Abstract

The properties of harmonic generation with temporally focused ultrashort pulses are explored both theoretically and experimentally. Analyzing the phase-matching conditions for harmonic generation we find a correspondence between temporal focusing and spatial focusing along one dimension. In particular, temporally focused pulses experience a π phase shift in passing through the temporal focus, similar to the Guoy phase shift experienced by spatially focused beams. This correspondence is confirmed by measurements of third-harmonic generation induced by temporally focused pulses.

© 2005 Optical Society of America

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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]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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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]
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    [CrossRef]

2005 (3)

2004 (1)

2002 (3)

J.-X. Cheng and X. S. Xie, "Green's function formulation for third-harmonic generation microscopy," J. Opt. Soc. Am. B 19, 1604-1609 (2002).
[CrossRef]

N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy," Nature 418, 512-514 (2002).
[CrossRef] [PubMed]

J. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, "Laser-scanning coherent anti-Stokes Raman scattering microscopy and applications to cell biology," Biophys. J. 83, 502-509 (2002).
[CrossRef] [PubMed]

2001 (1)

E. O. Potma, W. P. de Boeij, P. J. M. van Haastert, and D. A. Wiersma, "Real-time visualization of intracellular hydrodynamics in single living cells," Proc. Natl. Acad. Sci. U.S.A. 98, 1577-1582 (2001).
[CrossRef] [PubMed]

2000 (2)

D. Yelin and Y. Silberberg, "Third-harmonic microscopy in biology," Microscopy and Analysis 80, 15-18 (2000).

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

1999 (2)

D. Yelin and Y. Silberberg, "Laser scanning third-harmonic-generation microscopy in biology," Opt. Express 5, 169-175 (1999).
[CrossRef] [PubMed]

A. Zumbusch, G. R. Holtom, and X. S. Xie, "Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering," Phys. Rev. Lett. 82, 4142-4145 (1999).
[CrossRef]

1998 (2)

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D-microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
[CrossRef]

J. A. Squier, M. Muller, G. J. Brakenhoff, and K. R. Wilson, "Third harmonic generation microscopy," Opt. Express 3, 315-324 (1998).
[CrossRef] [PubMed]

1997 (2)

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, "Measuring serotonin distribution in live cells with three-photon excitation," Science 275, 530-532 (1997).
[CrossRef] [PubMed]

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, "Nonlinear scanning laser microscopy by third harmonic generation," Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

1996 (1)

G. Peleg, A. Lewis, O. Bouevitch, L. Loew, D. Parnas, and M. Linial, "Gigantic optical non-linearities from nanoparticle-enhanced molecular probes with potential for selectively imaging the structure and physiology of nanometric regions in cellular systems," Bioimaging 4, 215-224 (1996).
[CrossRef]

1990 (1)

W. Denk, J. H. Stricker, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Barad, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, "Nonlinear scanning laser microscopy by third harmonic generation," Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

Bouevitch, O.

G. Peleg, A. Lewis, O. Bouevitch, L. Loew, D. Parnas, and M. Linial, "Gigantic optical non-linearities from nanoparticle-enhanced molecular probes with potential for selectively imaging the structure and physiology of nanometric regions in cellular systems," Bioimaging 4, 215-224 (1996).
[CrossRef]

Boyd, R.

R. Boyd, Nonlinear Optics (Academic, 1992).

Brakenhoff, G. J.

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D-microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
[CrossRef]

J. A. Squier, M. Muller, G. J. Brakenhoff, and K. R. Wilson, "Third harmonic generation microscopy," Opt. Express 3, 315-324 (1998).
[CrossRef] [PubMed]

Cheng, J.

J. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, "Laser-scanning coherent anti-Stokes Raman scattering microscopy and applications to cell biology," Biophys. J. 83, 502-509 (2002).
[CrossRef] [PubMed]

Cheng, J.-X.

de Boeij, W. P.

