Abstract

Acoustooptic interaction as well as the characteristics of both the longitudinal and the flexural modes of guided acoustic waves in an isotropic planar acoustic waveguide have been investigated theoretically. Material parameters for the SF-59 dense flint glass have been used in numerical calculations as an example. The interaction between L(1) longitudinal mode and an optical beam through the center of the acoustic waveguide has been studied with particular detail and is compared with bulk acoustooptic interaction. It is found that the presence of acoustic boundaries results at nonuniform and frequency dependent acoustooptic interaction, unless the acoustic waveguide is made sufficiently thin. Substantial reduction in device driving power is possible using guided acoustic wave technology, due to the small cross section of the acoustic waveguide.

© 1978 Optical Society of America

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References

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  1. I. C. Chang, IEEE Trans. Sonics Ultrason. Su-23, 2 (1976).
    [Crossref]
  2. N. Uchida, N. Niizeki, Proc. IEEE 61, 1073 (1973).
    [Crossref]
  3. C. S. Tsai, M. A. Alheider, L. T. Nguyen, B. Kim, Proc. IEEE 64, 318 (1976).
    [Crossref]
  4. T. G. Giallorenzi, A. F. Milton, J. Appl. Phys. 45, 1762 (1974).
    [Crossref]
  5. R. V. Schmidt, IEEE Trans. Sonics Ultrason. SU-23, 22 (1976).
    [Crossref]
  6. L. C. Foster, C. B. Crumly, R. L. Cohoon, Appl. Opt. 9, 2154 (1970).
    [Crossref] [PubMed]
  7. H. G. Aas, R. K. Erf, J. Acoust. Soc. Am. 36, 1906 (1964).
    [Crossref]
  8. T. R. Meeker, A. H. Meitzler, Physical Acoustics IA (Academic, New York, 1964).
  9. J. D. Achenbach, S. P. Keshava, J. Appl. Mech. 34, Trans. ASME 89, 397 (1967).
  10. B. A. Auld, Acoustic Fields and Waves in Solids, Vol. 1 (Wiley, New York, 1973).

1976 (3)

I. C. Chang, IEEE Trans. Sonics Ultrason. Su-23, 2 (1976).
[Crossref]

C. S. Tsai, M. A. Alheider, L. T. Nguyen, B. Kim, Proc. IEEE 64, 318 (1976).
[Crossref]

R. V. Schmidt, IEEE Trans. Sonics Ultrason. SU-23, 22 (1976).
[Crossref]

1974 (1)

T. G. Giallorenzi, A. F. Milton, J. Appl. Phys. 45, 1762 (1974).
[Crossref]

1973 (1)

N. Uchida, N. Niizeki, Proc. IEEE 61, 1073 (1973).
[Crossref]

1970 (1)

1964 (1)

H. G. Aas, R. K. Erf, J. Acoust. Soc. Am. 36, 1906 (1964).
[Crossref]

Aas, H. G.

H. G. Aas, R. K. Erf, J. Acoust. Soc. Am. 36, 1906 (1964).
[Crossref]

Achenbach, J. D.

J. D. Achenbach, S. P. Keshava, J. Appl. Mech. 34, Trans. ASME 89, 397 (1967).

Alheider, M. A.

C. S. Tsai, M. A. Alheider, L. T. Nguyen, B. Kim, Proc. IEEE 64, 318 (1976).
[Crossref]

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids, Vol. 1 (Wiley, New York, 1973).

Chang, I. C.

I. C. Chang, IEEE Trans. Sonics Ultrason. Su-23, 2 (1976).
[Crossref]

Cohoon, R. L.

Crumly, C. B.

Erf, R. K.

H. G. Aas, R. K. Erf, J. Acoust. Soc. Am. 36, 1906 (1964).
[Crossref]

Foster, L. C.

Giallorenzi, T. G.

T. G. Giallorenzi, A. F. Milton, J. Appl. Phys. 45, 1762 (1974).
[Crossref]

Keshava, S. P.

J. D. Achenbach, S. P. Keshava, J. Appl. Mech. 34, Trans. ASME 89, 397 (1967).

Kim, B.

C. S. Tsai, M. A. Alheider, L. T. Nguyen, B. Kim, Proc. IEEE 64, 318 (1976).
[Crossref]

Meeker, T. R.

T. R. Meeker, A. H. Meitzler, Physical Acoustics IA (Academic, New York, 1964).

Meitzler, A. H.

