Abstract

The anisotropic diffraction of light by high frequency longitudinal ultrasonic waves in the tangential phase matching configuration may present some definite advantages over the same interaction using transverse acoustic waves. A systematic search for favorable crystal cuts in lithium niobate was worked out. The main results of this study are reported here; they enable the choice of the best configuration for a given operating center frequency.

© 1990 Optical Society of America

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References

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  1. C. P. Wen, R. F. Mayo, “Acoustic Attenuation of a Single Domain Lithium Niobate Crystal at Microwave Frequencies,” Appl. Phys. Lett. 9, 135–136 (1966).
    [CrossRef]
  2. R. W. Dixon, M. G. Cohen, “A New Technique for Measuring Magnitudes of Photoelastic Tensors and its Application to Lithium Niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
    [CrossRef]
  3. R. W. Dixon, “Photoelastic Properties of Selected Materials and their Relevance for Applications to Acoustic Light Modulators and Scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
    [CrossRef]
  4. I. C. Chang, “Spatial Light Modulators and Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 465, 18–22 (1984).
  5. I. C. Chang, L. S. Lee, “Acousto-Optic Bragg Cells for EW Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 477, 23–28 (1984).
  6. J. M. Rouvaen, G. Waxin, C. Bruneel, R. Torguet, “Wideband Lithium Niobate Acousto-Optic Cells,” Acoust. Lett. (G.B.) 9, 5–11 (1985).
  7. I. C. Chang, “Acousto-Optic Devices and Applications,” I.E.E.E. Trans. Sonics Ultrason. SU-23, 2–22 (1976).
    [CrossRef]
  8. G. Waxin, J. M. Rouvaen, M. G. Gazalet, C. Bruneel, “New High Frequency Anisotropic Diffraction Geometries in Lithium Niobate Crystals,” Acoust. Lett. (G.B.), 11, 137–140 (1988).
  9. R. Kalman, I. C. Chang, “Acousto-Optic Bragg Cells at Microwave Frequencies,” Proc. Soc. Photo. Opt. Instrum. Eng. 639, 11–15 (1986).
  10. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957).
  11. W. P. Mason, Crystal Physics of Interaction Processes, (Academic Press, New York, 1966).
  12. R. S. Weis, T. K. Gaylord, “Lithium Niobate: Summary of Physical Properties and Crystal Structure,” Appl. Phys. A 37, 191–203 (1985).
    [CrossRef]
  13. B. A. Auld, Acoustic Fields and Waves in Solids, Wiley Interscience, New York, 1973.
  14. R. O’B. Carpenter, “Photoelastic Effect in Electro-Optic Crystals,” J. Opt. Soc. Am. 40, 225–228 (1950).
    [CrossRef]
  15. A. W. Warner, M. Onoe, G. A. Coquin, “Determination of Elastic and Piezoelectric Constants for Crystals in Class (3m),” J. Acoust. Soc. Am. 42, 1223–1231 (1967).
    [CrossRef]
  16. L. P. Avakyants, D. F. Kiselev, N. N. Shchitkov, “Measurement of the Photoelastic Coefficients of Lithium Niobate Single Crystals,” Sov. Phys. Solid State 18, 899–901 (1976).
  17. E. H. Turner, “High Frequency Electro-Optic Coefficients of Lithium Niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
    [CrossRef]
  18. D. F. Nelson, R. M. Mikulyak, “Refractive Indices of Stoichiometric and Congruently Melting Lithium Niobate Crystals,” J. Appl. Phys. 45, 3688–3689 (1974).
    [CrossRef]

1988 (1)

G. Waxin, J. M. Rouvaen, M. G. Gazalet, C. Bruneel, “New High Frequency Anisotropic Diffraction Geometries in Lithium Niobate Crystals,” Acoust. Lett. (G.B.), 11, 137–140 (1988).

