Abstract

We study interference between a local oscillator and coherent anti-Stokes Raman scattering signal fields by controlling their relative phase and amplitude. This control allows direct observation of the real and imaginary components of the third-order nonlinear susceptibility (χ(3)) of the sample. In addition, we demonstrate that the heterodyne method can be used to amplify the signal.

© 2010 Optical Society of America

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  1. G. I. Petrov, R. Arora, V. V. Yakovlev, X. Wang, A. V. Sokolov, and M. O. Scully, Proc. Natl. Acad. Sci. USA 104, 7776 (2007).
    [CrossRef] [PubMed]
  2. D. Pestov, G. O. Ariunbold, X. Wang, R. K. Murawski, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, Opt. Lett. 32, 1725 (2007).
    [CrossRef] [PubMed]
  3. G. L. Eesley, Coherent Raman Spectroscopy (Pergamon Press, 1981).
  4. C. L. Evans, E. O. Potma, and X. S. Xie, Opt. Lett. 29, 2923 (2004).
    [CrossRef]
  5. M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, Opt. Express 16, 15863 (2008).
    [CrossRef] [PubMed]
  6. E. O. Potma, C. L. Evans, and X. S. Xie, Opt. Lett. 31, 241 (2006).
    [CrossRef] [PubMed]
  7. C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, J. Raman Spectrosc. 40, 809 (2009).
    [CrossRef]
  8. S.-H. Lim, A. G. Caster, and S. R. Leone, Phys. Rev. A 72, 041803(R) (2005).
    [CrossRef]
  9. D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
    [CrossRef] [PubMed]
  10. S.-H. Shim and M. T. Zanni, Phys. Chem. Chem. Phys. 11, 748 (2009).
    [CrossRef] [PubMed]
  11. D. Abramavicius, B. Palmieri, D. V. Voronine, F. Šanda, and S. Mukamel, Chem. Rev. (Washington, D.C.) 109, 2350 (2009).
  12. D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. Lett. 88, 063004 (2002).
    [CrossRef] [PubMed]
  13. J.-L. Oudar, R. W. Smith, and Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
    [CrossRef]
  14. J.-X. Cheng, L. D. Book, and X. S. Xie, Opt. Lett. 26, 1341 (2001).
    [CrossRef]
  15. M. H. Brooker, G. Hancock, B. C. Rice, and J. Shapter, J. Raman Spectrosc. 20, 683 (1989).
    [CrossRef]

2009 (3)

S.-H. Shim and M. T. Zanni, Phys. Chem. Chem. Phys. 11, 748 (2009).
[CrossRef] [PubMed]

D. Abramavicius, B. Palmieri, D. V. Voronine, F. Šanda, and S. Mukamel, Chem. Rev. (Washington, D.C.) 109, 2350 (2009).

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, J. Raman Spectrosc. 40, 809 (2009).
[CrossRef]

2008 (1)

2007 (3)

D. Pestov, G. O. Ariunbold, X. Wang, R. K. Murawski, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, Opt. Lett. 32, 1725 (2007).
[CrossRef] [PubMed]

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

G. I. Petrov, R. Arora, V. V. Yakovlev, X. Wang, A. V. Sokolov, and M. O. Scully, Proc. Natl. Acad. Sci. USA 104, 7776 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (1)

S.-H. Lim, A. G. Caster, and S. R. Leone, Phys. Rev. A 72, 041803(R) (2005).
[CrossRef]

2004 (1)

2002 (1)

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. Lett. 88, 063004 (2002).
[CrossRef] [PubMed]

2001 (1)

1989 (1)

M. H. Brooker, G. Hancock, B. C. Rice, and J. Shapter, J. Raman Spectrosc. 20, 683 (1989).
[CrossRef]

1979 (1)

J.-L. Oudar, R. W. Smith, and Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
[CrossRef]

Abramavicius, D.

D. Abramavicius, B. Palmieri, D. V. Voronine, F. Šanda, and S. Mukamel, Chem. Rev. (Washington, D.C.) 109, 2350 (2009).

Ariunbold, G. O.

D. Pestov, G. O. Ariunbold, X. Wang, R. K. Murawski, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, Opt. Lett. 32, 1725 (2007).
[CrossRef] [PubMed]

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

Arora, R.

G. I. Petrov, R. Arora, V. V. Yakovlev, X. Wang, A. V. Sokolov, and M. O. Scully, Proc. Natl. Acad. Sci. USA 104, 7776 (2007).
[CrossRef] [PubMed]

Book, L. D.

Brooker, M. H.

M. H. Brooker, G. Hancock, B. C. Rice, and J. Shapter, J. Raman Spectrosc. 20, 683 (1989).
[CrossRef]

Buckup, T.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, J. Raman Spectrosc. 40, 809 (2009).
[CrossRef]

Caster, A. G.

S.-H. Lim, A. G. Caster, and S. R. Leone, Phys. Rev. A 72, 041803(R) (2005).
[CrossRef]

Cheng, J. -X.

