Abstract

We propose and experimentally demonstrate a method that is capable of resolving both real and imaginary parts of third-order nonlinearity (χ(3)) in the vicinity of Raman resonances. Dispersion of χ(3) can be obtained from a medium probed within microscopic volumes with a spectral resolution of better than 0.10cm1.

© 2013 Optical Society of America

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References

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  1. A. Laubereau, D. von der Linde, and W. Kaiser, Phys. Rev. Lett. 28, 1162 (1972).
    [CrossRef]
  2. M. L. Geirnaert, G. M. Gale, and C. Flytzanis, Phys. Rev. Lett. 52, 815 (1984).
    [CrossRef]
  3. T. Lang, K.-L. Kompa, and M. Motzkus, Chem. Phys. Lett. 310, 65 (1999).
    [CrossRef]
  4. Y. J. Lee, H. S. Parekh, J. A. Fagan, and M. Cicerone, Phys. Rev. B 82, 165432 (2010).
    [CrossRef]
  5. B. B. Krynetsky, L. A. Kulevsky, V. A. Mishin, A. M. Prokhorov, A. D. Savel’ev, and V. V. Smirnov, Opt. Commun. 21, 225 (1977).
    [CrossRef]
  6. P. Leproux, V. Couderc, A. deAngelis, M. Akuno, H. Kano, and H. Hamaguchi, J. Raman Spectrosc. 42, 1871 (2011).
    [CrossRef]
  7. M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, Phys. Rev. Lett. 103, 043905 (2009).
    [CrossRef]
  8. C. L. Evans, E. O. Potma, and X. S. Xie, Opt. Lett. 29, 2923 (2004).
    [CrossRef]
  9. E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, Appl. Phys. B 87, 389 (2007).
    [CrossRef]
  10. C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
    [CrossRef]
  11. J. A. Giordmaine and W. Kaiser, Phys. Rev. 144, 676 (1966).
    [CrossRef]
  12. A. Laubereau and W. Kaiser, Rev. Mod. Phys. 50, 607 (1978).
    [CrossRef]
  13. Y.-X. Yan and K. Nelson, J. Chem. Phys. 87, 6240 (1987).
    [CrossRef]
  14. S. A. Malinovskaya, Opt. Lett. 33, 2245 (2008).
    [CrossRef]
  15. K. V. Bhupathiraju, A. D. Seymour, and F. Ganikhanov, Opt. Lett. 34, 2093 (2009).
    [CrossRef]
  16. J. D. Rowley, S. Yang, and F. Ganikhanov, J. Opt. Soc. Am. B 28, 1026 (2011).
    [CrossRef]
  17. G. E. Kugelt, F. Brehatt, B. Wyncket, M. D. Fontanat, G. Marniers, C. Carabatos-Nedelect, and J. Mangin, J. Phys. C 21, 5566 (1988).
  18. Y. E. D’yakov, JETP Lett. 37, 15 (1983).
  19. R. M. El-Abassy, P. Donfack, and A. Materny, J. Raman Spectrosc. 40, 1284 (2009).
    [CrossRef]

2011 (2)

P. Leproux, V. Couderc, A. deAngelis, M. Akuno, H. Kano, and H. Hamaguchi, J. Raman Spectrosc. 42, 1871 (2011).
[CrossRef]

J. D. Rowley, S. Yang, and F. Ganikhanov, J. Opt. Soc. Am. B 28, 1026 (2011).
[CrossRef]

2010 (1)

Y. J. Lee, H. S. Parekh, J. A. Fagan, and M. Cicerone, Phys. Rev. B 82, 165432 (2010).
[CrossRef]

2009 (3)

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, Phys. Rev. Lett. 103, 043905 (2009).
[CrossRef]

K. V. Bhupathiraju, A. D. Seymour, and F. Ganikhanov, Opt. Lett. 34, 2093 (2009).
[CrossRef]

R. M. El-Abassy, P. Donfack, and A. Materny, J. Raman Spectrosc. 40, 1284 (2009).
[CrossRef]

2008 (2)

S. A. Malinovskaya, Opt. Lett. 33, 2245 (2008).
[CrossRef]

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

2007 (1)

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, Appl. Phys. B 87, 389 (2007).
[CrossRef]

2004 (1)

1999 (1)

T. Lang, K.-L. Kompa, and M. Motzkus, Chem. Phys. Lett. 310, 65 (1999).
[CrossRef]

1988 (1)

G. E. Kugelt, F. Brehatt, B. Wyncket, M. D. Fontanat, G. Marniers, C. Carabatos-Nedelect, and J. Mangin, J. Phys. C 21, 5566 (1988).

