Abstract

The first single element 2-D acoustooptic (2DAO) laser beam deflector using a tellurium crystal was designed and fabricated for laser wavelength applications from 5 to 20 μm. The giant values of the figure of merit M associated with these two AO interactions equal to 285,000 × 10−15 s3/kg, are between 2 and 3 orders of magnitude higher than germanium, the next best AO material for 10.6 μm. This latter value indicates that acoustic power densities inside the crystal of the order of 0.1 W/mm2 are sufficient to diffract 100% of the incident light. The experimental data confirm the predicted 13°/25 MHz deflection slope. The theoretical amplitude and frequency modulation characteristics of the 2DAO deflector are also evaluated.

© 1990 Optical Society of America

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References

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  1. D. Souilhac, “Acoustooptic Diffraction and Deflection in Tellurium for the Carbon Dioxide Laser,” Ph.D. Thesis, McGill U., Electrical Engineering Department, Montreal (Aug.1987).
  2. J. E. B. Oliveira, “Generalized Anisotropic Acoustooptic Diffraction in Uniaxial Crystals,” Ph.D. Thesis, McGill U., Electrical Engineering Department, Montreal (Jan.1986).
  3. W. R. Klein, B. D. Cook, “Unified Approach to Ultrasonics Light Diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
    [CrossRef]
  4. J. E. B. Oliveira, E. L. Adler, D. Souilhac, A. Gundjian, “Acoustooptic Diffraction and Deflection in Tellurium at 10.6 μm,” in Proceedings, 1984 IEEE Ultrasonics Symposium (1984), pp. 332–340.
    [CrossRef]
  5. M. V. Klein, Optics (Wiley, New York, 1969).
  6. A. Jenkins, W. E. White, Fundamentals of Optics (McGrawHill, New York, 1965), Chap. 26.
  7. I. C. Chang, “Acoustooptic Devices and Applications,” IEEE Trans. Sonics Ultrason. SU-23, 2–22 (1976).
    [CrossRef]
  8. T. C. Lee, J. D. Zook, “Light Beam Deflection with Electrooptic Prisms,” IEEE J. Quantum Electron. QE-4, 442–443 (1968).
    [CrossRef]
  9. L. D. Dickson, “Optical Considerations for an Acoustooptic Deflector,” Appl. Opt. 11, 2196–2202 (1972).
    [CrossRef] [PubMed]
  10. C. H. Tsai, “Bragg Modulators for Optic Communications,” IEEE Trans. Circuits Syst. CAS-26, 1089–1098 (1979).
  11. C. P. Wang, R. L. Varwig, “Measurement of Phase Fluctuations in R. F. Chemical Laser Beam,” J. Appl. Phys. 50, 7917–7920 (1979).
    [CrossRef]
  12. J. P. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectrics Frequency Control UFFC-33, 485–499 (1986).
    [CrossRef]
  13. A. Korpel, “Acoustooptic, a Review of Fundamentals,” Proc. IEEE 69, 751–754 (1981).
  14. K. Pratt, Laser Communication Systems (Wiley, New York, 1968).
  15. S. Fukuda, T. Shiosaki, A. Kawabata, “Acoustooptic Properties of Tellurium at 10.6 μm,” J. Appl. Phys. 50, 3899–3905 (1979).
    [CrossRef]
  16. S. Fukuda, T. Karasaki, T. Shiosaki, A. Kawabata, “Photoelasticity and Acoustooptic Diffraction in Piezoelectric Semi-Conductors,” Phys. Rev. B 20, 4109–4119 (1979).
    [CrossRef]
  17. S. Ades, C. Champness, “Intermediate Infrared Optical Absorption in Intrinsic Tellurium,” J. Appl. Phys. 49, 4543–4548 (1978).
    [CrossRef]
  18. A. J. Fox, “Thermal Design for Germanium Acoustooptic Modulators,” Appl. Opt. 26, 872–884 (1987).
    [CrossRef] [PubMed]
  19. I. Shih, “Crystal Growth and Photoconductivity of Tellurium and Selenium–Tellurium Alloy,” Ph.D. Thesis, McGill U., Electrical Engineering Department (1981).
  20. D. Souilhac, “Two Dimensional Acoustooptic Deflector Using a Crystal of Tellurium for the CO2 Laser,” Technical Report, McGill U., Electrical Engineering Department (1986).
  21. P. D. Henshaw, H. M. Haskal, R. C. Knowlton, P. B. Scott, “Applicability of Laser Beam Steering for Rapid Access to 2D, 3D, and 4D Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 200–213 (1988).
  22. F. Sanchez, P. H. Kayoun, J. P. Huignard, “Two-Wave Mixing with Gain in Liquid Crystals at 10.6-μm Wavelength,” J. Appl. Phys. 64, 26–31 (1988).
    [CrossRef]
  23. J. M. Cruickshank, “Transversely Excited Atmospheric CO2 Laser Radar with Heterodyne Detection,” Appl. Opt. 18, 290–293 (1979).
    [CrossRef] [PubMed]
  24. B. Remy, “Imaging CO2 Laser Radar with Chirps Pulse Compression,” Ph.D. Thesis, U. Paris XI, Orsay (1986).
  25. D. Souilhac, D. Billerey, “Comparison of Hollow Metallic Waveguides with Optical Fibers for IR Laser Propagation,” Proc. Soc. Photo-Opt. Instrum. Eng., Los Angeles (1990), to be published.
  26. A. Waksberg, “Range Predictions for a CO2 Laser Communication System,” Appl. Opt. 20, 2688–2693 (1981).
    [CrossRef] [PubMed]
  27. M. J. Delanay, S. K. Kao, “Wideband Acoustooptic Bragg Cell,” in Proceedings, 1983 IEEE Ultrasonics Symposium (1983), pp. 431–436.

