Abstract

Theoretical and experimental studies of the acoustically tuned optical filter show that suitable crystal orientations can be divided into two broad classes based on the acoustic properties of the propagation path used. In acoustically isotropic cases, the acoustic phase and group velocities are collinear. All 32 crystalline point groups are examined for acoustically isotropic orientations that may be useful in tunable optical filters. In acoustically anisotropic cases, the phase and group velocities are not collinear. Methods are presented with which the effects caused by acoustic divergence in these cases may be compensated by similar effects due to changes of birefringence. In particular, anisotropic propagation collinear with acoustic group velocity on a path 101.2° from the optic axis in the Y, Z plane of quartz allows operation at a lower acoustic frequency and power level than that required by isotropic orientations for equivalent performance.

© 1974 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. Lett. 15, 325 (1969).
    [Crossref]
  3. S. E. Harris, S. T. K. Nieh, and R. S. Feigelson, Appl. Phys. Lett. 17, 223 (1970).
    [Crossref]
  4. S. T. K. Nieh and S. E. Harris, J. Opt. Soc. Am. 62, 672 (1972).
    [Crossref]
  5. R. W. Dixon, IEEE J. Quantum Electron. 3, 85 (1967).
    [Crossref]
  6. W. Streifer and J. R. Whinnery, Appl. Phys. Lett. 17, 335 (1970).
    [Crossref]
  7. D. J. Taylor, S. E. Harris, S. T. K. Nieh, and T. W. Hansch, Appl. Phys. Lett. 19, 269 (1971).
    [Crossref]
  8. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1964), p. 235.
  9. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 181.
  10. P. C. Waterman, Phys. Rev. 113, 1240 (1959).
    [Crossref]
  11. Point-group notation used throughout corresponds to the International Tables for X-Ray Crystallography (Kynoch, Birmingham, 1965).
  12. H. F. Tiersten, Linear Piezoelectric Plate Vibrations (Plenum, New York, 1969).
  13. See, for example, Ref. 9, p. 681.
  14. B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, New York, 1973).

1972 (1)

1971 (1)

D. J. Taylor, S. E. Harris, S. T. K. Nieh, and T. W. Hansch, Appl. Phys. Lett. 19, 269 (1971).
[Crossref]

1970 (2)

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

W. Streifer and J. R. Whinnery, Appl. Phys. Lett. 17, 335 (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. Lett. 15, 325 (1969).
[Crossref]

1967 (1)

R. W. Dixon, IEEE J. Quantum Electron. 3, 85 (1967).
[Crossref]

1959 (1)

P. C. Waterman, Phys. Rev. 113, 1240 (1959).
[Crossref]

Auld, B. A.

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

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 181.

Dixon, R. W.

R. W. Dixon, IEEE J. Quantum Electron. 3, 85 (1967).
[Crossref]

Feigelson, R. S.

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

Hansch, T. W.

D. J. Taylor, S. E. Harris, S. T. K. Nieh, and T. W. Hansch, Appl. Phys. Lett. 19, 269 (1971).
[Crossref]

Harris, S. E.

S. T. K. Nieh and S. E. Harris, J. Opt. Soc. Am. 62, 672 (1972).
[Crossref]

D. J. Taylor, S. E. Harris, S. T. K. Nieh, and T. W. Hansch, Appl. Phys. Lett. 19, 269 (1971).
[Crossref]

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

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

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

Nieh, S. T. K.

S. T. K. Nieh and S. E. Harris, J. Opt. Soc. Am. 62, 672 (1972).
[Crossref]

D. J. Taylor, S. E. Harris, S. T. K. Nieh, and T. W. Hansch, Appl. Phys. Lett. 19, 269 (1971).
[Crossref]

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

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

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1964), p. 235.

Streifer, W.

W. Streifer and J. R. Whinnery, Appl. Phys. Lett. 17, 335 (1970).
[Crossref]

Taylor, D. J.

D. J. Taylor, S. E. Harris, S. T. K. Nieh, and T. W. Hansch, Appl. Phys. Lett. 19, 269 (1971).
[Crossref]

Tiersten, H. F.

H. F. Tiersten, Linear Piezoelectric Plate Vibrations (Plenum, New York, 1969).

Wallace, R. W.

Waterman, P. C.

P. C. Waterman, Phys. Rev. 113, 1240 (1959).
[Crossref]

Whinnery, J. R.

W. Streifer and J. R. Whinnery, Appl. Phys. Lett. 17, 335 (1970).
[Crossref]

Winslow, D. K.

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

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 181.