T. R. Meeker, A. H. Meitzler, Physical Acoustics IA (Academic, New York, 1964).

Milton, A. F.

T. G. Giallorenzi, A. F. Milton, J. Appl. Phys. 45, 1762 (1974).
[Crossref]

Nguyen, L. T.

C. S. Tsai, M. A. Alheider, L. T. Nguyen, B. Kim, Proc. IEEE 64, 318 (1976).
[Crossref]

Niizeki, N.

N. Uchida, N. Niizeki, Proc. IEEE 61, 1073 (1973).
[Crossref]

Schmidt, R. V.

R. V. Schmidt, IEEE Trans. Sonics Ultrason. SU-23, 22 (1976).
[Crossref]

Tsai, C. S.

C. S. Tsai, M. A. Alheider, L. T. Nguyen, B. Kim, Proc. IEEE 64, 318 (1976).
[Crossref]

Uchida, N.

N. Uchida, N. Niizeki, Proc. IEEE 61, 1073 (1973).
[Crossref]

Appl. Opt. (1)

IEEE Trans. Sonics Ultrason. (2)

I. C. Chang, IEEE Trans. Sonics Ultrason. Su-23, 2 (1976).
[Crossref]

R. V. Schmidt, IEEE Trans. Sonics Ultrason. SU-23, 22 (1976).
[Crossref]

J. Acoust. Soc. Am. (1)

H. G. Aas, R. K. Erf, J. Acoust. Soc. Am. 36, 1906 (1964).
[Crossref]

J. Appl. Mech. (1)

J. D. Achenbach, S. P. Keshava, J. Appl. Mech. 34, Trans. ASME 89, 397 (1967).

J. Appl. Phys. (1)

T. G. Giallorenzi, A. F. Milton, J. Appl. Phys. 45, 1762 (1974).
[Crossref]

Proc. IEEE (2)

N. Uchida, N. Niizeki, Proc. IEEE 61, 1073 (1973).
[Crossref]

C. S. Tsai, M. A. Alheider, L. T. Nguyen, B. Kim, Proc. IEEE 64, 318 (1976).
[Crossref]

Other (2)

B. A. Auld, Acoustic Fields and Waves in Solids, Vol. 1 (Wiley, New York, 1973).

T. R. Meeker, A. H. Meitzler, Physical Acoustics IA (Academic, New York, 1964).

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Figures (6)

Fig. 1
Fig. 1

Definitions for an acoustic waveguide plate.

Fig. 2
Fig. 2

Phase velocities of various waveguide modes in a SF-59 glass plate.

Fig. 3
Fig. 3

Displacements of the L(1) mode in a SF-59 glass plate.

Fig. 4
Fig. 4

Induced index of refraction variation in SF-59 glass plate due to L(1) mode.

Fig. 5
Fig. 5

Effectiveness of the guided acoustooptic device with L(1) mode in SF-59 glass plate.

Fig. 6
Fig. 6

Acoustic waveguide length for 100% broadening of a L(1) mode acoustic pulse in a SF-59 glass plate of 1-mm thickness.

Equations (74)