1988 (2)

P. D. Henshaw, H. M. Haskal, R. C. Knowlton, P. B. Scott, “Applicability of Laser Beam Steering for Rapid Access to 2D, 3D, and 4D Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 200–213 (1988).

F. Sanchez, P. H. Kayoun, J. P. Huignard, “Two-Wave Mixing with Gain in Liquid Crystals at 10.6-μm Wavelength,” J. Appl. Phys. 64, 26–31 (1988).
[CrossRef]

1987 (1)

1986 (1)

J. P. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectrics Frequency Control UFFC-33, 485–499 (1986).
[CrossRef]

1984 (1)

J. E. B. Oliveira, E. L. Adler, D. Souilhac, A. Gundjian, “Acoustooptic Diffraction and Deflection in Tellurium at 10.6 μm,” in Proceedings, 1984 IEEE Ultrasonics Symposium (1984), pp. 332–340.
[CrossRef]

1983 (1)

M. J. Delanay, S. K. Kao, “Wideband Acoustooptic Bragg Cell,” in Proceedings, 1983 IEEE Ultrasonics Symposium (1983), pp. 431–436.

1981 (2)

A. Waksberg, “Range Predictions for a CO2 Laser Communication System,” Appl. Opt. 20, 2688–2693 (1981).
[CrossRef] [PubMed]

A. Korpel, “Acoustooptic, a Review of Fundamentals,” Proc. IEEE 69, 751–754 (1981).

1979 (5)

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 Semi-Conductors,” Phys. Rev. B 20, 4109–4119 (1979).
[CrossRef]

J. M. Cruickshank, “Transversely Excited Atmospheric CO2 Laser Radar with Heterodyne Detection,” Appl. Opt. 18, 290–293 (1979).
[CrossRef] [PubMed]

C. H. Tsai, “Bragg Modulators for Optic Communications,” IEEE Trans. Circuits Syst. CAS-26, 1089–1098 (1979).

C. P. Wang, R. L. Varwig, “Measurement of Phase Fluctuations in R. F. Chemical Laser Beam,” J. Appl. Phys. 50, 7917–7920 (1979).
[CrossRef]

1978 (1)

S. Ades, C. Champness, “Intermediate Infrared Optical Absorption in Intrinsic Tellurium,” J. Appl. Phys. 49, 4543–4548 (1978).
[CrossRef]

1976 (1)

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

1972 (1)

1968 (1)

T. C. Lee, J. D. Zook, “Light Beam Deflection with Electrooptic Prisms,” IEEE J. Quantum Electron. QE-4, 442–443 (1968).
[CrossRef]

1967 (1)

W. R. Klein, B. D. Cook, “Unified Approach to Ultrasonics Light Diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
[CrossRef]

Ades, S.

