Abstract

We show that nonlinear effects like self-phase modulation in a sample have to be considered for phase control of three-photon excitations. Furthermore, we demonstrate the control of three-photon excitation of L-Tryptophan in water using a pulse-shaping setup. Simulations of the propagation of the laser pulses in the cuvette exhibit good agreement with the experimental fluorescence scans at different laser intensities and show large discrepancies when neglecting nonlinear effects prior to the three-photon process. This can lead to improvements in selective excitation of amino acids by a near-infrared femtosecond laser source.

© 2014 Optical Society of America

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  4. I. Pastirk, J. D. Cruz, K. Walowicz, V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003).
    [CrossRef]
  5. J. P. Ogilvie, D. Débarre, X. Solinas, J. Martin, E. Beaurepaire, and M. Joffre, “Use of coherent control for selective two-photon fluorescence microscopy in live organisms,” Opt. Express 14, 759–766 (2006).
    [CrossRef]
  6. J. D. Cruz, V. Lozovoy, and M. Dantus, “Coherent control improves biomedical imaging with ultrashort shaped pulses,” J. Photochem. Photobiol. A Chem. 180, 307–313 (2006).
  7. R. Pillai, C. Boudoux, G. Labroille, N. Olivier, I. Veilleux, E. Farge, M. Joffre, and E. Beaurepaire, “Multiplexed two-photon microscopy of dynamic biological samples with shaped broadband pulses,” Opt. Express 17, 12741–12752 (2009).
    [CrossRef]
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  19. P. Devi, V. Lozovoy, and M. Dantus, “Measurement of group velocity dispersion of solvents using 2-cycle femtosecond pulses: experiment and theory,” AIP Adv. 1, 032166 (2011).
  20. Z. Wilkes, S. Varma, Y. Chen, H. Milchberg, T. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407  nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
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  21. R. Boyd, Nonlinear Optics (Academic, 2003).
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    [CrossRef]
  23. A. Patas, G. Achazi, N. Hermes, M. Pawłowska, and A. Lindinger, “Contrast optimization of two-photon processes after a microstructured hollow-core fiber demonstrated for dye molecules,” Appl. Phys. B 112, 579–586 (2013).
    [CrossRef]
  24. G. Achazi, N. Hermes, A. Patas, D. Tolksdorf, and A. Lindinger, “Polarization-shaped laser pulses for improved fluorescence anisotropy contrast,” Eur. Phys. J. D 67, 1–5 (2013).
    [CrossRef]

2013 (3)

N. Horton, K. Wang, D. Kobat, C. Clark, F. Wise, C. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[CrossRef]

A. Patas, G. Achazi, N. Hermes, M. Pawłowska, and A. Lindinger, “Contrast optimization of two-photon processes after a microstructured hollow-core fiber demonstrated for dye molecules,” Appl. Phys. B 112, 579–586 (2013).
[CrossRef]

G. Achazi, N. Hermes, A. Patas, D. Tolksdorf, and A. Lindinger, “Polarization-shaped laser pulses for improved fluorescence anisotropy contrast,” Eur. Phys. J. D 67, 1–5 (2013).
[CrossRef]

2011 (3)

T. Wu, J. Tang, B. Hajj, and M. Cui, “Phase resolved interferometric spectral modulation (prism) for ultrafast pulse measurement and compression,” Opt. Express 19, 12961–12968 (2011).
[CrossRef]

P. Devi, V. Lozovoy, and M. Dantus, “Measurement of group velocity dispersion of solvents using 2-cycle femtosecond pulses: experiment and theory,” AIP Adv. 1, 032166 (2011).

