Abstract

The diffraction of light by acoustic waves on a film is characterized and analyzed in detail. This investigation includes the mechanism of excitation of acoustic waves, the propagation of acoustic waves, and diffraction of light. The acoustic waveguiding phenomenon in unidirectionally stressed film is analyzed. Applications to optical processing are discussed. These include spectrum analysis, simultaneous parallel array data processing, and sequential multiproduct processing. Agenda for future development are discussed.

© 1982 Optical Society of America

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References

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  1. A. E. Attard, B. L. Heffner, Opt. Lett. 6, 225 (1981).
    [CrossRef] [PubMed]
  2. P. Merilainen, Microwave Opt. Acoust. 2, 147 (1978).
    [CrossRef]
  3. W. R. Smythe, Static and Dynamic Electricity (McGraw-Hill, New York, 1950), p. 18.
  4. N. W. McLachlan, Theory of Vibrations (Dover, New York, 1952),p. 27.
  5. M. V. Klein, Optics (Wiley, New York, 1970), p. 574.
  6. W. G. Mayer, G. B. Lamers, Technical Report 2, NONR 5037 (01) (May1967).
  7. I. N. Sneddon, Special Functions of Mathematical Physics and Chemistry (Oliver and Boyd, Edinburgh, 1956), p. 93.
  8. P. M. Morse, K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), p. 195.
  9. Ref. 8, p. 191.
  10. A. E. Attard, H. C. Lee, J. Chem. Educ. 56, 650 (1979).
    [CrossRef]
  11. B. O. Pierce, A Short Table of Integrals (Ginn & Co., New York, 1929), p. 96.
  12. B. T. Khuri-Yakub, G. S. Kino, Appl. Phys. Lett. 30, 78 (1977).
    [CrossRef]

1981 (1)

1979 (1)

A. E. Attard, H. C. Lee, J. Chem. Educ. 56, 650 (1979).
[CrossRef]

1978 (1)

P. Merilainen, Microwave Opt. Acoust. 2, 147 (1978).
[CrossRef]

1977 (1)

B. T. Khuri-Yakub, G. S. Kino, Appl. Phys. Lett. 30, 78 (1977).
[CrossRef]

Attard, A. E.

A. E. Attard, B. L. Heffner, Opt. Lett. 6, 225 (1981).
[CrossRef] [PubMed]

A. E. Attard, H. C. Lee, J. Chem. Educ. 56, 650 (1979).
[CrossRef]

Heffner, B. L.

Ingard, K. U.

P. M. Morse, K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), p. 195.

Khuri-Yakub, B. T.

B. T. Khuri-Yakub, G. S. Kino, Appl. Phys. Lett. 30, 78 (1977).
[CrossRef]

Kino, G. S.

B. T. Khuri-Yakub, G. S. Kino, Appl. Phys. Lett. 30, 78 (1977).
[CrossRef]

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970), p. 574.

Lamers, G. B.

W. G. Mayer, G. B. Lamers, Technical Report 2, NONR 5037 (01) (May1967).

Lee, H. C.

A. E. Attard, H. C. Lee, J. Chem. Educ. 56, 650 (1979).
[CrossRef]

Mayer, W. G.

W. G. Mayer, G. B. Lamers, Technical Report 2, NONR 5037 (01) (May1967).

McLachlan, N. W.

N. W. McLachlan, Theory of Vibrations (Dover, New York, 1952),p. 27.

Merilainen, P.

P. Merilainen, Microwave Opt. Acoust. 2, 147 (1978).
[CrossRef]

Morse, P. M.

P. M. Morse, K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), p. 195.

Pierce, B. O.

B. O. Pierce, A Short Table of Integrals (Ginn & Co., New York, 1929), p. 96.

Smythe, W. R.

W. R. Smythe, Static and Dynamic Electricity (McGraw-Hill, New York, 1950), p. 18.

Sneddon, I. N.

I. N. Sneddon, Special Functions of Mathematical Physics and Chemistry (Oliver and Boyd, Edinburgh, 1956), p. 93.

Appl. Phys. Lett. (1)

B. T. Khuri-Yakub, G. S. Kino, Appl. Phys. Lett. 30, 78 (1977).
[CrossRef]

J. Chem. Educ. (1)

A. E. Attard, H. C. Lee, J. Chem. Educ. 56, 650 (1979).
[CrossRef]

Microwave Opt. Acoust. (1)

P. Merilainen, Microwave Opt. Acoust. 2, 147 (1978).
[CrossRef]

Opt. Lett. (1)

Other (8)

B. O. Pierce, A Short Table of Integrals (Ginn & Co., New York, 1929), p. 96.

W. R. Smythe, Static and Dynamic Electricity (McGraw-Hill, New York, 1950), p. 18.

N. W. McLachlan, Theory of Vibrations (Dover, New York, 1952),p. 27.

M. V. Klein, Optics (Wiley, New York, 1970), p. 574.

W. G. Mayer, G. B. Lamers, Technical Report 2, NONR 5037 (01) (May1967).

I. N. Sneddon, Special Functions of Mathematical Physics and Chemistry (Oliver and Boyd, Edinburgh, 1956), p. 93.

P. M. Morse, K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), p. 195.

Ref. 8, p. 191.