S. Ades, C. Champness, “Intermediate Infrared Optical Absorption in Intrinsic Tellurium,” J. Appl. Phys. 49, 4543–4548 (1978).
[CrossRef]

Adler, E. L.

J. E. B. Oliveira, E. L. Adler, D. Souilhac, A. Gundjian, “Acoustooptic Diffraction and Deflection in Tellurium at 10.6 μm,” in Proceedings, 1984 IEEE Ultrasonics Symposium (1984), pp. 332–340.
[CrossRef]

Billerey, D.

D. Souilhac, D. Billerey, “Comparison of Hollow Metallic Waveguides with Optical Fibers for IR Laser Propagation,” Proc. Soc. Photo-Opt. Instrum. Eng., Los Angeles (1990), to be published.

Champness, C.

S. Ades, C. Champness, “Intermediate Infrared Optical Absorption in Intrinsic Tellurium,” J. Appl. Phys. 49, 4543–4548 (1978).
[CrossRef]

Chang, I. C.

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

Cook, B. D.

W. R. Klein, B. D. Cook, “Unified Approach to Ultrasonics Light Diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
[CrossRef]

Cruickshank, J. M.

Delanay, M. J.

M. J. Delanay, S. K. Kao, “Wideband Acoustooptic Bragg Cell,” in Proceedings, 1983 IEEE Ultrasonics Symposium (1983), pp. 431–436.

Dickson, L. D.

Fox, A. J.

Fukuda, S.

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 Semi-Conductors,” Phys. Rev. B 20, 4109–4119 (1979).
[CrossRef]

Gundjian, A.

J. E. B. Oliveira, E. L. Adler, D. Souilhac, A. Gundjian, “Acoustooptic Diffraction and Deflection in Tellurium at 10.6 μm,” in Proceedings, 1984 IEEE Ultrasonics Symposium (1984), pp. 332–340.
[CrossRef]

Haskal, H. M.

P. D. Henshaw, H. M. Haskal, R. C. Knowlton, P. B. Scott, “Applicability of Laser Beam Steering for Rapid Access to 2D, 3D, and 4D Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 200–213 (1988).

Henshaw, P. D.

P. D. Henshaw, H. M. Haskal, R. C. Knowlton, P. B. Scott, “Applicability of Laser Beam Steering for Rapid Access to 2D, 3D, and 4D Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 200–213 (1988).

Huignard, J. P.

F. Sanchez, P. H. Kayoun, J. P. Huignard, “Two-Wave Mixing with Gain in Liquid Crystals at 10.6-μm Wavelength,” J. Appl. Phys. 64, 26–31 (1988).
[CrossRef]

Jenkins, A.

A. Jenkins, W. E. White, Fundamentals of Optics (McGrawHill, New York, 1965), Chap. 26.

Kao, S. K.

M. J. Delanay, S. K. Kao, “Wideband Acoustooptic Bragg Cell,” in Proceedings, 1983 IEEE Ultrasonics Symposium (1983), pp. 431–436.

Karasaki, T.

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

Kawabata, A.

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 Semi-Conductors,” Phys. Rev. B 20, 4109–4119 (1979).
[CrossRef]

Kayoun, P. H.

F. Sanchez, P. H. Kayoun, J. P. Huignard, “Two-Wave Mixing with Gain in Liquid Crystals at 10.6-μm Wavelength,” J. Appl. Phys. 64, 26–31 (1988).
[CrossRef]

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1969).

Klein, W. R.

W. R. Klein, B. D. Cook, “Unified Approach to Ultrasonics Light Diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
[CrossRef]

Knowlton, R. C.

P. D. Henshaw, H. M. Haskal, R. C. Knowlton, P. B. Scott, “Applicability of Laser Beam Steering for Rapid Access to 2D, 3D, and 4D Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 200–213 (1988).

Korpel, A.

A. Korpel, “Acoustooptic, a Review of Fundamentals,” Proc. IEEE 69, 751–754 (1981).

Lee, T. C.

