Abstract

An analysis of the imaging properties of nonlinear coherent four-wave mixing optical microscopes is presented. The generation and propagation of coherent signals are considered under conditions of high numerical aperture with a model that circumvents the need to use the slowly varying envelope approximation. Calculations of coherent anti-Stokes Raman scattering signals show that diffraction effects play a prominent role in the spatial distribution of the coherent signal intensity. It is emphasized that, unlike for fluorescence microscopy, the detected signal is not a straightforward convolution of a point-spread function and the object but is shaped by the complex interplay of object size and coherent buildup dynamics.

© 2000 Optical Society of America

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  1. W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
    [CrossRef] [PubMed]
  2. K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, “In vivo dendritic calcium dynamics in neocortical pyramidal neurons,” Nature 385, 161–165 (1997).
    [CrossRef] [PubMed]
  3. P. J. Campagnola, M. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77, 3341–3349 (1999).
    [CrossRef] [PubMed]
  4. 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]
  5. M. Müller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, “3D microscopy of transparent objects using third-harmonic generation,” J. Microsc. (Oxford) 191, 266–274 (1998).
    [CrossRef]
  6. M. D. Duncan, J. Reintjes, and T. J. Manuccia, “Scanning coherent anti-Stokes Raman microscope,” Opt. Lett. 7, 350–352 (1982).
    [CrossRef] [PubMed]
  7. 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]
  8. M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. (Oxford) 197, 150–158 (2000).
    [CrossRef]
  9. M. D. Levenson and S. S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, San Diego, Calif., 1987).
  10. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), pp. 47–49.
  11. T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
    [CrossRef]
  12. R. E. Teets, “CARS signals: phase matching, transverse modes and optical damage effects,” Appl. Opt. 25, 855–862 (1986).
    [CrossRef]
  13. W. Kaabar and R. Devonshire, “A versatile model of CARS signal generation: optimum beam diameter ratios for different phase-matching geometries,” Chem. Phys. Lett. 186, 522–530 (1991).
    [CrossRef]
  14. W. M. Shaub, A. B. Harvey, and G. C. Bjorklund, “Power generation in anti-Stokes Raman spectroscopy with focused laser beams,” J. Chem. Phys. 67, 2547–2550 (1977).
    [CrossRef]
  15. S. Guha and J. Falk, “The effects of focusing on the efficiency of coherent anti-Stokes Raman scattering,” J. Chem. Phys. 75, 2599–2602 (1981).
    [CrossRef]
  16. N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).
  17. G. L. Eesley, Coherent Raman Spectroscopy (Pergamon, New York, 1981), p. 25.
  18. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1998), p. 437.
  19. T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984), pp. 12–26.
  20. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986), pp. 244–250.
  21. P. J. Shaw in Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), p. 373.

2000 (1)

M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. (Oxford) 197, 150–158 (2000).
[CrossRef]

1999 (2)

P. J. Campagnola, M. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77, 3341–3349 (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 (1)

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

1997 (3)

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

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]

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, “In vivo dendritic calcium dynamics in neocortical pyramidal neurons,” Nature 385, 161–165 (1997).
[CrossRef] [PubMed]

1991 (1)

W. Kaabar and R. Devonshire, “A versatile model of CARS signal generation: optimum beam diameter ratios for different phase-matching geometries,” Chem. Phys. Lett. 186, 522–530 (1991).
[CrossRef]

1990 (1)

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

1986 (1)

1982 (1)

1981 (1)

S. Guha and J. Falk, “The effects of focusing on the efficiency of coherent anti-Stokes Raman scattering,” J. Chem. Phys. 75, 2599–2602 (1981).
[CrossRef]

1977 (1)

W. M. Shaub, A. B. Harvey, and G. C. Bjorklund, “Power generation in anti-Stokes Raman spectroscopy with focused laser beams,” J. Chem. Phys. 67, 2547–2550 (1977).
[CrossRef]

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]

Bjorklund, G. C.

W. M. Shaub, A. B. Harvey, and G. C. Bjorklund, “Power generation in anti-Stokes Raman spectroscopy with focused laser beams,” J. Chem. Phys. 67, 2547–2550 (1977).
[CrossRef]

Brabec, T.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

Brakenhoff, G. J.

M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. (Oxford) 197, 150–158 (2000).
[CrossRef]

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

Campagnola, P. J.

P. J. Campagnola, M. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77, 3341–3349 (1999).
[CrossRef] [PubMed]

de Lange, C. A.

M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. (Oxford) 197, 150–158 (2000).
[CrossRef]

Denk, W.

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, “In vivo dendritic calcium dynamics in neocortical pyramidal neurons,” Nature 385, 161–165 (1997).
[CrossRef] [PubMed]

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

Devonshire, R.