Dogariu, A.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

Dudovich, N.

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. Lett. 88, 063004 (2002).
[CrossRef] [PubMed]

Eesley, G. L.

G. L. Eesley, Coherent Raman Spectroscopy (Pergamon Press, 1981).

Evans, C. L.

Hancock, G.

M. H. Brooker, G. Hancock, B. C. Rice, and J. Shapter, J. Raman Spectrosc. 20, 683 (1989).
[CrossRef]

Herek, J. L.

Huang, Y.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

Jurna, M.

Korterik, J. P.

Leone, S. R.

S.-H. Lim, A. G. Caster, and S. R. Leone, Phys. Rev. A 72, 041803(R) (2005).
[CrossRef]

Lim, S. -H.

S.-H. Lim, A. G. Caster, and S. R. Leone, Phys. Rev. A 72, 041803(R) (2005).
[CrossRef]

Motzkus, M.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, J. Raman Spectrosc. 40, 809 (2009).
[CrossRef]

Mukamel, S.

D. Abramavicius, B. Palmieri, D. V. Voronine, F. Šanda, and S. Mukamel, Chem. Rev. (Washington, D.C.) 109, 2350 (2009).

Müller, C.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, J. Raman Spectrosc. 40, 809 (2009).
[CrossRef]

Murawski, R. K.

D. Pestov, G. O. Ariunbold, X. Wang, R. K. Murawski, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, Opt. Lett. 32, 1725 (2007).
[CrossRef] [PubMed]

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

Offerhaus, H. L.

Oron, D.

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. Lett. 88, 063004 (2002).
[CrossRef] [PubMed]

Otto, C.

Oudar, J. -L.

J.-L. Oudar, R. W. Smith, and Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
[CrossRef]

Palmieri, B.

D. Abramavicius, B. Palmieri, D. V. Voronine, F. Šanda, and S. Mukamel, Chem. Rev. (Washington, D.C.) 109, 2350 (2009).

Pestov, D.

D. Pestov, G. O. Ariunbold, X. Wang, R. K. Murawski, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, Opt. Lett. 32, 1725 (2007).
[CrossRef] [PubMed]

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

Petrov, G. I.

G. I. Petrov, R. Arora, V. V. Yakovlev, X. Wang, A. V. Sokolov, and M. O. Scully, Proc. Natl. Acad. Sci. USA 104, 7776 (2007).
[CrossRef] [PubMed]

Potma, E. O.

Rice, B. C.

M. H. Brooker, G. Hancock, B. C. Rice, and J. Shapter, J. Raman Spectrosc. 20, 683 (1989).
[CrossRef]

Rostovtsev, Y. V.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

Šanda, F.

D. Abramavicius, B. Palmieri, D. V. Voronine, F. Šanda, and S. Mukamel, Chem. Rev. (Washington, D.C.) 109, 2350 (2009).

Sautenkov, V. A.

D. Pestov, G. O. Ariunbold, X. Wang, R. K. Murawski, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, Opt. Lett. 32, 1725 (2007).
[CrossRef] [PubMed]

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

Scully, M. O.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

G. I. Petrov, R. Arora, V. V. Yakovlev, X. Wang, A. V. Sokolov, and M. O. Scully, Proc. Natl. Acad. Sci. USA 104, 7776 (2007).
[CrossRef] [PubMed]

D. Pestov, G. O. Ariunbold, X. Wang, R. K. Murawski, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, Opt. Lett. 32, 1725 (2007).
[CrossRef] [PubMed]

Shapter, J.

M. H. Brooker, G. Hancock, B. C. Rice, and J. Shapter, J. Raman Spectrosc. 20, 683 (1989).
[CrossRef]

Shen, Y. R.

J.-L. Oudar, R. W. Smith, and Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
[CrossRef]

Shim, S. -H.

S.-H. Shim and M. T. Zanni, Phys. Chem. Chem. Phys. 11, 748 (2009).
[CrossRef] [PubMed]

Silberberg, Y.

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. Lett. 88, 063004 (2002).
[CrossRef] [PubMed]

Smith, R. W.

J.-L. Oudar, R. W. Smith, and Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
[CrossRef]

Sokolov, A. V.

D. Pestov, G. O. Ariunbold, X. Wang, R. K. Murawski, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, Opt. Lett. 32, 1725 (2007).
[CrossRef] [PubMed]

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

G. I. Petrov, R. Arora, V. V. Yakovlev, X. Wang, A. V. Sokolov, and M. O. Scully, Proc. Natl. Acad. Sci. USA 104, 7776 (2007).
[CrossRef] [PubMed]

von Vacano, B.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, J. Raman Spectrosc. 40, 809 (2009).
[CrossRef]

Voronine, D. V.

D. Abramavicius, B. Palmieri, D. V. Voronine, F. Šanda, and S. Mukamel, Chem. Rev. (Washington, D.C.) 109, 2350 (2009).

Wang, X.