T. C. Lee, J. D. Zook, “Light Beam Deflection with Electrooptic Prisms,” IEEE J. Quantum Electron. QE-4, 442–443 (1968).
[CrossRef]

Monchalin, J. P.

J. P. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectrics Frequency Control UFFC-33, 485–499 (1986).
[CrossRef]

Oliveira, J. E. B.

J. E. B. Oliveira, E. L. Adler, D. Souilhac, A. Gundjian, “Acoustooptic Diffraction and Deflection in Tellurium at 10.6 μm,” in Proceedings, 1984 IEEE Ultrasonics Symposium (1984), pp. 332–340.
[CrossRef]

J. E. B. Oliveira, “Generalized Anisotropic Acoustooptic Diffraction in Uniaxial Crystals,” Ph.D. Thesis, McGill U., Electrical Engineering Department, Montreal (Jan.1986).

Pratt, K.

K. Pratt, Laser Communication Systems (Wiley, New York, 1968).

Remy, B.

B. Remy, “Imaging CO2 Laser Radar with Chirps Pulse Compression,” Ph.D. Thesis, U. Paris XI, Orsay (1986).

Sanchez, F.

F. Sanchez, P. H. Kayoun, J. P. Huignard, “Two-Wave Mixing with Gain in Liquid Crystals at 10.6-μm Wavelength,” J. Appl. Phys. 64, 26–31 (1988).
[CrossRef]

Scott, P. B.

P. D. Henshaw, H. M. Haskal, R. C. Knowlton, P. B. Scott, “Applicability of Laser Beam Steering for Rapid Access to 2D, 3D, and 4D Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 200–213 (1988).

Shih, I.

I. Shih, “Crystal Growth and Photoconductivity of Tellurium and Selenium–Tellurium Alloy,” Ph.D. Thesis, McGill U., Electrical Engineering Department (1981).

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 Semi-Conductors,” Phys. Rev. B 20, 4109–4119 (1979).
[CrossRef]

Souilhac, D.

J. E. B. Oliveira, E. L. Adler, D. Souilhac, A. Gundjian, “Acoustooptic Diffraction and Deflection in Tellurium at 10.6 μm,” in Proceedings, 1984 IEEE Ultrasonics Symposium (1984), pp. 332–340.
[CrossRef]

D. Souilhac, “Acoustooptic Diffraction and Deflection in Tellurium for the Carbon Dioxide Laser,” Ph.D. Thesis, McGill U., Electrical Engineering Department, Montreal (Aug.1987).

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

D. Souilhac, D. Billerey, “Comparison of Hollow Metallic Waveguides with Optical Fibers for IR Laser Propagation,” Proc. Soc. Photo-Opt. Instrum. Eng., Los Angeles (1990), to be published.

Tsai, C. H.

C. H. Tsai, “Bragg Modulators for Optic Communications,” IEEE Trans. Circuits Syst. CAS-26, 1089–1098 (1979).

Varwig, R. L.

C. P. Wang, R. L. Varwig, “Measurement of Phase Fluctuations in R. F. Chemical Laser Beam,” J. Appl. Phys. 50, 7917–7920 (1979).
[CrossRef]

Waksberg, A.

Wang, C. P.

C. P. Wang, R. L. Varwig, “Measurement of Phase Fluctuations in R. F. Chemical Laser Beam,” J. Appl. Phys. 50, 7917–7920 (1979).
[CrossRef]

White, W. E.

A. Jenkins, W. E. White, Fundamentals of Optics (McGrawHill, New York, 1965), Chap. 26.

Zook, J. D.