1987 (1)

Y.-X. Yan and K. Nelson, J. Chem. Phys. 87, 6240 (1987).
[CrossRef]

1984 (1)

M. L. Geirnaert, G. M. Gale, and C. Flytzanis, Phys. Rev. Lett. 52, 815 (1984).
[CrossRef]

1983 (1)

Y. E. D’yakov, JETP Lett. 37, 15 (1983).

1978 (1)

A. Laubereau and W. Kaiser, Rev. Mod. Phys. 50, 607 (1978).
[CrossRef]

1977 (1)

B. B. Krynetsky, L. A. Kulevsky, V. A. Mishin, A. M. Prokhorov, A. D. Savel’ev, and V. V. Smirnov, Opt. Commun. 21, 225 (1977).
[CrossRef]

1972 (1)

A. Laubereau, D. von der Linde, and W. Kaiser, Phys. Rev. Lett. 28, 1162 (1972).
[CrossRef]

1966 (1)

J. A. Giordmaine and W. Kaiser, Phys. Rev. 144, 676 (1966).
[CrossRef]

Akuno, M.

P. Leproux, V. Couderc, A. deAngelis, M. Akuno, H. Kano, and H. Hamaguchi, J. Raman Spectrosc. 42, 1871 (2011).
[CrossRef]

Berner, S.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, Appl. Phys. B 87, 389 (2007).
[CrossRef]

Bhupathiraju, K. V.

Brehatt, F.

G. E. Kugelt, F. Brehatt, B. Wyncket, M. D. Fontanat, G. Marniers, C. Carabatos-Nedelect, and J. Mangin, J. Phys. C 21, 5566 (1988).

Carabatos-Nedelect, C.

G. E. Kugelt, F. Brehatt, B. Wyncket, M. D. Fontanat, G. Marniers, C. Carabatos-Nedelect, and J. Mangin, J. Phys. C 21, 5566 (1988).

Cicerone, M.

Y. J. Lee, H. S. Parekh, J. A. Fagan, and M. Cicerone, Phys. Rev. B 82, 165432 (2010).
[CrossRef]

Couderc, V.

P. Leproux, V. Couderc, A. deAngelis, M. Akuno, H. Kano, and H. Hamaguchi, J. Raman Spectrosc. 42, 1871 (2011).
[CrossRef]

D’yakov, Y. E.

Y. E. D’yakov, JETP Lett. 37, 15 (1983).

deAngelis, A.

P. Leproux, V. Couderc, A. deAngelis, M. Akuno, H. Kano, and H. Hamaguchi, J. Raman Spectrosc. 42, 1871 (2011).
[CrossRef]

Donfack, P.

R. M. El-Abassy, P. Donfack, and A. Materny, J. Raman Spectrosc. 40, 1284 (2009).
[CrossRef]

El-Abassy, R. M.

R. M. El-Abassy, P. Donfack, and A. Materny, J. Raman Spectrosc. 40, 1284 (2009).
[CrossRef]

Evans, C. L.

Fagan, J. A.

Y. J. Lee, H. S. Parekh, J. A. Fagan, and M. Cicerone, Phys. Rev. B 82, 165432 (2010).
[CrossRef]

Flytzanis, C.

M. L. Geirnaert, G. M. Gale, and C. Flytzanis, Phys. Rev. Lett. 52, 815 (1984).
[CrossRef]

Fontanat, M. D.

G. E. Kugelt, F. Brehatt, B. Wyncket, M. D. Fontanat, G. Marniers, C. Carabatos-Nedelect, and J. Mangin, J. Phys. C 21, 5566 (1988).

Freudiger, C. W.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

Gale, G. M.

M. L. Geirnaert, G. M. Gale, and C. Flytzanis, Phys. Rev. Lett. 52, 815 (1984).
[CrossRef]

Ganikhanov, F.

