Abstract

We suggest a new approach for analyzing spatial anisotropy of an acousto-optic figure of merit (AOFM). The relations for the effective elasto-optic coefficients and the AOFM are derived for all possible types of acousto-optic (AO) interactions in optically isotropic media, including nonsolid-state and solid-state amorphous media and crystals belonging to the cubic system. Our approach allows for finding the optimal geometries of AO interactions characterized by the highest AOFM for a given material. The analysis is carried out on the examples of cubic KBr and KAl(SO4)2×12H2O crystals, which represent different subgroups of the cubic symmetry class.

© 2014 Optical Society of America

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  1. O. G. Vlokh, Spatial Dispersion Phenomena in Parametric Crystal Optics (Vyshcha Shkola, 1984).
  2. Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1979).
  3. V. I. Balakshii, V. N. Parygin, and L. E. Chirkov, Physical Fundamentals of Acoustooptics (Radio i Sviaz’, 1985).
  4. J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, 1992).
  5. A. Korpel, Acousto-optics (Marcel Dekker, 1996).
  6. C. C. Tsai, Guided-Wave Acousto-Optics (Springer-Verlag, 1990).
  7. I. Martynyuk-Lototska, O. Mys, T. Dudok, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acoustooptic interaction in α-BaB2O4 and Li2B4O7 crystals,” Appl. Opt. 47, 3446–3454 (2008).
    [CrossRef]
  8. R. Vlokh and I. Martynyuk-Lototska, “Ferroelastic crystals as effective acoustooptic materials,” Ukr. J. Phys. Opt. 10, 89–99 (2009).
    [CrossRef]
  9. W. A. Bonner, S. Singh, L. G. Van Uitert, and A. W. Warner, “High quality tellurium dioxide for acousto-optic and non-linear applications,” J. Electron. Mater. 1, 154–164 (1972).
    [CrossRef]
  10. M. P. Shaskolskaya, Acoustic Crystals (Nauka, 1982).
  11. M. V. Kaidan, A. V. Zadorozhna, A. S. Andrushchak, and A. V. Kityk, “Cs2HgCl4 crystal as a new material for acoustooptical applications,” Opt. Mater. 22, 263–268 (2003).
    [CrossRef]
  12. T. S. Narasimhamurty, Photoelastic and Electrooptic Properties of Crystals (Plenum, 1981).
  13. A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
    [CrossRef]
  14. O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
    [CrossRef]
  15. J. F. Nye, Physical Properties of Crystals. Their Representation by Tensors and Matrices (Clarendon, 1964).
  16. W. Durr, “Acousto-optic interaction in gases and liquid bases in the far infrared,” Int. J. Infrared Millim. Waves 7, 1537–1558 (1986).
    [CrossRef]
  17. M. Lainé and A. B. Seddon, “Chalcogenide glasses for acousto-optic devices,” J. Non-Cryst. Solids 184, 30–35 (1995).
    [CrossRef]
  18. V. Adamiv, I. Teslyuk, Ya. Dyachok, G. Romanyuk, O. Krupych, O. Mys, I. Martynyuk-Lototska, Ya. Burak, and R. Vlokh, “Synthesis and optical characterization of LiKB4O7, Li2B6O10, and LiCsB6O10 glasses,” Appl. Opt. 49, 5360–5365 (2010).
    [CrossRef]
  19. D. Royer and E. Dieulesaint, Elastic Waves in Solids I. Free and Guided Propagation (Springer-Verlag, 1996).
  20. R. Truell, C. Elbaum, and B. B. Chick, Ultrasonic Methods in Solid State Physics (Academic, 1969).
  21. R. James Brown, D. C. Lawton, and S. P. Cheadle, “Scaled physical modelling of anisotropic wave propagation: multioffset profiles over an orthorhombic medium,” Geophys. J. Int. 107, 693–702 (1991).
    [CrossRef]
  22. S. Haussühl, Physical Properties of Crystals: An Introduction (Wiley-VCH, 2008).

2013

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

2010

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

V. Adamiv, I. Teslyuk, Ya. Dyachok, G. Romanyuk, O. Krupych, O. Mys, I. Martynyuk-Lototska, Ya. Burak, and R. Vlokh, “Synthesis and optical characterization of LiKB4O7, Li2B6O10, and LiCsB6O10 glasses,” Appl. Opt. 49, 5360–5365 (2010).
[CrossRef]

2009

R. Vlokh and I. Martynyuk-Lototska, “Ferroelastic crystals as effective acoustooptic materials,” Ukr. J. Phys. Opt. 10, 89–99 (2009).
[CrossRef]

2008

2003

M. V. Kaidan, A. V. Zadorozhna, A. S. Andrushchak, and A. V. Kityk, “Cs2HgCl4 crystal as a new material for acoustooptical applications,” Opt. Mater. 22, 263–268 (2003).
[CrossRef]

