Abstract

We report the determination of the magnitude and sign of the unknown photoelastic coefficients of tellurium, p65, p56, and p44, as well as all of the unknown signs of the previously determined photoelastic coefficients.

© 1989 Optical Society of America

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References

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  1. S. Fukuda, T. Shiosaki, A. Kawabata, “Acoustooptic Properties of Tellurium at 10.6 μm,” J. Appl. Phys. 50, 3899–3905 (1979).
    [CrossRef]
  2. D. Souilhac, “Acoustooptic Diffraction and Deflection in Tellurium for the Carbon Dioxide Laser,” PHD Thesis, McGill U., Montreal, P.Q., Canada (Aug.1987).
  3. J. E. B. Oliveira, “Generalized Anisotropic Acoustooptic Diffraction in Uniaxial Crystals,” PHD Thesis, McGill U., Montreal, P.Q. Canada (Jan.1986).
  4. D. Souilhac, D. Billerey, A. Gundjian, “Infrared Two Dimensional Acoustooptic Deflector Using a Crystal of Tellurium,” Submitted to Appl. Opt., Oct.1988.
  5. I. Shih, “Crystal Growth and Photoconductivity of Tellurium and Selenium Alloys,” PHD Thesis, McGill U., Montreal, P.Q. Canada (March1981).
  6. D. F. Nelson, M. Lax, “Theory of Photoelastic Interaction,” Phys. Rev. B3(8), 2778–2794 (1971).
  7. S. Fukuda, T. Karasaki, T. Shiosaki, A. Kawabata, “Photoelasticity and Acoustooptic Diffraction in Piezoelectric Semiconductors,” Phys. Rev. B 20, 4109–4119 (1979).
    [CrossRef]
  8. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1967).
  9. R. W. Dixon, “Photoelastic Properties of Selected Materials and their Relevance Parameters for Applications to AO Light Modulators and Scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
    [CrossRef]
  10. R. J. Presley, Ed. CRC Handbook of Lasers with Selected Data on Optical Technology (Chemical Rubber Co., Cleveland, 1971).
  11. R. W. Dixon, H. G. Cohen, “A New Technique for Measuring the Magnitude of Photoelastic Tensor and its Applications to Lithium Niobate,” Appl. Phys. Lett. 8, 205–212 (1966).
    [CrossRef]
  12. B. S. Collins, F. K. Hulme, N. A. Lowde, “An Acoustooptic Modulator for a CO2 Laser Range Finder Using Heterodyne Detection,” Opt. and Quantum Electron. 12, 419–426 (1960).
    [CrossRef]
  13. D. Souilhac, “Two Dimensional Acoustooptic Deflector Using a Crystal of Tellurium for the CO2 Laser,” Technical Report, McGill U., Department of Electrical Engineering, (1986).
  14. D. Souilhac, A. Gundjian, “Carbon Dioxide Laser Stabilization by Optoacoustic Tracking of an SF6 Lamb Dip,” Appl. Opt. 21, 1478–1481 (1982).
    [CrossRef] [PubMed]
  15. D. Souilhac, A. Gundjian, “Measurement and Theoretical Confirmation of Xe-Enhanced CO2 Laser Output Power Levels,” Appl. Opt. 20, 3097–3098 (1981).
    [CrossRef] [PubMed]

1982 (1)

1981 (1)

1979 (2)

S. Fukuda, T. Shiosaki, A. Kawabata, “Acoustooptic Properties of Tellurium at 10.6 μm,” J. Appl. Phys. 50, 3899–3905 (1979).
[CrossRef]

S. Fukuda, T. Karasaki, T. Shiosaki, A. Kawabata, “Photoelasticity and Acoustooptic Diffraction in Piezoelectric Semiconductors,” Phys. Rev. B 20, 4109–4119 (1979).
[CrossRef]

1971 (1)

D. F. Nelson, M. Lax, “Theory of Photoelastic Interaction,” Phys. Rev. B3(8), 2778–2794 (1971).

1967 (1)

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

1966 (1)

R. W. Dixon, H. G. Cohen, “A New Technique for Measuring the Magnitude of Photoelastic Tensor and its Applications to Lithium Niobate,” Appl. Phys. Lett. 8, 205–212 (1966).
[CrossRef]

1960 (1)

B. S. Collins, F. K. Hulme, N. A. Lowde, “An Acoustooptic Modulator for a CO2 Laser Range Finder Using Heterodyne Detection,” Opt. and Quantum Electron. 12, 419–426 (1960).
[CrossRef]

Billerey, D.

