Abstract

Based on the polarization interference between two four-wave mixing (FWM) processes, we demonstrate a phase-sensitive method for studying Raman-enhanced nondegenerate four-wave mixing (RENFWM). The reference beam is another FWM signal, which propagates along the same optical path as the RENFWM signal. We have employed this method to study the phase dispersion of the third-order susceptibility χ(3) and for optical heterodyne detection of the RENFWM signal.

© 2000 Optical Society of America

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  1. L. Sarger, P. Segonds, L. Canioni, F. Adamietz, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, “Time-resolved absolute interferometric measurement of third-order nonlinear-optical susceptibilities,” J. Opt. Soc. Am. B 11, 995–999 (1994).
    [CrossRef]
  2. K. Minoshima, M. Taiji, and T. Kobayashi, “Femtosecond time-resolved interferometry for the determination of complex nonlinear susceptibility,” Opt. Lett. 16, 1683–1685 (1991).
    [CrossRef] [PubMed]
  3. E. Tokunaga, A. Terasaki, and T. Kobayashi, “Femtosecond phase spectroscopy by use of frequency-domain interference,” J. Opt. Soc. Am. B 12, 753–771 (1995).
    [CrossRef]
  4. E. Tokunaga, A. Terasaki, V. S. Valencia, T. Wada, H. Sasabe, and T. Kobayashi, “Femtosecond phase spectros-copy of multi-level systems: phthalocyanines,” Appl. Phys. B 63, 255–264 (1996).
    [CrossRef]
  5. G. L. Eesley, Coherent Raman Spectroscopy (Pergamon, Oxford, 1981).
  6. A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
    [CrossRef]
  7. A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
    [CrossRef]
  8. D. DeBeer, V. G. Van Wagenen, R. Beach, and S. R. Hartmann, “Ultrafast modulation spectroscopy,” Phys. Rev. Lett. 56, 1128–1131 (1986).
    [CrossRef] [PubMed]
  9. P. Fu, Z. Yu, X. Mi, X. Li, and Q. Jiang, “Doppler-free ultrafast modulation spectroscopy with phase-conjugation geometry,” Phys. Rev. A 50, 698–708 (1994).
    [CrossRef] [PubMed]
  10. P. Fu, X. Mi, Z. Yu, Q. Jiang, Y. Zhang, and X. Li, “Ultrafast modulation spectroscopy in a cascade three-level system,” Phys. Rev. A 52, 4867–4870 (1995).
    [CrossRef] [PubMed]
  11. X. Mi, Z. Yu, Q. Jiang, X. Li, and P. Fu, “Four-level ultrafast modulation spectroscopy,” Opt. Commun. 152, 361–364 (1998).
    [CrossRef]
  12. X. Mi, Q. Jiang, Z. Yu, and P. Fu, “Observation of the beat between two independent light sources by a method of time-delayed laser-induced double gratings,” Opt. Lett. 16, 1526–1528 (1991).
    [CrossRef] [PubMed]
  13. X. Mi, Z. Yu, Q. Jiang, Z. Zhang, and P. Fu, “Time-delayed laser-induced double gratings,” J. Opt. Soc. Am. B 10, 725–732 (1993).
    [CrossRef]
  14. N. Tang and J. P. Partanen, “Four-wave-mixing interferometer,” Opt. Lett. 21, 1108–1110 (1996).
    [CrossRef] [PubMed]
  15. H. Ma, L. H. Acioli, A. S. L. Gomes, and C. B. de Araújo, “Method to determine the phase dispersion of the third-order susceptibility,” Opt. Lett. 16, 630–632 (1991).
    [CrossRef] [PubMed]
  16. H. Ma, A. S. L. Gomes, and C. B. de Araújo, “Raman-assisted polarization beats in time-delayed four-wave mixing,” Opt. Lett. 17, 1052–1052 (1992).
    [CrossRef] [PubMed]
  17. Z. Yu, H. Lu, P. Ye, and P. Fu, “Study of Raman enhanced nondegenerate four-wave mixing,” Opt. Commun. 61, 287–290 (1987).
    [CrossRef]
  18. M. D. Levenson and N. Bloembergen, “Dispersion of the nonlinear optical susceptibilities of organic liquids and solutions,” J. Chem. Phys. 60, 1323–1327 (1974).
    [CrossRef]