Geirnaert, M. L.

M. L. Geirnaert, G. M. Gale, and C. Flytzanis, Phys. Rev. Lett. 52, 815 (1984).
[CrossRef]

Gilch, P.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, Appl. Phys. B 87, 389 (2007).
[CrossRef]

Giordmaine, J. A.

J. A. Giordmaine and W. Kaiser, Phys. Rev. 144, 676 (1966).
[CrossRef]

Hamaguchi, H.

P. Leproux, V. Couderc, A. deAngelis, M. Akuno, H. Kano, and H. Hamaguchi, J. Raman Spectrosc. 42, 1871 (2011).
[CrossRef]

He, C.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

Herek, J. L.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, Phys. Rev. Lett. 103, 043905 (2009).
[CrossRef]

Holtom, G. R.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

Jurna, M.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, Phys. Rev. Lett. 103, 043905 (2009).
[CrossRef]

Kaiser, W.

A. Laubereau and W. Kaiser, Rev. Mod. Phys. 50, 607 (1978).
[CrossRef]

A. Laubereau, D. von der Linde, and W. Kaiser, Phys. Rev. Lett. 28, 1162 (1972).
[CrossRef]

J. A. Giordmaine and W. Kaiser, Phys. Rev. 144, 676 (1966).
[CrossRef]

Kang, J. X.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

Kano, H.

P. Leproux, V. Couderc, A. deAngelis, M. Akuno, H. Kano, and H. Hamaguchi, J. Raman Spectrosc. 42, 1871 (2011).
[CrossRef]

Kompa, K.-L.

T. Lang, K.-L. Kompa, and M. Motzkus, Chem. Phys. Lett. 310, 65 (1999).
[CrossRef]

Korterik, J. P.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, Phys. Rev. Lett. 103, 043905 (2009).
[CrossRef]

Krynetsky, B. B.

B. B. Krynetsky, L. A. Kulevsky, V. A. Mishin, A. M. Prokhorov, A. D. Savel’ev, and V. V. Smirnov, Opt. Commun. 21, 225 (1977).
[CrossRef]

Kugelt, G. E.

G. E. Kugelt, F. Brehatt, B. Wyncket, M. D. Fontanat, G. Marniers, C. Carabatos-Nedelect, and J. Mangin, J. Phys. C 21, 5566 (1988).

Kulevsky, L. A.

B. B. Krynetsky, L. A. Kulevsky, V. A. Mishin, A. M. Prokhorov, A. D. Savel’ev, and V. V. Smirnov, Opt. Commun. 21, 225 (1977).
[CrossRef]

Laimgruber, S.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, Appl. Phys. B 87, 389 (2007).
[CrossRef]

Lang, T.

T. Lang, K.-L. Kompa, and M. Motzkus, Chem. Phys. Lett. 310, 65 (1999).
[CrossRef]

Laubereau, A.

A. Laubereau and W. Kaiser, Rev. Mod. Phys. 50, 607 (1978).
[CrossRef]

A. Laubereau, D. von der Linde, and W. Kaiser, Phys. Rev. Lett. 28, 1162 (1972).
[CrossRef]

Lee, Y. J.

Y. J. Lee, H. S. Parekh, J. A. Fagan, and M. Cicerone, Phys. Rev. B 82, 165432 (2010).
[CrossRef]

Leproux, P.

P. Leproux, V. Couderc, A. deAngelis, M. Akuno, H. Kano, and H. Hamaguchi, J. Raman Spectrosc. 42, 1871 (2011).
[CrossRef]

Lu, S.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

Malinovskaya, S. A.

Mangin, J.

G. E. Kugelt, F. Brehatt, B. Wyncket, M. D. Fontanat, G. Marniers, C. Carabatos-Nedelect, and J. Mangin, J. Phys. C 21, 5566 (1988).

Marniers, G.

G. E. Kugelt, F. Brehatt, B. Wyncket, M. D. Fontanat, G. Marniers, C. Carabatos-Nedelect, and J. Mangin, J. Phys. C 21, 5566 (1988).

Materny, A.

