Abstract

Peculiarities of collinear acousto-optic interaction of a strongly divergent optical beam are examined theoretically by examples of two crystals widely used in acousto-optics: calcium molybdate (CaMoO4) and paratellurite (TeO2). These materials demonstrate essentially different diffraction characteristics because of peculiar features of optical and acousto-optic anisotropy in these crystals. The dependence of the integral diffraction efficiency and the transmission band of collinear acousto-optic filters on the optical beam divergence and acoustic power is studied. It is shown that with increasing light divergence these characteristics of the filter are worsened according to the same law, and the product of the relative bandwidth and the diffraction efficiency remains constant and independent of the optical wavelength and the acousto-optic interaction length.

© 2009 Optical Society of America

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  1. S. E. Harris and R. W. Wallace, “Acoustooptic tunable filter,” J. Opt. Soc. Am. 59, 744-747 (1969).
    [CrossRef]
  2. S. E. Harris, S. T. K. Nieh, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223-225 (1970).
    [CrossRef]
  3. I. C. Chang, “Tunable acoustooptic filtering: an overview,” Proc. SPIE 90, 12-22 (1976).
  4. N. Gupta and V. Voloshinov, “Hyperspectral imager, from ultraviolet to visible, with a KDP acousto-optic tunable filter,” Appl. Opt. 43, 2752-2759 (2004).
    [CrossRef] [PubMed]
  5. V. I. Balakshy, V. N. Parygin, and L. E. Chirkov, Physical Principles of Acousto-Optics (Radio & Svyaz, 1985).
  6. J. Xu and R. Stroud, Acousto-Optic Devices (Wiley, 1992).
  7. C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, “Interaction of light and microwave sound,” Proc. IEEE 53, 1604-1623(1965).
    [CrossRef]
  8. H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327-2335 (1972).
    [CrossRef]
  9. D.C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin film optical waveguids,” Appl. Phys. Lett. 24, 194-198 (1974).
    [CrossRef]
  10. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).
  11. V. N. Parygin, A. V. Vershoubskiy, and Yu. G. Resvov, “Collinear and quasi-collinear diffraction of bounded beams in crystals: Acousto-optic interaction for the example of paratellurite,” J. Opt. A 3, S32-S39 (2001).
    [CrossRef]
  12. Yu. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear diffraction of a divergent light beam on ultrasound in paratellurite crystal,” Opt. Spectrosc. 98, 618-623 (2005).
    [CrossRef]
  13. V. I. Balakshy, “Acousto-optic cell as a filter of spatial frequencies,” Radiotekh. Elektron. 29, 1610-1616 (1984).
  14. V. I. Balakshy, “Application of acousto-optic interaction for holographic conversion of light fields,” Opt. Laser Technol. 28, 109-117 (1996).
    [CrossRef]
  15. V. I. Balakshy, K. R. Asratyan, and V. Ya. Molchanov, “Acousto-optic collinear diffraction of a strongly divergent optical beam,” J. Opt. A 3, S87-S92 (2001).
    [CrossRef]
  16. V. I. Balakshy, V. B. Voloshinov, T. M. Babkina, and D. E. Kostyuk, “Optical image processing by means of acousto-optic spatial filtration,” J. Mod. Opt. 52, 120 (2005).
    [CrossRef]
  17. V. I. Balakshy and D. E. Kostyuk, “Spatial structure of acousto-optic phase matching in uniaxial crystals,” Opt. Spectrosc. 101, 283-289 (2006).
    [CrossRef]
  18. V. I. Balakshy and S. N. Mantsevich, “Influence of the divergence of a light beam on the characteristics of collinear diffraction,” Opt. Spectrosc. 103, 804-810 (2007).
    [CrossRef]

2007 (1)

V. I. Balakshy and S. N. Mantsevich, “Influence of the divergence of a light beam on the characteristics of collinear diffraction,” Opt. Spectrosc. 103, 804-810 (2007).
[CrossRef]

2006 (1)

V. I. Balakshy and D. E. Kostyuk, “Spatial structure of acousto-optic phase matching in uniaxial crystals,” Opt. Spectrosc. 101, 283-289 (2006).
[CrossRef]

2005 (2)

V. I. Balakshy, V. B. Voloshinov, T. M. Babkina, and D. E. Kostyuk, “Optical image processing by means of acousto-optic spatial filtration,” J. Mod. Opt. 52, 120 (2005).
[CrossRef]