D. Kobat, N. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16, 106014 (2011).
[CrossRef]

2010 (1)

D. Sharma, J. Léonard, and S. Haacke, “Ultrafast excited-state dynamics of tryptophan in water observed by transient absorption spectroscopy,” Chem. Phys. Lett. 489, 99–102 (2010).
[CrossRef]

2009 (2)

Z. Wilkes, S. Varma, Y. Chen, H. Milchberg, T. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407  nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

R. Pillai, C. Boudoux, G. Labroille, N. Olivier, I. Veilleux, E. Farge, M. Joffre, and E. Beaurepaire, “Multiplexed two-photon microscopy of dynamic biological samples with shaped broadband pulses,” Opt. Express 17, 12741–12752 (2009).
[CrossRef]

2006 (4)

J. P. Ogilvie, D. Débarre, X. Solinas, J. Martin, E. Beaurepaire, and M. Joffre, “Use of coherent control for selective two-photon fluorescence microscopy in live organisms,” Opt. Express 14, 759–766 (2006).
[CrossRef]

J. D. Cruz, V. Lozovoy, and M. Dantus, “Coherent control improves biomedical imaging with ultrashort shaped pulses,” J. Photochem. Photobiol. A Chem. 180, 307–313 (2006).

R. Heintzmann and G. Ficz, “Breaking the resolution limit in light microscopy,” Brief. Funct. Genomic. Proteomic. 5, 289–301 (2006).

S. Schenkl, F. van Mourik, N. Friedman, M. Sheves, R. Schlesinger, S. Haacke, and M. Chergui, “Insights into excited-state and isomerization dynamics of bacteriorhodopsin from ultrafast transient UV absorption,” Proc. Natl. Acad. Sci. USA 103, 4101–4106 (2006).

2005 (1)

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).

2004 (1)

2003 (2)

V. Lozovoy, I. Pastirk, K. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. II. Control of two- and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003).
[CrossRef]

I. Pastirk, J. D. Cruz, K. Walowicz, V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003).
[CrossRef]

1999 (1)

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60, 1287–1292 (1999).
[CrossRef]

1996 (1)

C. Xu, W. Zipfel, J. B. Shear, R. Williams, and W. Webb, “Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy,” Proc. Natl. Acad. Sci. USA 93, 10763–10768 (1996).

1992 (1)

S. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[CrossRef]

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef]

Achazi, G.

G. Achazi, N. Hermes, A. Patas, D. Tolksdorf, and A. Lindinger, “Polarization-shaped laser pulses for improved fluorescence anisotropy contrast,” Eur. Phys. J. D 67, 1–5 (2013).
[CrossRef]

A. Patas, G. Achazi, N. Hermes, M. Pawłowska, and A. Lindinger, “Contrast optimization of two-photon processes after a microstructured hollow-core fiber demonstrated for dye molecules,” Appl. Phys. B 112, 579–586 (2013).
[CrossRef]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Springer, 2000).

Beaurepaire, E.

Boudoux, C.

Boyd, R.

R. Boyd, Nonlinear Optics (Academic, 2003).

Chen, J.

Chen, Y.

Z. Wilkes, S. Varma, Y. Chen, H. Milchberg, T. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407  nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Chergui, M.

S. Schenkl, F. van Mourik, N. Friedman, M. Sheves, R. Schlesinger, S. Haacke, and M. Chergui, “Insights into excited-state and isomerization dynamics of bacteriorhodopsin from ultrafast transient UV absorption,” Proc. Natl. Acad. Sci. USA 103, 4101–4106 (2006).

Clark, C.

N. Horton, K. Wang, D. Kobat, C. Clark, F. Wise, C. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[CrossRef]

Couairon, A.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).

Cruz, J. D.

J. D. Cruz, V. Lozovoy, and M. Dantus, “Coherent control improves biomedical imaging with ultrashort shaped pulses,” J. Photochem. Photobiol. A Chem. 180, 307–313 (2006).

I. Pastirk, J. D. Cruz, K. Walowicz, V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003).
[CrossRef]

Cui, M.

Dantus, M.

P. Devi, V. Lozovoy, and M. Dantus, “Measurement of group velocity dispersion of solvents using 2-cycle femtosecond pulses: experiment and theory,” AIP Adv. 1, 032166 (2011).

J. D. Cruz, V. Lozovoy, and M. Dantus, “Coherent control improves biomedical imaging with ultrashort shaped pulses,” J. Photochem. Photobiol. A Chem. 180, 307–313 (2006).

