Abstract

A full-vectorial theoretical investigation of the recently proposed background-free coherent anti-Stokes Raman scattering (CARS) spectroscopy near transverse interfaces [Phys. Rev. A , 77, 061802(R) (2008) ] is presented. In this scheme, the field symmetries of the focused excitation beams are applied to recover the pure Raman spectrum of a medium forming a transverse interface with a nonresonant medium. We show that this method is robust to spatial shift of the excitation volume relative to the interface and does not depend on the linear polarizations states of the pump and Stokes beams. Finally, we extend the applicability of this scheme to a succession of planar interfaces between resonant and nonresonant media, which is potentially interesting for fast chemical analysis in microfluidic devices. Interestingly, this method can be extended to nondegenerated resonant four-wave-mixing processes to remove the nonresonant background.

© 2008 Optical Society of America

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  1. J. P. Coffinet and F. de Martini, “Coherent excitation of polaritons in Gallium Phosphide,” Phys. Rev. Lett. 22, 60-64 (1969).
    [CrossRef]
  2. J. J. Wynne, “Nonlinear optical Spectroscopy of χ(3) in LiNbO3,” Phys. Rev. Lett. 29650-653 (1972).
    [CrossRef]
  3. P. R. Regnier, and J. P.-E. Taran, “On the possibility of measuring gas concentrations by stimulated anti-Stokes scattering,” Appl. Phys. Lett. 23, 240-242 (1973).
    [CrossRef]
  4. R. F. Begley, A. B. Harvey, and R. L. Byer, “Coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 25, 387-390 (1974).
    [CrossRef]
  5. M. D. Levenson, C. Flytzanis, and N. Bloembergen, “Interference of resonant and nonresonant three-wave mixing in diamond,” Phys. Rev. B 10, 003962 (1972).
    [CrossRef]
  6. J. J. Song, G. L. Easley, and M. D. Levenson, “Background suppression in coherent Raman spectroscopy,” Appl. Phys. Lett. 29, 567-569 (1976).
    [CrossRef]
  7. S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, “Polarization active Raman spectroscopy and coherent Raman ellipsometry,” Sov. Phys. JETP 47, 667-677 (1978).
  8. J.-L. Oudar, R. W. Smith, and Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
    [CrossRef]
  9. F. M. Kamga and M. G. Sceats, “Pulse-sequenced coherent anti-Stokes Raman scattering spectroscopy: a method for suppression of the nonresonant background,” Opt. Lett. 5, 126-128 (1980).
    [CrossRef]
  10. Y. Yacoby, R. Fitzgibbon, and B. Lax, “Coherent cancellation of background in four-wave mixing spectroscopy,” J. Appl. Phys. 51, 3072-3077 (1980).
    [CrossRef]
  11. J. P. Ogilvie, E. Beaurepaire, A. Alexandrou, and M. Joffre, “Fourier-transform coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 31, 480-482 (2006).
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  12. Y. Paskover, I. S. Averbukh, and Y. Prior, “Single-shot two dimensional time resolved coherent anti Stokes Raman Scattering,” Opt. Express 15, 1700-1705 (2007).
    [CrossRef] [PubMed]
  13. N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature (London) 418, 512-514 (2002).
    [CrossRef]
  14. D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90, 213902 (2003).
    [CrossRef]
  15. S.-H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72, 041803(R) (2005).
    [CrossRef]
  16. 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]
  17. J.-X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26, 1341-1343 (2001).
    [CrossRef]
  18. A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505-1507 (2002).
    [CrossRef]
  19. C. L. Evans, E. O. Potma, and X. S. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility for vibrational microscopy,” Opt. Lett. 29, 2923-2925 (2004).
    [CrossRef]
  20. E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31, 241-243 (2006).
    [CrossRef]
  21. A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87, 023901 (2001).
    [CrossRef]
  22. V. V. Krishnamachari and E. O. Potma, “Focus-engineered coherent anti-Stokes Raman scattering microscopy: A numerical investigation,” J. Opt. Soc. Am. A 24, 1138-1147 (2007).
    [CrossRef]
  23. V. V. Krishnamachari and E. O. Potma, “Imaging chemical interfaces perpendicular to the optical axis with focus-engineered coherent anti-Stokes Raman scattering microscopy,” Chem. Phys. 341, 81-88 (2007).
    [CrossRef]
  24. V. V. Krishnamachari and E. O. Potma, “Detecting lateral interfaces with focus-engineered coherent anti-Stokes Raman scattering microscopy,” J. Raman Spectrosc. 39, 593-598 (2008).
    [CrossRef]
  25. D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A 77, 061802(R) (2008).
    [CrossRef]
  26. D. Gachet, N. Sandeau, and H. Rigneault, “Influence of the Raman depolarisation ratio on far-field radiation patterns in coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Eur. Opt. Soc. Rapid Publ. 1, 06013 (2006).
    [CrossRef]
  27. D. Gachet, F. Billard, N. Sandeau, and H. Rigneault, “Coherent anti-Stokes Raman scattering (CARS) microscopy imaging at interfaces: evidence of interference effects,” Opt. Express 15, 10408-10420 (2007).
    [CrossRef]
  28. H. Lotem, R. T. Lynch Jr., and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976).
    [CrossRef]
  29. D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977-1979 (1962).
    [CrossRef]
  30. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanetic system,” Proc. R. Soc. London 253, 358-379 (1959).
    [CrossRef]
  31. S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83, 2300-2317 (2002).
    [CrossRef]
  32. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).
  33. For a collimated beam with E(r)=exp(ik.r) the minus sign vanishes as E(−r)=E*(r).
  34. L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Acad. Sci., Paris, C. R. 110, 1251-1253 (1890).
  35. L. G. Gouy, “Sur la propagation anormale des ondes,” Acad. Sci., Paris, C. R. 111, 33-35 (1890).
  36. J. F. Ward and G. H. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57-72 (1969).
    [CrossRef]
  37. D. Débarre, W. Supatto, and E. Beaurepaire, “Structure sensitivity in third-harmonic generation microscopy,” Opt. Lett. 30, 2134-2136 (2005).
    [CrossRef] [PubMed]
  38. Interestingly, all the symmetry relations reported in Table still hold if the illumination is annular. In that case, the integration over the angle θ in relations is performed between a new value θmin (comprised between 0 and θmax) and θmax.
  39. J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 19, 1363-1375 (2002).
    [CrossRef]
  40. R. W. Hellwarth, “Third-order optical susceptibilities of solids and liquids,” Prog. Quantum Electron. 5, 1-68 (1977).
    [CrossRef]
  41. G. W. H. Wurpel, J. M. Schins, and M. Müller, “Direct measurement of chain order in single phospholipid mono- and bilayers with multiplex CARS,” J. Phys. Chem. B 108, 3400-3403 (2004).
    [CrossRef]
  42. C. L. Evans, E. O. Potma, M. Puoris'haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102, 16807-16812 (2005).
    [CrossRef]
  43. N. Djaker, D. Gachet, N. Sandeau, P.-F. Lenne, and H. Rigneault, “Refractive effects in coherent anti-Stokes Raman scattering (CARS) microscopy,” Appl. Opt. 45, 7005-7011 (2006).
    [CrossRef]
  44. C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32, 495-501 (2001).
    [CrossRef]
  45. M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem. B 106, 3715-3723 (2002).
    [CrossRef]
  46. J.-X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493-8498 (2002).
    [CrossRef]