1995

M. Lainé and A. B. Seddon, “Chalcogenide glasses for acousto-optic devices,” J. Non-Cryst. Solids 184, 30–35 (1995).
[CrossRef]

1991

R. James Brown, D. C. Lawton, and S. P. Cheadle, “Scaled physical modelling of anisotropic wave propagation: multioffset profiles over an orthorhombic medium,” Geophys. J. Int. 107, 693–702 (1991).
[CrossRef]

1986

W. Durr, “Acousto-optic interaction in gases and liquid bases in the far infrared,” Int. J. Infrared Millim. Waves 7, 1537–1558 (1986).
[CrossRef]

1972

W. A. Bonner, S. Singh, L. G. Van Uitert, and A. W. Warner, “High quality tellurium dioxide for acousto-optic and non-linear applications,” J. Electron. Mater. 1, 154–164 (1972).
[CrossRef]

Adamiv, V.

Andrushchak, A. S.

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

M. V. Kaidan, A. V. Zadorozhna, A. S. Andrushchak, and A. V. Kityk, “Cs2HgCl4 crystal as a new material for acoustooptical applications,” Opt. Mater. 22, 263–268 (2003).
[CrossRef]

Andrushchak, N. A.

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

Balakshii, V. I.

V. I. Balakshii, V. N. Parygin, and L. E. Chirkov, Physical Fundamentals of Acoustooptics (Radio i Sviaz’, 1985).

Bonner, W. A.

W. A. Bonner, S. Singh, L. G. Van Uitert, and A. W. Warner, “High quality tellurium dioxide for acousto-optic and non-linear applications,” J. Electron. Mater. 1, 154–164 (1972).
[CrossRef]

Burak, Ya.

Buryy, O. A.

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

Chaban, K. O.

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

Cheadle, S. P.

R. James Brown, D. C. Lawton, and S. P. Cheadle, “Scaled physical modelling of anisotropic wave propagation: multioffset profiles over an orthorhombic medium,” Geophys. J. Int. 107, 693–702 (1991).
[CrossRef]

Chernyhivsky, E. M.

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

Chick, B. B.

R. Truell, C. Elbaum, and B. B. Chick, Ultrasonic Methods in Solid State Physics (Academic, 1969).

Chirkov, L. E.

V. I. Balakshii, V. N. Parygin, and L. E. Chirkov, Physical Fundamentals of Acoustooptics (Radio i Sviaz’, 1985).

Dieulesaint, E.

D. Royer and E. Dieulesaint, Elastic Waves in Solids I. Free and Guided Propagation (Springer-Verlag, 1996).

Dudok, T.

Durr, W.

W. Durr, “Acousto-optic interaction in gases and liquid bases in the far infrared,” Int. J. Infrared Millim. Waves 7, 1537–1558 (1986).
[CrossRef]

Dyachok, Ya.

Elbaum, C.

R. Truell, C. Elbaum, and B. B. Chick, Ultrasonic Methods in Solid State Physics (Academic, 1969).

Gotra, O. Z.

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

Gotra, Z. Yu.

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

Haussühl, S.

S. Haussühl, Physical Properties of Crystals: An Introduction (Wiley-VCH, 2008).

James Brown, R.

R. James Brown, D. C. Lawton, and S. P. Cheadle, “Scaled physical modelling of anisotropic wave propagation: multioffset profiles over an orthorhombic medium,” Geophys. J. Int. 107, 693–702 (1991).
[CrossRef]

Kaidan, M. V.

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

M. V. Kaidan, A. V. Zadorozhna, A. S. Andrushchak, and A. V. Kityk, “Cs2HgCl4 crystal as a new material for acoustooptical applications,” Opt. Mater. 22, 263–268 (2003).
[CrossRef]

Kityk, A. V.

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

M. V. Kaidan, A. V. Zadorozhna, A. S. Andrushchak, and A. V. Kityk, “Cs2HgCl4 crystal as a new material for acoustooptical applications,” Opt. Mater. 22, 263–268 (2003).
[CrossRef]

Korpel, A.

A. Korpel, Acousto-optics (Marcel Dekker, 1996).

Krupych, O.

Kushnir, O. S.

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

Lainé, M.

M. Lainé and A. B. Seddon, “Chalcogenide glasses for acousto-optic devices,” J. Non-Cryst. Solids 184, 30–35 (1995).
[CrossRef]

Larchenko, A. V.

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

Lawton, D. C.

R. James Brown, D. C. Lawton, and S. P. Cheadle, “Scaled physical modelling of anisotropic wave propagation: multioffset profiles over an orthorhombic medium,” Geophys. J. Int. 107, 693–702 (1991).
[CrossRef]

Maksymyuk, T. A.