I. Pastirk, J. D. Cruz, K. Walowicz, V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003).
[CrossRef]

V. Lozovoy, I. Pastirk, K. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. II. Control of two- and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003).
[CrossRef]

Débarre, D.

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef]

Devi, P.

P. Devi, V. Lozovoy, and M. Dantus, “Measurement of group velocity dispersion of solvents using 2-cycle femtosecond pulses: experiment and theory,” AIP Adv. 1, 032166 (2011).

Farge, E.

Ficz, G.

R. Heintzmann and G. Ficz, “Breaking the resolution limit in light microscopy,” Brief. Funct. Genomic. Proteomic. 5, 289–301 (2006).

Franco, M.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).

Friedman, N.

S. Schenkl, F. van Mourik, N. Friedman, M. Sheves, R. Schlesinger, S. Haacke, and M. Chergui, “Insights into excited-state and isomerization dynamics of bacteriorhodopsin from ultrafast transient UV absorption,” Proc. Natl. Acad. Sci. USA 103, 4101–4106 (2006).

Haacke, S.

D. Sharma, J. Léonard, and S. Haacke, “Ultrafast excited-state dynamics of tryptophan in water observed by transient absorption spectroscopy,” Chem. Phys. Lett. 489, 99–102 (2010).
[CrossRef]

S. Schenkl, F. van Mourik, N. Friedman, M. Sheves, R. Schlesinger, S. Haacke, and M. Chergui, “Insights into excited-state and isomerization dynamics of bacteriorhodopsin from ultrafast transient UV absorption,” Proc. Natl. Acad. Sci. USA 103, 4101–4106 (2006).

Hajj, B.

Heintzmann, R.

R. Heintzmann and G. Ficz, “Breaking the resolution limit in light microscopy,” Brief. Funct. Genomic. Proteomic. 5, 289–301 (2006).

Hell, S.

S. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[CrossRef]

Hermes, N.

G. Achazi, N. Hermes, A. Patas, D. Tolksdorf, and A. Lindinger, “Polarization-shaped laser pulses for improved fluorescence anisotropy contrast,” Eur. Phys. J. D 67, 1–5 (2013).
[CrossRef]

A. Patas, G. Achazi, N. Hermes, M. Pawłowska, and A. Lindinger, “Contrast optimization of two-photon processes after a microstructured hollow-core fiber demonstrated for dye molecules,” Appl. Phys. B 112, 579–586 (2013).
[CrossRef]

Horton, N.

N. Horton, K. Wang, D. Kobat, C. Clark, F. Wise, C. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[CrossRef]

D. Kobat, N. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16, 106014 (2011).
[CrossRef]

Joffre, M.

Jones, T.

Z. Wilkes, S. Varma, Y. Chen, H. Milchberg, T. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407  nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Kannari, F.

Kawano, H.

Kobat, D.

N. Horton, K. Wang, D. Kobat, C. Clark, F. Wise, C. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[CrossRef]

D. Kobat, N. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt. 16, 106014 (2011).
[CrossRef]

Labroille, G.

Léonard, J.

D. Sharma, J. Léonard, and S. Haacke, “Ultrafast excited-state dynamics of tryptophan in water observed by transient absorption spectroscopy,” Chem. Phys. Lett. 489, 99–102 (2010).
[CrossRef]

Lindinger, A.

A. Patas, G. Achazi, N. Hermes, M. Pawłowska, and A. Lindinger, “Contrast optimization of two-photon processes after a microstructured hollow-core fiber demonstrated for dye molecules,” Appl. Phys. B 112, 579–586 (2013).
[CrossRef]

G. Achazi, N. Hermes, A. Patas, D. Tolksdorf, and A. Lindinger, “Polarization-shaped laser pulses for improved fluorescence anisotropy contrast,” Eur. Phys. J. D 67, 1–5 (2013).
[CrossRef]

Lozovoy, V.

P. Devi, V. Lozovoy, and M. Dantus, “Measurement of group velocity dispersion of solvents using 2-cycle femtosecond pulses: experiment and theory,” AIP Adv. 1, 032166 (2011).