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c T 2 = G / ρ ,
c L 2 = [ 2 G ( 1 ν ) ] / [ ρ ( 1 2 ν ) ] c T 2 / α 2 .
α 2 = ( 1 2 ν ) / [ 2 ( 1 ν ) ] ,
δ 2 = ( 1 2 ν ) / ( 2 ν ) .
T x = G α 2 u x + G δ 2 w z ,
T z = G α 2 w z + G δ 2 u x ,
T x z = G ( u z + w x ) ,
T y = G α 2 u x + G α 2 w z ,
T y z = G υ z ·
c T 2 ( 2 u x 2 + 2 u z 2 ) + ( c L 2 c T 2 ) ( 2 u x 2 + 2 w x z ) = 2 u t 2 ,
c T 2 ( 2 w x 2 + 2 w z 2 ) + ( c L 2 c T 2 ) ( 2 u x z 2 w z 2 ) = 2 w t 2 ,
c T 2 ( 2 υ x 2 + 2 υ z 2 ) = 2 υ t 2 ·
u = [ A exp ( k q z ) + B exp ( k q z ) ] exp [ i k ( x c t ) ] [ C exp ( k s z ) D exp ( k s z ) ] exp [ i k ( x c t ) ] ,
υ = [ E exp ( i k r z ) + F exp ( j k r z ) ] exp [ j k ( x c t ) ] ,
w = i q [ A exp ( k q z ) B exp ( k q z ) ] exp [ i k ( x c t ) ] ( i / s ) [ C exp ( k s z ) + D exp ( k s z ) ] exp [ i k ( x c t ) ] .
r = ( c 2 / c T 2 1 ) 1 / 2 ,
s = ( 1 c 2 / c T 2 ) 1 / 2 ,
q = ( 1 c 2 / c L 2 ) 1 / 2 ,
T y z ( ± 1 2 h ) = 0
T z ( ± 1 2 h ) = 0 ,
T x z ( ± 1 2 h ) = 0 ,
υ = 1 2 E j sin ( k r z ) cos ( k r z ) exp [ j k ( x c t ) ] ,
c = c T { 1 + [ n / ( k h ) ] 2 } 1 / 2 , n = 0,1,2 , ,
| ( 1 + s 2 ) exp ( ξ q ) ( 1 + s 2 ) exp ( ξ q ) 2 exp ( ξ s ) 2 exp ( ξ s ) 2 q exp ( ξ q ) 2 q exp ( ξ q ) ( s + 1 s ) exp ( ξ s ) ( s + 1 s ) exp ( ξ s ) ( 1 + s 2 ) exp ( ξ q ) ( 1 + s 2 ) exp ( ξ q ) 2 exp ( ξ s ) 2 exp ( ξ s ) 2 q exp ( ξ q ) 2 q exp ( ξ q ) ( s + 1 s ) exp ( ξ s ) ( s + 1 s ) exp ( ξ s ) | = 0 ,
u = 2 [ A cosh ( k q z ) C cosh ( k s z ) ] exp [ i k ( x c t ) ] ,
w = 2 [ i q A sinh ( k q z ) + i C s sinh ( k s z ) ] exp [ i k ( x c t ) ] ,
u = 2 [ A sinh ( k q z ) + C sinh ( k s z ) ] exp [ i k ( x c t ) ] ,
w = 2 [ i q A cosh ( k q z ) i C s cosh ( k s z ) ] exp [ i k ( x c t ) ] .
S 4 = 1 2 ( υ / z ) ,
S 6 = 1 2 ( υ / x ) ,
S 1 = S 2 = S 3 = S 5 = 0.
[ p 11 p 12 p 12 0 0 0 p 12 p 11 p 12 0 0 0 p 12 p 12 p 11 0 0 0 0 0 0 1 2 ( p 11 p 12 ) 0 0 0 0 0 0 1 2 ( p 11 p 12 ) 0 0 0 0 0 0 1 2 ( p 11 p 12 ) ] ,
Δ B 1 = Δ B 2 = Δ B 3 = Δ B 5 = 0 ,
Δ B 4 = 1 2 ( p 11 p 12 ) S 4 ,
Δ B 6 = 1 2 ( p 11 p 12 ) S 6 ,
B 1 = B 2 = B 3 = 1 / n 2 .
ψ = 1 2 tan 1 [ 2 B 6 / ( B 1 B 2 ) ] ,
n x = ( B 1 + B 6 tan 45 ° ) 1 / 2 ,
n y = ( B 2 B 6 tan 45 ° ) 1 / 2 .
S 2 = S 4 = S 6 = 0 ,
S 1 = ( u ) / ( x ) ,
S 3 = ( w ) / ( z ) ,
S 5 = 1 2 { [ ( u ) / ( z ) ] + [ ( w ) / x ) ] } .
Δ B 1 = p 11 S 1 + p 12 S 3 ,
Δ B 2 = p 12 ( S 1 + S 3 ) ,
Δ B 3 = p 12 S 1 + P 11 S 3 ,
Δ B 5 = 1 2 ( p 11 p 12 ) S 5 ,
Δ B 4 = Δ B 6 = 0 ,