W. Kaabar and R. Devonshire, “A versatile model of CARS signal generation: optimum beam diameter ratios for different phase-matching geometries,” Chem. Phys. Lett. 186, 522–530 (1991).
[CrossRef]

Duncan, M. D.

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]

Falk, J.

S. Guha and J. Falk, “The effects of focusing on the efficiency of coherent anti-Stokes Raman scattering,” J. Chem. Phys. 75, 2599–2602 (1981).
[CrossRef]

Guha, S.

S. Guha and J. Falk, “The effects of focusing on the efficiency of coherent anti-Stokes Raman scattering,” J. Chem. Phys. 75, 2599–2602 (1981).
[CrossRef]

Harvey, A. B.

W. M. Shaub, A. B. Harvey, and G. C. Bjorklund, “Power generation in anti-Stokes Raman spectroscopy with focused laser beams,” J. Chem. Phys. 67, 2547–2550 (1977).
[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]

Kaabar, W.

W. Kaabar and R. Devonshire, “A versatile model of CARS signal generation: optimum beam diameter ratios for different phase-matching geometries,” Chem. Phys. Lett. 186, 522–530 (1991).
[CrossRef]

Kleinfeld, D.

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, “In vivo dendritic calcium dynamics in neocortical pyramidal neurons,” Nature 385, 161–165 (1997).
[CrossRef] [PubMed]

Krausz, F.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

Lewis, A.

P. J. Campagnola, M. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77, 3341–3349 (1999).
[CrossRef] [PubMed]

Loew, L. M.

P. J. Campagnola, M. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77, 3341–3349 (1999).
[CrossRef] [PubMed]

Manuccia, T. J.

Müller, M.

M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. (Oxford) 197, 150–158 (2000).
[CrossRef]

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

Reintjes, J.

Shaub, W. M.

W. M. Shaub, A. B. Harvey, and G. C. Bjorklund, “Power generation in anti-Stokes Raman spectroscopy with focused laser beams,” J. Chem. Phys. 67, 2547–2550 (1977).
[CrossRef]

Silberberg, 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]

Squier, J.

M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. (Oxford) 197, 150–158 (2000).
[CrossRef]

M. Müller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, “3D microscopy of transparent objects using third-harmonic generation,” J. Microsc. (Oxford) 191, 266–274 (1998).
[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] [PubMed]

Svoboda, K.

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, “In vivo dendritic calcium dynamics in neocortical pyramidal neurons,” Nature 385, 161–165 (1997).
[CrossRef] [PubMed]

Tank, D. W.

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, “In vivo dendritic calcium dynamics in neocortical pyramidal neurons,” Nature 385, 161–165 (1997).
[CrossRef] [PubMed]

Teets, R. E.

Webb, W. W.

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

Wei, M.

P. J. Campagnola, M. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77, 3341–3349 (1999).
[CrossRef] [PubMed]

Wilson, K. R.

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

Xie, X. S.

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]

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. Opt. (1)

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]

Biophys. J. (1)

P. J. Campagnola, M. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J. 77, 3341–3349 (1999).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

W. Kaabar and R. Devonshire, “A versatile model of CARS signal generation: optimum beam diameter ratios for different phase-matching geometries,” Chem. Phys. Lett. 186, 522–530 (1991).
[CrossRef]

J. Chem. Phys. (2)

W. M. Shaub, A. B. Harvey, and G. C. Bjorklund, “Power generation in anti-Stokes Raman spectroscopy with focused laser beams,” J. Chem. Phys. 67, 2547–2550 (1977).
[CrossRef]

S. Guha and J. Falk, “The effects of focusing on the efficiency of coherent anti-Stokes Raman scattering,” J. Chem. Phys. 75, 2599–2602 (1981).
[CrossRef]

J. Microsc. (Oxford) (2)

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

M. Müller, J. Squier, C. A. de Lange, and G. J. Brakenhoff, “CARS microscopy with folded BoxCARS phasematching,” J. Microsc. (Oxford) 197, 150–158 (2000).
[CrossRef]

Nature (1)

K. Svoboda, W. Denk, D. Kleinfeld, and D. W. Tank, “In vivo dendritic calcium dynamics in neocortical pyramidal neurons,” Nature 385, 161–165 (1997).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

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]

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

Science (1)

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

Other (8)

M. D. Levenson and S. S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, San Diego, Calif., 1987).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), pp. 47–49.

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

G. L. Eesley, Coherent Raman Spectroscopy (Pergamon, New York, 1981), p. 25.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1998), p. 437.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984), pp. 12–26.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986), pp. 244–250.