E. O. Potma, W. P. de Boeij, P. J. M. van Haastert, and D. A. Wiersma, "Real-time visualization of intracellular hydrodynamics in single living cells," Proc. Natl. Acad. Sci. U.S.A. 98, 1577-1582 (2001).
[CrossRef] [PubMed]

Denk, W.

W. Denk, J. H. Stricker, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy," Nature 418, 512-514 (2002).
[CrossRef] [PubMed]

Durst, M.

Eisenberg, H.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, "Nonlinear scanning laser microscopy by third harmonic generation," Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

Holtom, G. R.

A. Zumbusch, G. R. Holtom, and X. S. Xie, "Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering," Phys. Rev. Lett. 82, 4142-4145 (1999).
[CrossRef]

Horowitz, M.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, "Nonlinear scanning laser microscopy by third harmonic generation," Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

Jia, Y. K.

J. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, "Laser-scanning coherent anti-Stokes Raman scattering microscopy and applications to cell biology," Biophys. J. 83, 502-509 (2002).
[CrossRef] [PubMed]

Lewis, A.

G. Peleg, A. Lewis, O. Bouevitch, L. Loew, D. Parnas, and M. Linial, "Gigantic optical non-linearities from nanoparticle-enhanced molecular probes with potential for selectively imaging the structure and physiology of nanometric regions in cellular systems," Bioimaging 4, 215-224 (1996).
[CrossRef]

Linial, M.

G. Peleg, A. Lewis, O. Bouevitch, L. Loew, D. Parnas, and M. Linial, "Gigantic optical non-linearities from nanoparticle-enhanced molecular probes with potential for selectively imaging the structure and physiology of nanometric regions in cellular systems," Bioimaging 4, 215-224 (1996).
[CrossRef]

Loew, L.

G. Peleg, A. Lewis, O. Bouevitch, L. Loew, D. Parnas, and M. Linial, "Gigantic optical non-linearities from nanoparticle-enhanced molecular probes with potential for selectively imaging the structure and physiology of nanometric regions in cellular systems," Bioimaging 4, 215-224 (1996).
[CrossRef]

Maiti, S.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, "Measuring serotonin distribution in live cells with three-photon excitation," Science 275, 530-532 (1997).
[CrossRef] [PubMed]

Muller, M.

J. A. Squier, M. Muller, G. J. Brakenhoff, and K. R. Wilson, "Third harmonic generation microscopy," Opt. Express 3, 315-324 (1998).
[CrossRef] [PubMed]

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D-microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
[CrossRef]

Oron, D.

Parnas, D.

G. Peleg, A. Lewis, O. Bouevitch, L. Loew, D. Parnas, and M. Linial, "Gigantic optical non-linearities from nanoparticle-enhanced molecular probes with potential for selectively imaging the structure and physiology of nanometric regions in cellular systems," Bioimaging 4, 215-224 (1996).
[CrossRef]

Peleg, G.

G. Peleg, A. Lewis, O. Bouevitch, L. Loew, D. Parnas, and M. Linial, "Gigantic optical non-linearities from nanoparticle-enhanced molecular probes with potential for selectively imaging the structure and physiology of nanometric regions in cellular systems," Bioimaging 4, 215-224 (1996).
[CrossRef]

Potma, E. O.

E. O. Potma, W. P. de Boeij, P. J. M. van Haastert, and D. A. Wiersma, "Real-time visualization of intracellular hydrodynamics in single living cells," Proc. Natl. Acad. Sci. U.S.A. 98, 1577-1582 (2001).
[CrossRef] [PubMed]

Shear, J. B.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, "Measuring serotonin distribution in live cells with three-photon excitation," Science 275, 530-532 (1997).
[CrossRef] [PubMed]

Silberberg, Y.

Squier, J.

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D-microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
[CrossRef]

Squier, J. A.

Stricker, J. H.

W. Denk, J. H. Stricker, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Tal, E.

van Haastert, P. J. M.

