Abstract

We report a new version of spectral phase interferometry for direct electric field reconstruction (SPIDER) requiring only a single phase-shaped laser beam. A narrowband probe pulse is selected out of a broadband ultrafast laser pulse by a phase pulse-shaping technique and mixed with the original broadband pulse to generate a second-harmonic generation (SHG) signal. Using another SHG signal solely generated by the broadband pulse as a local oscillator, the spectral phase of the broadband laser pulse can be analytically retrieved by a combination of double-quadrature spectral interferometry and homodyne optical technique for SPIDER (HOT SPIDER). An arbitrary spectral phase at the sample position of a microscope can be compensated with a precision of 0.05rad over the FWHM of the laser spectrum. It is readily applicable to a nonlinear microscopy technique with a phase-controlled broadband laser pulse.

© 2008 Optical Society of America

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References

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  1. D. Oron, E. Tal, and Y. Silberberg, Opt. Express 13, 1468 (2005).
    [CrossRef] [PubMed]
  2. P. Xi, Y. Andegeko, L. R. Weisel, V. V. Lozovoy, and M. Dantus, Opt. Commun. 281, 1841 (2008).
    [CrossRef]
  3. N. Dudovich, D. Oron, and Y. Silberberg, Nature 418, 512 (2002).
    [CrossRef] [PubMed]
  4. B.-C. Chen and S.-H. Lim, J. Phys. Chem. B 112, 3653 (2008).
    [CrossRef] [PubMed]
  5. B. W. Xu, J. M. Gunn, J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, J. Opt. Soc. Am. B 23, 750 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. Here we use arctan for clarity of the discussion. In the experiment, we transformed the numerator and denominator inside the arctan term in Eqs. (2) and (3) into the polar coordinate to retrieve the phase.

2008 (3)

P. Xi, Y. Andegeko, L. R. Weisel, V. V. Lozovoy, and M. Dantus, Opt. Commun. 281, 1841 (2008).
[CrossRef]

B.-C. Chen and S.-H. Lim, J. Phys. Chem. B 112, 3653 (2008).
[CrossRef] [PubMed]

V. V. Lozovoy, B. Xu, Y. Coello, and M. Dantus, Opt. Express 16, 592597 (2008).
[CrossRef]

2007 (1)

2006 (2)

2005 (1)

2003 (1)

2002 (1)

N. Dudovich, D. Oron, and Y. Silberberg, Nature 418, 512 (2002).
[CrossRef] [PubMed]

2001 (1)

1998 (1)

1995 (1)

Andegeko, Y.

P. Xi, Y. Andegeko, L. R. Weisel, V. V. Lozovoy, and M. Dantus, Opt. Commun. 281, 1841 (2008).
[CrossRef]

Buckup, T.

Chen, B.-C.

Chériaux, G.

Coello, Y.

V. V. Lozovoy, B. Xu, Y. Coello, and M. Dantus, Opt. Express 16, 592597 (2008).
[CrossRef]

Dantus, M.

V. V. Lozovoy, B. Xu, Y. Coello, and M. Dantus, Opt. Express 16, 592597 (2008).
[CrossRef]

P. Xi, Y. Andegeko, L. R. Weisel, V. V. Lozovoy, and M. Dantus, Opt. Commun. 281, 1841 (2008).
[CrossRef]

B. W. Xu, J. M. Gunn, J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, J. Opt. Soc. Am. B 23, 750 (2006).
[CrossRef]

Dela Cruz, J. M.

Dorrer, C.

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, Nature 418, 512 (2002).
[CrossRef] [PubMed]

Gunn, J. M.

Herzog, R.

Iaconis, C.

Joffre, M.

Kaplan, D.

Lepetit, L.

Lim, S.-H.

Londero, P.

Lozovoy, V. V.

V. V. Lozovoy, B. Xu, Y. Coello, and M. Dantus, Opt. Express 16, 592597 (2008).
[CrossRef]

P. Xi, Y. Andegeko, L. R. Weisel, V. V. Lozovoy, and M. Dantus, Opt. Commun. 281, 1841 (2008).
[CrossRef]

B. W. Xu, J. M. Gunn, J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, J. Opt. Soc. Am. B 23, 750 (2006).
[CrossRef]

Monmayrant, A.

Motzkus, M.

Oksenhendler, T.

Oron, D.

Silberberg, Y.

Tal, E.

Tournois, P.

von Vacano, B.

Walmsley, I. A.

Weisel, L. R.

P. Xi, Y. Andegeko, L. R. Weisel, V. V. Lozovoy, and M. Dantus, Opt. Commun. 281, 1841 (2008).
[CrossRef]

Xi, P.

P. Xi, Y. Andegeko, L. R. Weisel, V. V. Lozovoy, and M. Dantus, Opt. Commun. 281, 1841 (2008).
[CrossRef]

Xu, B.