P. J. Shaw in Handbook of Biological Confocal Microscopy, J. Pawley, ed. (Plenum, New York, 1995), p. 373.

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Figures (8)

Fig. 1
Fig. 1

Experimental layout of the CARS microscope in transmission mode. A combined pump–probe beam is aligned collinearly with the Stokes beam by a dichroic beam splitter and focused by an excitation objective in the sample. After collection by a secondary objective, the spectrally filter CARS signal is detected by a large-area detector.

Fig. 2
Fig. 2

Wave-vector mismatch factor in water for collinear CARS geometry as a function of NA. Stokes wavelength, 800 nm. Solid curve: pump wavelength, 600 nm; spectral shift, 4167 cm-1. Dashed curve: pump wavelength, 500 nm; spectral shift, 7500 cm-1. Interaction length L is defined by the FWHM of the focal excitation intensity along the optical axis.

Fig. 3
Fig. 3

Intensity distribution in the focal region of a lens with a NA of 0.9. (a) CARS signal intensity patterns in diffraction-limited volume for continuum material illumination of λp/λS=0.75; (b) excitation intensity (Ip2IS).

Fig. 4
Fig. 4

CARS intensity profiles along (a) the optical axis and (b) the lateral axis in the focal plane. Solid curves, CARS signal; dashed curves, excitation intensity. Same parameters as in Fig. 3.

Fig. 5
Fig. 5

CARS signal intensity in the focal plane for several wavelength shifts between pump and Stokes beams. Solid curve, λp/λS=0.5; dashed curve, λp/λS=0.9.

Fig. 6
Fig. 6

Axial edge response in CARS microscopy. Solid curve, coherent limit; dashed curve, calculated from an incoherent CARS response. Dotted curve, illumination intensity. Same parameters as in Fig. 3.

Fig. 7
Fig. 7

Relative amount of CARS signal collected by a collimating objective that is positioned parfocally with the excitation objective. The NA’s of excitation and collimating objectives are identical, and λp/λS=0.75.

Fig. 8
Fig. 8

Axial edge response of CARS signal calculated from the exact analysis (solid line) and determined with the SVEA (dashed line). The NA was taken to be 0.9, and λp/λS=0.75.

Equations (26)

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P=χ(1)E1+χ(2)E1E2+χ(3)E1E2E3+.
Ei(r¯, t)=Ei(r¯)exp(iωt)+c.c.,
P(r¯, t)=P(r¯)exp(iωt)+c.c.,
PCARS(r¯)=χCARS(3)Ep2(r¯)ES*(r¯)exp[i(2kp-kS)z],
Ei(v, u)=2 0 J0(vρ)exp-iuρ22ρdρ,
vi=2π sin αλir,
ui=8π sin2(α/2)λiz,
2Ec(r¯, t)-n2c2 2Ec(r¯, t)t2=4πc2 2P(r¯, t)t2.
2Ec(r, ϕ, z)z2+1r rr r+1r2 2ϕ2Ec(r, ϕ, z)
+kc2Ec(r, ϕ, z)=-4πω2c2P(r, ϕ, z).
Ec(ρ, z)=2π0Ec(r, z)J0(2πρr)rdr
2z2-4π2ρ2+kc2Ec(ρ, z)=-4πω2c2P(ρ, z).
Ec(ρ, z)=Ec+(ρ, z)exp(ikcz)+Ec-(ρ, z)exp(-ikcz),
Ec+(ρ, z)=E0+-12ik 4πkc2P(ρ, z)exp(iΔk-z)×exp[-i(k-kc)z]dz×exp[i(k-kc)z],
Ec-(ρ, z)=E0-+12ik 4πkc2P(ρ, z)exp(iΔk+z)×exp[i(k-kc)z]dz×exp[-i(k-kc)z],
Ec+(ρ, z)=exp[i(k-kc)z] 2iπkc2k -zP(ρ, z)×exp(iΔk-z)×exp[-i(k-kc)z]dz.
ESVEA(ρ, z)=exp-2iπ2ρ2zkc2iπkc-zP(ρ, z)×exp(iΔk-z)exp2iπ2ρ2zkcdz.
Eρ0(z)=2iπkc-zP(z)exp[iΔk-z]dz.
Ec(r, z)=2π0Ec(ρ, z)J0(2πρr)ρdρ.
I(u)=2π0vdv|Ec(v, u)|2=2π0ρdρ|Ec(ρ, u)|2.
S(u)=2π0a|Ec(ρ, u)|2ρdρI(u),
E(r¯, t)=Ec(r¯)exp[i(kcz-ωt)].
2Ec(r¯)z2+2ikc Ec(r¯)z+1r rr r+1r2 2ϕ2Ec(r¯)
=-4πω2c2P(r¯)exp(-ikcz).
2Ec(r¯)z2kc Ec(r¯)z.
Ec(ρ, z)z=-2iπ2ρ2kcEc(ρ, z)+2iπkcP(ρ, z)exp(-ikcz).

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