2008 (2)

V. V. Krishnamachari and E. O. Potma, “Detecting lateral interfaces with focus-engineered coherent anti-Stokes Raman scattering microscopy,” J. Raman Spectrosc. 39, 593-598 (2008).
[CrossRef]

D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A 77, 061802(R) (2008).
[CrossRef]

2007 (4)

2006 (5)

2005 (3)

C. L. Evans, E. O. Potma, M. Puoris'haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102, 16807-16812 (2005).
[CrossRef]

S.-H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72, 041803(R) (2005).
[CrossRef]

D. Débarre, W. Supatto, and E. Beaurepaire, “Structure sensitivity in third-harmonic generation microscopy,” Opt. Lett. 30, 2134-2136 (2005).
[CrossRef] [PubMed]

2004 (2)

C. L. Evans, E. O. Potma, and X. S. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility for vibrational microscopy,” Opt. Lett. 29, 2923-2925 (2004).
[CrossRef]

G. W. H. Wurpel, J. M. Schins, and M. Müller, “Direct measurement of chain order in single phospholipid mono- and bilayers with multiplex CARS,” J. Phys. Chem. B 108, 3400-3403 (2004).
[CrossRef]

2003 (1)

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef]

2002 (6)

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

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505-1507 (2002).
[CrossRef]

M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem. B 106, 3715-3723 (2002).
[CrossRef]

J.-X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 19, 1363-1375 (2002).
[CrossRef]

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83, 2300-2317 (2002).
[CrossRef]

2001 (3)

J.-X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26, 1341-1343 (2001).
[CrossRef]

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87, 023901 (2001).
[CrossRef]

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

1999 (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]

1980 (2)

Y. Yacoby, R. Fitzgibbon, and B. Lax, “Coherent cancellation of background in four-wave mixing spectroscopy,” J. Appl. Phys. 51, 3072-3077 (1980).
[CrossRef]

F. M. Kamga and M. G. Sceats, “Pulse-sequenced coherent anti-Stokes Raman scattering spectroscopy: a method for suppression of the nonresonant background,” Opt. Lett. 5, 126-128 (1980).
[CrossRef]

1979 (1)

J.-L. Oudar, R. W. Smith, and Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
[CrossRef]

1978 (1)

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, “Polarization active Raman spectroscopy and coherent Raman ellipsometry,” Sov. Phys. JETP 47, 667-677 (1978).

1977 (1)

R. W. Hellwarth, “Third-order optical susceptibilities of solids and liquids,” Prog. Quantum Electron. 5, 1-68 (1977).
[CrossRef]

1976 (2)

J. J. Song, G. L. Easley, and M. D. Levenson, “Background suppression in coherent Raman spectroscopy,” Appl. Phys. Lett. 29, 567-569 (1976).
[CrossRef]

H. Lotem, R. T. Lynch Jr., and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976).
[CrossRef]

1974 (1)

R. F. Begley, A. B. Harvey, and R. L. Byer, “Coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 25, 387-390 (1974).
[CrossRef]

1973 (1)

P. R. Regnier, and J. P.-E. Taran, “On the possibility of measuring gas concentrations by stimulated anti-Stokes scattering,” Appl. Phys. Lett. 23, 240-242 (1973).
[CrossRef]

1972 (2)

M. D. Levenson, C. Flytzanis, and N. Bloembergen, “Interference of resonant and nonresonant three-wave mixing in diamond,” Phys. Rev. B 10, 003962 (1972).
[CrossRef]

J. J. Wynne, “Nonlinear optical Spectroscopy of χ(3) in LiNbO3,” Phys. Rev. Lett. 29650-653 (1972).
[CrossRef]

1969 (2)

J. P. Coffinet and F. de Martini, “Coherent excitation of polaritons in Gallium Phosphide,” Phys. Rev. Lett. 22, 60-64 (1969).
[CrossRef]

J. F. Ward and G. H. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57-72 (1969).
[CrossRef]

1962 (1)

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977-1979 (1962).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanetic system,” Proc. R. Soc. London 253, 358-379 (1959).
[CrossRef]

1890 (2)

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Acad. Sci., Paris, C. R. 110, 1251-1253 (1890).

L. G. Gouy, “Sur la propagation anormale des ondes,” Acad. Sci., Paris, C. R. 111, 33-35 (1890).

Akhmanov, S. A.

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, “Polarization active Raman spectroscopy and coherent Raman ellipsometry,” Sov. Phys. JETP 47, 667-677 (1978).

Alexandrou, A.

Averbukh, I. S.

Beaurepaire, E.

Begley, R. F.

R. F. Begley, A. B. Harvey, and R. L. Byer, “Coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 25, 387-390 (1974).
[CrossRef]

Billard, F.

D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A 77, 061802(R) (2008).
[CrossRef]

D. Gachet, F. Billard, N. Sandeau, and H. Rigneault, “Coherent anti-Stokes Raman scattering (CARS) microscopy imaging at interfaces: evidence of interference effects,” Opt. Express 15, 10408-10420 (2007).
[CrossRef]

Bloembergen, N.

H. Lotem, R. T. Lynch Jr., and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976).
[CrossRef]

M. D. Levenson, C. Flytzanis, and N. Bloembergen, “Interference of resonant and nonresonant three-wave mixing in diamond,” Phys. Rev. B 10, 003962 (1972).
[CrossRef]

Book, L. D.