V. V. Lozovoy, B. Xu, Y. Coello, and M. Dantus, Opt. Express 16, 592597 (2008).
[CrossRef]

Xu, B. W.

J. Opt. Soc. Am. B (2)

J. Phys. Chem. B (1)

B.-C. Chen and S.-H. Lim, J. Phys. Chem. B 112, 3653 (2008).
[CrossRef] [PubMed]

Nature (1)

N. Dudovich, D. Oron, and Y. Silberberg, Nature 418, 512 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. Xi, Y. Andegeko, L. R. Weisel, V. V. Lozovoy, and M. Dantus, Opt. Commun. 281, 1841 (2008).
[CrossRef]

Opt. Express (2)

D. Oron, E. Tal, and Y. Silberberg, Opt. Express 13, 1468 (2005).
[CrossRef] [PubMed]

V. V. Lozovoy, B. Xu, Y. Coello, and M. Dantus, Opt. Express 16, 592597 (2008).
[CrossRef]

Opt. Lett. (5)

Other (1)

Here we use arctan for clarity of the discussion. In the experiment, we transformed the numerator and denominator inside the arctan term in Eqs. (2) and (3) into the polar coordinate to retrieve the phase.

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Figures (2)

Fig. 1
Fig. 1

(a) (Top) spectrum of the laser and (bottom) phase mask used in the experiment. (b) Two SHG components from the laser pulse with the phase mask in (a).

Fig. 2
Fig. 2

(a) Measured SHG spectra with the probe phase ( ϕ pr ) of 0, π 2 , π, and π 2 . The probe wavelength is 778 nm . Each trace is vertically displaced for clarity. (b) Spectral phase of the laser pulse at the microscope sample position before (thin curve) and after (thick curve with error bars) the pulse compression. Note the difference in the vertical scales.

Equations (7)

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E 0 ( ω ) = E h ( ω ) + E pr ( ω ) ,
E SHG ( ω ) d Ω E 0 ( ω Ω ) E 0 ( Ω ) = d Ω [ E h ( ω Ω ) + E pr ( ω Ω ) ] [ E h ( Ω ) + E pr ( Ω ) ] = d Ω [ E h ( ω Ω ) + E 0 ( ω pr ) δ ( ω Ω ω pr ) ] × [ E h ( Ω ) + E 0 ( ω pr ) δ ( Ω ω pr ) ] = E h ( ω Ω ) E h ( Ω ) d Ω + 2 E 0 ( ω pr ) E h ( ω ω pr ) + ( E 0 ( ω pr ) ) 2 δ ( ω 2 ω pr ) E SHG LO ( ω ) + E SHG ( 1 ) ( ω ) + ( E 0 ( ω pr ) ) 2 δ ( ω 2 ω pr ) ,
S ( 1 ) ( ω ) = E SHG LO ( ω ) + E SHG ( 1 ) ( ω ) 2 = E SHG LO ( ω ) 2 + E SHG ( 1 ) ( ω ) 2 + 2 E SHG LO ( ω ) E SHG ( 1 ) ( ω ) cos ( ϕ LO ( ω ) ϕ pr ϕ ( ω ω pr ) ) ,
ϕ LO ( ω ) ϕ ( ω ω pr ) = tan 1 [ S ( 1 ) ( ω , ϕ pr = π 2 ) S ( 1 ) ( ω , ϕ pr = π 2 ) S ( 1 ) ( ω , ϕ pr = 0 ) S ( 1 ) ( ω , ϕ pr = π ) ] ,
ϕ LO ( ω ) ϕ ( ω ω pr δ ω ) = tan 1 [ S ( 2 ) ( ω , ϕ pr = π 2 ) S ( 2 ) ( ω , ϕ pr = π 2 ) S ( 2 ) ( ω , ϕ pr = 0 ) S ( 2 ) ( ω , ϕ pr = π ) ] ,
ϕ ( ω ω pr ) ϕ ( ω ω pr δ ω ) = tan 1 [ S ( 2 ) ( ω , ϕ pr = π 2 ) S ( 2 ) ( ω , ϕ pr = π 2 ) S ( 2 ) ( ω , ϕ pr = 0 ) S ( 2 ) ( ω , ϕ pr = π ) ] tan 1 [ S ( 1 ) ( ω , ϕ pr = π 2 ) S ( 1 ) ( ω , ϕ pr = π 2 ) S ( 1 ) ( ω , ϕ pr = 0 ) S ( 1 ) ( ω , ϕ pr = π ) ] θ ( ω ω pr ) .
ϕ ( ω 0 + n δ ω ) = ϕ ( ω 0 ) + k = 1 n θ ( ω 0 + k δ ω ) ,

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