Yu. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear diffraction of a divergent light beam on ultrasound in paratellurite crystal,” Opt. Spectrosc. 98, 618-623 (2005).
[CrossRef]

2004 (1)

2001 (2)

V. I. Balakshy, K. R. Asratyan, and V. Ya. Molchanov, “Acousto-optic collinear diffraction of a strongly divergent optical beam,” J. Opt. A 3, S87-S92 (2001).
[CrossRef]

V. N. Parygin, A. V. Vershoubskiy, and Yu. G. Resvov, “Collinear and quasi-collinear diffraction of bounded beams in crystals: Acousto-optic interaction for the example of paratellurite,” J. Opt. A 3, S32-S39 (2001).
[CrossRef]

1996 (1)

V. I. Balakshy, “Application of acousto-optic interaction for holographic conversion of light fields,” Opt. Laser Technol. 28, 109-117 (1996).
[CrossRef]

1984 (1)

V. I. Balakshy, “Acousto-optic cell as a filter of spatial frequencies,” Radiotekh. Elektron. 29, 1610-1616 (1984).

1976 (1)

I. C. Chang, “Tunable acoustooptic filtering: an overview,” Proc. SPIE 90, 12-22 (1976).

1974 (1)

D.C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin film optical waveguids,” Appl. Phys. Lett. 24, 194-198 (1974).
[CrossRef]

1972 (1)

H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

1970 (1)

S. E. Harris, S. T. K. Nieh, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223-225 (1970).
[CrossRef]

1969 (1)

1965 (1)

C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, “Interaction of light and microwave sound,” Proc. IEEE 53, 1604-1623(1965).
[CrossRef]

Balakshy, V. I.

V. I. Balakshy and D. E. Kostyuk, “Spatial structure of acousto-optic phase matching in uniaxial crystals,” Opt. Spectrosc. 101, 283-289 (2006).
[CrossRef]

Asratyan, K. R.

V. I. Balakshy, K. R. Asratyan, and V. Ya. Molchanov, “Acousto-optic collinear diffraction of a strongly divergent optical beam,” J. Opt. A 3, S87-S92 (2001).
[CrossRef]

Babkina, T. M.

V. I. Balakshy, V. B. Voloshinov, T. M. Babkina, and D. E. Kostyuk, “Optical image processing by means of acousto-optic spatial filtration,” J. Mod. Opt. 52, 120 (2005).
[CrossRef]

Balakshy, V. I.

V. I. Balakshy, “Application of acousto-optic interaction for holographic conversion of light fields,” Opt. Laser Technol. 28, 109-117 (1996).
[CrossRef]

Balakshy, V. I.

V. I. Balakshy and S. N. Mantsevich, “Influence of the divergence of a light beam on the characteristics of collinear diffraction,” Opt. Spectrosc. 103, 804-810 (2007).
[CrossRef]

Balakshy, V. I.

V. I. Balakshy, V. B. Voloshinov, T. M. Babkina, and D. E. Kostyuk, “Optical image processing by means of acousto-optic spatial filtration,” J. Mod. Opt. 52, 120 (2005).
[CrossRef]

V. I. Balakshy, K. R. Asratyan, and V. Ya. Molchanov, “Acousto-optic collinear diffraction of a strongly divergent optical beam,” J. Opt. A 3, S87-S92 (2001).
[CrossRef]

V. I. Balakshy, “Acousto-optic cell as a filter of spatial frequencies,” Radiotekh. Elektron. 29, 1610-1616 (1984).

V. I. Balakshy, V. N. Parygin, and L. E. Chirkov, Physical Principles of Acousto-Optics (Radio & Svyaz, 1985).

Chang, I. C.

I. C. Chang, “Tunable acoustooptic filtering: an overview,” Proc. SPIE 90, 12-22 (1976).

Chirkov, L. E.

V. I. Balakshy, V. N. Parygin, and L. E. Chirkov, Physical Principles of Acousto-Optics (Radio & Svyaz, 1985).

Dobrolenskiy, Yu. S.

Yu. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear diffraction of a divergent light beam on ultrasound in paratellurite crystal,” Opt. Spectrosc. 98, 618-623 (2005).
[CrossRef]

Fiegelson, R. S.

S. E. Harris, S. T. K. Nieh, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223-225 (1970).
[CrossRef]

Flanders, C.

D.C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin film optical waveguids,” Appl. Phys. Lett. 24, 194-198 (1974).
[CrossRef]

Gupta, N.

Harris, S. E.

