Abstract

Femtosecond beats in time-delayed forward degenerate four-wave mixing (DFWM) with incoherent light in liquid and solid materials have been observed, and their origin is discussed. It is shown that the oscillations are due to the interference between pure DFWM signal and Rayleigh scattering from the excitation beams. It is also shown that, if this effect is not taken into account, incorrect conclusions can be reached.

© 2000 Optical Society of America

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References

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  1. V. L. Bogdanov, A. B. Evdokimov, G. L. Lukomskii, and B. D. Fainberg, “Subfemtosecond beats in an interference of the fields of Rayleigh scattering and four-wave mixing,” JETP Lett. 49, 157–161 (1989).
  2. C. H. Grossman and J. J. Schwendiman, “Ultrashort dephasing-time measurements in Nile Blue polymer films,” Opt. Lett. 23, 624–626 (1998).
    [CrossRef]
  3. H. S. Kwok, “Nonlinear optics without lasers,” in Resonances: A Volume in Honor of the 70th Birthday of Nicolaas Bloembergen, M. D. Levenson, E. Mazur, P. S. Persham, and Y. R. Shen, eds. (World Scientific, Singapore, 1990), pp. 271–278.
  4. Z. Q. Huang, Y. J. Xie, G. L. Huang, and H. S. Kwok, “Observation of molecular vibrations in time domain with incoherent laser pulses,” Opt. Lett. 15, 501–503 (1990).
    [CrossRef] [PubMed]
  5. N. Morita and T. Yajima, “Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light,” Phys. Rev. A 30, 2525–2535 (1984).
    [CrossRef]
  6. This statement is based on Eq. (2), which was obtained through consideration of a two-level system with the density-matrix relaxation described by the parameters T1 and T2. However, more-complex nonlinear response functions appropriate for other particular systems might yield oscillations.
  7. L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, and C. B. de Araújo, “Femtosecond dynamics of semiconductor-doped glasses using a new source of incoherent light,” Appl. Phys. Lett. 56, 2279–2281 (1990).
    [CrossRef]

1998 (1)

1990 (2)

Z. Q. Huang, Y. J. Xie, G. L. Huang, and H. S. Kwok, “Observation of molecular vibrations in time domain with incoherent laser pulses,” Opt. Lett. 15, 501–503 (1990).
[CrossRef] [PubMed]

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, and C. B. de Araújo, “Femtosecond dynamics of semiconductor-doped glasses using a new source of incoherent light,” Appl. Phys. Lett. 56, 2279–2281 (1990).
[CrossRef]

1989 (1)

V. L. Bogdanov, A. B. Evdokimov, G. L. Lukomskii, and B. D. Fainberg, “Subfemtosecond beats in an interference of the fields of Rayleigh scattering and four-wave mixing,” JETP Lett. 49, 157–161 (1989).

1984 (1)

N. Morita and T. Yajima, “Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light,” Phys. Rev. A 30, 2525–2535 (1984).
[CrossRef]

Acioli, L. H.

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, and C. B. de Araújo, “Femtosecond dynamics of semiconductor-doped glasses using a new source of incoherent light,” Appl. Phys. Lett. 56, 2279–2281 (1990).
[CrossRef]

Bogdanov, V. L.

V. L. Bogdanov, A. B. Evdokimov, G. L. Lukomskii, and B. D. Fainberg, “Subfemtosecond beats in an interference of the fields of Rayleigh scattering and four-wave mixing,” JETP Lett. 49, 157–161 (1989).

de Araújo, C. B.

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, and C. B. de Araújo, “Femtosecond dynamics of semiconductor-doped glasses using a new source of incoherent light,” Appl. Phys. Lett. 56, 2279–2281 (1990).
[CrossRef]

Evdokimov, A. B.

V. L. Bogdanov, A. B. Evdokimov, G. L. Lukomskii, and B. D. Fainberg, “Subfemtosecond beats in an interference of the fields of Rayleigh scattering and four-wave mixing,” JETP Lett. 49, 157–161 (1989).

Fainberg, B. D.

V. L. Bogdanov, A. B. Evdokimov, G. L. Lukomskii, and B. D. Fainberg, “Subfemtosecond beats in an interference of the fields of Rayleigh scattering and four-wave mixing,” JETP Lett. 49, 157–161 (1989).

Gomes, A. S. L.

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, and C. B. de Araújo, “Femtosecond dynamics of semiconductor-doped glasses using a new source of incoherent light,” Appl. Phys. Lett. 56, 2279–2281 (1990).
[CrossRef]

Grossman, C. H.

Hickmann, J. M.