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

Martynyuk-Lototska, I.

Mys, O.

Mytsyk, B. G.

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

Narasimhamurty, T. S.

T. S. Narasimhamurty, Photoelastic and Electrooptic Properties of Crystals (Plenum, 1981).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals. Their Representation by Tensors and Matrices (Clarendon, 1964).

Parygin, V. N.

V. I. Balakshii, V. N. Parygin, and L. E. Chirkov, Physical Fundamentals of Acoustooptics (Radio i Sviaz’, 1985).

Romanyuk, G.

Royer, D.

D. Royer and E. Dieulesaint, Elastic Waves in Solids I. Free and Guided Propagation (Springer-Verlag, 1996).

Schranz, W.

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

Seddon, A. B.

M. Lainé and A. B. Seddon, “Chalcogenide glasses for acousto-optic devices,” J. Non-Cryst. Solids 184, 30–35 (1995).
[CrossRef]

Shaskolskaya, M. P.

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1979).

M. P. Shaskolskaya, Acoustic Crystals (Nauka, 1982).

Singh, S.

W. A. Bonner, S. Singh, L. G. Van Uitert, and A. W. Warner, “High quality tellurium dioxide for acousto-optic and non-linear applications,” J. Electron. Mater. 1, 154–164 (1972).
[CrossRef]

Sirotin, Yu. I.

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1979).

Smirnov, Ye.

Stroud, R.

J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, 1992).

Teslyuk, I.

Truell, R.

R. Truell, C. Elbaum, and B. B. Chick, Ultrasonic Methods in Solid State Physics (Academic, 1969).

Tsai, C. C.

C. C. Tsai, Guided-Wave Acousto-Optics (Springer-Verlag, 1990).

Ubizskii, S. B.

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

Van Uitert, L. G.

W. A. Bonner, S. Singh, L. G. Van Uitert, and A. W. Warner, “High quality tellurium dioxide for acousto-optic and non-linear applications,” J. Electron. Mater. 1, 154–164 (1972).
[CrossRef]

Vlokh, O. G.

O. G. Vlokh, Spatial Dispersion Phenomena in Parametric Crystal Optics (Vyshcha Shkola, 1984).

Vlokh, R.

Vynnyk, D. M.

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

Warner, A. W.

W. A. Bonner, S. Singh, L. G. Van Uitert, and A. W. Warner, “High quality tellurium dioxide for acousto-optic and non-linear applications,” J. Electron. Mater. 1, 154–164 (1972).
[CrossRef]

Xu, J.

J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, 1992).

Yurkevych, O. V.

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

Zadorozhna, A. V.

M. V. Kaidan, A. V. Zadorozhna, A. S. Andrushchak, and A. V. Kityk, “Cs2HgCl4 crystal as a new material for acoustooptical applications,” Opt. Mater. 22, 263–268 (2003).
[CrossRef]

Appl. Opt.

Geophys. J. Int.

R. James Brown, D. C. Lawton, and S. P. Cheadle, “Scaled physical modelling of anisotropic wave propagation: multioffset profiles over an orthorhombic medium,” Geophys. J. Int. 107, 693–702 (1991).
[CrossRef]

Int. J. Infrared Millim. Waves

W. Durr, “Acousto-optic interaction in gases and liquid bases in the far infrared,” Int. J. Infrared Millim. Waves 7, 1537–1558 (1986).
[CrossRef]

J. Appl. Phys.

A. S. Andrushchak, E. M. Chernyhivsky, Z. Yu. Gotra, M. V. Kaidan, A. V. Kityk, N. A. Andrushchak, T. A. Maksymyuk, B. G. Mytsyk, and W. Schranz, “Spatial anisotropy of the acousto-optical efficiency in lithium niobate crystals,” J. Appl. Phys. 108, 103118 (2010).
[CrossRef]

O. A. Buryy, A. S. Andrushchak, O. S. Kushnir, S. B. Ubizskii, D. M. Vynnyk, O. V. Yurkevych, A. V. Larchenko, K. O. Chaban, O. Z. Gotra, and A. V. Kityk, “Method of extreme surfaces for optimizing geometry of acousto-optic interactions in crystalline materials: example of LiNbO3 crystals,” J. Appl. Phys. 113, 083103 (2013).
[CrossRef]

J. Electron. Mater.

W. A. Bonner, S. Singh, L. G. Van Uitert, and A. W. Warner, “High quality tellurium dioxide for acousto-optic and non-linear applications,” J. Electron. Mater. 1, 154–164 (1972).
[CrossRef]

J. Non-Cryst. Solids

M. Lainé and A. B. Seddon, “Chalcogenide glasses for acousto-optic devices,” J. Non-Cryst. Solids 184, 30–35 (1995).
[CrossRef]

Opt. Mater.