1998

X. Mi, Z. Yu, Q. Jiang, X. Li, and P. Fu, “Four-level ultrafast modulation spectroscopy,” Opt. Commun. 152, 361–364 (1998).
[CrossRef]

1997

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[CrossRef]

1996

E. Tokunaga, A. Terasaki, V. S. Valencia, T. Wada, H. Sasabe, and T. Kobayashi, “Femtosecond phase spectros-copy of multi-level systems: phthalocyanines,” Appl. Phys. B 63, 255–264 (1996).
[CrossRef]

N. Tang and J. P. Partanen, “Four-wave-mixing interferometer,” Opt. Lett. 21, 1108–1110 (1996).
[CrossRef] [PubMed]

1995

E. Tokunaga, A. Terasaki, and T. Kobayashi, “Femtosecond phase spectroscopy by use of frequency-domain interference,” J. Opt. Soc. Am. B 12, 753–771 (1995).
[CrossRef]

P. Fu, X. Mi, Z. Yu, Q. Jiang, Y. Zhang, and X. Li, “Ultrafast modulation spectroscopy in a cascade three-level system,” Phys. Rev. A 52, 4867–4870 (1995).
[CrossRef] [PubMed]

1994

1993

1992

1991

1987

Z. Yu, H. Lu, P. Ye, and P. Fu, “Study of Raman enhanced nondegenerate four-wave mixing,” Opt. Commun. 61, 287–290 (1987).
[CrossRef]

1986

D. DeBeer, V. G. Van Wagenen, R. Beach, and S. R. Hartmann, “Ultrafast modulation spectroscopy,” Phys. Rev. Lett. 56, 1128–1131 (1986).
[CrossRef] [PubMed]

1974

M. D. Levenson and N. Bloembergen, “Dispersion of the nonlinear optical susceptibilities of organic liquids and solutions,” J. Chem. Phys. 60, 1323–1327 (1974).
[CrossRef]

Acioli, L. H.

Adamietz, F.

Beach, R.

D. DeBeer, V. G. Van Wagenen, R. Beach, and S. R. Hartmann, “Ultrafast modulation spectroscopy,” Phys. Rev. Lett. 56, 1128–1131 (1986).
[CrossRef] [PubMed]

Bloembergen, N.

M. D. Levenson and N. Bloembergen, “Dispersion of the nonlinear optical susceptibilities of organic liquids and solutions,” J. Chem. Phys. 60, 1323–1327 (1974).
[CrossRef]

Canioni, L.

Chernyak, V.

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[CrossRef]

de Araújo, C. B.

DeBeer, D.

D. DeBeer, V. G. Van Wagenen, R. Beach, and S. R. Hartmann, “Ultrafast modulation spectroscopy,” Phys. Rev. Lett. 56, 1128–1131 (1986).
[CrossRef] [PubMed]

Ducasse, A.

Duchesne, C.

Fargin, E.

Fleming, G. R.

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[CrossRef]

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

Fu, P.

X. Mi, Z. Yu, Q. Jiang, X. Li, and P. Fu, “Four-level ultrafast modulation spectroscopy,” Opt. Commun. 152, 361–364 (1998).
[CrossRef]

P. Fu, X. Mi, Z. Yu, Q. Jiang, Y. Zhang, and X. Li, “Ultrafast modulation spectroscopy in a cascade three-level system,” Phys. Rev. A 52, 4867–4870 (1995).
[CrossRef] [PubMed]

P. Fu, Z. Yu, X. Mi, X. Li, and Q. Jiang, “Doppler-free ultrafast modulation spectroscopy with phase-conjugation geometry,” Phys. Rev. A 50, 698–708 (1994).
[CrossRef] [PubMed]

X. Mi, Z. Yu, Q. Jiang, Z. Zhang, and P. Fu, “Time-delayed laser-induced double gratings,” J. Opt. Soc. Am. B 10, 725–732 (1993).
[CrossRef]

X. Mi, Q. Jiang, Z. Yu, and P. Fu, “Observation of the beat between two independent light sources by a method of time-delayed laser-induced double gratings,” Opt. Lett. 16, 1526–1528 (1991).
[CrossRef] [PubMed]

Z. Yu, H. Lu, P. Ye, and P. Fu, “Study of Raman enhanced nondegenerate four-wave mixing,” Opt. Commun. 61, 287–290 (1987).
[CrossRef]

Gomes, A. S. L.

