Abstract

A method based on Fresnel or parabolic approximation of the Helmholtz scalar wave equation is presented for calculating the diffracted amplitude when a plane monochromatic light wave is incident on a vessel filled with liquid irradiated by ultrasound. The intensities of the diffracted orders are calculated and compared with the Raman-Nath and Brillouin results and coincide for the range of validity of the latter. Good agreement between the theoretical curves and the experimental values of Klein and Hiedemann has been obtained even for a range of values where the Raman-Nath expressions are not used at all.

© 1980 Optical Society of America

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References

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  1. M. D. Feit, J. A. Fleck, Appl. Opt. 17, 3990 (1978).
    [CrossRef] [PubMed]
  2. J. A. Fleck, J. R. Morris, Appl. Opt. 17, 2575 (1978).
    [PubMed]
  3. W. R. Klein, E. A. Hiedemann, Physica (Utrecht) 29, 981 (1963).
    [CrossRef]
  4. M. V. Berry, the Diffraction of Light by Ultrasound (Academic, New York, 1966).

1978

1963

W. R. Klein, E. A. Hiedemann, Physica (Utrecht) 29, 981 (1963).
[CrossRef]

Berry, M. V.

M. V. Berry, the Diffraction of Light by Ultrasound (Academic, New York, 1966).

Feit, M. D.

Fleck, J. A.

Hiedemann, E. A.

W. R. Klein, E. A. Hiedemann, Physica (Utrecht) 29, 981 (1963).
[CrossRef]

Klein, W. R.

W. R. Klein, E. A. Hiedemann, Physica (Utrecht) 29, 981 (1963).
[CrossRef]

Morris, J. R.

Appl. Opt.

Physica (Utrecht)

W. R. Klein, E. A. Hiedemann, Physica (Utrecht) 29, 981 (1963).
[CrossRef]

Other

M. V. Berry, the Diffraction of Light by Ultrasound (Academic, New York, 1966).

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Figures (4)

Fig. 1
Fig. 1

Geometry of ultrasonic diffraction problem.

Fig. 2
Fig. 2

Comparison of theory with the results of Klein and Hiedemann for M = 0.94. The dashed line represents J 0 2 ( s ). There is a slight discrepancy between the experimental points and the Bessel-function expression given by Eq. (3).

Fig. 3
Fig. 3

Comparison of theory with the results of Klein and Hiedemann for M = 1.26. The experimental points do not coincide with the Bessel-function expression for the values of s larger than 2.

Fig. 4
Fig. 4

Comparison of theory with the results of Klein and Hiedemann for M = 1.48. The Bessel-function expression cannot be applied even for small s.

Equations (19)

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n = n 0 + n 1 cos ( K x - Ω t ) ,
2 ϕ + k 2 n 2 ϕ = 0.
I m = [ J m ( s ) ] 2 ,
ϕ ( x , y , z ) = exp ( ± i A z ) ϕ ( x , y , 0 ) ,
exp ( ± i A z ) = 1 ± i A z - 1 / 2 A 2 z 2 + .
A 2 2 k n + k n ,
2 = 2 x 2 + 2 y 2
A 2 2 g k n 0 + k n ,
ϕ ( x , y , D ) = exp { - i D [ 2 2 g k n 0 + k ( n - n 0 ) ] } × exp ( - i D n 0 k ) .
ϕ ( x , y , D ) = exp ( - i k n 0 D ) exp { i ( 2 g s M cos K x ) × [ sin ( M 2 g ) + i [ 1 - cos ( M 2 g ) ] ] } ,
ϕ ( x , y , D ) = exp ( - i k n 0 D ) m = - + ( i ) m J m ( 2 g s M { sin ( M 2 g ) + i [ 1 - cos ( M 2 g ) ] } ) exp ( i K m x ) ,
I m = | J m ( 2 g s M { sin ( M 2 g ) + i [ 1 - cos ( M 2 g ) ] } ) | 2 .
I m J m ( s ) 2 .
sin ( M 2 g ) 1 - cos ( M 2 g ) ,             J m ( x ) x m m ! 2 m ,
I ± 1 4 P 2 sin 2 ( p s 4 ) .
exp ( A + B ) = exp { A c [ 1 - exp ( - c ) ] } exp ( B ) .
[ B , A ] = c B ,
exp ( A + B ) = exp { B c [ 1 - exp ( - c ) ] } exp ( A ) .
A i z 2 g k n 0 2 ,             B - i z k ( n - n 0 ) ,

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