Appl. Phys. Lett. (4)

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

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

W. Streifer and J. R. Whinnery, Appl. Phys. Lett. 17, 335 (1970).
[Crossref]

D. J. Taylor, S. E. Harris, S. T. K. Nieh, and T. W. Hansch, Appl. Phys. Lett. 19, 269 (1971).
[Crossref]

IEEE J. Quantum Electron. (1)

R. W. Dixon, IEEE J. Quantum Electron. 3, 85 (1967).
[Crossref]

J. Opt. Soc. Am. (2)

Phys. Rev. (1)

P. C. Waterman, Phys. Rev. 113, 1240 (1959).
[Crossref]

Other (6)

Point-group notation used throughout corresponds to the International Tables for X-Ray Crystallography (Kynoch, Birmingham, 1965).

H. F. Tiersten, Linear Piezoelectric Plate Vibrations (Plenum, New York, 1969).

See, for example, Ref. 9, p. 681.

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

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1964), p. 235.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 181.

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Figures (5)

Fig. 1
Fig. 1

k-vector diagram. The figure shows the momentum-matching conditions when input light, ki, is propagated collinearly with acoustic group velocity, Vg, and phase matched with the acoustic beam, ka, to produce the output-light beam, ko. Acoustically anisotropic case.

Fig. 2
Fig. 2

k-vector diagram for light entering the filter at a different angle, α1, in the same plane as Fig. 1.

Fig. 3
Fig. 3

k-vector diagram for light entering the filter at a different angle, α2, in the plane orthogonal to Fig. 1.

Fig. 4
Fig. 4

Optical-wave surface for a uniaxial negative crystal showing the three propagation directions examined experimentally.

Fig. 5
Fig. 5

Filter optical passband as a function of the optical wavelength. The data are for a quartz ATOF at 101.2° from the optic axis in the Y, Z plane. Curve 1 gives the half-power bandwidth obtained for fully collimated light. Curve 2 shows the bandwidth measured when the optical acceptance half-angle is increased to 3°.

Tables (3)

Tables Icon

Table I Elements of the photoelastic tensor, PMN, allowed for correct ATOF operation.

Tables Icon

Table II Possible ATOF orientations in acoustically isotropic directions.

Tables Icon

Table III Experimental results, acoustically anisotropic case. λ = 6328 Å, L = 10 cm, uncollimated half-angle = 1°.

Equations (29)

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f a = f 0 V a c Δ n ,
P D = λ 0 2 ρ V a 3 2 n 0 3 n i 3 p 2 L 2 ,
B 1 2 Δ n L ,
f a α = 0 ,
Δ n α = 0 ,
V a = ( c / ρ ) 1 2 ,
c = c 44 + [ ( m 2 - 1 2 ) e 24 + 2 m l e 14 ] 2 / 11 ,
θ = 1 2 tan - 1 ( e 24 e 14 )             or             θ = 1 2 tan - 1 ( - e 14 e 24 ) ,
k i = k 0 + k a ,
k = 2 π / Λ
k i = k o cos θ o + k a cos θ a ,
k o sin θ o = k a sin θ a ,
k i k o + k a cos θ a .
f a = V a Δ n λ o cos θ a ,
f a α | λ fixed = 0.
f a = V a cos ( θ a + a 1 ) Δ n ( α 1 ) λ o .
f a = V a cos θ a Δ n ( α 2 ) λ o .
1 Δ n α 1 Δ n ( α 1 ) | α 1 = 0 = - tan θ a .
α 2 Δ n ( α 2 ) | α 2 = 0 = 0.
1 n ± 2 = 1 2 ( 1 n x 2 + 1 n z 2 ) + ( 1 n x 2 - 1 n z 2 ) cos ( β 1 ± β 2 ) .
Δ n = n + - n - ( n z - n x ) sin β 1 sin β 2 .
1 n e 2 = sin 2 θ n e 2 + cos 2 θ n o 2 ;             n o = n o ,
Δ n = n e - n o ( n e - n o ) sin 2 θ .
V a = ω k a = ( c / ρ ) 1 2 ,
c = c 66 sin 2 θ p + c 44 cos 2 θ p + c 14 sin 2 θ p ,
V g = ω k x x ˆ + ω k y y , + ω k z z ˆ .
θ g = tan - 1 ( ω / k y ω / k z ) ,
θ a = θ g - tan - 1 ( c 44 tan θ g - c 14 c 66 - c 44 tan θ g ) .
2 ctn θ = - tan [ θ - tan - 1 ( c 44 tan θ - c 14 c 66 - c 14 tan θ ) ] .