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505-1507 (2002).
[CrossRef]

J.-X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

J.-X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26, 1341-1343 (2001).
[CrossRef]

Bunkin, A. F.

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, “Polarization active Raman spectroscopy and coherent Raman ellipsometry,” Sov. Phys. JETP 47, 667-677 (1978).

Byer, R. L.

R. F. Begley, A. B. Harvey, and R. L. Byer, “Coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 25, 387-390 (1974).
[CrossRef]

Caster, A. G.

S.-H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72, 041803(R) (2005).
[CrossRef]

Cheng, J.-X.

J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 19, 1363-1375 (2002).
[CrossRef]

J.-X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87, 023901 (2001).
[CrossRef]

J.-X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26, 1341-1343 (2001).
[CrossRef]

Coffinet, J. P.

J. P. Coffinet and F. de Martini, “Coherent excitation of polaritons in Gallium Phosphide,” Phys. Rev. Lett. 22, 60-64 (1969).
[CrossRef]

Côté, D.

C. L. Evans, E. O. Potma, M. Puoris'haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102, 16807-16812 (2005).
[CrossRef]

de Martini, F.

J. P. Coffinet and F. de Martini, “Coherent excitation of polaritons in Gallium Phosphide,” Phys. Rev. Lett. 22, 60-64 (1969).
[CrossRef]

Débarre, D.

Djaker, N.

Dudovich, N.

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef]

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

Easley, G. L.

J. J. Song, G. L. Easley, and M. D. Levenson, “Background suppression in coherent Raman spectroscopy,” Appl. Phys. Lett. 29, 567-569 (1976).
[CrossRef]

Evans, C. L.

Fitzgibbon, R.

Y. Yacoby, R. Fitzgibbon, and B. Lax, “Coherent cancellation of background in four-wave mixing spectroscopy,” J. Appl. Phys. 51, 3072-3077 (1980).
[CrossRef]

Flytzanis, C.

M. D. Levenson, C. Flytzanis, and N. Bloembergen, “Interference of resonant and nonresonant three-wave mixing in diamond,” Phys. Rev. B 10, 003962 (1972).
[CrossRef]

Gachet, D.

D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A 77, 061802(R) (2008).
[CrossRef]

D. Gachet, F. Billard, N. Sandeau, and H. Rigneault, “Coherent anti-Stokes Raman scattering (CARS) microscopy imaging at interfaces: evidence of interference effects,” Opt. Express 15, 10408-10420 (2007).
[CrossRef]

N. Djaker, D. Gachet, N. Sandeau, P.-F. Lenne, and H. Rigneault, “Refractive effects in coherent anti-Stokes Raman scattering (CARS) microscopy,” Appl. Opt. 45, 7005-7011 (2006).
[CrossRef]

D. Gachet, N. Sandeau, and H. Rigneault, “Influence of the Raman depolarisation ratio on far-field radiation patterns in coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Eur. Opt. Soc. Rapid Publ. 1, 06013 (2006).
[CrossRef]

Gouy, L. G.

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Acad. Sci., Paris, C. R. 110, 1251-1253 (1890).

L. G. Gouy, “Sur la propagation anormale des ondes,” Acad. Sci., Paris, C. R. 111, 33-35 (1890).

Greve, J.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

Harvey, A. B.

R. F. Begley, A. B. Harvey, and R. L. Byer, “Coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 25, 387-390 (1974).
[CrossRef]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

Hellwarth, R. W.

R. W. Hellwarth, “Third-order optical susceptibilities of solids and liquids,” Prog. Quantum Electron. 5, 1-68 (1977).
[CrossRef]

Hess, S. T.

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83, 2300-2317 (2002).
[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]

Ivanov, S. G.

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, “Polarization active Raman spectroscopy and coherent Raman ellipsometry,” Sov. Phys. JETP 47, 667-677 (1978).

Joffre, M.

Kamga, F. M.

Kleinman, D. A.

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977-1979 (1962).
[CrossRef]

Koroteev, N. I.

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, “Polarization active Raman spectroscopy and coherent Raman ellipsometry,” Sov. Phys. JETP 47, 667-677 (1978).

Krishnamachari, V. V.

V. V. Krishnamachari and E. O. Potma, “Detecting lateral interfaces with focus-engineered coherent anti-Stokes Raman scattering microscopy,” J. Raman Spectrosc. 39, 593-598 (2008).
[CrossRef]

V. V. Krishnamachari and E. O. Potma, “Imaging chemical interfaces perpendicular to the optical axis with focus-engineered coherent anti-Stokes Raman scattering microscopy,” Chem. Phys. 341, 81-88 (2007).
[CrossRef]

V. V. Krishnamachari and E. O. Potma, “Focus-engineered coherent anti-Stokes Raman scattering microscopy: A numerical investigation,” J. Opt. Soc. Am. A 24, 1138-1147 (2007).
[CrossRef]

Kruglik, S. G.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

Lax, B.

Y. Yacoby, R. Fitzgibbon, and B. Lax, “Coherent cancellation of background in four-wave mixing spectroscopy,” J. Appl. Phys. 51, 3072-3077 (1980).
[CrossRef]

Lenne, P.-F.

Leone, S. R.

S.-H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72, 041803(R) (2005).
[CrossRef]

Levenson, M. D.

J. J. Song, G. L. Easley, and M. D. Levenson, “Background suppression in coherent Raman spectroscopy,” Appl. Phys. Lett. 29, 567-569 (1976).
[CrossRef]

M. D. Levenson, C. Flytzanis, and N. Bloembergen, “Interference of resonant and nonresonant three-wave mixing in diamond,” Phys. Rev. B 10, 003962 (1972).
[CrossRef]

Lim, S.-H.

S.-H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72, 041803(R) (2005).
[CrossRef]

Lin, C. P.

C. L. Evans, E. O. Potma, M. Puoris'haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102, 16807-16812 (2005).
[CrossRef]

Lotem, H.

H. Lotem, R. T. Lynch Jr., and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976).
[CrossRef]

Lynch, R. T.

H. Lotem, R. T. Lynch Jr., and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976).
[CrossRef]

Müller, M.

G. W. H. Wurpel, J. M. Schins, and M. Müller, “Direct measurement of chain order in single phospholipid mono- and bilayers with multiplex CARS,” J. Phys. Chem. B 108, 3400-3403 (2004).
[CrossRef]

M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem. B 106, 3715-3723 (2002).
[CrossRef]

New, G. H.

