Abstract

Coupled-mode equations are established for the acoustooptic interaction of plane waves in anisotropic, optically active crystals. A method of solution is proposed which allows for spatial variation of the optical polarization modes. An analysis of the slow shear wave TeO2 Bragg cell is given with numerical results for diffraction efficiency and polarization of the optical beams as a function of distance travelled in the cell. Large departures of the optical polarization from pure circular polarization are evident as the acoustic power is increased.

© 1990 Optical Society of America

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References

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  1. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  2. A. W. Warner, D. L. White, W. A. Bonner, “Acousto-optic Light Deflectors Using Optical Activity in Paratellurite,” J. Appl. Phys. 43, 4489–4495 (1972).
    [CrossRef]
  3. J. M. Rouvaen, M. G. Ghazaleh, E. Bridoux, R. Torguet, “On a General Treatment of Acousto-optic Interactions in Linear Anisotropic Crystals,” J. Appl. Phys. 50, 5472–5477 (1979).
    [CrossRef]
  4. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).
  5. G. N. Ramachandran, S. Ramaseshan, “Crystal Optics,” in Encyclopedia of Physics, S. Flugge, Eds., Vol. 35/1 (Springer-Verlag, Berlin, 1961), p. 77.
  6. J. F. Nye, Physical Properties of Crystals (Oxford U. P., London, 1964).
  7. I. C. Chang, “Acoustooptic Devices and Applications,” IEEE Trans. Sonics Ultrason. SU-23, 2–22 (1976).
    [CrossRef]

1979 (1)

J. M. Rouvaen, M. G. Ghazaleh, E. Bridoux, R. Torguet, “On a General Treatment of Acousto-optic Interactions in Linear Anisotropic Crystals,” J. Appl. Phys. 50, 5472–5477 (1979).
[CrossRef]

1976 (1)

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

1972 (1)

A. W. Warner, D. L. White, W. A. Bonner, “Acousto-optic Light Deflectors Using Optical Activity in Paratellurite,” J. Appl. Phys. 43, 4489–4495 (1972).
[CrossRef]

Bonner, W. A.

A. W. Warner, D. L. White, W. A. Bonner, “Acousto-optic Light Deflectors Using Optical Activity in Paratellurite,” J. Appl. Phys. 43, 4489–4495 (1972).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

Bridoux, E.

J. M. Rouvaen, M. G. Ghazaleh, E. Bridoux, R. Torguet, “On a General Treatment of Acousto-optic Interactions in Linear Anisotropic Crystals,” J. Appl. Phys. 50, 5472–5477 (1979).
[CrossRef]

Chang, I. C.

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

Ghazaleh, M. G.

J. M. Rouvaen, M. G. Ghazaleh, E. Bridoux, R. Torguet, “On a General Treatment of Acousto-optic Interactions in Linear Anisotropic Crystals,” J. Appl. Phys. 50, 5472–5477 (1979).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U. P., London, 1964).

Ramachandran, G. N.

G. N. Ramachandran, S. Ramaseshan, “Crystal Optics,” in Encyclopedia of Physics, S. Flugge, Eds., Vol. 35/1 (Springer-Verlag, Berlin, 1961), p. 77.

Ramaseshan, S.

G. N. Ramachandran, S. Ramaseshan, “Crystal Optics,” in Encyclopedia of Physics, S. Flugge, Eds., Vol. 35/1 (Springer-Verlag, Berlin, 1961), p. 77.

Rouvaen, J. M.

J. M. Rouvaen, M. G. Ghazaleh, E. Bridoux, R. Torguet, “On a General Treatment of Acousto-optic Interactions in Linear Anisotropic Crystals,” J. Appl. Phys. 50, 5472–5477 (1979).
[CrossRef]

Torguet, R.

J. M. Rouvaen, M. G. Ghazaleh, E. Bridoux, R. Torguet, “On a General Treatment of Acousto-optic Interactions in Linear Anisotropic Crystals,” J. Appl. Phys. 50, 5472–5477 (1979).
[CrossRef]

Warner, A. W.

A. W. Warner, D. L. White, W. A. Bonner, “Acousto-optic Light Deflectors Using Optical Activity in Paratellurite,” J. Appl. Phys. 43, 4489–4495 (1972).
[CrossRef]

White, D. L.