E. O. Potma, W. P. de Boeij, P. J. M. van Haastert, and D. A. Wiersma, "Real-time visualization of intracellular hydrodynamics in single living cells," Proc. Natl. Acad. Sci. U.S.A. 98, 1577-1582 (2001).
[CrossRef] [PubMed]

van Howe, J.

Webb, W. W.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, "Measuring serotonin distribution in live cells with three-photon excitation," Science 275, 530-532 (1997).
[CrossRef] [PubMed]

W. Denk, J. H. Stricker, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Weiner, A. M.

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Wiersma, D. A.

E. O. Potma, W. P. de Boeij, P. J. M. van Haastert, and D. A. Wiersma, "Real-time visualization of intracellular hydrodynamics in single living cells," Proc. Natl. Acad. Sci. U.S.A. 98, 1577-1582 (2001).
[CrossRef] [PubMed]

Williams, R. M.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, "Measuring serotonin distribution in live cells with three-photon excitation," Science 275, 530-532 (1997).
[CrossRef] [PubMed]

Wilson, K. R.

J. A. Squier, M. Muller, G. J. Brakenhoff, and K. R. Wilson, "Third harmonic generation microscopy," Opt. Express 3, 315-324 (1998).
[CrossRef] [PubMed]

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D-microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
[CrossRef]

Xie, X. S.

J.-X. Cheng and X. S. Xie, "Green's function formulation for third-harmonic generation microscopy," J. Opt. Soc. Am. B 19, 1604-1609 (2002).
[CrossRef]

J. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, "Laser-scanning coherent anti-Stokes Raman scattering microscopy and applications to cell biology," Biophys. J. 83, 502-509 (2002).
[CrossRef] [PubMed]

A. Zumbusch, G. R. Holtom, and X. S. Xie, "Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering," Phys. Rev. Lett. 82, 4142-4145 (1999).
[CrossRef]

Xu, C.

Yelin, D.

D. Yelin and Y. Silberberg, "Third-harmonic microscopy in biology," Microscopy and Analysis 80, 15-18 (2000).

D. Yelin and Y. Silberberg, "Laser scanning third-harmonic-generation microscopy in biology," Opt. Express 5, 169-175 (1999).
[CrossRef] [PubMed]

Zheng, G.

J. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, "Laser-scanning coherent anti-Stokes Raman scattering microscopy and applications to cell biology," Biophys. J. 83, 502-509 (2002).
[CrossRef] [PubMed]

Zhu, G.

Zipfel, W.

Zipfel, W. R.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, "Measuring serotonin distribution in live cells with three-photon excitation," Science 275, 530-532 (1997).
[CrossRef] [PubMed]

Zumbusch, A.

A. Zumbusch, G. R. Holtom, and X. S. Xie, "Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering," Phys. Rev. Lett. 82, 4142-4145 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, "Nonlinear scanning laser microscopy by third harmonic generation," Appl. Phys. Lett. 70, 922-924 (1997).
[CrossRef]

Bioimaging (1)

G. Peleg, A. Lewis, O. Bouevitch, L. Loew, D. Parnas, and M. Linial, "Gigantic optical non-linearities from nanoparticle-enhanced molecular probes with potential for selectively imaging the structure and physiology of nanometric regions in cellular systems," Bioimaging 4, 215-224 (1996).
[CrossRef]

Biophys. J. (1)

J. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, "Laser-scanning coherent anti-Stokes Raman scattering microscopy and applications to cell biology," Biophys. J. 83, 502-509 (2002).
[CrossRef] [PubMed]

J. Microsc. (1)

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, "3D-microscopy of transparent objects using third-harmonic generation," J. Microsc. 191, 266-274 (1998).
[CrossRef]

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

Microscopy and Analysis (1)

D. Yelin and Y. Silberberg, "Third-harmonic microscopy in biology," Microscopy and Analysis 80, 15-18 (2000).

Nature (1)

N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy," Nature 418, 512-514 (2002).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