J. F. Ward and G. H. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57-72 (1969).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

Ogilvie, J. P.

Oron, D.

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef]

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

Otto, C.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

Oudar, J.-L.

J.-L. Oudar, R. W. Smith, and Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
[CrossRef]

Paskover, Y.

Potma, E. O.

V. V. Krishnamachari and E. O. Potma, “Detecting lateral interfaces with focus-engineered coherent anti-Stokes Raman scattering microscopy,” J. Raman Spectrosc. 39, 593-598 (2008).
[CrossRef]

V. V. Krishnamachari and E. O. Potma, “Imaging chemical interfaces perpendicular to the optical axis with focus-engineered coherent anti-Stokes Raman scattering microscopy,” Chem. Phys. 341, 81-88 (2007).
[CrossRef]

V. V. Krishnamachari and E. O. Potma, “Focus-engineered coherent anti-Stokes Raman scattering microscopy: A numerical investigation,” J. Opt. Soc. Am. A 24, 1138-1147 (2007).
[CrossRef]

E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31, 241-243 (2006).
[CrossRef]

C. L. Evans, E. O. Potma, M. Puoris'haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102, 16807-16812 (2005).
[CrossRef]

C. L. Evans, E. O. Potma, and X. S. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility for vibrational microscopy,” Opt. Lett. 29, 2923-2925 (2004).
[CrossRef]

Prior, Y.

Puoris'haag, M.

C. L. Evans, E. O. Potma, M. Puoris'haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102, 16807-16812 (2005).
[CrossRef]

Regnier, P. R.

P. R. Regnier, and J. P.-E. Taran, “On the possibility of measuring gas concentrations by stimulated anti-Stokes scattering,” Appl. Phys. Lett. 23, 240-242 (1973).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanetic system,” Proc. R. Soc. London 253, 358-379 (1959).
[CrossRef]

Rigneault, H.

D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A 77, 061802(R) (2008).
[CrossRef]

D. Gachet, F. Billard, N. Sandeau, and H. Rigneault, “Coherent anti-Stokes Raman scattering (CARS) microscopy imaging at interfaces: evidence of interference effects,” Opt. Express 15, 10408-10420 (2007).
[CrossRef]

N. Djaker, D. Gachet, N. Sandeau, P.-F. Lenne, and H. Rigneault, “Refractive effects in coherent anti-Stokes Raman scattering (CARS) microscopy,” Appl. Opt. 45, 7005-7011 (2006).
[CrossRef]

D. Gachet, N. Sandeau, and H. Rigneault, “Influence of the Raman depolarisation ratio on far-field radiation patterns in coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Eur. Opt. Soc. Rapid Publ. 1, 06013 (2006).
[CrossRef]

Sandeau, N.

Sceats, M. G.

Schins, J. M.

G. W. H. Wurpel, J. M. Schins, and M. Müller, “Direct measurement of chain order in single phospholipid mono- and bilayers with multiplex CARS,” J. Phys. Chem. B 108, 3400-3403 (2004).
[CrossRef]

M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem. B 106, 3715-3723 (2002).
[CrossRef]

Shen, Y. R.

J.-L. Oudar, R. W. Smith, and Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
[CrossRef]

Silberberg, Y.

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef]

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

Smith, R. W.

J.-L. Oudar, R. W. Smith, and Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
[CrossRef]

Song, J. J.

J. J. Song, G. L. Easley, and M. D. Levenson, “Background suppression in coherent Raman spectroscopy,” Appl. Phys. Lett. 29, 567-569 (1976).
[CrossRef]

Supatto, W.

Taran, J. P.-E.

P. R. Regnier, and J. P.-E. Taran, “On the possibility of measuring gas concentrations by stimulated anti-Stokes scattering,” Appl. Phys. Lett. 23, 240-242 (1973).
[CrossRef]

Volkmer, A.

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505-1507 (2002).
[CrossRef]

J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 19, 1363-1375 (2002).
[CrossRef]

J.-X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87, 023901 (2001).
[CrossRef]

Voroshilov, A.

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

Ward, J. F.

J. F. Ward and G. H. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57-72 (1969).
[CrossRef]

Webb, W. W.

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83, 2300-2317 (2002).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanetic system,” Proc. R. Soc. London 253, 358-379 (1959).
[CrossRef]

Wurpel, G. W. H.

G. W. H. Wurpel, J. M. Schins, and M. Müller, “Direct measurement of chain order in single phospholipid mono- and bilayers with multiplex CARS,” J. Phys. Chem. B 108, 3400-3403 (2004).
[CrossRef]

Wynne, J. J.

J. J. Wynne, “Nonlinear optical Spectroscopy of χ(3) in LiNbO3,” Phys. Rev. Lett. 29650-653 (1972).
[CrossRef]

Xie, X. S.

E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31, 241-243 (2006).
[CrossRef]

C. L. Evans, E. O. Potma, M. Puoris'haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102, 16807-16812 (2005).
[CrossRef]

C. L. Evans, E. O. Potma, and X. S. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility for vibrational microscopy,” Opt. Lett. 29, 2923-2925 (2004).
[CrossRef]

J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 19, 1363-1375 (2002).
[CrossRef]

J.-X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505-1507 (2002).
[CrossRef]

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87, 023901 (2001).
[CrossRef]

J.-X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26, 1341-1343 (2001).
[CrossRef]

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]

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Y. Yacoby, R. Fitzgibbon, and B. Lax, “Coherent cancellation of background in four-wave mixing spectroscopy,” J. Appl. Phys. 51, 3072-3077 (1980).
[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]

Acad. Sci., Paris, C. R. (2)

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L. G. Gouy, “Sur la propagation anormale des ondes,” Acad. Sci., Paris, C. R. 111, 33-35 (1890).

