Abstract

We present what we believe to be a new version of spectral phase interferometry for direct electric field reconstruction (SPIDER) using only a single-phase and polarization controlled laser beam. Two narrow pulses and one broadband pulse are selected out of an ultrafast laser pulse by a polarization and phase control technique to generate second harmonic generation (SHG) signals, which are equivalent to a spectral shear interferogram in the conventional SPIDER method. The spectral phase of the broadband laser pulse is extracted analytically with double quadrature spectral interferometry (DQSI). An arbitrary spectral phase can be retrieved with great precision and compensated in situ at the sample position of a microscope. This new method requires no separate reference beam and is suitable for nonlinear optical microscopy with a phase controlled laser pulse.

© 2007 Optical Society of America

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2006

S.-H. Lim, A. G. Caster, and S. R. Leone, J. Phys. Chem. B 110, 5196 (2006).
[CrossRef] [PubMed]

J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, J. Photochem. Photobiol. A 180, 307 (2006).
[CrossRef]

B. von Vacano, T. Buckup, and M. Motzukus, Opt. Lett. 31, 1154 (2006).
[CrossRef] [PubMed]

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

2005

2004

2003

D. Oron, N. Dudovich, and Y. Silberberg, Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef] [PubMed]

2002

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

2001

1999

C. Iaconis and I. A. Walmsley, IEEE J. Quantum Electron. 35, 501 (1999).
[CrossRef]

1997

1995

Baum, P.

Brixner, T.

Buckup, T.

Caster, A. G.

S.-H. Lim, A. G. Caster, and S. R. Leone, J. Phys. Chem. B 110, 5196 (2006).
[CrossRef] [PubMed]

Cheriaux, G.

Dantus, M.

J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, J. Photochem. Photobiol. A 180, 307 (2006).
[CrossRef]

B. 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.

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

J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, J. Photochem. Photobiol. A 180, 307 (2006).
[CrossRef]

Dudovich, N.

D. Oron, N. Dudovich, and Y. Silberberg, Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef] [PubMed]

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

Gerber, G.

Gunn, J. M.

Iaconis, C.

C. Iaconis and I. A. Walmsley, IEEE J. Quantum Electron. 35, 501 (1999).
[CrossRef]

Joffre, M.

Leone, S. R.

S.-H. Lim, A. G. Caster, and S. R. Leone, J. Phys. Chem. B 110, 5196 (2006).
[CrossRef] [PubMed]

Lepetit, L.

Lim, S.-H.

S.-H. Lim, A. G. Caster, and S. R. Leone, J. Phys. Chem. B 110, 5196 (2006).
[CrossRef] [PubMed]

Lochbrunner, S.

Lozovoy, V. V.

J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, J. Photochem. Photobiol. A 180, 307 (2006).
[CrossRef]

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

Meshulach, D.

Motzukus, M.

Oron, D.

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

D. Oron, N. Dudovich, and Y. Silberberg, Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef] [PubMed]

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

Riedle, E.

Silberberg, Y.

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

D. Oron, N. Dudovich, and Y. Silberberg, Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef] [PubMed]

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

D. Yelin, D. Meshulach, and Y. Silberberg, Opt. Lett. 22, 1793 (1997).
[CrossRef]

Tal, E.

von Vacano, B.

Walmsley, I. A.

C. Iaconis and I. A. Walmsley, IEEE J. Quantum Electron. 35, 501 (1999).
[CrossRef]

Xu, B.

Yelin, D.

IEEE J. Quantum Electron.

C. Iaconis and I. A. Walmsley, IEEE J. Quantum Electron. 35, 501 (1999).
[CrossRef]

J. Opt. Soc. Am. B

J. Photochem. Photobiol. A

J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, J. Photochem. Photobiol. A 180, 307 (2006).
[CrossRef]

J. Phys. Chem. B

S.-H. Lim, A. G. Caster, and S. R. Leone, J. Phys. Chem. B 110, 5196 (2006).
[CrossRef] [PubMed]

Nature

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

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

D. Oron, N. Dudovich, and Y. Silberberg, Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Experimental setup: GR, grating; SLM, dual-bank liquid crystal spatial light modulator; OBJ, microscope objective lens; F, BG28 filter; SP, spectrometer. (b) Spectrum of the laser (top). Polarization (middle) and phase (bottom) masks used in the experiment.

Fig. 2
Fig. 2

(a) SHG spectra with different phases at Pr 1 ( ϕ p r = 0 , π 2 , π and 3 π 2 ). Each trace is displaced vertically for clarity. (b) Amplitude [ f ( ω ) ] and phase [ θ ( ω ) ] spectra of the cross term in Eq. (1) retrieved with Eqs. (2, 3).

Fig. 3
Fig. 3

(a) Spectral phase of the laser pulse at the microscope sample position before (thin curve) and after (thick curve) compressing the laser pulse by applying the compensating phase mask. Note the difference in the vertical scales. (b) Phase mask applied in the SLM (solid curve) and the retrieved spectral phase of the laser pulse by the single beam SPIDER (dot).

Equations (9)

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E S H G ( 1 ) ( ω + ω p + δ ω ) E 0 ( ω p + δ ω ) E 0 ( ω ) exp ( i ϕ ( ω ) + i ϕ p r ) ,
E S H G ( 2 ) ( ω + ω p ) E 0 ( ω p ) E 0 ( ω ) exp ( i ϕ ( ω ) ) ,
S ( ω + ω p ) = E S H G ( 1 ) ( ω + ω p ) + E S H G ( 2 ) ( ω + ω p ) 2 E 0 ( ω p + δ ω ) E 0 ( ω δ ω ) 2 + E 0 ( ω p ) E 0 ( ω ) 2 + f ( ω ) ( exp [ i ( θ ( ω ) ϕ p r ) ] + exp [ i ( θ ( ω ) ϕ p r ) ] ) ,
θ ( ω ) = tan 1 [ S ( ω + ω p , ϕ p r = π 2 ) S ( ω + ω p , ϕ p r = 3 π 2 ) S ( ω + ω p , ϕ p r = 0 ) S ( ω + ω p , ϕ p r = π ) ] ,
f ( ω ) = 1 4 ( S ( ϕ p r = 0 ) S ( ϕ p r = π ) ) 2 + ( S ( ϕ p r = π 2 ) S ( ϕ p r = 3 π 2 ) ) 2 .
ϕ ( ω 0 + n δ ω ) = ϕ ( ω 0 ) + k = 1 n θ ( ω 0 + k δ ω ) , where n is a positive integer ,
S = E S H G ( 1 ) + E S H G ( 2 ) + E b g r 2 = E S H G ( 1 ) 2 + E S H G ( 2 ) 2 + E b g r 2 + 2 Re [ E S H G ( 1 ) E S H G ( 2 ) * ] + 2 Re [ E S H G ( 1 ) E b g r * ] + 2 Re [ E S H G ( 2 ) E b g r * ] ,
S b g r ( 1 ) = E S H G ( 1 ) 2 + E b g r 2 + 2 Re [ E S H G ( 1 ) E b g r * ]
S b g r ( 2 ) = E S H G ( 2 ) 2 + E b g r 2 + 2 Re [ E S H G ( 2 ) E b g r * ] .

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