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Figures (10)

Fig. 1
Fig. 1

Detail of the transducer arrangement.

Fig. 2
Fig. 2

Model of the transducer.

Fig. 3
Fig. 3

Scattering of light by two scattering centers on an acoustic wave. The centers are separated by horizontal distance X. The amplitude difference is Y. The angle of incidence is θ0, and the angle of scattering is θ0 + α, where α may be positive or negative.

Fig. 4
Fig. 4

Velocity of the acoustic wave as a function of frequency. The dashed line represents the velocity in the absence of air reaction and was obtained from the Y intercept of Fig. 5.

Fig. 5
Fig. 5

Square of the acoustic velocity as a function of the square of the ratio of velocity to frequency. This is a test of the velocity dispersion model. In a linear regression analysis,10 the coefficient of determination r2 = 0.97.

Fig. 6
Fig. 6

Amplitude of the acoustic wave as a function of the rf voltage Vrf.

Fig. 7
Fig. 7

Amplitude of the acoustic wave as a function of frequency. The dashed line illustrates the 1/f relation.

Fig. 8
Fig. 8

Amplitude of the acoustic wave as a function of frequency. Here we see the presence of resonant vibration modes of the film. The amplitude of these modes is small compared with the amplitude of the acoustic wave.

Fig. 9
Fig. 9

Two-dimensional diffraction pattern as a consequence of sequential diffraction by different acoustic beams on the film.

Fig. 10
Fig. 10

Identification of the first-order diffraction beams in Fig. 9 with indication of the shift in optical frequency for each beam.

Equations (29)

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C 1 = C A = E f E 0 h E 0 + d E f ,
ϕ = 2 π λ 0 { X [ sin ( θ + α ) sin θ ] + Y [ cos ( θ + α ) + cos θ ] } .
Y = j a j sin K j X ,
A ( θ , α ) = 1 L L / 2 L / 2 exp ( iGX ) j exp [ i W j sin ( K j X ) ] d X ,
G = 2 π λ 0 [ sin ( θ 0 + α ) sin θ 0 ] , W j = 2 π λ 0 [ cos ( θ 0 + α ) + cos θ 0 ] a j .
exp ( i A sin θ ) = n = J n ( A ) exp ( in θ ) , J n ( A ) = ( 1 ) n J n ( A ) .
A ( θ 0 , α ) = 1 L L / 2 L / 2 exp ( iGX ) r [ n = J n ( W r ) exp ( in K r X ) ] d X .
A ( θ 0 , α ) = n = A n sin ( 1 / 2 ) ( G + n K ) ( 1 / 2 ) ( G + n K ) ,
sin ( θ α ) sin θ = n λ 0 Λ ,
A 2 = J 2 ( W 1 ) J 0 ( W 2 ) J 0 ( W 1 ) J 1 ( W 2 ) + J 2 ( W 1 ) J 2 ( W 2 ) + h , A 1 = J 1 ( W 1 ) J 0 ( W 2 ) J 1 ( W 1 ) J 1 ( W 2 ) + h A 0 = J 0 ( W 1 ) J 0 ( W 2 ) + h A 1 = J 1 ( W 1 ) J 0 ( W 2 ) J 1 ( W 1 ) J 1 ( W 2 ) + h A 2 = J 2 ( W 1 ) J 0 ( W 2 ) + J 0 ( W 1 ) J 1 ( W 2 ) + J 2 ( W 1 ) J 2 ( W 2 ) + h ,
I 2 = I 2 = [ J 1 ( W 2 ) ] 2 ; I 1 = I 1 = 0 ; I 0 = [ J 0 ( W 2 ) ] 2 .
I 2 = I 2 = [ J 2 ( W 2 ) ] 2 ; I 1 = I 1 = [ J 1 ( W 1 ) ] 2 ; I 0 = [ J 0 ( W 1 ) ] 2 .
T d 2 y d X 2 + P = σ d 2 y d t 2 ,
V a 2 = C 2 1 + ( B / σ ω 2 ) ,
V a 2 = C 2 S ( V a 2 f a 2 )
I n ( W 1 ) I 0 ( 0 ) = [ J n ( W 1 ) ] 2 ,
W 1 = 2 π λ 0 [ cos ( θ 0 + α ) + cos θ 0 ] a 1 4 π λ 0 a 1 cos θ .
T x d 2 Z d X 2 + T y d 2 Z d Y 2 = σ d 2 Z d t 2 .
d 2 Z d X 2 + b d 2 Z d Y 2 = 1 C 2 d 2 Z d t 2 .
d 2 Z d X 2 = 1 C 2 d 2 Z d t 2 .
V x = C = T / σ .
d 2 Z d Y 2 = 1 b C 2 d 2 Z d t 2 .
Z ( X 2 ) = Z ( X 1 ) | d Z d x ( X 2 X 1 ) | .
d 2 Z d X 2 + d 2 Z d Y 2 = 1 C 2 d 2 Z d t 2 .
d Z d Y = d Z d X
d Z d Y = d Z d X 1 b ,
f = V 2 π 3 σ M L = 1 2 π 3 T M L ,
J n ( x ) = ( x / 2 ) n n ! [ 1 + 0 ( x 1 ) ] .
J 1 ( x ) = x / 2 2 π a cos θ λ = J 1 ( W 1 ) .

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