Appl. Opt. (1)

Appl. Phys. Lett. (5)

P. R. Regnier, and J. P.-E. Taran, “On the possibility of measuring gas concentrations by stimulated anti-Stokes scattering,” Appl. Phys. Lett. 23, 240-242 (1973).
[CrossRef]

R. F. Begley, A. B. Harvey, and R. L. Byer, “Coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 25, 387-390 (1974).
[CrossRef]

J. J. Song, G. L. Easley, and M. D. Levenson, “Background suppression in coherent Raman spectroscopy,” Appl. Phys. Lett. 29, 567-569 (1976).
[CrossRef]

J.-L. Oudar, R. W. Smith, and Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758-760 (1979).
[CrossRef]

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: imaging based on Raman free induction decay,” Appl. Phys. Lett. 80, 1505-1507 (2002).
[CrossRef]

Biophys. J. (1)

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83, 2300-2317 (2002).
[CrossRef]

Chem. Phys. (1)

V. V. Krishnamachari and E. O. Potma, “Imaging chemical interfaces perpendicular to the optical axis with focus-engineered coherent anti-Stokes Raman scattering microscopy,” Chem. Phys. 341, 81-88 (2007).
[CrossRef]

J. Appl. Phys. (1)

Y. Yacoby, R. Fitzgibbon, and B. Lax, “Coherent cancellation of background in four-wave mixing spectroscopy,” J. Appl. Phys. 51, 3072-3077 (1980).
[CrossRef]

J. Eur. Opt. Soc. Rapid Publ. (1)

D. Gachet, N. Sandeau, and H. Rigneault, “Influence of the Raman depolarisation ratio on far-field radiation patterns in coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Eur. Opt. Soc. Rapid Publ. 1, 06013 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Phys. Chem. B (3)

M. Müller and J. M. Schins, “Imaging the thermodynamic state of lipid membranes with multiplex CARS microscopy,” J. Phys. Chem. B 106, 3715-3723 (2002).
[CrossRef]

J.-X. Cheng, A. Volkmer, L. D. Book, and X. S. Xie, “Multiplex coherent anti-Stokes Raman scattering microspectroscopy and study of lipid vesicles,” J. Phys. Chem. B 106, 8493-8498 (2002).
[CrossRef]

G. W. H. Wurpel, J. M. Schins, and M. Müller, “Direct measurement of chain order in single phospholipid mono- and bilayers with multiplex CARS,” J. Phys. Chem. B 108, 3400-3403 (2004).
[CrossRef]

J. Raman Spectrosc. (2)

C. Otto, A. Voroshilov, S. G. Kruglik, and J. Greve, “Vibrational bands of luminescent zinc(II)-octaethylporphyrin using a polarization-sensitive “microscopic” multiplex CARS technique,” J. Raman Spectrosc. 32, 495-501 (2001).
[CrossRef]

V. V. Krishnamachari and E. O. Potma, “Detecting lateral interfaces with focus-engineered coherent anti-Stokes Raman scattering microscopy,” J. Raman Spectrosc. 39, 593-598 (2008).
[CrossRef]

Nature (London) (1)

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

Opt. Express (2)

Opt. Lett. (6)

Phys. Rev. (2)

J. F. Ward and G. H. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57-72 (1969).
[CrossRef]

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977-1979 (1962).
[CrossRef]

Phys. Rev. A (3)

H. Lotem, R. T. Lynch Jr., and N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748-1755 (1976).
[CrossRef]

S.-H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72, 041803(R) (2005).
[CrossRef]

D. Gachet, F. Billard, and H. Rigneault, “Focused field symmetries for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. A 77, 061802(R) (2008).
[CrossRef]

Phys. Rev. B (1)

M. D. Levenson, C. Flytzanis, and N. Bloembergen, “Interference of resonant and nonresonant three-wave mixing in diamond,” Phys. Rev. B 10, 003962 (1972).
[CrossRef]

Phys. Rev. Lett. (5)

J. P. Coffinet and F. de Martini, “Coherent excitation of polaritons in Gallium Phosphide,” Phys. Rev. Lett. 22, 60-64 (1969).
[CrossRef]

J. J. Wynne, “Nonlinear optical Spectroscopy of χ(3) in LiNbO3,” Phys. Rev. Lett. 29650-653 (1972).
[CrossRef]

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90, 213902 (2003).
[CrossRef]

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]

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epidetected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87, 023901 (2001).
[CrossRef]

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

C. L. Evans, E. O. Potma, M. Puoris'haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102, 16807-16812 (2005).
[CrossRef]

Proc. R. Soc. London (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanetic system,” Proc. R. Soc. London 253, 358-379 (1959).
[CrossRef]

Prog. Quantum Electron. (1)

R. W. Hellwarth, “Third-order optical susceptibilities of solids and liquids,” Prog. Quantum Electron. 5, 1-68 (1977).
[CrossRef]

Sov. Phys. JETP (1)

S. A. Akhmanov, A. F. Bunkin, S. G. Ivanov, and N. I. Koroteev, “Polarization active Raman spectroscopy and coherent Raman ellipsometry,” Sov. Phys. JETP 47, 667-677 (1978).

Other (3)

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

For a collimated beam with E(r)=exp(ik.r) the minus sign vanishes as E(−r)=E*(r).

Interestingly, all the symmetry relations reported in Table still hold if the illumination is annular. In that case, the integration over the angle θ in relations is performed between a new value θmin (comprised between 0 and θmax) and θmax.

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Figures (9)

Fig. 1
Fig. 1

Gaussian beam focusing through a microscope objective. (a) f, objective focal length; F , objective focus; r 0 , microscope objective’s back aperture; θ max , focusing maximal angle; θ, focusing angle of an elementary ray; σ, Gaussian profile half-width (at 1/e); E 0 , amplitude of the incoming beam. (b) α, field polarization direction in the object space. (c) Cylindrical coordinates system adopted to define the position of a point M ( r ) = M ( ρ M , φ M , z ) near the microscope objective focus F .

Fig. 2
Fig. 2

Scheme of the studied configuration. (a) Excitation volume. The focal plane defines the z = 0 plane. (b) α-problem: the resonant medium 1 lies above the nonresonant medium 2, and the position of their common interface is z 0 . (c) β-problem: the resonant medium 1 lies below the nonresonant medium 2, and the position of their common interface is z 0 .

