 618 (2011).
[CrossRef]

Nat. Phys. (1)

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, Nat. Phys. 3, 632 (2007).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. B (1)

M. Sheik-Bahae, Phys. Rev. B 60, 11257 (1999).
[CrossRef]

Phys. Rev. Lett. (2)

R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, Phys. Rev. Lett. 76, 1703 (1996).
[CrossRef]

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Other (1)

Code for Retrieving a Pulse Intensity and Phase from Its FROG Trace, available from the Trebino group at http://frog.gatech.edu/code.html .

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Figures (4)

Fig. 1.
Fig. 1.

Experimental scheme: A 0.5 mm thick BBO generates the second harmonic (blue). An interferometer controls the delay τ of the fundamental portion Eω(2) (red) relative to a pulse pair composed of the remaining fundamental (Eω(1)) and the second harmonic E2ω. The emergent beam is focused onto a LT-GaAs sample with gold electrodes spaced 10 μm apart. A lock-in amplifier measures the photoresponse. Inset: geometry of the contacts and the optical polarizations.

Fig. 2.
Fig. 2.

(a) Current interferogram I(τ) recorded for the 45 fs pulse at 1.45 μm. (b) FFT amplitude of I(τ). ω0 and 2ω0 are the center frequencies of the ω and 2ω pulses.

Fig. 3.
Fig. 3.

(a) Theoretical phase curvature Dω0 as a function of the GVD ϕ(ω0). Solid line: expectation Dω0=(8/9)ϕ(ω0) valid for long pulses (tp). Dashed lines: full result for two exemplary tp,ω assuming ϕ(2ω0)=(1/2)ϕ(ω0) and tp,2ω=(1/2)tp,ω. (b) Spectral phases of the FFT of I(τ)-traces for pulses of different chirp. Positive (negative) chirp is introduced by 5.3 mm SF11 (10 mm Infrasil). The lines are polynomial fits.

Fig. 4.
Fig. 4.

Results for the GVD ϕ(ω0) measured by the coherent control technique (red symbols) and by FROG (blue symbols) for different chirp configurations. The abscissa is calibrated by the Sellmeier equations for SF11 and Infrasil. The dashed line shows the theoretical expectation assuming that the unaltered OPA output has a residual GVD of ϕ(ω0)=50fs2.

Equations (7)

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J⃗˙=ηE⃗ω*E⃗ω*E⃗2ω,
J˙x=ηxxxx[Eω(2)(t)Eω(2)(t)]*E2ω(t+τ),
J˙y=ηyyxx[Eω(1)(t+τ)Eω(2)(t)]*E2ω(t+τ).
I^x(ω)[E^ω(2)(ω)E^ω(2)(ω)]*·E^2ω(ω),
I^y(ω)(E^ω(2)(ω))*·[(E^ω(1)(ω))*E^2ω(ω)].
Dω0=109ϕ(ω0)49ϕ(2ω0),
D2ω0=12ϕ(ω0)ϕ(2ω0).

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