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, and C. B. de Araújo, “Femtosecond dynamics of semiconductor-doped glasses using a new source of incoherent light,” Appl. Phys. Lett. 56, 2279–2281 (1990).
[CrossRef]

Huang, G. L.

Huang, Z. Q.

Kwok, H. S.

Lukomskii, G. L.

V. L. Bogdanov, A. B. Evdokimov, G. L. Lukomskii, and B. D. Fainberg, “Subfemtosecond beats in an interference of the fields of Rayleigh scattering and four-wave mixing,” JETP Lett. 49, 157–161 (1989).

Morita, N.

N. Morita and T. Yajima, “Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light,” Phys. Rev. A 30, 2525–2535 (1984).
[CrossRef]

Schwendiman, J. J.

Xie, Y. J.

Yajima, T.

N. Morita and T. Yajima, “Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light,” Phys. Rev. A 30, 2525–2535 (1984).
[CrossRef]

Appl. Phys. Lett. (1)

L. H. Acioli, A. S. L. Gomes, J. M. Hickmann, and C. B. de Araújo, “Femtosecond dynamics of semiconductor-doped glasses using a new source of incoherent light,” Appl. Phys. Lett. 56, 2279–2281 (1990).
[CrossRef]

JETP Lett. (1)

V. L. Bogdanov, A. B. Evdokimov, G. L. Lukomskii, and B. D. Fainberg, “Subfemtosecond beats in an interference of the fields of Rayleigh scattering and four-wave mixing,” JETP Lett. 49, 157–161 (1989).

Opt. Lett. (2)

Phys. Rev. A (1)

N. Morita and T. Yajima, “Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light,” Phys. Rev. A 30, 2525–2535 (1984).
[CrossRef]

Other (2)

This statement is based on Eq. (2), which was obtained through consideration of a two-level system with the density-matrix relaxation described by the parameters T1 and T2. However, more-complex nonlinear response functions appropriate for other particular systems might yield oscillations.

H. S. Kwok, “Nonlinear optics without lasers,” in Resonances: A Volume in Honor of the 70th Birthday of Nicolaas Bloembergen, M. D. Levenson, E. Mazur, P. S. Persham, and Y. R. Shen, eds. (World Scientific, Singapore, 1990), pp. 271–278.

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Figures (5)

Fig. 1
Fig. 1

Scheme of the experiment. DL, delay line; L, lens with a focal length of 10 cm; λ/2, half-wave plate; S, sample.

Fig. 2
Fig. 2

Observed interference signals between the DFWM signal and the Rayleigh scattered waves in Sulforhodamine 640, emitted along k3 (dashed curve) and k4 (solid curve) in the vicinity of τ=0.

Fig. 3
Fig. 3

FFT spectra of the oscillatory signals depicted in Fig. 2.

Fig. 4
Fig. 4

Modulation depth of the signal emitted along the k3 direction versus the ratio between the intensities of the Rayleigh scattered light and of the DFWM signal around τ=0. The solid curve is a fitting curve proportional to the square root of the noise-to-signal ratio.

Fig. 5
Fig. 5

DFWM signal in a semiconductor-doped glass (Corning CS 2-73) along k3 (dashed curve) and k4 (solid curve) for the perpendicular polarizations of the excitation beams. The oscillation period corresponds to a particular choice of the DL step size.

Equations (4)

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ET(r,t)=E1[t+τ-n1·(r-R0)/ν]×exp[-iω(t+τ)+k1·(r-R0)]+E2[t-n2·(r-R0)/ν]×exp[-iωt+k2·(r-R0)]+c.c.=E1(t+τ)exp[-iω(t+τ)+k1·r]+E2(t)exp[-iωt+k2·r]+c.c.
P(3)exp(ik3·r+iωτ)-tdt1-t1dt2×-t2dt3{E1(t1)E1(t2)E2*(t3+τ)×exp[-iΔω(t-t1-t2+t3)]+E1(t1)E2*(t2+τ)E1(t3)×exp[-iΔω(t-t1+t2-t3)]}×exp[-(t1-t2)/T1-(t-t1+t2-t3)/T2]=A3(r, t, τ)exp(iωτ),
ERdVΔ{E(t+τ-T)exp[-iω(t+τ+R0/ν)-(k3-k1)·r]+E(t-T)exp[-iω(t+R0/ν)-(k3-k2)·r]}=A1(r, t, τ)exp(-iωτ)+A2(r, t, τ),
SA32[1+ρ1+ρ2+2ρ21/2 cos(ωτ+φ)+2ρ11/2ρ21/2 cos(ωτ)+2ρ11/2 cos(2ωτ+φ)],

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