Hartmann, S. R.

D. DeBeer, V. G. Van Wagenen, R. Beach, and S. R. Hartmann, “Ultrafast modulation spectroscopy,” Phys. Rev. Lett. 56, 1128–1131 (1986).
[CrossRef] [PubMed]

Jiang, Q.

X. Mi, Z. Yu, Q. Jiang, X. Li, and P. Fu, “Four-level ultrafast modulation spectroscopy,” Opt. Commun. 152, 361–364 (1998).
[CrossRef]

P. Fu, X. Mi, Z. Yu, Q. Jiang, Y. Zhang, and X. Li, “Ultrafast modulation spectroscopy in a cascade three-level system,” Phys. Rev. A 52, 4867–4870 (1995).
[CrossRef] [PubMed]

P. Fu, Z. Yu, X. Mi, X. Li, and Q. Jiang, “Doppler-free ultrafast modulation spectroscopy with phase-conjugation geometry,” Phys. Rev. A 50, 698–708 (1994).
[CrossRef] [PubMed]

X. Mi, Z. Yu, Q. Jiang, Z. Zhang, and P. Fu, “Time-delayed laser-induced double gratings,” J. Opt. Soc. Am. B 10, 725–732 (1993).
[CrossRef]

X. Mi, Q. Jiang, Z. Yu, and P. Fu, “Observation of the beat between two independent light sources by a method of time-delayed laser-induced double gratings,” Opt. Lett. 16, 1526–1528 (1991).
[CrossRef] [PubMed]

Kobayashi, T.

Lang, M. J.

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[CrossRef]

Larsen, D. S.

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[CrossRef]

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

Le Flem, G.

Levenson, M. D.

M. D. Levenson and N. Bloembergen, “Dispersion of the nonlinear optical susceptibilities of organic liquids and solutions,” J. Chem. Phys. 60, 1323–1327 (1974).
[CrossRef]

Li, X.

X. Mi, Z. Yu, Q. Jiang, X. Li, and P. Fu, “Four-level ultrafast modulation spectroscopy,” Opt. Commun. 152, 361–364 (1998).
[CrossRef]

P. Fu, X. Mi, Z. Yu, Q. Jiang, Y. Zhang, and X. Li, “Ultrafast modulation spectroscopy in a cascade three-level system,” Phys. Rev. A 52, 4867–4870 (1995).
[CrossRef] [PubMed]

P. Fu, Z. Yu, X. Mi, X. Li, and Q. Jiang, “Doppler-free ultrafast modulation spectroscopy with phase-conjugation geometry,” Phys. Rev. A 50, 698–708 (1994).
[CrossRef] [PubMed]

Lu, H.

Z. Yu, H. Lu, P. Ye, and P. Fu, “Study of Raman enhanced nondegenerate four-wave mixing,” Opt. Commun. 61, 287–290 (1987).
[CrossRef]

Ma, H.

Mi, X.

X. Mi, Z. Yu, Q. Jiang, X. Li, and P. Fu, “Four-level ultrafast modulation spectroscopy,” Opt. Commun. 152, 361–364 (1998).
[CrossRef]

P. Fu, X. Mi, Z. Yu, Q. Jiang, Y. Zhang, and X. Li, “Ultrafast modulation spectroscopy in a cascade three-level system,” Phys. Rev. A 52, 4867–4870 (1995).
[CrossRef] [PubMed]

P. Fu, Z. Yu, X. Mi, X. Li, and Q. Jiang, “Doppler-free ultrafast modulation spectroscopy with phase-conjugation geometry,” Phys. Rev. A 50, 698–708 (1994).
[CrossRef] [PubMed]

X. Mi, Z. Yu, Q. Jiang, Z. Zhang, and P. Fu, “Time-delayed laser-induced double gratings,” J. Opt. Soc. Am. B 10, 725–732 (1993).
[CrossRef]

X. Mi, Q. Jiang, Z. Yu, and P. Fu, “Observation of the beat between two independent light sources by a method of time-delayed laser-induced double gratings,” Opt. Lett. 16, 1526–1528 (1991).
[CrossRef] [PubMed]

Minoshima, K.

Mukamel, S.

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[CrossRef]

Olazcuaga, R.

Partanen, J. P.

Sarger, L.