1986 (1)

R. Kalman, I. C. Chang, “Acousto-Optic Bragg Cells at Microwave Frequencies,” Proc. Soc. Photo. Opt. Instrum. Eng. 639, 11–15 (1986).

1985 (2)

R. S. Weis, T. K. Gaylord, “Lithium Niobate: Summary of Physical Properties and Crystal Structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

J. M. Rouvaen, G. Waxin, C. Bruneel, R. Torguet, “Wideband Lithium Niobate Acousto-Optic Cells,” Acoust. Lett. (G.B.) 9, 5–11 (1985).

1984 (2)

I. C. Chang, “Spatial Light Modulators and Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 465, 18–22 (1984).

I. C. Chang, L. S. Lee, “Acousto-Optic Bragg Cells for EW Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 477, 23–28 (1984).

1976 (2)

I. C. Chang, “Acousto-Optic Devices and Applications,” I.E.E.E. Trans. Sonics Ultrason. SU-23, 2–22 (1976).
[CrossRef]

L. P. Avakyants, D. F. Kiselev, N. N. Shchitkov, “Measurement of the Photoelastic Coefficients of Lithium Niobate Single Crystals,” Sov. Phys. Solid State 18, 899–901 (1976).

1974 (1)

D. F. Nelson, R. M. Mikulyak, “Refractive Indices of Stoichiometric and Congruently Melting Lithium Niobate Crystals,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

1967 (2)

R. W. Dixon, “Photoelastic Properties of Selected Materials and their Relevance for Applications to Acoustic Light Modulators and Scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[CrossRef]

A. W. Warner, M. Onoe, G. A. Coquin, “Determination of Elastic and Piezoelectric Constants for Crystals in Class (3m),” J. Acoust. Soc. Am. 42, 1223–1231 (1967).
[CrossRef]

1966 (3)

C. P. Wen, R. F. Mayo, “Acoustic Attenuation of a Single Domain Lithium Niobate Crystal at Microwave Frequencies,” Appl. Phys. Lett. 9, 135–136 (1966).
[CrossRef]

R. W. Dixon, M. G. Cohen, “A New Technique for Measuring Magnitudes of Photoelastic Tensors and its Application to Lithium Niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

E. H. Turner, “High Frequency Electro-Optic Coefficients of Lithium Niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
[CrossRef]

1950 (1)

Auld, B. A.

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

Avakyants, L. P.

L. P. Avakyants, D. F. Kiselev, N. N. Shchitkov, “Measurement of the Photoelastic Coefficients of Lithium Niobate Single Crystals,” Sov. Phys. Solid State 18, 899–901 (1976).

Bruneel, C.

G. Waxin, J. M. Rouvaen, M. G. Gazalet, C. Bruneel, “New High Frequency Anisotropic Diffraction Geometries in Lithium Niobate Crystals,” Acoust. Lett. (G.B.), 11, 137–140 (1988).

J. M. Rouvaen, G. Waxin, C. Bruneel, R. Torguet, “Wideband Lithium Niobate Acousto-Optic Cells,” Acoust. Lett. (G.B.) 9, 5–11 (1985).

Carpenter, R. O’B.

Chang, I. C.

R. Kalman, I. C. Chang, “Acousto-Optic Bragg Cells at Microwave Frequencies,” Proc. Soc. Photo. Opt. Instrum. Eng. 639, 11–15 (1986).

I. C. Chang, “Spatial Light Modulators and Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 465, 18–22 (1984).

I. C. Chang, L. S. Lee, “Acousto-Optic Bragg Cells for EW Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 477, 23–28 (1984).

I. C. Chang, “Acousto-Optic Devices and Applications,” I.E.E.E. Trans. Sonics Ultrason. SU-23, 2–22 (1976).
[CrossRef]

Cohen, M. G.

R. W. Dixon, M. G. Cohen, “A New Technique for Measuring Magnitudes of Photoelastic Tensors and its Application to Lithium Niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

Coquin, G. A.

