Abstract

Generation of transient gratings in weakly absorbing liquids with a high-power laser gives rise to changes in the fluid's index of refraction that are sufficiently large to produce both multiple diffraction of a probe laser beam and a time response anomaly. The coupled-wave approach to the solution of the volume diffraction problem is shown to predict the existence of high-order diffraction of the probe beam and the time dependence of the diffraction intensity of each order. In addition, criteria for the Raman–Nath and Bragg diffraction regimes are derived from the first-order, coupled-wave equations.

© 1999 Optical Society of America

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  1. C. V. Raman and N. S. Nagendra Nath, Proc. Indian Acad. Sci. Section A 2, 406, 413 (1935)Proc. Indian Acad. Sci. Section A 3, 75, 119, 459 (1936)L. Brillouin, Ann. Phys. (Paris) 17, 103 (1921)La Diffraction de la Lumiere par des Ultrasons (Hermann, Paris, 1933)M. V. Berry, The Diffraction of Light by Ultrasound (Academic, London, 1966).
  2. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
    [CrossRef]
  3. M. G. Moharam and T. K. Gaylord, J. Opt. Soc. Am. 71, 811 (1981). Figures??2–5 of this reference show how changes in the strength parameter caused by density excursions determine the diffracted light intensity.
    [CrossRef]
  4. T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
    [CrossRef]
  5. H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1985).
  6. D. J. McGraw and J. M. Harris, Opt. Lett. 10, 140 (1985).
    [CrossRef] [PubMed]
  7. X. R. Zhu and J. M. Harris, J. Phys. Chem. 93, 75 (1989).
    [CrossRef]
  8. X. R. Zhu and J. M. Harris, Chem. Phys. 142, 301 (1990).
    [CrossRef]
  9. H. X. Chen and G. J. Diebold, Science 270, 963 (1995).
    [CrossRef]
  10. R. T. Cambron and J. M. Harris, Anal. Chem. 67, 365 (1995).
    [CrossRef]
  11. We use the word “quasi-sinusoidal” to describe the simplest intensity versus time waveform seen in transient-grating experiments, which is given by -1+cos?t2.
  12. Fitting of the experimental waveforms involves a convolution over the time profile of the laser pulse; since the exact time profile of the laser beam cannot be accurately modeled with simple functions such as a Gaussian or a Lorentzian, a quantitative fit of the experimental curves was not carried out.
  13. T. Jaaskelainen and T. Hytonen, Opt. Commun. 64, 19 (1987). These authors have shown the Gaylord–Moharam criterion for the Raman–Nath regime to be necessary but not sufficient.
    [CrossRef]
  14. H. X. Chen, “Laser induced effects in carbon suspensions and diffraction by volume gratings in liquids,” Ph.D dissertation (Brown University, Providence, R.I., 1997).

1995

H. X. Chen and G. J. Diebold, Science 270, 963 (1995).
[CrossRef]

R. T. Cambron and J. M. Harris, Anal. Chem. 67, 365 (1995).
[CrossRef]

1990

X. R. Zhu and J. M. Harris, Chem. Phys. 142, 301 (1990).
[CrossRef]

1989

X. R. Zhu and J. M. Harris, J. Phys. Chem. 93, 75 (1989).
[CrossRef]

1987

T. Jaaskelainen and T. Hytonen, Opt. Commun. 64, 19 (1987). These authors have shown the Gaylord–Moharam criterion for the Raman–Nath regime to be necessary but not sufficient.
[CrossRef]

1985

D. J. McGraw and J. M. Harris, Opt. Lett. 10, 140 (1985).
[CrossRef] [PubMed]

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

1981

1969

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

1935

C. V. Raman and N. S. Nagendra Nath, Proc. Indian Acad. Sci. Section A 2, 406, 413 (1935)Proc. Indian Acad. Sci. Section A 3, 75, 119, 459 (1936)L. Brillouin, Ann. Phys. (Paris) 17, 103 (1921)La Diffraction de la Lumiere par des Ultrasons (Hermann, Paris, 1933)M. V. Berry, The Diffraction of Light by Ultrasound (Academic, London, 1966).

Cambron, R. T.

R. T. Cambron and J. M. Harris, Anal. Chem. 67, 365 (1995).
[CrossRef]

Chen, H. X.

H. X. Chen and G. J. Diebold, Science 270, 963 (1995).
[CrossRef]

H. X. Chen, “Laser induced effects in carbon suspensions and diffraction by volume gratings in liquids,” Ph.D dissertation (Brown University, Providence, R.I., 1997).

Diebold, G. J.

H. X. Chen and G. J. Diebold, Science 270, 963 (1995).
[CrossRef]

Eichler, H. J.

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1985).

Gaylord, T. K.

Gunter, P.

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1985).

Harris, J. M.

R. T. Cambron and J. M. Harris, Anal. Chem. 67, 365 (1995).
[CrossRef]

X. R. Zhu and J. M. Harris, Chem. Phys. 142, 301 (1990).
[CrossRef]

X. R. Zhu and J. M. Harris, J. Phys. Chem. 93, 75 (1989).
[CrossRef]

D. J. McGraw and J. M. Harris, Opt. Lett. 10, 140 (1985).
[CrossRef] [PubMed]

Hytonen, T.

T. Jaaskelainen and T. Hytonen, Opt. Commun. 64, 19 (1987). These authors have shown the Gaylord–Moharam criterion for the Raman–Nath regime to be necessary but not sufficient.
[CrossRef]

Jaaskelainen, T.