J. D. Cruz, V. Lozovoy, and M. Dantus, “Coherent control improves biomedical imaging with ultrashort shaped pulses,” J. Photochem. Photobiol. A Chem. 180, 307–313 (2006).

I. Pastirk, J. D. Cruz, K. Walowicz, V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003).
[CrossRef]

V. Lozovoy, I. Pastirk, K. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. II. Control of two- and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003).
[CrossRef]

Martin, J.

Meshulach, D.

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60, 1287–1292 (1999).
[CrossRef]

Midorikawa, K.

Milchberg, H.

Z. Wilkes, S. Varma, Y. Chen, H. Milchberg, T. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407  nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Miyawaki, A.

Mizuno, H.

Mysyrowicz, A.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).

Nabekawa, Y.

Ogilvie, J. P.

Olivier, N.

Pastirk, I.

I. Pastirk, J. D. Cruz, K. Walowicz, V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003).
[CrossRef]

V. Lozovoy, I. Pastirk, K. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. II. Control of two- and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003).
[CrossRef]

Patas, A.

A. Patas, G. Achazi, N. Hermes, M. Pawłowska, and A. Lindinger, “Contrast optimization of two-photon processes after a microstructured hollow-core fiber demonstrated for dye molecules,” Appl. Phys. B 112, 579–586 (2013).
[CrossRef]

G. Achazi, N. Hermes, A. Patas, D. Tolksdorf, and A. Lindinger, “Polarization-shaped laser pulses for improved fluorescence anisotropy contrast,” Eur. Phys. J. D 67, 1–5 (2013).
[CrossRef]

Pawlowska, M.

A. Patas, G. Achazi, N. Hermes, M. Pawłowska, and A. Lindinger, “Contrast optimization of two-photon processes after a microstructured hollow-core fiber demonstrated for dye molecules,” Appl. Phys. B 112, 579–586 (2013).
[CrossRef]

Pillai, R.

Prade, B.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).

Schaffer, C.

N. Horton, K. Wang, D. Kobat, C. Clark, F. Wise, C. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[CrossRef]

Schenkl, S.

S. Schenkl, F. van Mourik, N. Friedman, M. Sheves, R. Schlesinger, S. Haacke, and M. Chergui, “Insights into excited-state and isomerization dynamics of bacteriorhodopsin from ultrafast transient UV absorption,” Proc. Natl. Acad. Sci. USA 103, 4101–4106 (2006).

Schlesinger, R.

S. Schenkl, F. van Mourik, N. Friedman, M. Sheves, R. Schlesinger, S. Haacke, and M. Chergui, “Insights into excited-state and isomerization dynamics of bacteriorhodopsin from ultrafast transient UV absorption,” Proc. Natl. Acad. Sci. USA 103, 4101–4106 (2006).

Sharma, D.

D. Sharma, J. Léonard, and S. Haacke, “Ultrafast excited-state dynamics of tryptophan in water observed by transient absorption spectroscopy,” Chem. Phys. Lett. 489, 99–102 (2010).
[CrossRef]

Shear, J. B.

C. Xu, W. Zipfel, J. B. Shear, R. Williams, and W. Webb, “Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy,” Proc. Natl. Acad. Sci. USA 93, 10763–10768 (1996).

Sheves, M.

S. Schenkl, F. van Mourik, N. Friedman, M. Sheves, R. Schlesinger, S. Haacke, and M. Chergui, “Insights into excited-state and isomerization dynamics of bacteriorhodopsin from ultrafast transient UV absorption,” Proc. Natl. Acad. Sci. USA 103, 4101–4106 (2006).

Silberberg, Y.

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60, 1287–1292 (1999).
[CrossRef]

Solinas, X.

Stelzer, E. H. K.

S. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[CrossRef]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef]

Sudrie, L.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).

Tanabe, T.

Tang, J.

Ting, A.

Z. Wilkes, S. Varma, Y. Chen, H. Milchberg, T. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407  nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Tolksdorf, D.

