Abstract

In many ultrafast contexts, a collinear pulse-shaping frequency-resolved optical gating (FROG) technique is desired. Some applicable techniques already exist, but they suffer from one of two issues: either they require many time points to allow for Fourier filtering, or they do not yield a traditional FROG trace. To overcome these issues, we propose and demonstrate a fast new phase-cycled FROG technique using a pulse shaper.

© 2013 Optical Society of America

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References

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2012

2010

2009

S.-H. Shim and M. T. Zanni, Phys. Chem. Chem. Phys. 11, 748 (2009).
[CrossRef]

2008

2007

2006

2005

2004

2003

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, Science 300, 1553 (2003).
[CrossRef]

D. Goswami, Phys. Rep. 374, 385 (2003).
[CrossRef]

I. Pastirk, J. Dela Cruz, K. Walowicz, V. Lozovoy, and M. Dantus, Opt. Express 11, 1695 (2003).
[CrossRef]

2000

L. Gallmann, G. Steinmeyer, D. H. Sutter, N. Matuschek, and U. Keller, Opt. Lett. 25, 269 (2000).
[CrossRef]

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

1998

1997

1993

W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
[CrossRef]

Akturk, S.

Amat-Roldán, I.

Artigas, D.

Bartels, R.

Beaurepaire, E.

Ben Yoo, S. J.

Beutter, M.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Cao, J.

Carriles, R.

Chandler, E. V.

Cormack, I. G.

Crozatier, V.

Dahleh, M.

W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
[CrossRef]

Dantus, M.

Débarre, D.

Dela Cruz, J.

Field, J. J.

Fontaine, N. K.

Forget, N.

Fuller, F. D.

Gabolde, P.

Gallmann, L.

Goswami, D.

D. Goswami, Phys. Rep. 374, 385 (2003).
[CrossRef]

Gu, X.

Gualda, E. J.

Heritage, J. P.

Hoover, E. E.

Hughes, T. E.

Iaconis, C.

Joffre, M.

Keller, U.

Keusters, D.

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, Science 300, 1553 (2003).
[CrossRef]

Kleinfeld, D.

Kolner, B. H.

Lewis, K. L. M.

Lochbrunner, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Loza-Alvarez, P.

Lozovoy, V.

Lozovoy, V. V.

Martin, J.-L.

Matuschek, N.

Myers, J. A.

Ogilvie, J. P.

Okamoto, K.

Oksenhendler, T.

Pastirk, I.

Piel, J.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

T. Wilhelm, J. Piel, and E. Riedle, Opt. Lett. 22, 1494 (1997).
[CrossRef]

Rabitz, H.

W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
[CrossRef]

Ratner, J.

Riedle, E.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

T. Wilhelm, J. Piel, and E. Riedle, Opt. Lett. 22, 1494 (1997).
[CrossRef]

Schenkl, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Scott, R. P.

Sheetz, K. E.

Shim, S.-H.

S.-H. Shim and M. T. Zanni, Phys. Chem. Chem. Phys. 11, 748 (2009).
[CrossRef]

Solinas, X.

Sporlein, S.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Squier, J. A.

Steinmeyer, G.

Stibenz, G.

Sutter, D. H.

Suzaki, Y.

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, Science 300, 1553 (2003).
[CrossRef]

Sylvester, A. W.

Tekavec, P. F.

Tian, P.

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, Science 300, 1553 (2003).
[CrossRef]

Tillo, S. E.

Trebino, R.

Walmsley, I. A.

Walowicz, K.

Warren, W. S.

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, Science 300, 1553 (2003).
[CrossRef]

W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
[CrossRef]

Weiner, A. M.

A. M. Weiner, Media (Wiley, 2009).

Wilhelm, T.

Wong, T. C.

Zanni, M. T.

S.-H. Shim and M. T. Zanni, Phys. Chem. Chem. Phys. 11, 748 (2009).
[CrossRef]

Zinth, W.

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

Appl. Phys. B

E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sporlein, and W. Zinth, Appl. Phys. B 71, 457 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Chem. Chem. Phys.

S.-H. Shim and M. T. Zanni, Phys. Chem. Chem. Phys. 11, 748 (2009).
[CrossRef]

Phys. Rep.

D. Goswami, Phys. Rep. 374, 385 (2003).
[CrossRef]

Science

W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
[CrossRef]

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, Science 300, 1553 (2003).
[CrossRef]

Other

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, 2002) p. 456.

A. M. Weiner, Media (Wiley, 2009).

T. C. Wong and R. Trebino, “Trebino-group code,” http://frog.gatech.edu/code.html .

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Figures (3)

Fig. 1.
Fig. 1.

(a) Temporal intensity and phase of the simulated test pulse, which is temporally a double pulse with significant quadratic and cubic spectral phase. (b) Spectral intensity and phase of the simulated test pulse. (c) Simulated standard SHG-FROG trace of the test pulse. (d) Simulated phase-cycled collinear SHG-FROG trace of the test pulse, showing excellent agreement with (c).

Fig. 2.
Fig. 2.

(a–d) Interferometric FROG traces of the simulated test pulse with 0, π/2, π, and 3π/2 relative carrier-envelope phase shifts, respectively, zoomed in along τ to show the interferometric modulation. (e) Sum of the first two phase shifts showing removal of the second-harmonic frequency. (f) Sum of all four phase shifts, showing removal of all modulation along τ; the modulation along the detection axis is part of the traditional SHG-FROG trace (see Fig. 1).

Fig. 3.
Fig. 3.

(a) Diagram of experimental setup for the new phase-cycled technique. (b) Measured SHG-FROG trace using the technique. (c) Reconstructed SHG-FROG trace using the standard FROG algorithm; the reconstruction error is low at G=0.057 [23]. (d) Measured temporal intensity and phase showing a 31.6 fs pulse duration FWHM; linear component of temporal phase subtracted. (e) Measured spectral intensity and phase; linear component of spectral phase subtracted.

Equations (6)

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I(ω,τ,ϕ)=|[E(t)+E(tτ)exp(iϕ)]2exp(iωt)dt|2.
ESH(Δω)=E2(t)exp(iΔωt)dt.
EFROG(Δω,τ)=E(t)E(tτ)exp(iΔωt)dt.
I(Δω,τ,ϕ)=|[1+exp(2iϕi(2ω0+Δω)τ)]ESH(Δω)+2exp(iϕiω0τ)EFROG(Δω,τ)|2.
I(Δω,τ,ϕ)=2|ESH(Δω)|2+4|EFROG(Δω,τ)|2+8cos[ϕ(ω0+Δω/2)τ]×Re[EFROG(Δω,τ)ESH*(Δω)exp(iΔωτ/2)]+2cos[2ϕ(2ω0+Δω)τ]|ESH(Δω)|2.
I(Δω,τ,0)+I(Δω,τ,π/2)+I(Δω,τ,π)+I(Δω,τ,3π/2)=8|ESH(Δω)|2+16|EFROG(Δω,τ)|2.

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