R. M. El-Abassy, P. Donfack, and A. Materny, J. Raman Spectrosc. 40, 1284 (2009).
[CrossRef]

Min, W.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

Mishin, V. A.

B. B. Krynetsky, L. A. Kulevsky, V. A. Mishin, A. M. Prokhorov, A. D. Savel’ev, and V. V. Smirnov, Opt. Commun. 21, 225 (1977).
[CrossRef]

Motzkus, M.

T. Lang, K.-L. Kompa, and M. Motzkus, Chem. Phys. Lett. 310, 65 (1999).
[CrossRef]

Nelson, K.

Y.-X. Yan and K. Nelson, J. Chem. Phys. 87, 6240 (1987).
[CrossRef]

Offerhaus, H. L.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, Phys. Rev. Lett. 103, 043905 (2009).
[CrossRef]

Otto, C.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, Phys. Rev. Lett. 103, 043905 (2009).
[CrossRef]

Parekh, H. S.

Y. J. Lee, H. S. Parekh, J. A. Fagan, and M. Cicerone, Phys. Rev. B 82, 165432 (2010).
[CrossRef]

Ploetz, E.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, Appl. Phys. B 87, 389 (2007).
[CrossRef]

Potma, E. O.

Prokhorov, A. M.

B. B. Krynetsky, L. A. Kulevsky, V. A. Mishin, A. M. Prokhorov, A. D. Savel’ev, and V. V. Smirnov, Opt. Commun. 21, 225 (1977).
[CrossRef]

Rowley, J. D.

Saar, B. G.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

Savel’ev, A. D.

B. B. Krynetsky, L. A. Kulevsky, V. A. Mishin, A. M. Prokhorov, A. D. Savel’ev, and V. V. Smirnov, Opt. Commun. 21, 225 (1977).
[CrossRef]

Seymour, A. D.

Smirnov, V. V.

B. B. Krynetsky, L. A. Kulevsky, V. A. Mishin, A. M. Prokhorov, A. D. Savel’ev, and V. V. Smirnov, Opt. Commun. 21, 225 (1977).
[CrossRef]

Tsai, J. C.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

von der Linde, D.

A. Laubereau, D. von der Linde, and W. Kaiser, Phys. Rev. Lett. 28, 1162 (1972).
[CrossRef]

Wyncket, B.

G. E. Kugelt, F. Brehatt, B. Wyncket, M. D. Fontanat, G. Marniers, C. Carabatos-Nedelect, and J. Mangin, J. Phys. C 21, 5566 (1988).

Xie, X. S.

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

C. L. Evans, E. O. Potma, and X. S. Xie, Opt. Lett. 29, 2923 (2004).
[CrossRef]

Yan, Y.-X.

Y.-X. Yan and K. Nelson, J. Chem. Phys. 87, 6240 (1987).
[CrossRef]

Yang, S.

Zinth, W.

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, Appl. Phys. B 87, 389 (2007).
[CrossRef]

Appl. Phys. B (1)

E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, and P. Gilch, Appl. Phys. B 87, 389 (2007).
[CrossRef]

Chem. Phys. Lett. (1)

T. Lang, K.-L. Kompa, and M. Motzkus, Chem. Phys. Lett. 310, 65 (1999).
[CrossRef]

J. Chem. Phys. (1)

Y.-X. Yan and K. Nelson, J. Chem. Phys. 87, 6240 (1987).
[CrossRef]

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

J. Phys. C (1)

G. E. Kugelt, F. Brehatt, B. Wyncket, M. D. Fontanat, G. Marniers, C. Carabatos-Nedelect, and J. Mangin, J. Phys. C 21, 5566 (1988).

J. Raman Spectrosc. (2)

P. Leproux, V. Couderc, A. deAngelis, M. Akuno, H. Kano, and H. Hamaguchi, J. Raman Spectrosc. 42, 1871 (2011).
[CrossRef]

R. M. El-Abassy, P. Donfack, and A. Materny, J. Raman Spectrosc. 40, 1284 (2009).
[CrossRef]

JETP Lett. (1)

Y. E. D’yakov, JETP Lett. 37, 15 (1983).

Opt. Commun. (1)

B. B. Krynetsky, L. A. Kulevsky, V. A. Mishin, A. M. Prokhorov, A. D. Savel’ev, and V. V. Smirnov, Opt. Commun. 21, 225 (1977).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (1)