T. Jaaskelainen and T. Hytonen, Opt. Commun. 64, 19 (1987). These authors have shown the Gaylord–Moharam criterion for the Raman–Nath regime to be necessary but not sufficient.
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

McGraw, D. J.

Moharam, M. G.

Nagendra Nath, N. S.

C. V. Raman and N. S. Nagendra Nath, Proc. Indian Acad. Sci. Section A 2, 406, 413 (1935)Proc. Indian Acad. Sci. Section A 3, 75, 119, 459 (1936)L. Brillouin, Ann. Phys. (Paris) 17, 103 (1921)La Diffraction de la Lumiere par des Ultrasons (Hermann, Paris, 1933)M. V. Berry, The Diffraction of Light by Ultrasound (Academic, London, 1966).

Pohl, D. W.

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1985).

Raman, C. V.

C. V. Raman and N. S. Nagendra Nath, Proc. Indian Acad. Sci. Section A 2, 406, 413 (1935)Proc. Indian Acad. Sci. Section A 3, 75, 119, 459 (1936)L. Brillouin, Ann. Phys. (Paris) 17, 103 (1921)La Diffraction de la Lumiere par des Ultrasons (Hermann, Paris, 1933)M. V. Berry, The Diffraction of Light by Ultrasound (Academic, London, 1966).

Zhu, X. R.

X. R. Zhu and J. M. Harris, Chem. Phys. 142, 301 (1990).
[CrossRef]

X. R. Zhu and J. M. Harris, J. Phys. Chem. 93, 75 (1989).
[CrossRef]

Anal. Chem.

R. T. Cambron and J. M. Harris, Anal. Chem. 67, 365 (1995).
[CrossRef]

Bell Syst. Tech. J.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Chem. Phys.

X. R. Zhu and J. M. Harris, Chem. Phys. 142, 301 (1990).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. Chem.

X. R. Zhu and J. M. Harris, J. Phys. Chem. 93, 75 (1989).
[CrossRef]

Opt. Commun.

T. Jaaskelainen and T. Hytonen, Opt. Commun. 64, 19 (1987). These authors have shown the Gaylord–Moharam criterion for the Raman–Nath regime to be necessary but not sufficient.
[CrossRef]

Opt. Lett.

Proc. IEEE

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Proc. Indian Acad. Sci. Section A

C. V. Raman and N. S. Nagendra Nath, Proc. Indian Acad. Sci. Section A 2, 406, 413 (1935)Proc. Indian Acad. Sci. Section A 3, 75, 119, 459 (1936)L. Brillouin, Ann. Phys. (Paris) 17, 103 (1921)La Diffraction de la Lumiere par des Ultrasons (Hermann, Paris, 1933)M. V. Berry, The Diffraction of Light by Ultrasound (Academic, London, 1966).

Science

H. X. Chen and G. J. Diebold, Science 270, 963 (1995).
[CrossRef]

Other

We use the word “quasi-sinusoidal” to describe the simplest intensity versus time waveform seen in transient-grating experiments, which is given by -1+cos?t2.

Fitting of the experimental waveforms involves a convolution over the time profile of the laser pulse; since the exact time profile of the laser beam cannot be accurately modeled with simple functions such as a Gaussian or a Lorentzian, a quantitative fit of the experimental curves was not carried out.

H. X. Chen, “Laser induced effects in carbon suspensions and diffraction by volume gratings in liquids,” Ph.D dissertation (Brown University, Providence, R.I., 1997).

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1985).

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Figures (2)

Fig. 1
Fig. 1

Diffraction efficiency versus change in dielectric constant Δϵ. Left column, first Bragg angle; right column, second Bragg angle. (a), (d) first-order diffracted beams; (b), (e) second-order diffracted beams; (c), (f) third-order diffracted beams.

Fig. 2
Fig. 2

Oscilloscope traces of diffracted light intensity versus time from transient gratings in methanol, with the laser fluence increasing from the bottom to the top plots. First column: first Bragg angle, first diffracted beam. Top, 430  mJ; middle, 360  mJ; bottom, 300  mJ. Second column: second Bragg angle, first diffracted beam. Top, 240  mJ; middle, 145  mJ; bottom, 100  mJ. Third column: second Bragg angle, second diffracted beam. Top, 400  mJ; middle, 330  mJ; bottom, 270  mJ. The cell insets at the bottom right are plots of diffracted light intensity versus time from Gaylord–Moharam theory. The damping of the acoustic wave is not discernable on the time scale shown here.

Equations (5)

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

-idflz^dz^+Q2l1-lflz^+γfl-1z^+fl+1z^=0,
γ=πdΔϵ2 λϵDcosθ,Q=2πλdϵDΛ2cosθ.
f0:1-2γ2+112γ2Q2+32γ4f1:+γ2-γ4f-1:+γ2-112γ2Q2-γ4f2:+14γ4f-2:+14γ4.
f0:1-2γ2+124γ2Q2+32γ4f1+f-1:+2γ2-124γ2Q2-2γ4f2+f-2:+12γ4.
f0:cos2γ+14ρ2[-2cos2γ+γ2cos2γ+2cosγcos2ργ],f1:sin2γ+14ρ2-2sin2γ+γ2sin2γ,f-1:+14ρ2cos2γ-2cosγcos2ργ+1,f2:+14ρ2sin2γ,

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