Abstract

A theoretical and experimental study of the aperture–bandwidth characteristics of the electronically tunable acousto-optic filter shows that (a) optical divergence in the ordinary plane of the acousto-optic crystal results in a broadening of the filter frequency-transmission characteristic toward longer wavelengths; (b) optical divergence in the extraordinary plane results in a broadening toward shorter wavelengths; (c) divergence of the acoustic beam has the same effect as optical ordinary divergence, and generally will not be of consequence; and (d) roughly, the resolution times the solid-angle acceptance of the acousto-optic filter is approximately the same as that of a solid Fabry–Perot interferometer made of the same material.

© 1972 Optical Society of America

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References

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  1. S. E. Harris and R. W. Wallace, J. Opt. Soc. Am. 59, 744 (1969).
    [Crossref]
  2. S. E. Harris, S. T. K. Nieh, and D. K. Winslow, Appl. Phys. Letters 15, 325 (1969).
    [Crossref]
  3. S. E. Harris, S. T. K. Nieh, and R. S. Feigelson, Appl. Phys. Letters 17, 223 (1970).
    [Crossref]
  4. R. W. Dixon, IEEE J. QE-3, 85 (1967).
    [Crossref]
  5. D. A. Kleinman, A. Ashkin, and G. D. Boyd, Phys. Rev. 145, 338 (1966).
    [Crossref]
  6. W. L. Bond, J. Appl. Phys. 36, 1674 (1965).
    [Crossref]

1970 (1)

S. E. Harris, S. T. K. Nieh, and R. S. Feigelson, Appl. Phys. Letters 17, 223 (1970).
[Crossref]

1969 (2)

S. E. Harris and R. W. Wallace, J. Opt. Soc. Am. 59, 744 (1969).
[Crossref]

S. E. Harris, S. T. K. Nieh, and D. K. Winslow, Appl. Phys. Letters 15, 325 (1969).
[Crossref]

1967 (1)

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

1966 (1)

D. A. Kleinman, A. Ashkin, and G. D. Boyd, Phys. Rev. 145, 338 (1966).
[Crossref]

1965 (1)

W. L. Bond, J. Appl. Phys. 36, 1674 (1965).
[Crossref]

Ashkin, A.

D. A. Kleinman, A. Ashkin, and G. D. Boyd, Phys. Rev. 145, 338 (1966).
[Crossref]

Bond, W. L.

W. L. Bond, J. Appl. Phys. 36, 1674 (1965).
[Crossref]

Boyd, G. D.

D. A. Kleinman, A. Ashkin, and G. D. Boyd, Phys. Rev. 145, 338 (1966).
[Crossref]

Dixon, R. W.

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

Feigelson, R. S.

S. E. Harris, S. T. K. Nieh, and R. S. Feigelson, Appl. Phys. Letters 17, 223 (1970).
[Crossref]

Harris, S. E.

S. E. Harris, S. T. K. Nieh, and R. S. Feigelson, Appl. Phys. Letters 17, 223 (1970).
[Crossref]

S. E. Harris, S. T. K. Nieh, and D. K. Winslow, Appl. Phys. Letters 15, 325 (1969).
[Crossref]

S. E. Harris and R. W. Wallace, J. Opt. Soc. Am. 59, 744 (1969).
[Crossref]

Kleinman, D. A.

D. A. Kleinman, A. Ashkin, and G. D. Boyd, Phys. Rev. 145, 338 (1966).
[Crossref]

Nieh, S. T. K.

S. E. Harris, S. T. K. Nieh, and R. S. Feigelson, Appl. Phys. Letters 17, 223 (1970).
[Crossref]

S. E. Harris, S. T. K. Nieh, and D. K. Winslow, Appl. Phys. Letters 15, 325 (1969).
[Crossref]

Wallace, R. W.

Winslow, D. K.

S. E. Harris, S. T. K. Nieh, and D. K. Winslow, Appl. Phys. Letters 15, 325 (1969).
[Crossref]

Appl. Phys. Letters (2)

S. E. Harris, S. T. K. Nieh, and D. K. Winslow, Appl. Phys. Letters 15, 325 (1969).
[Crossref]

S. E. Harris, S. T. K. Nieh, and R. S. Feigelson, Appl. Phys. Letters 17, 223 (1970).
[Crossref]

IEEE J. (1)

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

J. Appl. Phys. (1)

W. L. Bond, J. Appl. Phys. 36, 1674 (1965).
[Crossref]

J. Opt. Soc. Am. (1)

Phys. Rev. (1)

D. A. Kleinman, A. Ashkin, and G. D. Boyd, Phys. Rev. 145, 338 (1966).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

Schematic of electronically tunable optical filter and tuning curve for a CaMoO4 filter. The acoustic wave is brought in via the transducer at the lower left corner of the CaMoO4 crystal; is reflected off the CaMoO4 air interface; and after traveling down the length of the CaMoO4 crystal is terminated in an aluminum and wax termination.