Fig. 3
Fig. 3

CARS spectra when the excitation is centered on an interface ( z 0 = 0 ) . (a) Fwd-CARS signals generated on the interface separating two resonant and nonresonant media versus the normalized frequency detuning ζ = ( ω P ω S Ω R ) Γ . I as α (black circles) and I as β (gray circles), CARS signals associated with α and β-problems; Δ I as (gray dots), signal difference I as α I as β ; the solid line is Im [ χ x x y y ( 3 ) 1 R ] and the dashed line is the bulk spectrum of the resonant medium. For the resonant medium, the probed Raman line is assumed to be Lorentzian following χ x x y y ( 3 ) 1 R = a [ ω P ω S Ω R + i Γ ] and χ x x y y ( 3 ) 1 NR = a Γ . For the nonresonant medium, χ x x y y ( 3 ) 2 NR = 2 χ x x y y ( 3 ) 1 NR . (b) Raman recovered spectra for several values of the nonresonant medium tensor element χ x x y y ( 3 ) 2 NR : 0.5 χ x x y y ( 3 ) 1 NR (black circles), χ x x y y ( 3 ) 1 NR (gray circles), and 2 χ x x y y ( 3 ) 1 NR (black dots). The incident pump ( λ p = 730 nm ) and Stokes ( λ s = 787 nm ) lasers are linearly polarized along the same direction. The Raman depolarization ratio ρ R associated with medium 1 equals 1 3 . Objective numerical apertures (NA): 1.2 for excitation and 0.5 for collection.

Fig. 4
Fig. 4

CARS generation when excitation is centered on an interface ( z 0 = 0 ) . CARS signal difference Δ I as = I as α I as β maxima (for a Raman resonance detuning ζ = 0 ) as a function of χ x x y y ( 3 ) 2 NR χ x x y y ( 3 ) 1 NR for different values of the Raman depolarization ratio ρ R associated with medium 1. Black circles: ρ R = 0 ; black dots: ρ R = 1 3 ; gray dots: ρ R = 0.75 .

Fig. 5
Fig. 5

CARS generation near a unique interface. Influence of the excitation volume spatial shift z 0 to the interface on the signals generated for the α (black circles) and β-problems (gray circles) and their difference Δ I as (black dots): (a) z 0 = 500 nm and (b) z 0 = 500 nm . For comparison, the bulk CARS spectrum of medium 1 is plotted (dashed lines). (c) Signal difference for the previous values of the excitation spatial shift z 0 : 500 nm (circles), 0 nm (dots) and 500 nm (crosses). On each graph, Im ( χ x x y y ( 3 ) 1 R ) is plotted (solid curve). (d) For information, square of the nonlinear induced polarization (normalized) in a bulk medium for the same focusing parameters. The laser, the excitation and collection objective parameters, and the Raman depolarization ratio are chosen as in Fig. 3.

Fig. 6
Fig. 6

CARS generation near a unique interface. CARS signal difference Δ I as = I as α I as β for different values of the excitation volume spatial shift z 0 as a function of the Raman depolarization ratio ρ R associated with medium 1: (a) ρ R = 0 , (b) ρ R = 1 3 , and (c) ρ R = 0.75 . Circles, z 0 = 500 nm ; crosses, z 0 = 500 nm . On each graph, Im ( χ x x y y ( 3 ) 1 R ) is plotted (solid curve).

Fig. 7
Fig. 7

Scheme of the studied configuration for two successive transverse interfaces. (a) Excitation volume. The focal plane defines the z = 0 plane. (b) α-problem: a resonant medium 1 with width e 0 is embedded between two identical semi-infinite nonresonant media 2. The lower and upper interface positions are, respectively, z 1 and z 2 with z 2 = z 1 + e 0 . (c) β-problem: the lower and upper interface positions are, respectively, z 2 and z 1 .

Fig. 8
Fig. 8

CARS generation near two successive interfaces. CARS signals related to the α (black circles) and β-problems (gray circles) and signal difference Δ I as (gray dots). For comparison, the bulk CARS signal of medium 1 (dashed curve) and the imaginary part of the medium 1 nonlinear tensor element χ x x y y ( 3 ) 1 R (solid curve) are plotted. The layer 1 width e 0 is 500 nm , and the excitation is centered on the lower interface for the α-problem and on the upper interface for the β-problem ( z 1 = 0 nm and z 2 = 500 nm ).

Fig. 9
Fig. 9

CARS generation near two successive interfaces. (a) Signal difference Δ I as for different values of the layer 1 width e 0 . In each case, the excitation is centered on the lower interface for the α-problem and on the upper interface for the β-problem ( z 1 = 0 nm and z 2 = e 0 ). (b) Signal difference Δ I as for different values of the spatial shift z 1 to the lower interface. The resonant layer 1 width is e 0 = 500 nm

Tables (1)

Tables Icon

Table 1 Symmetry Relations on the Focused Field Components a

Equations (53)