Sasabe, H.

E. Tokunaga, A. Terasaki, V. S. Valencia, T. Wada, H. Sasabe, and T. Kobayashi, “Femtosecond phase spectros-copy of multi-level systems: phthalocyanines,” Appl. Phys. B 63, 255–264 (1996).
[CrossRef]

Segonds, P.

Taiji, M.

Tang, N.

Terasaki, A.

E. Tokunaga, A. Terasaki, V. S. Valencia, T. Wada, H. Sasabe, and T. Kobayashi, “Femtosecond phase spectros-copy of multi-level systems: phthalocyanines,” Appl. Phys. B 63, 255–264 (1996).
[CrossRef]

E. Tokunaga, A. Terasaki, and T. Kobayashi, “Femtosecond phase spectroscopy by use of frequency-domain interference,” J. Opt. Soc. Am. B 12, 753–771 (1995).
[CrossRef]

Tokmakoff, A.

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[CrossRef]

Tokunaga, E.

E. Tokunaga, A. Terasaki, V. S. Valencia, T. Wada, H. Sasabe, and T. Kobayashi, “Femtosecond phase spectros-copy of multi-level systems: phthalocyanines,” Appl. Phys. B 63, 255–264 (1996).
[CrossRef]

E. Tokunaga, A. Terasaki, and T. Kobayashi, “Femtosecond phase spectroscopy by use of frequency-domain interference,” J. Opt. Soc. Am. B 12, 753–771 (1995).
[CrossRef]

Valencia, V. S.

E. Tokunaga, A. Terasaki, V. S. Valencia, T. Wada, H. Sasabe, and T. Kobayashi, “Femtosecond phase spectros-copy of multi-level systems: phthalocyanines,” Appl. Phys. B 63, 255–264 (1996).
[CrossRef]

Van Wagenen, V. G.

D. DeBeer, V. G. Van Wagenen, R. Beach, and S. R. Hartmann, “Ultrafast modulation spectroscopy,” Phys. Rev. Lett. 56, 1128–1131 (1986).
[CrossRef] [PubMed]

Wada, T.

E. Tokunaga, A. Terasaki, V. S. Valencia, T. Wada, H. Sasabe, and T. Kobayashi, “Femtosecond phase spectros-copy of multi-level systems: phthalocyanines,” Appl. Phys. B 63, 255–264 (1996).
[CrossRef]

Ye, P.

Z. Yu, H. Lu, P. Ye, and P. Fu, “Study of Raman enhanced nondegenerate four-wave mixing,” Opt. Commun. 61, 287–290 (1987).
[CrossRef]

Yu, Z.

X. Mi, Z. Yu, Q. Jiang, X. Li, and P. Fu, “Four-level ultrafast modulation spectroscopy,” Opt. Commun. 152, 361–364 (1998).
[CrossRef]

P. Fu, X. Mi, Z. Yu, Q. Jiang, Y. Zhang, and X. Li, “Ultrafast modulation spectroscopy in a cascade three-level system,” Phys. Rev. A 52, 4867–4870 (1995).
[CrossRef] [PubMed]

P. Fu, Z. Yu, X. Mi, X. Li, and Q. Jiang, “Doppler-free ultrafast modulation spectroscopy with phase-conjugation geometry,” Phys. Rev. A 50, 698–708 (1994).
[CrossRef] [PubMed]

X. Mi, Z. Yu, Q. Jiang, Z. Zhang, and P. Fu, “Time-delayed laser-induced double gratings,” J. Opt. Soc. Am. B 10, 725–732 (1993).
[CrossRef]

X. Mi, Q. Jiang, Z. Yu, and P. Fu, “Observation of the beat between two independent light sources by a method of time-delayed laser-induced double gratings,” Opt. Lett. 16, 1526–1528 (1991).
[CrossRef] [PubMed]

Z. Yu, H. Lu, P. Ye, and P. Fu, “Study of Raman enhanced nondegenerate four-wave mixing,” Opt. Commun. 61, 287–290 (1987).
[CrossRef]

Zhang, Y.

P. Fu, X. Mi, Z. Yu, Q. Jiang, Y. Zhang, and X. Li, “Ultrafast modulation spectroscopy in a cascade three-level system,” Phys. Rev. A 52, 4867–4870 (1995).
[CrossRef] [PubMed]

Zhang, Z.

