Abstract

This paper proposes a new type of electronically tunable optical filter. The basic idea is to utilize collinear acousto-optic diffraction in an optically anisotropic media. Changing the driving acoustic frequency changes the band of optical frequencies that the filter passes. A LiNbO3 acousto-optic filter with a pass band approximately 1.3 cm−1 wide should be tunable from 4000 to 7000 Å by changing the acoustic frequency from 428 to 990 Mc/sec. For this case, the angular aperture will be about 1.5°, and, theoretically 100% transmittance should be attained at the filter center frequency by use of about 14 mW of acoustic power per mm2 of filter aperture.

© 1969 Optical Society of America

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References

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  1. R. W. Dixon, IEEE J. Quant. Elect. QE-3, 85 (1967).
    [Crossref]
  2. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 593–609.
  3. In fact, the Bragg condition is a special case of k¯ vector matching and is strictly correct only when the acoustic frequency is negligibly small as compared with the optical frequency.
  4. E. G. H. Lean and H. J. Shaw, Appl. Phys. Letters 9, 372 (1966).
    [Crossref]
  5. R. W. Dixon, J. Appl. Phys. 38, 5149 (1967).
    [Crossref]
  6. M. V. Hobden and J. Warner, Phys. Rev. Letters 22, 243 (1966).
  7. A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, M. A. Ballman, J. J. Levinstein, and K. Nassau, Appl. Phys. Letters 9, 72 (1966).
    [Crossref]
  8. C. P. Wen and R. F. Mayo, Appl. Phys. Letters 9, 135 (1966).
    [Crossref]

1967 (2)

R. W. Dixon, J. Appl. Phys. 38, 5149 (1967).
[Crossref]

R. W. Dixon, IEEE J. Quant. Elect. QE-3, 85 (1967).
[Crossref]

1966 (4)

E. G. H. Lean and H. J. Shaw, Appl. Phys. Letters 9, 372 (1966).
[Crossref]

M. V. Hobden and J. Warner, Phys. Rev. Letters 22, 243 (1966).

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, M. A. Ballman, J. J. Levinstein, and K. Nassau, Appl. Phys. Letters 9, 72 (1966).
[Crossref]

C. P. Wen and R. F. Mayo, Appl. Phys. Letters 9, 135 (1966).
[Crossref]

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, M. A. Ballman, J. J. Levinstein, and K. Nassau, Appl. Phys. Letters 9, 72 (1966).
[Crossref]

Ballman, M. A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, M. A. Ballman, J. J. Levinstein, and K. Nassau, Appl. Phys. Letters 9, 72 (1966).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 593–609.

Boyd, G. D.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, M. A. Ballman, J. J. Levinstein, and K. Nassau, Appl. Phys. Letters 9, 72 (1966).
[Crossref]

Dixon, R. W.

R. W. Dixon, J. Appl. Phys. 38, 5149 (1967).
[Crossref]

R. W. Dixon, IEEE J. Quant. Elect. QE-3, 85 (1967).
[Crossref]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, M. A. Ballman, J. J. Levinstein, and K. Nassau, Appl. Phys. Letters 9, 72 (1966).
[Crossref]

Hobden, M. V.

M. V. Hobden and J. Warner, Phys. Rev. Letters 22, 243 (1966).

Lean, E. G. H.

E. G. H. Lean and H. J. Shaw, Appl. Phys. Letters 9, 372 (1966).
[Crossref]

Levinstein, J. J.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, M. A. Ballman, J. J. Levinstein, and K. Nassau, Appl. Phys. Letters 9, 72 (1966).
[Crossref]

Mayo, R. F.

C. P. Wen and R. F. Mayo, Appl. Phys. Letters 9, 135 (1966).
[Crossref]

Nassau, K.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, M. A. Ballman, J. J. Levinstein, and K. Nassau, Appl. Phys. Letters 9, 72 (1966).
[Crossref]

Shaw, H. J.