A. Zumbusch, G. R. Holtom, and X. S. Xie, "Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering," Phys. Rev. Lett. 82, 4142-4145 (1999).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

E. O. Potma, W. P. de Boeij, P. J. M. van Haastert, and D. A. Wiersma, "Real-time visualization of intracellular hydrodynamics in single living cells," Proc. Natl. Acad. Sci. U.S.A. 98, 1577-1582 (2001).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

Science (2)

W. Denk, J. H. Stricker, and W. W. Webb, "Two-photon laser scanning fluorescence microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, "Measuring serotonin distribution in live cells with three-photon excitation," Science 275, 530-532 (1997).
[CrossRef] [PubMed]

Other (1)

R. Boyd, Nonlinear Optics (Academic, 1992).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup of third-harmonic generation (THG) by temporally focused beams. The input beam impinges upon a grating, aligned perpendicular to the optic axis of the microscope. The grating is imaged through a high-magnification telescope, comprised of a cylindrical lens and the microscope objective, on the sample. The integrated THG signal is collected in the forward direction and measured by a photomultiplier tube (PMT).

Fig. 2
Fig. 2

Geometry of the temporally focused beam and the resulting harmonic beam. The fundamental beam is comprised of plane waves at different frequencies propagating at different angles. At the temporal focal plane, all frequencies constructively interfere to generate a focal spot moving along the x axis. The generated harmonic is similarly a temporally focused beam, implying that each harmonic frequency q ω copropagates with the fundamental ω.

Fig. 3
Fig. 3

Comparison of the cross-sectioning capabilities of THG excited by single point illumination by spatial focusing along two spatial axes (solid curve) and line illumination by combined temporal focusing and spatial focusing along a single spatial axis (dashed curve). As can be seen, the two cases result in an identical depth resolution, as expected following the analysis of Section 2.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

k ( ω ) = k ω cos ( θ ω ) z ̂ + k ω sin ( θ ω ) x ̂ k ω ( 1 θ ω 2 2 ) z ̂ + k ω θ ω x ̂ .
E ( x , z , t ) = d ω g ( ω ) exp ( i k ( ω ) r i ω t ) = d ω g ( ω ) exp [ i k ω z ( 1 P 2 δ 2 2 ) + i k ω x P δ i ω t ] ,
E ( x , z , t ) = g 1 exp [ i ( k 0 z ω 0 t ) ] d δ exp ( δ 2 Δ 2 ) exp [ i ( δ c k 0 P 2 δ 2 2 P 2 δ 3 2 c ) z + i ( k 0 P δ + P δ 2 c ) x i δ t ] ,
A = 1 Δ 2 ( 1 + i k 0 Δ 2 P 2 2 z ) ; t 0 = ( k 0 P x z c ) .
E ( x , z , t ) = exp [ i ( k 0 z ω 0 t ) ] g 1 Δ π 1 + i ξ exp [ Δ 2 ( t t 0 ) 2 4 ( 1 + i ξ ) ] .
E ( x , z ) = exp [ i ( k 0 z ω 0 t ) ] A 1 1 + i ζ exp [ x 2 w 0 2 ( 1 + i ζ ) ] ,
[ E ( x , z , t ) ] q = exp [ i ( q k 0 z q ω 0 t ) ] Δ q π q 2 ( 1 + i ξ ) ( q 2 ) exp [ q Δ 2 ( t t 0 ) 2 4 ( 1 + i ξ ) ] .
E q ( x , z , t ) = C ( z ) exp [ i ( k q z q ω 0 t ) ] Δ q π 1 + i ξ exp [ q Δ 2 ( t t 0 ) 2 4 ( 1 + i ξ ) ] ,
C ( z ) d z exp [ i ( k q q k 0 ) ] ( 1 + i ξ ) ( q 1 ) 2 ,
C ( z ) d z exp [ i ( k q q k 0 ) ] ( 1 + i ξ ) ( q 1 ) 2 ( 1 + i ζ ) ( q 1 ) 2 .

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