Appl. Phys. B

E. Tokunaga, A. Terasaki, V. S. Valencia, T. Wada, H. Sasabe, and T. Kobayashi, “Femtosecond phase spectros-copy of multi-level systems: phthalocyanines,” Appl. Phys. B 63, 255–264 (1996).
[CrossRef]

Chem. Phys. Lett.

A. Tokmakoff, M. J. Lang, D. S. Larsen, and G. R. Fleming, “Intrinsic optical heterodyne detection of a two-dimensional fifth order Raman response,” Chem. Phys. Lett. 272, 48–54 (1997).
[CrossRef]

J. Chem. Phys.

M. D. Levenson and N. Bloembergen, “Dispersion of the nonlinear optical susceptibilities of organic liquids and solutions,” J. Chem. Phys. 60, 1323–1327 (1974).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

Z. Yu, H. Lu, P. Ye, and P. Fu, “Study of Raman enhanced nondegenerate four-wave mixing,” Opt. Commun. 61, 287–290 (1987).
[CrossRef]

X. Mi, Z. Yu, Q. Jiang, X. Li, and P. Fu, “Four-level ultrafast modulation spectroscopy,” Opt. Commun. 152, 361–364 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev. A

P. Fu, Z. Yu, X. Mi, X. Li, and Q. Jiang, “Doppler-free ultrafast modulation spectroscopy with phase-conjugation geometry,” Phys. Rev. A 50, 698–708 (1994).
[CrossRef] [PubMed]

P. Fu, X. Mi, Z. Yu, Q. Jiang, Y. Zhang, and X. Li, “Ultrafast modulation spectroscopy in a cascade three-level system,” Phys. Rev. A 52, 4867–4870 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett.

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[CrossRef]

D. DeBeer, V. G. Van Wagenen, R. Beach, and S. R. Hartmann, “Ultrafast modulation spectroscopy,” Phys. Rev. Lett. 56, 1128–1131 (1986).
[CrossRef] [PubMed]

Other

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

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Figures (5)

Fig. 1
Fig. 1

Experimental setup: BS’s, beam splitters; M’s, mirrors; L’s, lenses; GP’s, Glan prisms; CP, Soleil–Babinet compensator; P, polarizer; PD, photodiode; ODL, optical delay line; S, sample.

Fig. 2
Fig. 2

RENFWM signal intensity versus frequency detuning Δ. Solid curve, theoretical curve with γR=9.4×1010 s-1 and χM/χR=0.5.

Fig. 3
Fig. 3

FWM signal intensity versus relative time delay with frequency detuning Δ=-1.25 cm-1 (filled triangles), Δ=-0.25 cm-1 (open squares), and Δ=0.5 cm-1 (filled squares).

Fig. 4
Fig. 4

Phase angle θR versus frequency detuning Δ. Solid curve, theoretical curve with γR=9.4×1010 s-1 and χM/χR=0.5.

Fig. 5
Fig. 5

FWM spectra with (a) (ω1-ω2)τ=0 and (b) (ω1-ω2)τ=-π/2. Solid curves, theoretical curves with parameters γR=9.4×1010 s-1, χM/χR=0.5, and η=0.2.

Equations (13)

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Ep1(r, t)=1exp[i(k1r-ω1t+ω1τ)]+2exp[i(k2r-ω2t+ω2τ)],
Ep2(r, t)=1exp[i(k1r-ω1t)]+2exp[i(k2r-ω2t)].
E3(r, t)=3exp[i(k3r-ω3t)].
χ(3)=χM-χRγRΔ+iγR.
P(3)(r, t)=6223×exp i[(k2-k2+k3)r-ω3t+ω2τ]×{χM+ηχ(3)exp i[(ω1-ω2)τ]}.
η=1122exp{-i[(k2-k2)-(k1-k1)]r}.
θR=tan-1χRγR2χM(Δ2+γR2)-χRγRΔ.
I(χM)2+η2|χ(3)|2+2ηχM|χ(3)|×cos[(ω1-ω2)τ-θR].
IχM+ηχ(3)exp{i[(ω1-ω2)τ]}+η[χ(3)]*×exp{-i[(ω1-ω2)τ]}.
χ=χM-χRγRΔΔ2+γR2,
χ=χRγR2Δ2+γR2.
IχM+2η x.
IχM+2ηχ.

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