E. G. H. Lean and H. J. Shaw, Appl. Phys. Letters 9, 372 (1966).
[Crossref]

Smith, R. G.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, M. A. Ballman, J. J. Levinstein, and K. Nassau, Appl. Phys. Letters 9, 72 (1966).
[Crossref]

Warner, J.

M. V. Hobden and J. Warner, Phys. Rev. Letters 22, 243 (1966).

Wen, C. P.

C. P. Wen and R. F. Mayo, Appl. Phys. Letters 9, 135 (1966).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 593–609.

Appl. Phys. Letters (3)

E. G. H. Lean and H. J. Shaw, Appl. Phys. Letters 9, 372 (1966).
[Crossref]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, M. A. Ballman, J. J. Levinstein, and K. Nassau, Appl. Phys. Letters 9, 72 (1966).
[Crossref]

C. P. Wen and R. F. Mayo, Appl. Phys. Letters 9, 135 (1966).
[Crossref]

IEEE J. Quant. Elect. (1)

R. W. Dixon, IEEE J. Quant. Elect. QE-3, 85 (1967).
[Crossref]

J. Appl. Phys. (1)

R. W. Dixon, J. Appl. Phys. 38, 5149 (1967).
[Crossref]

Phys. Rev. Letters (1)

M. V. Hobden and J. Warner, Phys. Rev. Letters 22, 243 (1966).

Other (2)

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 593–609.

In fact, the Bragg condition is a special case of k¯ vector matching and is strictly correct only when the acoustic frequency is negligibly small as compared with the optical frequency.

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Figures (4)

Fig. 1
Fig. 1

LiNbO3 acousto-optic filter. Longitudinal wave (L), shear wave (S).

Fig. 2
Fig. 2

Filter transmittance vs normalized frequency.

Fig. 3
Fig. 3

b and 2π(n0ne) vs λ.

Fig. 4
Fig. 4

k ¯ vector matching for nearly collinear propagation (not to scale).

Equations (12)

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E ˆ z ( y , t ) = [ E z ( y ) / 2 ]     exp     j ( ω e t - k e y ) + c . c . ( input optical wave ) E ˆ x ( y , t ) = [ E x ( y ) / 2 ]     exp     j ( ω 0 t - k 0 y ) + c . c . ( output optical wave ) S ˆ 6 ( y , t ) = [ S 6 ( y ) / 2 ]     exp     j ( ω a t - k a y ) + c . c . ( acoustic shear wave )
P ˆ x = - e 0 n 0 2 n e 2 p 41 S ˆ 6 E ˆ z P ˆ z = - e 0 n 0 2 n e 2 p 41 S ˆ 6 E ˆ x ,
2 E ˆ y 2 - 1 c 2 2 E ˆ t 2 = μ 0 2 P ˆ t 2
d E x d y = j n 0 n e 2 p 41 ω 0 4 c S 6 E z     exp ( j Δ k y ) d E z d y = j n e n 0 2 p 41 ω e 4 c S 6 * E x exp ( - j Δ k y ) ,
P x ( L ) P z ( 0 ) = ( ω 0 ω e ) Γ 2 L 2 sin 2 [ ( Γ 2 + Δ k 2 4 ) 1 2 L ] ( Γ 2 + Δ k 2 4 ) L 2
Γ 2 = n 0 3 n e 3 p 41 2 ω 0 ω e 16 c 2 S 6 2 .
P x ( L ) / P z ( 0 ) = sin 2 Γ L
Γ 2 = n 0 3 n e 3 p 41 2 π 2 2 λ 0 2 1 ρ V 3 P A A ,
Δ k = ( k 0 y - k e y ) Δ y b Δ y ,
H ( f ) = π 2 sin 2 1 2 ( π 2 + b 2 L 2 Δ y 2 ) 1 2 π 2 + b 2 L 2 Δ y 2 .
f a = ( V / λ 0 ) ( n 0 - n e ) ,
Δ k = k 0     cos φ - k e     cos ψ - k a k 0 - k e - k a + ( k c - k e 2 k 0 ) ψ 2 2 ( π / λ ) Δ n ψ 2 .