A. W. Warner, M. Onoe, G. A. Coquin, “Determination of Elastic and Piezoelectric Constants for Crystals in Class (3m),” J. Acoust. Soc. Am. 42, 1223–1231 (1967).
[CrossRef]

Dixon, R. W.

R. W. Dixon, “Photoelastic Properties of Selected Materials and their Relevance for Applications to Acoustic Light Modulators and Scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[CrossRef]

R. W. Dixon, M. G. Cohen, “A New Technique for Measuring Magnitudes of Photoelastic Tensors and its Application to Lithium Niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

Gaylord, T. K.

R. S. Weis, T. K. Gaylord, “Lithium Niobate: Summary of Physical Properties and Crystal Structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Gazalet, M. G.

G. Waxin, J. M. Rouvaen, M. G. Gazalet, C. Bruneel, “New High Frequency Anisotropic Diffraction Geometries in Lithium Niobate Crystals,” Acoust. Lett. (G.B.), 11, 137–140 (1988).

Kalman, R.

R. Kalman, I. C. Chang, “Acousto-Optic Bragg Cells at Microwave Frequencies,” Proc. Soc. Photo. Opt. Instrum. Eng. 639, 11–15 (1986).

Kiselev, D. F.

L. P. Avakyants, D. F. Kiselev, N. N. Shchitkov, “Measurement of the Photoelastic Coefficients of Lithium Niobate Single Crystals,” Sov. Phys. Solid State 18, 899–901 (1976).

Lee, L. S.

I. C. Chang, L. S. Lee, “Acousto-Optic Bragg Cells for EW Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 477, 23–28 (1984).

Mason, W. P.

W. P. Mason, Crystal Physics of Interaction Processes, (Academic Press, New York, 1966).

Mayo, R. F.

C. P. Wen, R. F. Mayo, “Acoustic Attenuation of a Single Domain Lithium Niobate Crystal at Microwave Frequencies,” Appl. Phys. Lett. 9, 135–136 (1966).
[CrossRef]

Mikulyak, R. M.

D. F. Nelson, R. M. Mikulyak, “Refractive Indices of Stoichiometric and Congruently Melting Lithium Niobate Crystals,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

Nelson, D. F.

D. F. Nelson, R. M. Mikulyak, “Refractive Indices of Stoichiometric and Congruently Melting Lithium Niobate Crystals,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957).

Onoe, M.

A. W. Warner, M. Onoe, G. A. Coquin, “Determination of Elastic and Piezoelectric Constants for Crystals in Class (3m),” J. Acoust. Soc. Am. 42, 1223–1231 (1967).
[CrossRef]

Rouvaen, J. M.

G. Waxin, J. M. Rouvaen, M. G. Gazalet, C. Bruneel, “New High Frequency Anisotropic Diffraction Geometries in Lithium Niobate Crystals,” Acoust. Lett. (G.B.), 11, 137–140 (1988).

J. M. Rouvaen, G. Waxin, C. Bruneel, R. Torguet, “Wideband Lithium Niobate Acousto-Optic Cells,” Acoust. Lett. (G.B.) 9, 5–11 (1985).

Shchitkov, N. N.

L. P. Avakyants, D. F. Kiselev, N. N. Shchitkov, “Measurement of the Photoelastic Coefficients of Lithium Niobate Single Crystals,” Sov. Phys. Solid State 18, 899–901 (1976).

Torguet, R.

J. M. Rouvaen, G. Waxin, C. Bruneel, R. Torguet, “Wideband Lithium Niobate Acousto-Optic Cells,” Acoust. Lett. (G.B.) 9, 5–11 (1985).

Turner, E. H.

E. H. Turner, “High Frequency Electro-Optic Coefficients of Lithium Niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
[CrossRef]

Warner, A. W.

A. W. Warner, M. Onoe, G. A. Coquin, “Determination of Elastic and Piezoelectric Constants for Crystals in Class (3m),” J. Acoust. Soc. Am. 42, 1223–1231 (1967).
[CrossRef]

Waxin, G.