J. A. Giordmaine and W. Kaiser, Phys. Rev. 144, 676 (1966).
[CrossRef]

Phys. Rev. B (1)

Y. J. Lee, H. S. Parekh, J. A. Fagan, and M. Cicerone, Phys. Rev. B 82, 165432 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

A. Laubereau, D. von der Linde, and W. Kaiser, Phys. Rev. Lett. 28, 1162 (1972).
[CrossRef]

M. L. Geirnaert, G. M. Gale, and C. Flytzanis, Phys. Rev. Lett. 52, 815 (1984).
[CrossRef]

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, Phys. Rev. Lett. 103, 043905 (2009).
[CrossRef]

Rev. Mod. Phys. (1)

A. Laubereau and W. Kaiser, Rev. Mod. Phys. 50, 607 (1978).
[CrossRef]

Science (1)

C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, Science 322, 1857 (2008).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Three-color femtosecond CARS is enabled by two independently tunable OPOs that provided broadband pulses at central frequencies of ω1 and ω2 in order to phase in vibrations within subfemtoliter excitation volume. Decay of coherent amplitude Q(t) is probed by a pulse at ωpr that is a small part of the Ti:sapphire oscillator output. Fourier transform of the square root of the time-domain CARS signal measured with high dynamic range Sas(td) provides dispersion of χ(3).

Fig. 2.
Fig. 2.

(a) Experimental time-domain CARS signal (open circles) from KTP crystal. Solid red and blue curves represent the calculated CARS signal with decay times of 495 and 505 fs, respectively. (b) Dispersion of the resonant χ(3) (open circles) using Fourier transform of the experimental time-domain data. Solid red line represents the calculated two-peak Lorentzian lineshape with the following parameters: the ratio for the excited doublet line amplitudes is 21.50, and lower and higher frequency peak linewidths (ΔνL1,2) are 21.00 and 24.20cm1, respectively. Inset shows differences in spectra that would correspond to the different time-domain signal decay times indicated above. An order of magnitude difference seen for the CARS signals (td>2ps) corresponds to less than 15% change in magnitude of the spectra.

Fig. 3.
Fig. 3.

(a) Experimental time-domain CARS signal (open circles) from KTP crystal for the case in which pulses at ω1 and ω2 were tuned to efficiently excite both lines in the Raman doublet. (b) Dispersion of the resonant χ(3)(ω1ω2) obtained from time-domain data using Eq. (5). Solid red line represents the calculated Lorentzian lineshape with the following parameters: the ratio for the doublet line amplitudes corresponds to 5.40, and the lower and higher frequency peak linewidths (ΔνL1,2) are 21.00 and 24.20cm1. The solid red line on part (a) is the calculated CARS signal corresponding to the same amplitude ratio as mentioned above, while the phonon decay times are T1,2*=2/(πcΔvL1,2), and the peak position difference is 60cm1.

Fig. 4.
Fig. 4.

(a) Experimental time-domain CARS signal (open circles) from oil. The ω1 and ω2 pulses were tuned to excite vibrations near 870cm1 (C-C bending mode). (b) Dispersion of the resonant χ(3) (ω1ω2) obtained from time-domain data using Eq. (5). Solid red line represents the calculated Lorentzian lineshape with Γ/πc=3.82±0.08cm1. The inset in part (a) shows the transient when the wavelength of one of the OPOs is slightly detuned so that the neighboring Raman line that is spaced apart by 21cm1 can be efficiently excited, thus resulting in the quantum beat pattern.

Equations (6)

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

P(3)(ωas)=6χ(3)(ωas;ω1,ω2,ω3)E1E2*E3.
P(3)(ωas)=12NαqQ(ω1ω2)E3,
Sas(td)|Eas(t)|2dt,Eas(z,t)z=κasE3(ttd)Q(z,t),
Q(t)=1Ni=1Nqi(t),qit+(γi+iγx)qi=κqE1(t)E2*(t).
Sas(td)=ζ|Q(td)|2I32,
χ(3)(ωas;ω1,ω2,ω3)=112Nαqκq0(Sas(t)Sas(0))1/2eiωtdt.

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