D. Souilhac, D. Billerey, A. Gundjian, “Infrared Two Dimensional Acoustooptic Deflector Using a Crystal of Tellurium,” Submitted to Appl. Opt., Oct.1988.

Cohen, H. G.

R. W. Dixon, H. G. Cohen, “A New Technique for Measuring the Magnitude of Photoelastic Tensor and its Applications to Lithium Niobate,” Appl. Phys. Lett. 8, 205–212 (1966).
[CrossRef]

Collins, B. S.

B. S. Collins, F. K. Hulme, N. A. Lowde, “An Acoustooptic Modulator for a CO2 Laser Range Finder Using Heterodyne Detection,” Opt. and Quantum Electron. 12, 419–426 (1960).
[CrossRef]

Dixon, R. W.

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

R. W. Dixon, H. G. Cohen, “A New Technique for Measuring the Magnitude of Photoelastic Tensor and its Applications to Lithium Niobate,” Appl. Phys. Lett. 8, 205–212 (1966).
[CrossRef]

Fukuda, S.

S. Fukuda, T. Karasaki, T. Shiosaki, A. Kawabata, “Photoelasticity and Acoustooptic Diffraction in Piezoelectric Semiconductors,” Phys. Rev. B 20, 4109–4119 (1979).
[CrossRef]

S. Fukuda, T. Shiosaki, A. Kawabata, “Acoustooptic Properties of Tellurium at 10.6 μm,” J. Appl. Phys. 50, 3899–3905 (1979).
[CrossRef]

Gundjian, A.

Hulme, F. K.

B. S. Collins, F. K. Hulme, N. A. Lowde, “An Acoustooptic Modulator for a CO2 Laser Range Finder Using Heterodyne Detection,” Opt. and Quantum Electron. 12, 419–426 (1960).
[CrossRef]

Karasaki, T.

S. Fukuda, T. Karasaki, T. Shiosaki, A. Kawabata, “Photoelasticity and Acoustooptic Diffraction in Piezoelectric Semiconductors,” Phys. Rev. B 20, 4109–4119 (1979).
[CrossRef]

Kawabata, A.

S. Fukuda, T. Karasaki, T. Shiosaki, A. Kawabata, “Photoelasticity and Acoustooptic Diffraction in Piezoelectric Semiconductors,” Phys. Rev. B 20, 4109–4119 (1979).
[CrossRef]

S. Fukuda, T. Shiosaki, A. Kawabata, “Acoustooptic Properties of Tellurium at 10.6 μm,” J. Appl. Phys. 50, 3899–3905 (1979).
[CrossRef]

Lax, M.

D. F. Nelson, M. Lax, “Theory of Photoelastic Interaction,” Phys. Rev. B3(8), 2778–2794 (1971).

Lowde, N. A.

B. S. Collins, F. K. Hulme, N. A. Lowde, “An Acoustooptic Modulator for a CO2 Laser Range Finder Using Heterodyne Detection,” Opt. and Quantum Electron. 12, 419–426 (1960).
[CrossRef]

Nelson, D. F.

D. F. Nelson, M. Lax, “Theory of Photoelastic Interaction,” Phys. Rev. B3(8), 2778–2794 (1971).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1967).

Oliveira, J. E. B.

J. E. B. Oliveira, “Generalized Anisotropic Acoustooptic Diffraction in Uniaxial Crystals,” PHD Thesis, McGill U., Montreal, P.Q. Canada (Jan.1986).

Shih, I.

I. Shih, “Crystal Growth and Photoconductivity of Tellurium and Selenium Alloys,” PHD Thesis, McGill U., Montreal, P.Q. Canada (March1981).

Shiosaki, T.

S. Fukuda, T. Shiosaki, A. Kawabata, “Acoustooptic Properties of Tellurium at 10.6 μm,” J. Appl. Phys. 50, 3899–3905 (1979).
[CrossRef]

S. Fukuda, T. Karasaki, T. Shiosaki, A. Kawabata, “Photoelasticity and Acoustooptic Diffraction in Piezoelectric Semiconductors,” Phys. Rev. B 20, 4109–4119 (1979).
[CrossRef]

Souilhac, D.

D. Souilhac, A. Gundjian, “Carbon Dioxide Laser Stabilization by Optoacoustic Tracking of an SF6 Lamb Dip,” Appl. Opt. 21, 1478–1481 (1982).
[CrossRef] [PubMed]

D. Souilhac, A. Gundjian, “Measurement and Theoretical Confirmation of Xe-Enhanced CO2 Laser Output Power Levels,” Appl. Opt. 20, 3097–3098 (1981).
[CrossRef] [PubMed]

D. Souilhac, “Two Dimensional Acoustooptic Deflector Using a Crystal of Tellurium for the CO2 Laser,” Technical Report, McGill U., Department of Electrical Engineering, (1986).