S. E. Harris, S. T. K. Nieh, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223-225 (1970).
[CrossRef]

S. E. Harris and R. W. Wallace, “Acoustooptic tunable filter,” J. Opt. Soc. Am. 59, 744-747 (1969).
[CrossRef]

Kogelnik, H.

D.C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin film optical waveguids,” Appl. Phys. Lett. 24, 194-198 (1974).
[CrossRef]

H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

Kostyuk, D. E.

V. I. Balakshy and D. E. Kostyuk, “Spatial structure of acousto-optic phase matching in uniaxial crystals,” Opt. Spectrosc. 101, 283-289 (2006).
[CrossRef]

V. I. Balakshy, V. B. Voloshinov, T. M. Babkina, and D. E. Kostyuk, “Optical image processing by means of acousto-optic spatial filtration,” J. Mod. Opt. 52, 120 (2005).
[CrossRef]

Mantsevich, S. N.

V. I. Balakshy and S. N. Mantsevich, “Influence of the divergence of a light beam on the characteristics of collinear diffraction,” Opt. Spectrosc. 103, 804-810 (2007).
[CrossRef]

Molchanov, V. Ya.

V. I. Balakshy, K. R. Asratyan, and V. Ya. Molchanov, “Acousto-optic collinear diffraction of a strongly divergent optical beam,” J. Opt. A 3, S87-S92 (2001).
[CrossRef]

Nieh, S. T. K.

S. E. Harris, S. T. K. Nieh, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223-225 (1970).
[CrossRef]

Parygin, V. N.

Yu. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear diffraction of a divergent light beam on ultrasound in paratellurite crystal,” Opt. Spectrosc. 98, 618-623 (2005).
[CrossRef]

V. N. Parygin, A. V. Vershoubskiy, and Yu. G. Resvov, “Collinear and quasi-collinear diffraction of bounded beams in crystals: Acousto-optic interaction for the example of paratellurite,” J. Opt. A 3, S32-S39 (2001).
[CrossRef]

V. I. Balakshy, V. N. Parygin, and L. E. Chirkov, Physical Principles of Acousto-Optics (Radio & Svyaz, 1985).

Quate, C. F.

C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, “Interaction of light and microwave sound,” Proc. IEEE 53, 1604-1623(1965).
[CrossRef]

Resvov, Yu. G.

V. N. Parygin, A. V. Vershoubskiy, and Yu. G. Resvov, “Collinear and quasi-collinear diffraction of bounded beams in crystals: Acousto-optic interaction for the example of paratellurite,” J. Opt. A 3, S32-S39 (2001).
[CrossRef]

Schmidt, R. V.

D.C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin film optical waveguids,” Appl. Phys. Lett. 24, 194-198 (1974).
[CrossRef]

Shank, C. V.

D.C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin film optical waveguids,” Appl. Phys. Lett. 24, 194-198 (1974).
[CrossRef]

H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

Stroud, R.

J. Xu and R. Stroud, Acousto-Optic Devices (Wiley, 1992).

Vershoubskiy, A. V.

V. N. Parygin, A. V. Vershoubskiy, and Yu. G. Resvov, “Collinear and quasi-collinear diffraction of bounded beams in crystals: Acousto-optic interaction for the example of paratellurite,” J. Opt. A 3, S32-S39 (2001).
[CrossRef]

Voloshinov, V.

Voloshinov, V. B.

Yu. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear diffraction of a divergent light beam on ultrasound in paratellurite crystal,” Opt. Spectrosc. 98, 618-623 (2005).
[CrossRef]

V. I. Balakshy, V. B. Voloshinov, T. M. Babkina, and D. E. Kostyuk, “Optical image processing by means of acousto-optic spatial filtration,” J. Mod. Opt. 52, 120 (2005).
[CrossRef]

Wallace, R. W.

Wilkinson, C. D. W.

C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, “Interaction of light and microwave sound,” Proc. IEEE 53, 1604-1623(1965).
[CrossRef]

Winslow, D. K.

C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, “Interaction of light and microwave sound,” Proc. IEEE 53, 1604-1623(1965).
[CrossRef]

Xu, J.

J. Xu and R. Stroud, Acousto-Optic Devices (Wiley, 1992).

Yariv, A.

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

Yeh, P.