G. Achazi, N. Hermes, A. Patas, D. Tolksdorf, and A. Lindinger, “Polarization-shaped laser pulses for improved fluorescence anisotropy contrast,” Eur. Phys. J. D 67, 1–5 (2013).
[CrossRef]

van Mourik, F.

S. Schenkl, F. van Mourik, N. Friedman, M. Sheves, R. Schlesinger, S. Haacke, and M. Chergui, “Insights into excited-state and isomerization dynamics of bacteriorhodopsin from ultrafast transient UV absorption,” Proc. Natl. Acad. Sci. USA 103, 4101–4106 (2006).

Varma, S.

Z. Wilkes, S. Varma, Y. Chen, H. Milchberg, T. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407  nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Veilleux, I.

Walowicz, K.

I. Pastirk, J. D. Cruz, K. Walowicz, V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003).
[CrossRef]

V. Lozovoy, I. Pastirk, K. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. II. Control of two- and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003).
[CrossRef]

Wang, K.

N. Horton, K. Wang, D. Kobat, C. Clark, F. Wise, C. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[CrossRef]

Webb, W.

C. Xu, W. Zipfel, J. B. Shear, R. Williams, and W. Webb, “Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy,” Proc. Natl. Acad. Sci. USA 93, 10763–10768 (1996).

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef]

Wilkes, Z.

Z. Wilkes, S. Varma, Y. Chen, H. Milchberg, T. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407  nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
[CrossRef]

Williams, R.

C. Xu, W. Zipfel, J. B. Shear, R. Williams, and W. Webb, “Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy,” Proc. Natl. Acad. Sci. USA 93, 10763–10768 (1996).

Wise, F.

N. Horton, K. Wang, D. Kobat, C. Clark, F. Wise, C. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[CrossRef]

Wu, T.

Xu, C.

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Figures (7)

Fig. 1.
Fig. 1.

Experimental setup.

Fig. 2.
Fig. 2.

(a) Measurement of the spectral FWHM after the cuvette plotted against the linear pulse chirp at the focus position. (b) Simulation of the propagated spectra for pulses of various linear chirps. A comparison is made at three different values for the laser power.

Fig. 3.
Fig. 3.

(a) Third-order phase of 5×104fs3 and the resulting three-photon spectrum. (b) Third-order phase of 5×104fs3. Without the effects of SPM and self-steepening, both phase functions centered around 805 nm result in the same three-photon spectrum. The red line depicts the three-photon spectrum of the transform-limited pulse.

Fig. 4.
Fig. 4.

Simulated three-photon spectra. (a) +5×104fs3, center wavelength 805 nm, (b) 5×104fs3, center wavelength 805 nm, (c) +5×104fs3, center wavelength 811 nm, and (d) 5×104fs3, center wavelength 811 nm. When considering nonlinear effects, large differences in the three-photon spectra emerge.

Fig. 5.
Fig. 5.

Simulated spectra for third-order phases of ±5×104fs3 centered around 805 nm as well as the reference spectrum measured before the cuvette.

Fig. 6.
Fig. 6.

Simulation of the expected fluorescence intensity of Tryptophan from pulses with a shifted ±5×104fs3 third-order phase. First the nonlinear propagation of the pulses in the cuvette and then the three-photon process is simulated. This is done for each pulse shape at each laser power.

Fig. 7.
Fig. 7.

Measured shifted-phase scans of a ±5×104fs3 third-order phase for various laser powers. For low peak intensities in the cuvette nonlinear effects disappear, while in the case of large fluorescence a shift between positive and negative phase functions arises.

Equations (5)

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E(3)(3ω)=|E(ωΩ1Ω2)||E(Ω1)||E(Ω2)|×ei(Φ(ωΩ1Ω2)+Φ(Ω1)+Φ(Ω2))dΩ1dΩ2,
IE(3)(3ω)Abs3p(3ω)dω.
Φ(λ)=b32π6(cλcλ0)3.
δω(t)=n2ω0LctI(t).
I(t)tdt=[I(t)]=0,

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