G. Waxin, J. M. Rouvaen, M. G. Gazalet, C. Bruneel, “New High Frequency Anisotropic Diffraction Geometries in Lithium Niobate Crystals,” Acoust. Lett. (G.B.), 11, 137–140 (1988).

J. M. Rouvaen, G. Waxin, C. Bruneel, R. Torguet, “Wideband Lithium Niobate Acousto-Optic Cells,” Acoust. Lett. (G.B.) 9, 5–11 (1985).

Weis, R. S.

R. S. Weis, T. K. Gaylord, “Lithium Niobate: Summary of Physical Properties and Crystal Structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Wen, C. P.

C. P. Wen, R. F. Mayo, “Acoustic Attenuation of a Single Domain Lithium Niobate Crystal at Microwave Frequencies,” Appl. Phys. Lett. 9, 135–136 (1966).
[CrossRef]

Acoust. Lett. (G.B.) (2)

G. Waxin, J. M. Rouvaen, M. G. Gazalet, C. Bruneel, “New High Frequency Anisotropic Diffraction Geometries in Lithium Niobate Crystals,” Acoust. Lett. (G.B.), 11, 137–140 (1988).

J. M. Rouvaen, G. Waxin, C. Bruneel, R. Torguet, “Wideband Lithium Niobate Acousto-Optic Cells,” Acoust. Lett. (G.B.) 9, 5–11 (1985).

Appl. Phys. A (1)

R. S. Weis, T. K. Gaylord, “Lithium Niobate: Summary of Physical Properties and Crystal Structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Appl. Phys. Lett. (3)

E. H. Turner, “High Frequency Electro-Optic Coefficients of Lithium Niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
[CrossRef]

C. P. Wen, R. F. Mayo, “Acoustic Attenuation of a Single Domain Lithium Niobate Crystal at Microwave Frequencies,” Appl. Phys. Lett. 9, 135–136 (1966).
[CrossRef]

R. W. Dixon, M. G. Cohen, “A New Technique for Measuring Magnitudes of Photoelastic Tensors and its Application to Lithium Niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

I.E.E.E. Trans. Sonics Ultrason. SU-23 (1)

I. C. Chang, “Acousto-Optic Devices and Applications,” I.E.E.E. Trans. Sonics Ultrason. SU-23, 2–22 (1976).
[CrossRef]

J. Acoust. Soc. Am. (1)

A. W. Warner, M. Onoe, G. A. Coquin, “Determination of Elastic and Piezoelectric Constants for Crystals in Class (3m),” J. Acoust. Soc. Am. 42, 1223–1231 (1967).
[CrossRef]

J. Appl. Phys. (2)

D. F. Nelson, R. M. Mikulyak, “Refractive Indices of Stoichiometric and Congruently Melting Lithium Niobate Crystals,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

R. W. Dixon, “Photoelastic Properties of Selected Materials and their Relevance for Applications to Acoustic Light Modulators and Scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

I. C. Chang, “Spatial Light Modulators and Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 465, 18–22 (1984).

I. C. Chang, L. S. Lee, “Acousto-Optic Bragg Cells for EW Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 477, 23–28 (1984).

Proc. Soc. Photo. Opt. Instrum. Eng. (1)

R. Kalman, I. C. Chang, “Acousto-Optic Bragg Cells at Microwave Frequencies,” Proc. Soc. Photo. Opt. Instrum. Eng. 639, 11–15 (1986).

Sov. Phys. Solid State (1)

L. P. Avakyants, D. F. Kiselev, N. N. Shchitkov, “Measurement of the Photoelastic Coefficients of Lithium Niobate Single Crystals,” Sov. Phys. Solid State 18, 899–901 (1976).

Other (3)

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

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957).

W. P. Mason, Crystal Physics of Interaction Processes, (Academic Press, New York, 1966).

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Figures (7)

Fig. 1
Fig. 1

Geometry of the acoustooptic interaction: (a) general definition for angles α and β;(b) tangential phase matching.