D. Souilhac, “Acoustooptic Diffraction and Deflection in Tellurium for the Carbon Dioxide Laser,” PHD Thesis, McGill U., Montreal, P.Q., Canada (Aug.1987).

D. Souilhac, D. Billerey, A. Gundjian, “Infrared Two Dimensional Acoustooptic Deflector Using a Crystal of Tellurium,” Submitted to Appl. Opt., Oct.1988.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

R. W. Dixon, H. G. Cohen, “A New Technique for Measuring the Magnitude of Photoelastic Tensor and its Applications to Lithium Niobate,” Appl. Phys. Lett. 8, 205–212 (1966).
[CrossRef]

J. Appl. Phys. (2)

S. Fukuda, T. Shiosaki, A. Kawabata, “Acoustooptic Properties of Tellurium at 10.6 μm,” J. Appl. Phys. 50, 3899–3905 (1979).
[CrossRef]

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

Opt. and Quantum Electron. (1)

B. S. Collins, F. K. Hulme, N. A. Lowde, “An Acoustooptic Modulator for a CO2 Laser Range Finder Using Heterodyne Detection,” Opt. and Quantum Electron. 12, 419–426 (1960).
[CrossRef]

Phys. Rev. (1)

D. F. Nelson, M. Lax, “Theory of Photoelastic Interaction,” Phys. Rev. B3(8), 2778–2794 (1971).

Phys. Rev. B (1)

S. Fukuda, T. Karasaki, T. Shiosaki, A. Kawabata, “Photoelasticity and Acoustooptic Diffraction in Piezoelectric Semiconductors,” Phys. Rev. B 20, 4109–4119 (1979).
[CrossRef]

Other (7)

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1967).

R. J. Presley, Ed. CRC Handbook of Lasers with Selected Data on Optical Technology (Chemical Rubber Co., Cleveland, 1971).

D. Souilhac, “Acoustooptic Diffraction and Deflection in Tellurium for the Carbon Dioxide Laser,” PHD Thesis, McGill U., Montreal, P.Q., Canada (Aug.1987).

J. E. B. Oliveira, “Generalized Anisotropic Acoustooptic Diffraction in Uniaxial Crystals,” PHD Thesis, McGill U., Montreal, P.Q. Canada (Jan.1986).

D. Souilhac, D. Billerey, A. Gundjian, “Infrared Two Dimensional Acoustooptic Deflector Using a Crystal of Tellurium,” Submitted to Appl. Opt., Oct.1988.

I. Shih, “Crystal Growth and Photoconductivity of Tellurium and Selenium Alloys,” PHD Thesis, McGill U., Montreal, P.Q. Canada (March1981).

D. Souilhac, “Two Dimensional Acoustooptic Deflector Using a Crystal of Tellurium for the CO2 Laser,” Technical Report, McGill U., Department of Electrical Engineering, (1986).

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Figures (4)

Fig. 1
Fig. 1

Arrangement of the atoms in a Te crystal.

Fig. 2
Fig. 2

Cross section perpendicular to the c-axis of Te; X1, X2, X3 denote the crystalline a-axis of (001) direction.

Fig. 3
Fig. 3

Experimental arrangement.

Fig. 4
Fig. 4

(a) The X, Y, Z axes are the crystalline axes. The X* Z* plane is the rotated AO interaction plane localized by the three Euler angles ϕ, θ, and ψ. The acoustic wave is along X* and the optic beams propagate near the Z* axis, (b) Wavevector diagram showing phase matching. An extraordinary incident optical wave with wave vector KI is diffracted into an ordinary wave with wavevector KD by an acoustic wave with wavevector KA.

Tables (2)

Tables Icon

Table I Some Physical Constants of Tellurium

Tables Icon

Table II Photoelastlc Tensor and Constants of Tellurium

Equations (7)

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M = N I 3 N D 3 ρ V P 3 ρ eff 2 ,
M 1 M 2 = I 1 I 2 ,
p 65 = 0.04 or 0.013 ± 20 % .
p 65 = ± 0.04 ± 20 % .
p 56 = + 0.28 or 0.033 ± 12 % .
p 56 = + 0.28 ± 10 % .
p 44 = + 0.14 ± 10 % .

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