Abstract

Acoustic modulation of light scattering from a linear centrosymmetric array is analyzed by considering far-field contributions due to optoelastic (OE) effect and acoustically induced translation of the array elements. The modulated light intensity is shown to vary sinusoidally at the acoustic frequency when the physical constants representative of the above effects are within ranges of their physical limits. The OE and translation components of the acousto-optic (AO) signal are shown to be in phase quadrature, each exhibiting a double-sided maxima when expressed as a function of the detector angle.

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References

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  1. S. Bhagavantam and B. R. Rao, Proc. Math. Sc. 28, 54 (1948).
  2. W. R. Klein and B. D. Cook, IEEE Trans. Sonics Ultrason. 14, 123 (1967).
  3. A. Korpel, Acousto-Optics (Marcel Dekker, 1996).
  4. R. Reibold and W. Molkenstruck, Acustica 49, 205 (1981).

1996

A. Korpel, Acousto-Optics (Marcel Dekker, 1996).

1981

R. Reibold and W. Molkenstruck, Acustica 49, 205 (1981).

1967

W. R. Klein and B. D. Cook, IEEE Trans. Sonics Ultrason. 14, 123 (1967).

1948

S. Bhagavantam and B. R. Rao, Proc. Math. Sc. 28, 54 (1948).

Bhagavantam, S.

S. Bhagavantam and B. R. Rao, Proc. Math. Sc. 28, 54 (1948).

Cook, B. D.

W. R. Klein and B. D. Cook, IEEE Trans. Sonics Ultrason. 14, 123 (1967).

Klein, W. R.

W. R. Klein and B. D. Cook, IEEE Trans. Sonics Ultrason. 14, 123 (1967).

Korpel, A.

A. Korpel, Acousto-Optics (Marcel Dekker, 1996).

Molkenstruck, W.

R. Reibold and W. Molkenstruck, Acustica 49, 205 (1981).

Rao, B. R.

S. Bhagavantam and B. R. Rao, Proc. Math. Sc. 28, 54 (1948).

Reibold, R.

R. Reibold and W. Molkenstruck, Acustica 49, 205 (1981).

Acustica

R. Reibold and W. Molkenstruck, Acustica 49, 205 (1981).

IEEE Trans. Sonics Ultrason.

W. R. Klein and B. D. Cook, IEEE Trans. Sonics Ultrason. 14, 123 (1967).

Proc. Math. Sc.

S. Bhagavantam and B. R. Rao, Proc. Math. Sc. 28, 54 (1948).

Other

A. Korpel, Acousto-Optics (Marcel Dekker, 1996).

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Figures (2)

Fig. 1
Fig. 1

Scattering of a plane wave by a collinear array of scattering centers.

Fig. 2
Fig. 2

AO intensity ( I ac ) as a function of detector angle ( θ ) for m opt = 0 . The insets show the time variation of intensity [ Δ I ( t ) ] corresponding to different θ values. The parameters used are a = 0.1 , ϕ = 30 ° , n 0 = 1.2 , r 0 = 0.1 m , λ = 1 × 10 6 m , λ s = 1 × 10 3 m , and N = 40 . (a) AO intensity due to translation of elements ( A 0 = 1 × 10 9 m ) ; (b) AO intensity due to variations in refractive index ( C = 1 × 10 4 ) .

Equations (23)

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sin θ = n 0 sin ϕ ± m ao ( λ λ s ) , m ao = 0 , 1 , 2 , .
E = E inc exp ( j ω t ) ( exp { j k r 0 } r 0 + p = 1 N exp { j k [ r p + s p ] } r p + p = 1 N exp { j k [ r p + + s p + ] } r p + ) ,
r p + r 0 p d sin θ , r p r 0 + p d sin θ .
E p p = E p + + E p = 2 E inc r 0 exp ( j ω t ) exp ( j k r 0 ) cos ( k Θ p ) , p 0 .
I opt ( r 0 , θ ) = E E * 2 = 1 2 ( E inc r 0 ) 2 sin 2 [ π a ( 2 N + 1 ) ( sin θ n 0 sin ϕ ) ] sin 2 [ π a ( sin θ n 0 sin ϕ ) ] .
θ Bragg = sin 1 ( n 0 sin ϕ m opt a ) ,
S ( x , t ) = S m cos ( k s x ω s t ) ,
Δ x p ± = A 0 cos ( p r ω s t ) , for p = 0 , 1 , , N ,
Δ s p ± = n 0 A 0 sin ϕ cos ( p r ω s t ) .
E ̃ p ± = ( E inc r 0 ) exp ( j ω t ) exp [ j k ( r 0 p a λ sin θ + s p ± + Δ s p ± ) ] ,
I ̃ ( t ) = 1 2 ( E inc r 0 ) 2 | exp ( j k Δ s 0 ) + p = 1 N exp [ j k ( Θ p + Δ s p ) ] + exp [ j k ( Θ p Δ s p + ) ] | 2 ,
Δ I ( t ) = I ac sin ( n π + ω s t ) , n = 0 , 1 , 2 , .
Case- 1 : Δ s p ± = ± n 0 A 0 sin ϕ sin p r , Case- 2 : Δ s p ± = n 0 A 0 sin ϕ sin p r .
Δ s p = { n 0 A 0 sin ϕ sin p r for Case- 1 n 0 A 0 sin ϕ sin p r for Case- 2 } .
I ac = 1 2 ( E inc r o ) 2 ( ( 1 + 2 p = 1 N cos [ k ( Θ p Δ s p ) ] ) 2 ( 1 + 2 p = 1 N cos k Θ p ) 2 ) .
n ̃ ( x , t ) = n 0 + C S m cos ( k s x ω s t ) ,
E ̃ p p = E inc r o exp { j ( k r 0 ω t ) } [ exp { j k ( Θ p + Δ s p ) } + exp { j k ( Θ p Δ s p + ) } ] ,
k Δ s p ± = ± 2 π p a C sin ϕ cos ( p r ω s t ) ,
I ̃ ( t ) = 1 2 ( E inc r o ) 2 | 1 + p = 1 N exp { j k ( Θ p + Δ s p ) } + exp { j k ( Θ p Δ s p + ) } | 2 .
Δ I ( t ) = I ac cos ( n π + ω s t ) , n = 0 , 1 , 2 , .
Case 1 : k Δ s p ± = ± 2 π p a C sin ϕ cos p r ,
Case 2 : k Δ s p ± = 2 π p a C sin ϕ cos p r .
k Δ s p = { + 2 π p a C sin ϕ cos p r for Case- 1 2 π p a C sin ϕ cos p r for Case- 2 } .

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