Fig. 2
Fig. 2

Geometric solution of the phase matching problem: (a) Sketch of the geometric configuration in three-dimensional space; and (b) Definition for the notations used in the plane of the incident light wavevector locus (containing the acoustic wavevector).

Fig. 3
Fig. 3

Variations of the figure of merit M2 against angle θ for a typical set of configurations: (a) α d = 10°, β d = 30°; (b) α d = 10°, β d = 60°; and (c) α d = 10°, β d = 90°, where M2 is given in 1015s3 Kg−1 units.

Fig. 4
Fig. 4

Variations of the figure of merit M2 against angle α d for a typical set of configurations with β a fixed at 110° and variable β d . The vertical unit is the same as for Fig. 3.

Fig. 5
Fig. 5

Variations of the figure of merit M2 against angle β d for a typical set of configurations with β a fixed to 110° and variable α d The vertical unit is the same as for Fig. 3.

Fig. 6
Fig. 6

Sketch of the most efficient configurations for the lower frequency interaction, giving the corresponding values of α d , β d and M2 against the ultrasonic frequency (horizontal axis scaled in GHz units).

Fig. 7
Fig. 7

Sketch of the most efficient configurations for the upper frequency interaction. The quantities represented are the same as for Fig. 6.

Tables (2)

Tables Icon

Table I Photo-Elasto-Piezo-Dielectric Constants of Lithium Niobate

Tables Icon

Table II Comparison of Several Interaction Configurations in Lithium Niobate for a 2-GHz Centre Operating Frequency, a 1-GHz Frequency Bandwidth, Assuming Acoustic Attenuations Equal to 0.15 dB/cm × GHz2 for the Longitudinal Mode and 4 dB/cm × GHz2 for the Transverse Mode

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

k d = k i + K .
n d - 2 = cos 2 α d n o - 2 + sin 2 α d n e - 2 .
k i = k 0 n o ( sin α i cos β i x + sin α i sin β i y + cos α i z ) ,
P i = - sin β i x + cos β i y ,
k d = k 0 n o ( sin α d cos β d x + sin α d sin β d y + cos α d z ) ,
P d = cos α d cos β d x + cos α d sin β d y - sin α d z ,
K = K ( sin α a cos β a x + sin α a sin β a y + cos α a z ) ,
k i = k 0 n 0 ( sin α i cos δ β i u + sin α i sin δ β i v + cos α i w ) ,
k d = k 0 n d ( sin α d u + cos α d w ) ,
δ β i = β i - β d ,
K = K ( sin α a cos δ β a u + sin α a sin δ β a v + cos α a w ) ,
δ β a = β a - β d ,
n d ( U sin α d n e - 2 + W cos α d n 0 - 2 ) = 1 ,
U 2 + V 2 + W 2 = n 0 2
k i = O I = O C + CI ,
O C = - A u + B w ,
CI = R ( sin θ p + cos θ q ) ,
A = F sin α d n 0 2 Δ - 1 ,
B = F cos α d n e 2 Δ - 1 ,
R 2 = n 0 4 ( n 0 2 - n e 2 ) sin 2 α d Δ - 1 ,
F = n d ( cos 2 α d n e 2 + sin 2 α d n 0 2 ) ,
Δ = cos 2 α d n e 4 + sin 2 α d n 0 4 ,
p = v
q = ( cos α d n e 2 u - sin α d n 0 2 w ) Δ 1 / 2 ,
Δ B i j = p i j k l S k l + r i j k E k ,
S k l = 1 2 × ( u k x l + u l x k ) ,
u k = D k AMP exp ( j ω t ) exp ( - j Kr )
E k = - ϕ x k .
η = π 2 2 λ 0 2 ( M 2 L H η e ) ,
M 2 = ( n 0 n d ) 3 p eff 2 ρ v 3
p eff = | Δ B l k P k i P l d S |

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