ψ = 1 2 tan 1 [ 2 B 5 / ( B 1 B 3 ) ] , = 1 2 tan 1 [ S 5 / ( S 1 S 3 ) ] , = 1 2 tan 1 { 1 2 C ( s + 1 s ) sinh ( k s z ) / i [ A c 2 c L 2 cosh ( k q z ) + 2 C cosh ( k s z ) ] }
n x = ( 1 / n 2 + Δ B 1 + Δ B 5 tan ψ ) 1 / 2 ,
n z = ( 1 / n 2 + Δ B 2 Δ B 5 tan ψ ) 1 / 2 .
ψ = 1 2 tan 1 { A q cosh ( k q z ) 1 2 C ( s + s 1 ) cosh ( k s z ) i [ A ( 1 + q 2 ) sinh ( k q z ) + 2 C sinh ( k s z ) ] } ,
n = n 0 1 2 n 0 3 p 12 ( S 1 + S 3 ) .
n = n 0 1 2 n 0 3 p 12 2 i ω ( c / c L 2 ) A cosh ( k q z ) exp [ i k ( x c t ) ] ,
n = n 0 + 1 2 n 0 3 p 12 2 i ω ( c / c L 2 ) A × sinh ( k q z ) exp [ i k ( x c t ) ] .
Δ n = n n 0 = Δ n ( 0 ) cosh ( k q z ) exp [ i k ( x c t ) ] ( L modes ) ,
Δ n = Δ n ( 0 ) sinh ( k q z ) exp [ i k ( x c t ) ] ( F modes ) .
T ¯ = [ G α 2 u x + G δ 2 w z 0 G ( u z + w x ) 0 G δ 2 ( u x + w z ) 0 G ( u z + w x ) 0 G α 2 w z + G σ 2 u x ] .
P x = u * ( 1 α 2 u x + 1 δ 2 w z ) + w * ( u z + w x ) ,
P z = u * ( u z + w x ) + w * ( 1 α 2 w z + 1 δ 2 u x ) .
P x = ( E 1 A 2 + E 2 A C + E 3 C 2 ) 4 i k .
P = 2 ω k c T 2 A 2 ρ [ h / 2 h / 2 E 1 d z + ( C A ) h / 2 h / 2 E 2 d z + ( C 2 A 2 ) h / 2 h / 2 E 3 d z ] .
h / 2 h / 2 E 1 d z = c 2 2 c T 2 h + ( 2 2 c 2 c L 2 + c 2 2 c T 2 ) h [ sinh ( k q h ) k q h ] ,
h / 2 h / 2 E 2 d z = ( 2 c 2 c L 2 c 2 c T 2 4 ) h 2 [ sinh k ( q + s ) h 2 k ( q + s ) h 2 + sinh k ( q s ) h 2 k ( q s ) h 2 ] q s ( 4 c 2 c T 2 ) h 2 [ sinh k ( q + s ) h 2 k ( q + s ) h 2 sinh k ( q s ) h 2 k ( q s ) h 2 ] ,
h / 2 h / 2 E 3 d z = 1 2 s 2 ( c c T ) 2 h + 1 2 s 2 ( 4 3 c 2 c T 2 ) h [ sinh ( k s h ) k s h ] ·
h / 2 h / 2 E 1 d z = { c 2 2 c T 2 h + ( 2 2 c 2 c L 2 + c 2 2 c T 2 ) h [ sinh ( k q h ) k q h ] } ( q * q ) ,
h / 2 h / 2 E 2 d z = q s [ 2 s * s + q * q ( 1 + s 2 ) ] × h 2 [ sinh k ( q + s ) h 2 k ( q + s ) h 2 + sinh k ( q s ) h 2 k ( q s ) h 2 ] × [ 2 ( q * q ) ( 2 + c T 2 2 c 2 c L 2 ) ( s * s ) ] × h 2 [ sinh k ( q + s ) h 2 k ( q + s ) h 2 sinh k ( q s ) h 2 k ( q s ) h 2 ] ,
h / 2 h / 2 E 3 d z = { 1 2 s 2 ( c c T ) 2 h + 1 2 s 2 ( 4 3 c 2 c T 2 ) h [ sinh ( k s h ) k s h ] } ( s * s ) .
P e = h ω 2 A 2 ρ c 2 c L [ 1 + sinh ( k q h ) k q h ] .
AOG P e / P = h c L c [ 1 + sinh ( k q h ) k q h ] 2 c T 2 [ h / 2 h / 2 E 1 d z + ( C A ) h / 2 h / 2 E 2 d z + ( C A ) 2 h / 2 h / 2 E 3 d z ] .
Δ x ( t ) [ ( Δ x 0 ) 2 + ( t Δ x 0 d 2 ω d k 2 | 0 ) 2 ] 1 / 2 ,
T ( ω ) ( Δ x 0 ) 2 / d 2 ω d k 2 | 0 ,
L ( ω ) N 2 π 2 c 0 3 / ω 0 2 d 2 ω d k 2 | 0 ,
L ( ω ) N 2 π 2 ( c c T ) ( 1 ξ 0 2 ) [ 1 d 2 ( ω h / c T ) d ξ 0 2 ] h .

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