T. C. Lee, J. D. Zook, “Light Beam Deflection with Electrooptic Prisms,” IEEE J. Quantum Electron. QE-4, 442–443 (1968).
[CrossRef]

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

T. C. Lee, J. D. Zook, “Light Beam Deflection with Electrooptic Prisms,” IEEE J. Quantum Electron. QE-4, 442–443 (1968).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

C. H. Tsai, “Bragg Modulators for Optic Communications,” IEEE Trans. Circuits Syst. CAS-26, 1089–1098 (1979).

IEEE Trans. Sonics Ultrason. (2)

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

W. R. Klein, B. D. Cook, “Unified Approach to Ultrasonics Light Diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectrics Frequency Control (1)

J. P. Monchalin, “Optical Detection of Ultrasound,” IEEE Trans. Ultrason. Ferroelectrics Frequency Control UFFC-33, 485–499 (1986).
[CrossRef]

J. Appl. Phys. (4)

C. P. Wang, R. L. Varwig, “Measurement of Phase Fluctuations in R. F. Chemical Laser Beam,” J. Appl. Phys. 50, 7917–7920 (1979).
[CrossRef]

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

F. Sanchez, P. H. Kayoun, J. P. Huignard, “Two-Wave Mixing with Gain in Liquid Crystals at 10.6-μm Wavelength,” J. Appl. Phys. 64, 26–31 (1988).
[CrossRef]

S. Ades, C. Champness, “Intermediate Infrared Optical Absorption in Intrinsic Tellurium,” J. Appl. Phys. 49, 4543–4548 (1978).
[CrossRef]

Phys. Rev. B (1)

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

Proc. IEEE (1)

A. Korpel, “Acoustooptic, a Review of Fundamentals,” Proc. IEEE 69, 751–754 (1981).

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

P. D. Henshaw, H. M. Haskal, R. C. Knowlton, P. B. Scott, “Applicability of Laser Beam Steering for Rapid Access to 2D, 3D, and 4D Optical Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 963, 200–213 (1988).

Proceedings, 1983 IEEE Ultrasonics Symposium (1)

M. J. Delanay, S. K. Kao, “Wideband Acoustooptic Bragg Cell,” in Proceedings, 1983 IEEE Ultrasonics Symposium (1983), pp. 431–436.

Proceedings, 1984 IEEE Ultrasonics Symposium (1)

J. E. B. Oliveira, E. L. Adler, D. Souilhac, A. Gundjian, “Acoustooptic Diffraction and Deflection in Tellurium at 10.6 μm,” in Proceedings, 1984 IEEE Ultrasonics Symposium (1984), pp. 332–340.
[CrossRef]

Other (9)

M. V. Klein, Optics (Wiley, New York, 1969).

A. Jenkins, W. E. White, Fundamentals of Optics (McGrawHill, New York, 1965), Chap. 26.

D. Souilhac, “Acoustooptic Diffraction and Deflection in Tellurium for the Carbon Dioxide Laser,” Ph.D. Thesis, McGill U., Electrical Engineering Department, Montreal (Aug.1987).

J. E. B. Oliveira, “Generalized Anisotropic Acoustooptic Diffraction in Uniaxial Crystals,” Ph.D. Thesis, McGill U., Electrical Engineering Department, Montreal (Jan.1986).

K. Pratt, Laser Communication Systems (Wiley, New York, 1968).

I. Shih, “Crystal Growth and Photoconductivity of Tellurium and Selenium–Tellurium Alloy,” Ph.D. Thesis, McGill U., Electrical Engineering Department (1981).

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

B. Remy, “Imaging CO2 Laser Radar with Chirps Pulse Compression,” Ph.D. Thesis, U. Paris XI, Orsay (1986).

D. Souilhac, D. Billerey, “Comparison of Hollow Metallic Waveguides with Optical Fibers for IR Laser Propagation,” Proc. Soc. Photo-Opt. Instrum. Eng., Los Angeles (1990), to be published.

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Figures (9)

Fig. 1
Fig. 1

X*Z* is the general interaction plane. X* and Z* define the rotated axes related to the crystalline axes X,Y,Z through the three Euler angles ϕ, θ, and ψ.

Fig. 2
Fig. 2

Wavevector diagram of the 2DAO deflector. The acoustic waves propagate along the X*,Y* axes localized by the three Euler angles ϕ = 0°, θ = 130°, and ψ = ±45°. K I ,K A are the incident and diffracted optic wavevectors and acoustic wavevectors, respectively. θ I * is the incident Bragg angle. N I and N D represent the indices of refraction seen by the first and second diffracted optic beams.

Fig. 3
Fig. 3

Experimental configuration.