Fig. 2
Fig. 2

Construction for the determination of the k-vector mismatch Δk and angular coordinates for analysis. In the upper portion of this figure, the vector keka denotes the acoustic driving polarization, while the vector k0 denotes the three electromagnetic waves.

Fig. 3
Fig. 3

Dispersive constant b vs wavelength for CaMoO4.

Fig. 4
Fig. 4

Filter transmittance versus optical wavelength deviation (ΔÅ) from 5000 Å. The figure assumes a 5-cm CaMoO4 crystal and notes the effect of different types of optical divergence as follows: (a) no divergence; (b) optical ordinary divergence; (c) optical extraordinary divergence; (d) both ordinary and extraordinary optical divergence; and (e) acoustic divergence. All cases except (a) assume a uniformly diverging beam of half-angle internal divergence varying between −0.035 radians and +0.035 radians.

Fig. 5
Fig. 5

Filter transmission curves as a function of parameter ( Δ n L / λ 0 ) 1 2 ψ and normalized frequency bLΔy.

Fig. 6
Fig. 6

Normalized half-power bandwidth vs normalized angular divergence. The angularly broadened bandwidth is normalized to the half-power bandwidth in the absence of angular broadening. ψ is the internal half-angle divergence.

Fig. 7
Fig. 7

Schematic of CaMoO4 transmission-type acousto-optic filter.

Fig. 8
Fig. 8

Experimental and theoretical comparison of filter transmission for uniformly diverging optical beams with different maximum angular aperture. The CaMoO4 crystal was 1.8 cm long and centered at 5940 Å. In this figure, θ is the maximum external half-angle.

Equations (19)

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E ˆ z ( r , t ) = E z ( r ) 2 exp j ( ω e t - k e · r ) + complex conjugate , E ˆ x ( r , t ) = E x ( r ) 2 exp j ( ω 0 t - k 0 · r ) + complex conjugate , S ˆ 4 ( r , t ) = S 4 2 exp j ( ω a t - k a · r ) + complex conjugate ,
k 0 k 0 · E x ( r ) = j ω 0 n 0 n e 2 p 45 S 4 * 4 c E z ( r ) e - j Δ k · r , k e k e · E z ( r ) = j ω e n e n 0 2 p 45 S 4 4 c E x ( r ) e j Δ k · r , Δ k = k e - k 0 - k a ,
E x ξ = j ω 0 n 0 n e 2 p 45 S 4 * 4 c E z e - j Δ k y ,
E z ξ = j ω e n e n 0 2 p 45 S 4 4 c E x e j Δ k y ,
Δ k = Δ k a y
Δ k = 2 π n e λ 0 - 2 π n 0 λ 0 - 2 π f a V a + π λ 0 n 0 ( n e θ e λ 0 - f a θ a V a ) 2 + π λ 0 n 0 ( n e φ e λ 0 - f a φ a V a ) 2 - π n e λ 0 ( n e 2 n 0 2 θ e 2 + φ e 2 ) + π f a V a ( θ a 2 + φ a 2 ) ,
E x ξ = j ω 0 n 0 n e 2 p 45 S 4 * 4 c E z e - j Δ k ξ cos γ , E z ξ = j ω e n e n 0 2 p 45 S 4 4 c E x e + j Δ k ξ cos γ .
2 π n e λ 0 - 2 π n 0 λ 0 - 2 π f a V a = 0
Δ k = ( k e y - k 0 y ) Δ y = b Δ y ,
H ( Δ y , θ e , φ e , θ a , φ a ) = Γ 2 L 2 sin 2 ( Γ 2 L 2 + Δ k 2 L 2 / 4 ) 1 2 Γ 2 L 2 + 1 4 Δ k 2 L 2 ,
Γ 2 = n 0 3 n e 3 p 45 2 π 2 4 λ 0 2 S 4 2 = n 0 3 n e 3 p 45 2 π 2 2 ρ V a 3 λ 0 2 ( P A A )
Δ k = π λ 0 n 0 ( n e θ e λ 0 - f a θ a V a ) 2 + π λ 0 n 0 ( n e φ e λ 0 - f a φ a V a ) 2 - π n e λ 0 ( n e 2 n 0 2 θ e 2 + φ e 2 ) + π f a V a ( θ a 2 + φ a 2 ) + b Δ y ,
T ( Δ y ) = θ e , φ e , θ a , φ a H ( Δ y , θ e , φ e , θ a , φ a ) × I ( Δ y , θ e , φ e ) d θ e d φ e d θ a d φ a / θ e , φ e , θ a , φ a I ( Δ y , θ e , φ e ) d θ e d φ e d θ a d φ a .
Δ k = π n e ( n e - n 0 ) n 0 λ 0 φ e 2 + b Δ y .
Δ k = - π n e 2 ( n e - n 0 ) n 0 2 λ 0 θ e 2 + b Δ y .
Δ k = π n e ( n e - n 0 ) n 0 λ 0 ( θ a 2 + φ a 2 ) + b Δ y .
Ω = n e n 0 π ψ 2 = n e n 0 π λ 0 Δ n L .
R = λ Δ λ = 2 Δ n L λ 0 .
R Ω = n e n 0 2 π .