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

χ ( 3 ) = χ R ( 3 ) + χ NR ( 3 ) .
χ i j k l ( 3 ) R = χ x x y y ( 3 ) R ( δ i j δ k l + δ i k δ j l + 2 ρ R 1 ρ R δ i l δ j k ) ,
χ i j k l ( 3 ) NR = χ x x y y ( 3 ) NR ( δ i j δ k l + δ i k δ j l + δ i l δ j k ) ,
P ( 3 ) ( r , ω as ) = χ ( 3 ) ( r ; ω as ; ω p , ω p , ω s ) E p ( r , ω p ) : E p ( r , ω p ) : E s * ( r , ω s ) .
P i ( 3 ) ( r ) = 3 j , k , l χ i j k l ( 3 ) E p j ( r ) E p k ( r ) E s l * ( r ) ,
P ( 3 ) ( r ) = P R ( 3 ) ( r ) + P NR ( 3 ) ( r ) .
P R ( 3 ) ( r ) = 6 χ x x y y ( 3 ) R S ( r , ρ R ) ,
P NR ( 3 ) ( r ) = 6 χ x x y y ( 3 ) NR S ( r , 1 3 ) ,
S ( r , ρ R ) = [ E p ( r ) E s * ( r ) ] E p ( r ) + ρ R 1 ρ R [ E p x 2 ( r ) + E p y 2 ( r ) + E p z 2 ( r ) ] E s * ( r ) ,
S ( r , 1 3 ) = [ E p ( r ) E s * ( r ) ] E p ( r ) + 1 2 [ E p x 2 ( r ) + E p y 2 ( r ) + E p z 2 ( r ) ] E s * ( r ) .
P ( 3 ) ( r , ρ R ) = 6 [ χ x x y y ( 3 ) R ( r ) S ( r , ρ R ) + χ x x y y ( 3 ) NR ( r ) S ( r , 1 3 ) ] .
A ( θ ) = i k 0 f 2 π E 0 cos ( θ ) n exp [ ( n β sin ( θ ) NA ) 2 ] ,
E x ( ρ M , φ M , z ) = cos ( α ) [ I 0 ( ρ M , z ) + cos ( 2 φ M ) I 2 ( ρ M , z ) ] + sin ( α ) sin ( 2 φ M ) I 2 ( ρ M , z ) ,
E y ( ρ M , φ M , z ) = cos ( α ) sin ( 2 φ M ) I 2 ( ρ M , z ) + sin ( α ) [ I 0 ( ρ M , z ) cos ( 2 φ M ) I 2 ( ρ M , z ) ] ,
E z ( ρ M , φ M , z ) = cos ( φ M ) I 1 ( ρ M , z ) .
I 0 ( ρ M , z ) = 0 θ max A ( θ ) sin ( θ ) [ 1 + cos ( θ ) ] J 0 [ k ρ M sin ( θ ) ] exp [ i k z cos ( θ ) ] d θ ,
I 1 ( ρ M , z ) = 0 θ max A ( θ ) sin 2 ( θ ) J 1 [ k ρ M sin ( θ ) ] exp [ i k z cos ( θ ) ] d θ ,
I 2 ( ρ M , z ) = 0 θ max A ( θ ) sin ( θ ) [ 1 cos ( θ ) ] J 2 [ k ρ M sin ( θ ) ] exp [ i k z cos ( θ ) ] d θ ,
E ( r ) = E * ( r )
S ( r , ρ R ) = S * ( r , ρ R ) ,
S ( r , 1 3 ) = S * ( r , 1 3 ) .
χ 1 ( 3 ) = χ 1 R ( 3 ) + χ 1 NR ( 3 ) ,
χ 2 ( 3 ) = χ 2 NR ( 3 ) .
E as m ( k ) = z = z = + y = y = + x = x = + M ( k ) P ( 3 ) , m ( r ) exp ( i k r ) d r ,
I as m ( k ) = E as m ( k ) 2 = E as m ( k ) E as m * ( k ) .
E as α ( k ) = z = z = + + + M ( k ) P ( 3 ) , α ( r ) exp ( i k r ) d r .
E as α ( k ) = z = z = + z 0 + + M ( k ) P 2 ( 3 ) ( r ) exp ( i k r ) d r + z = + z 0 z = + + + M ( k ) P 1 ( 3 ) ( r ) exp ( i k r ) d r .
E as α ( k ) = 6 [ χ x x y y ( 3 ) 2 NR z = z = + z 0 + + M ( k ) S ( r , 1 3 ) exp ( i k r ) d r + χ x x y y ( 3 ) 1 R z = + z 0 z = + + + M ( k ) S ( r , ρ R ) exp ( i k r ) d r + χ x x y y ( 3 ) 1 NR z = + z 0 z = + + + M ( k ) S ( r , 1 3 ) exp ( i k r ) d r ] .
E as α ( k ) = 6 [ χ x x y y ( 3 ) 1 R I + z 0 + ( ρ R ) + χ x x y y ( 3 ) 1 NR I + z 0 + ( 1 3 ) + χ x x y y ( 3 ) 2 NR I z 0 ( 1 3 ) ] .
I as α ( k ) = 36 { χ x x y y ( 3 ) 1 R 2 I + z 0 + ( ρ R ) 2 + 2 χ x x y y ( 3 ) 1 NR Re [ χ x x y y ( 3 ) 1 R I + z 0 + ( ρ R ) I + z 0 + * ( 1 3 ) ] + ( χ x x y y ( 3 ) 1 NR ) 2 I + z 0 + ( 1 3 ) 2 + 2 χ x x y y ( 3 ) 2 NR Re [ χ x x y y ( 3 ) 1 R I + z 0 + ( ρ R ) I + z 0 * ( 1 3 ) ] + ( χ x x y y ( 3 ) 2 NR ) 2 I + z 0 ( 1 3 ) 2 + 2 χ x x y y ( 3 ) 1 NR χ x x y y ( 3 ) 2 NR Re [ I + z 0 + ( 1 3 ) I + z 0 * ( 1 3 ) ] } .
E as β ( k ) = z = z = + + + M ( k ) P ( 3 ) , β ( r ) exp ( i k r ) d r .
E as β ( k ) = [ z = z = z 0 + + M ( k ) P 1 ( 3 ) ( r ) exp ( i k r ) d r + z = z 0 z = + + + M ( k ) P 2 ( 3 ) ( r ) exp ( i k r ) d r ] ,
E as β ( k ) = 6 [ χ x x y y ( 3 ) 2 NR z = z 0 z = + + + M ( k ) S ( r , 1 3 ) exp ( i k r ) d r + χ x x y y ( 3 ) 1 R z = z = z 0 + + M ( k ) S ( r , ρ R ) exp ( i k r ) d r + χ x x y y ( 3 ) 1 NR z = z = z 0 + + M ( k ) S ( r , 1 3 ) exp ( i k r ) d r ] .