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

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. E. Harris, S. T. K. Nieh, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223-225 (1970).
[CrossRef]

D.C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin film optical waveguids,” Appl. Phys. Lett. 24, 194-198 (1974).
[CrossRef]

J. Appl. Phys. (1)

H. Kogelnik and C. V. Shank, “Coupled wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

J. Mod. Opt. (1)

V. I. Balakshy, V. B. Voloshinov, T. M. Babkina, and D. E. Kostyuk, “Optical image processing by means of acousto-optic spatial filtration,” J. Mod. Opt. 52, 120 (2005).
[CrossRef]

J. Opt. A (2)

V. I. Balakshy, K. R. Asratyan, and V. Ya. Molchanov, “Acousto-optic collinear diffraction of a strongly divergent optical beam,” J. Opt. A 3, S87-S92 (2001).
[CrossRef]

V. N. Parygin, A. V. Vershoubskiy, and Yu. G. Resvov, “Collinear and quasi-collinear diffraction of bounded beams in crystals: Acousto-optic interaction for the example of paratellurite,” J. Opt. A 3, S32-S39 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Laser Technol. (1)

V. I. Balakshy, “Application of acousto-optic interaction for holographic conversion of light fields,” Opt. Laser Technol. 28, 109-117 (1996).
[CrossRef]

Opt. Spectrosc. (3)

V. I. Balakshy and D. E. Kostyuk, “Spatial structure of acousto-optic phase matching in uniaxial crystals,” Opt. Spectrosc. 101, 283-289 (2006).
[CrossRef]

V. I. Balakshy and S. N. Mantsevich, “Influence of the divergence of a light beam on the characteristics of collinear diffraction,” Opt. Spectrosc. 103, 804-810 (2007).
[CrossRef]

Yu. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear diffraction of a divergent light beam on ultrasound in paratellurite crystal,” Opt. Spectrosc. 98, 618-623 (2005).
[CrossRef]

Proc. IEEE (1)

C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, “Interaction of light and microwave sound,” Proc. IEEE 53, 1604-1623(1965).
[CrossRef]

Proc. SPIE (1)

I. C. Chang, “Tunable acoustooptic filtering: an overview,” Proc. SPIE 90, 12-22 (1976).

Radiotekh. Elektron. (1)

V. I. Balakshy, “Acousto-optic cell as a filter of spatial frequencies,” Radiotekh. Elektron. 29, 1610-1616 (1984).

Other (3)

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

V. I. Balakshy, V. N. Parygin, and L. E. Chirkov, Physical Principles of Acousto-Optics (Radio & Svyaz, 1985).

J. Xu and R. Stroud, Acousto-Optic Devices (Wiley, 1992).

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Figures (6)

Fig. 1
Fig. 1

Principal scheme of the Ca Mo O 4 collinear filter: 1, acoustic beam; 2, piezoelectric transducer; 3, acoustic absorber, 4, incident optical beam; 5,6, compensating prisms; 7, polarizer; 8, undiffracted beam (zero order); 9, diffracted beam (1st order); 10, analyzer.

Fig. 2
Fig. 2

Transfer functions of the Ca Mo O 4 collinear filter at l = 4 cm and A = π . (a)  f = f c = 46.62 MHz , (b)  f = 46.57 MHz , (c)  f = 46.67 MHz .

Fig. 3
Fig. 3

Spatial structure of the AO figure of merit for the Te O 2 crystal.

Fig. 4
Fig. 4

Transfer functions of the Te O 2 collinear filter at l = 2 cm and A 0 = 200 π . (a)  f = f c = 148.26 MHz , (b)  f = 148.12 MHz , (c)  f = 148.37 MHz .

Fig. 5
Fig. 5

Transmission functions of (a)  Ca Mo O 4 and (b)  Te O 2 collinear filters.

Fig. 6
Fig. 6

Integral diffraction efficiency as a function of the Raman–Nath parameter for (a)  Ca Mo O 4 and (b)  Te O 2 collinear filters.

Equations (7)

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

U d ( α , β ) = U i ( α , β ) H ( α , β ) ,
H ( α , β ) = A 2 sinc ( 1 2 π A 2 + R 2 ( α , β ) ) ,
H ( α , β ) = A 0 2 r ( α , β ) × sinc [ 1 2 π A 0 2 r ( α , β ) + R 2 ( α , β ) ] ,
R = 2 π l λ ( n d 2 n i 2 sin 2 α n i cos α + λ f V ) ,
f c = V λ ( n i n d ) .
n i = n o n e n o 2 + ( n e 2 n o 2 ) cos 2 β sin 2 α , n d = n o .
M ( α , β ) = ( p 11 p 12 ) 2 n o 3 n e 3 sin 2 ( β ) 4 ρ V 3 ,

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