Fig. 4
Fig. 4

General wavevector diagram. X, Y and Z are the principal crystalline axes. The rotated X*, Y*, and Z* axes define the interaction plane X*Z*. Only one of the two AO interaction planes in Fig. 2 is shown here. The acoustic direction wavevector K A is along the X* axis localized by the three Euler angles ϕ = 0°, θ = 130°, and ψ = ±45°. The extraordinary polarization directions of the optic beams lie in the two ( K I , Z ) , ( K D , Z ) planes. N I and N D are the indices of refraction seen by the incident and diffracted optic beams.

Fig. 5
Fig. 5

In the X*Z* plane, X 1 is the intersection axis between the X*Z* plane and the XZ plane. X 2 is perpendicular to X 1 and lies in the X*Z* plane.

Fig. 6
Fig. 6

Wavevector diagram loci in the X*Z* plane. X 1 and X 2 are the principal axes of the ellipse. N I is the index of refraction seen by the extraordinary polarized incident and diffracted optic beams. N D = n o is the ordinary index of refraction.

Fig. 7
Fig. 7

Calculated diffraction efficiency and deflection angles outside tellurium vs acoustic frequency for the 2DAO deflector. The first stage operates at 100% diffraction. The second stage has θ B * = 1.5 ° constant inside the crystal. Also shown are some experimental points. The acoustic column length L = 1 μm.

Fig. 8
Fig. 8

Diffraction spots produced on thermal paper and corresponding 2DAO profiles.

Fig. 9
Fig. 9

Reconstructed deflection traces from the 2DAO deflector.

Tables (1)

Tables Icon

Table I Acoustic Attenuation Data

Equations (17)

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

I D I I = cos α I cos α D η sin 2 [ η + ( Δ k l 2 ) 2 ] 1 / 2 η + ( Δ k l 2 ) 2 ,
η = π 2 2 λ 0 2 M P A L H L 2 cos 2 δ a cos δ I cos δ D cos ( θ I * - δ I - δ a ) cos ( θ D * - δ a - δ D ) .
M = N l 3 ( θ I ) N D 3 ( θ D ) ρ V p 3 p eff 2 ,
Δ k l = π l l 0 ( F - 1 ) F .
l 0 = N D Λ 0 2 cos ( θ D * - δ a ) λ 0
cos α I , D = cos δ I , D cos δ I , D cos ( θ I , D * - δ a - δ I , D ) ,
cos δ l = 1 N l 2 ( θ 1 ) ( cos 2 θ l n o 4 + sin 2 θ l n e 4 ) - 1 / 2 ,
N l ( θ 1 ) = n o n e ( n e 2 cos 2 θ l + n o 2 sin 2 θ l ) 1 / 2 .
Δ f = 1.8 N D V p 2 cos ( θ B * = δ a ) λ 0 f 0 l             and             sin θ B * = λ 0 2 V p f , Δ θ = λ 0 Δ f V p cos θ D * .
N l 2 [ sin 2 ( θ l ) + cos 2 ( θ l ) sin 2 β ] n e 2 + N l 2 cos 2 β cos 2 ( θ l ) n o 2 = 1 ,
tan 2 α = tan 2 θ sin 2 ψ             and             cos 2 β = cos 2 θ / cos 2 α .
N Δ θ λ / D = 450 ,
V p ( λ / D ) f = 10 7 spots / s ,
A = ω 2 γ 2 κ T ρ V p 5 + ω V p e 2 2 c ɛ ω ω c ,
N I 2 = n o 2 n e 2 ( n o 2 sin 2 θ I + n e 2 cos 2 θ I ) = n o 2 n e 2 n o 2 ( sin 2 α + cos 2 α sin 2 β ) + n e 2 cos 2 β cos 2 α .
N I 2 = n o 2 n e 2 [ n o 2 ( 1 - sin 2 θ sin 2 ψ ) + n e 2 sin 2 θ sin 2 ψ ] = n o 2 n e 2 n o 2 [ cos 2 α + sin 2 α sin 2 β ] + n e 2 cos 2 β sin 2 α .
tan 2 α = tan 2 θ sin 2 ψ and cos 2 β = cos 2 θ / cos 2 α ,

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