A. W. Warner, D. L. White, W. A. Bonner, “Acousto-optic Light Deflectors Using Optical Activity in Paratellurite,” J. Appl. Phys. 43, 4489–4495 (1972).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

IEEE Trans. Sonics Ultrason. (1)

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

J. Appl. Phys. (2)

A. W. Warner, D. L. White, W. A. Bonner, “Acousto-optic Light Deflectors Using Optical Activity in Paratellurite,” J. Appl. Phys. 43, 4489–4495 (1972).
[CrossRef]

J. M. Rouvaen, M. G. Ghazaleh, E. Bridoux, R. Torguet, “On a General Treatment of Acousto-optic Interactions in Linear Anisotropic Crystals,” J. Appl. Phys. 50, 5472–5477 (1979).
[CrossRef]

Other (4)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

G. N. Ramachandran, S. Ramaseshan, “Crystal Optics,” in Encyclopedia of Physics, S. Flugge, Eds., Vol. 35/1 (Springer-Verlag, Berlin, 1961), p. 77.

J. F. Nye, Physical Properties of Crystals (Oxford U. P., London, 1964).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

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Figures (6)

Fig. 1
Fig. 1

Scattering geometry for a birefringent crystal: (a) the crystal configuration; (b) the phase-matching condition.

Fig. 2
Fig. 2

Calculated intensities (arbitrary units) of input (solid) and diffracted (dashed) optical beams as a function of distance into the TeO2 crystal for acoustic power of 0.01 W. The input angle is −2.201° and the diffracted angle is zero.

Fig. 3
Fig. 3

Same as Fig. 2 but with 0.1 W of acoustic power. Identical results for intensities are obtained for input angles to in excess of 10°.

Fig. 4
Fig. 4

Calculated polarizations of input (solid) and diffracted (dashed) optical beams expressed as phase difference between Ex and Ey Same conditions as Fig. 2.

Fig. 5
Fig. 5

Polarizations for the conditions of Fig. 3.

Fig. 6
Fig. 6

Polarizations for the conditions of Fig. 3 but with an input angle of −10°.

Tables (2)

Tables Icon

Table I Data Used In the Calculations for the TeO2 Bragg Cell

Tables Icon

Table II Calculated Values for TeO2 Slow Shear Wave Device for an Input Angle of −2.201° and an Acoustic Power of 0.01 Watt.a

Equations (25)

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

× E = - B t × B = D t ,
D i = ( i j + Δ i j ) E j + d i j k E k x j .
D = ( + Δ ) E + ( g ) × E .
1 μ 0 × × E = - 2 E t 2 - 2 ( Δ E ) t 2 - ( g ) × 2 E t 2 .
E ( r , t ) = ½ A ( r ) exp [ i ( k i · r - ω i t ) ] + ½ E ( r ) × exp [ i ( k d · r - ω d t ) ] + c . c . ,
Δ ( r , t ) = ½ Δ exp [ i ( q · r - ω a t ) ] + c . c .
ω d = ω i + ω a and k d = k i + q .
ME = - ½ μ 0 ω d 2 Δ A
NA = - ½ μ 0 ω i 2 Δ * E .
M = M 0 + M 1
M 0 = k d × k d × + μ 0 ω d 2 + i ( ρ k d ) ×
M 1 = - i [ k d × × + × k d × ] + ( ρ ) ×
P = μ 0 ω d 2 g
M = M 1 z + M 0 ,
E ¯ = ½ μ 0 ω d 2 D - 1 N 1 A 0 ,
D = - s 2 N 1 Δ - 1 M 1 - s ( N 0 Δ - 1 M 1 + N 1 Δ - 1 M 0 ) - N 0 Δ - 1 M 0 + ¼ g μ 0 ω 1 2 ω d 2 Δ * .
D - 1 = cof D det D ,
E ¯ = m = 1 6 ( s - s m ) - 1 α m ,
E ( z ) = m = 1 6 α m exp ( i s m z )
Δ = - i 2 0 n 0 4 S ( p 11 - p 12 ) ( 1 0 0 0 - 1 0 0 0 0 ) ,
P a = ½ ρ v 3 S 2 L H
M i j = M i j - M i 3 M 3 j M 33 for i , j = 1 , 2.
Δ = ( Δ 0 0 - Δ ) .
M 1 = ( 2 i k 3 - ρ 3 - i k 1 ρ 3 2 i k 3 - i k 2 - i k 1 - i k 2 0 )
M 0 = ( μ 0 ω 2 1 - k 2 2 - k 3 2 k 1 k 2 - i ρ 3 k 3 k 1 k 3 + i ρ 1 k 2 k 1 k 2 + i ρ 3 k 3 μ 0 ω 2 1 - k 1 2 - k 3 2 k 2 k 3 - i ρ 1 k 1 k 1 k 3 - i ρ 1 k 2 k 2 k 3 + i ρ 1 k 1 μ 0 ω 2 3 - k 1 2 - k 2 2 ) .

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