I as β ( k ) = 36 { χ x x y y ( 3 ) 1 R 2 I z 0 ( ρ R ) 2 + 2 χ x x y y ( 3 ) 1 NR Re [ χ x x y y ( 3 ) 1 R I z 0 ( ρ R ) I z 0 * ( 1 3 ) ] + ( χ x x y y ( 3 ) 1 NR ) 2 I z 0 ( 1 3 ) 2 + 2 χ x x y y ( 3 ) 2 NR Re [ χ x x y y ( 3 ) 1 R I z 0 ( ρ R ) I z 0 + * ( 1 3 ) ] + ( χ x x y y ( 3 ) 2 NR ) 2 I z 0 + ( 1 3 ) 2 + 2 χ x x y y ( 3 ) 1 NR χ x x y y ( 3 ) 2 NR Re [ I z 0 ( 1 3 ) I z 0 + * ( 1 3 ) ] } .
I z low z up ( ρ R ) = I z up z low * ( ρ R ) ,
I z low z up ( 1 3 ) = I z up * z low ( 1 3 ) .
I as β ( k ) = 36 { χ x x y y ( 3 ) 1 R 2 I + z 0 + ( ρ R ) 2 + 2 χ x x y y ( 3 ) 1 NR Re [ χ x x y y ( 3 ) 1 R I + z 0 + * ( ρ R ) I + z 0 + ( 1 3 ) ] + ( χ x x y y ( 3 ) 1 NR ) 2 I + z 0 + ( 1 3 ) 2 + 2 χ x x y y ( 3 ) 2 NR Re [ χ x x y y ( 3 ) 1 R I + z 0 + * ( ρ R ) I + z 0 ( 1 3 ) ] + ( χ x x y y ( 3 ) 2 NR ) 2 I + z 0 ( 1 3 ) 2 + 2 χ x x y y ( 3 ) 1 NR χ x x y y ( 3 ) 2 NR Re [ I + z 0 + * ( 1 3 ) I + z 0 ( 1 3 ) ] } .
Δ I as ( k ) = I as β ( k ) I as α ( k ) ,
Δ I as ( k ) = 72 { χ x x y y ( 3 ) 1 NR Re { χ x x y y ( 3 ) 1 R [ I + z 0 + * ( ρ R ) I + z 0 + ( 1 3 ) I + z 0 + ( ρ R ) I + z 0 + * ( 1 3 ) ] } + χ x x y y ( 3 ) 2 NR Re { χ x x y y ( 3 ) 1 R [ I + z 0 + * ( ρ R ) I + z 0 ( 1 3 ) I + z 0 + ( ρ R ) I + z 0 * ( 1 3 ) ] } + χ x x y y ( 3 ) 1 NR χ x x y y ( 3 ) 2 NR Re { I + z 0 + * ( 1 3 ) I + z 0 ( 1 3 ) I + z 0 + ( 1 3 ) I + z 0 * ( 1 3 ) } } .
T 1 = 2 χ x x y y ( 3 ) 1 NR Im [ I + z 0 + ( 1 3 ) I + z 0 + * ( ρ R ) ] Im ( χ x x y y ( 3 ) 1 R ) ,
T 2 = 2 χ x x y y ( 3 ) 2 NR Im [ I + z 0 ( 1 3 ) I + z 0 + * ( ρ R ) ] Im ( χ x x y y ( 3 ) 1 R ) ,
T 3 = 0 .
Δ I as ( k ) = 144 [ F 1 ( k , z 0 , ρ R ) χ x x y y ( 3 ) 1 NR + F 2 ( k , z 0 , ρ R ) χ x x y y ( 3 ) 2 NR ] Im ( χ x x y y ( 3 ) 1 R ) ,
F 1 ( k , z 0 , ρ R ) = Im [ I + z 0 + ( 1 3 ) I + z 0 + * ( ρ R ) ] ,
F 2 ( k , z 0 , ρ R ) = Im [ I + z 0 ( 1 3 ) I + z 0 + * ( ρ R ) ] .
F 2 ( k , z 0 , 1 3 ) = F 2 ( k , z 0 , 1 3 ) .
E as α ( k ) = 6 [ χ x x y y ( 3 ) 1 R I z 1 z 2 ( ρ R ) + χ x x y y ( 3 ) 1 NR I z 1 z 2 ( 1 3 ) + χ x x y y ( 3 ) 2 NR I z 1 ( 1 3 ) + χ x x y y ( 3 ) 2 NR I z 2 + ( 1 3 ) ] .
I as α ( k ) = 36 { χ x x y y ( 3 ) 1 R I z 1 z 2 ( ρ R ) 2 + χ x x y y ( 3 ) 1 NR I z 1 z 2 ( 1 3 ) 2 + 2 χ x x y y ( 3 ) 1 NR Re [ χ x x y y ( 3 ) 1 R I z 1 z 2 ( ρ R ) I z 1 z 2 * ( 1 3 ) ] + χ x x y y ( 3 ) 2 NR I z 1 ( 1 3 ) 2 + 2 χ x x y y ( 3 ) 2 NR Re { χ x x y y ( 3 ) 1 R I z 1 z 2 ( ρ R ) [ I z 1 ( 1 3 ) + I z 2 + ( 1 3 ) ] * } + χ x x y y ( 3 ) 2 NR I z 2 + ( 1 3 ) 2 + 2 ( χ x x y y ( 3 ) 2 NR ) 2 Re [ I z 1 ( 1 3 ) I z 2 + * ( 1 3 ) ] + 2 χ x x y y ( 3 ) 1 NR χ x x y y ( 3 ) 2 NR Re { I z 1 z 2 ( 1 3 ) [ I z 1 ( 1 3 ) + I z 2 + ( 1 3 ) ] * } } .
E as β ( k ) = 6 [ χ x x y y ( 3 ) 1 R I z 2 z 1 ( ρ R ) + χ x x y y ( 3 ) 1 NR I z 2 z 1 ( 1 3 ) + χ x x y y ( 3 ) 2 NR I z 2 ( 1 3 ) + χ x x y y ( 3 ) 2 NR I z 1 + ( 1 3 ) ] ,
I as β ( k ) = 36 { χ x x y y ( 3 ) 1 R I z 2 z 1 ( ρ R ) 2 + χ x x y y ( 3 ) 1 NR I z 2 z 1 ( 1 3 ) 2 + 2 χ x x y y ( 3 ) 1 NR Re [ χ x x y y ( 3 ) 1 R I z 2 z 1 ( ρ R ) I z 2 z 1 * ( 1 3 ) ] + χ x x y y ( 3 ) 2 NR I z 1 + ( 1 3 ) 2 + 2 χ x x y y ( 3 ) 2 NR Re { χ x x y y ( 3 ) 1 R I z 2 z 1 ( ρ R ) [ I z 1 + ( 1 3 ) + I z 2 ( 1 3 ) ] * } + χ x x y y ( 3 ) 2 NR I z 2 ( 1 3 ) 2 + 2 ( χ x x y y ( 3 ) 2 NR ) 2 Re [ I z 1 + ( 1 3 ) I z 2 * ( 1 3 ) ] + 2 χ x x y y ( 3 ) 1 NR χ x x y y ( 3 ) 2 NR Re { I z 2 z 1 ( 1 3 ) [ I z 1 + ( 1 3 ) + I z 2 ( 1 3 ) ] * } } .
Δ I as ( k ) = 144 [ F 1 ( k , z 1 , z 2 , ρ R ) χ x x y y ( 3 ) 1 NR + F 2 ( k , z 1 , z 2 , ρ R ) χ x x y y ( 3 ) 2 NR ] Im ( χ x x y y ( 3 ) 1 R ) ,
F 1 ( k , z 1 , z 2 , ρ R ) = Im [ I z 1 z 2 ( 1 3 ) I z 1 z 2 * ( ρ R ) ] ,
F 2 ( k , z 1 , z 2 , ρ R ) = Im { [ I z 1 ( 1 3 ) + I z 2 + ( 1 3 ) ] I z 1 z 2 * ( ρ R ) } .

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