D. Pestov, G. O. Ariunbold, X. Wang, R. K. Murawski, V. A. Sautenkov, A. V. Sokolov, and M. O. Scully, Opt. Lett. 32, 1725 (2007).
[CrossRef] [PubMed]

G. I. Petrov, R. Arora, V. V. Yakovlev, X. Wang, A. V. Sokolov, and M. O. Scully, Proc. Natl. Acad. Sci. USA 104, 7776 (2007).
[CrossRef] [PubMed]

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

Xie, X. S.

Yakovlev, V. V.

G. I. Petrov, R. Arora, V. V. Yakovlev, X. Wang, A. V. Sokolov, and M. O. Scully, Proc. Natl. Acad. Sci. USA 104, 7776 (2007).
[CrossRef] [PubMed]

Yelin, D.

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. Lett. 88, 063004 (2002).
[CrossRef] [PubMed]

Zanni, M. T.

S.-H. Shim and M. T. Zanni, Phys. Chem. Chem. Phys. 11, 748 (2009).
[CrossRef] [PubMed]

Zhi, M.

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J.-L. Oudar, R. W. Smith, and Y. R. Shen, Appl. Phys. Lett. 34, 758 (1979).
[CrossRef]

Chem. Rev. (Washington, D.C.) (1)

D. Abramavicius, B. Palmieri, D. V. Voronine, F. Šanda, and S. Mukamel, Chem. Rev. (Washington, D.C.) 109, 2350 (2009).

J. Raman Spectrosc. (2)

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, J. Raman Spectrosc. 40, 809 (2009).
[CrossRef]

M. H. Brooker, G. Hancock, B. C. Rice, and J. Shapter, J. Raman Spectrosc. 20, 683 (1989).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Chem. Chem. Phys. (1)

S.-H. Shim and M. T. Zanni, Phys. Chem. Chem. Phys. 11, 748 (2009).
[CrossRef] [PubMed]

Phys. Rev. A (1)

S.-H. Lim, A. G. Caster, and S. R. Leone, Phys. Rev. A 72, 041803(R) (2005).
[CrossRef]

Phys. Rev. Lett. (1)

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. Lett. 88, 063004 (2002).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

G. I. Petrov, R. Arora, V. V. Yakovlev, X. Wang, A. V. Sokolov, and M. O. Scully, Proc. Natl. Acad. Sci. USA 104, 7776 (2007).
[CrossRef] [PubMed]

Science (1)

D. Pestov, R. K. Murawski, G. O. Ariunbold, X. Wang, M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, Science 316, 265 (2007).
[CrossRef] [PubMed]

Other (1)

G. L. Eesley, Coherent Raman Spectroscopy (Pergamon Press, 1981).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the CARS spectral interferometer: BS, beam splitter; L1–L5, lenses; NF, neutral density filter; SPF, shortwave-pass filter; Spec, grating spectrometer. Inset, spectral ranges and profiles of the pump, Stokes, and probe beams in the experiment.

Fig. 2
Fig. 2

(a) Experimental and (b) calculated interferometric spectra of aqueous methanol solution at different phases ϕ between the LO and signal arms. (c) Spectra rescaled as S ( ω ) / S LO ( ω ) ; the values at left sides correspond to the dotted horizontal lines in each case.

Fig. 3
Fig. 3

(a) Extracted third-order polarization, hence the susceptibility from experiment (solid curves, scaled to left) and calculation (dashed and dotted curves, scaled to right). (b) Heterodyne signal including only the imaginary part of CARS field; inset, CARS field from the signal arm.

Equations (5)

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

P CARS ( 3 ) = P B ( 3 ) + P R ( 3 ) = 0 d Ω ( χ B ( 3 ) ( Ω ) + N χ R ( 3 ) ( Ω ) ) E p r ( ω Ω ) R ( Ω ) ,
S CARS = | P B ( 3 ) | 2 + | P R ( 3 ) | 2 + 2   Re ( P B ( 3 ) ( ω ) P R ( 3 ) ( ω ) ) .
S ( ω ) | P LO ( 3 ) | 2 + | P CARS ( 3 ) | 2 + 2 P LO ( 3 ) ( ω ) [ Re ( P B ( 3 ) ( ω ) + P R ( 3 ) ( ω ) ) cos   ϕ + Im ( P B ( 3 ) ( ω ) + P R ( 3 ) ( ω ) ) sin   ϕ ] ,
S ( ω ) ϕ = π 2 S ( ω ) ϕ = 3 π 2 P LO ( 3 ) ( ω ) = 4   Im ( P B ( 3 ) ( ω ) + P R ( 3 ) ( ω ) ) = 4 E EX [ Im ( χ B ( 3 ) ( ω ) ) + Im ( χ R ( 3 ) ( ω ) ) ] ,
S ( ω ) ϕ = 0 S ( ω ) ϕ = π P LO ( 3 ) ( ω ) = 4 E EX [ Re ( χ B ( 3 ) ( ω ) ) + Re ( χ R ( 3 ) ( ω ) ) ] .

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