M. V. Kaidan, A. V. Zadorozhna, A. S. Andrushchak, and A. V. Kityk, “Cs2HgCl4 crystal as a new material for acoustooptical applications,” Opt. Mater. 22, 263–268 (2003).
[CrossRef]

Ukr. J. Phys. Opt.

R. Vlokh and I. Martynyuk-Lototska, “Ferroelastic crystals as effective acoustooptic materials,” Ukr. J. Phys. Opt. 10, 89–99 (2009).
[CrossRef]

Other

T. S. Narasimhamurty, Photoelastic and Electrooptic Properties of Crystals (Plenum, 1981).

M. P. Shaskolskaya, Acoustic Crystals (Nauka, 1982).

J. F. Nye, Physical Properties of Crystals. Their Representation by Tensors and Matrices (Clarendon, 1964).

S. Haussühl, Physical Properties of Crystals: An Introduction (Wiley-VCH, 2008).

O. G. Vlokh, Spatial Dispersion Phenomena in Parametric Crystal Optics (Vyshcha Shkola, 1984).

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1979).

V. I. Balakshii, V. N. Parygin, and L. E. Chirkov, Physical Fundamentals of Acoustooptics (Radio i Sviaz’, 1985).

J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, 1992).

A. Korpel, Acousto-optics (Marcel Dekker, 1996).

C. C. Tsai, Guided-Wave Acousto-Optics (Springer-Verlag, 1990).

D. Royer and E. Dieulesaint, Elastic Waves in Solids I. Free and Guided Propagation (Springer-Verlag, 1996).

R. Truell, C. Elbaum, and B. B. Chick, Ultrasonic Methods in Solid State Physics (Academic, 1969).

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Figures (15)

Fig. 1.
Fig. 1.

Scheme of AO interaction in isotropic liquid or gaseous media: X, Y, Z are the axes of the laboratory coordinate system, Kac is the AW vector, ki and kd are the wave vectors, respectively, of the incident and diffracted optical waves, and θB is the Bragg angle.

Fig. 2.
Fig. 2.

Three types of AO interactions possible in the isotropic amorphous solids (see explanations in the text).

Fig. 3.
Fig. 3.

Vector diagram of AO interaction and the same diagram rotated by the angle Θ around the Y axis.

Fig. 4.
Fig. 4.

Crystallographic coordinate system coupled with the Cartesian system XYZ, and a new coordinate system XYZ coupled with the plane of AO interaction XZ.

Fig. 5.
Fig. 5.

Dependences of M2(I) (a) coefficient, (b) EEC, and (c) acoustic slowness on the direction of the AW vector (angle Θ) at different orientations of the interaction plane (angle φ).

Fig. 6.
Fig. 6.

Dependences of (a) AOFM M2(II) and (b) EEC on the AW vector direction in the XZ plane at different Bragg angles, as simulated for KBr crystals.

Fig. 7.
Fig. 7.

Dependences of (a) M2(II) coefficient and (b) EEC on the direction of the AW vector (angle Θ) at different orientations of the interaction plane (angle φ).

Fig. 8.
Fig. 8.

Dependences of (a) M2(III) coefficient and (b) EEC on the direction of the AW vector (angle Θ) at different values of θB and at angle φ=0deg.

Fig. 9.
Fig. 9.

Dependences of (a) M2(III) coefficient, (b) EEC, and (c) cross section of the acoustic slowness surface on the angle Θ for different orientations of AO interaction plane (angle φ).

Fig. 10.
Fig. 10.

Dependences of (a) EEC, (b) AOFM M2(V), and (c) acoustic slowness v121 on the angle Θ at different angles φ.

Fig. 11.
Fig. 11.

Dependence of EEC on the angle Θ for (a) different Bragg angles and for (b) different φ angles at θB=4deg. (c) Dependence of M2(VI) coefficient on the angle Θ for different φ angles at θB=4deg.

Fig. 12.
Fig. 12.

Dependences of AOFM on the Θ angle for different angles φ, as calculated for KAl(SO4)2×12H2O crystals: (a) M2(I), (b) M2(II), (c) M2(III), (d) M2(V), and (e) M2(VI).

Fig. 13.
Fig. 13.

Dependences of acoustic slowness: (a) v111, (b) v131, and (c) v121 on the angle Θ at the angles φ corresponding to the maximal AOFMs.

Fig. 14.
Fig. 14.

Dependences of EECs on the angle Θ at different angles φ for the interaction of types (a) (I); (b) (II); (c) (III); (d) (V); and (e) (VI).

Fig. 15.
Fig. 15.

Dependences of (a) M2(IV) and (b) EEC on the angle Θ at different angles φ.

Equations (45)

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M2=n6pef2ρv3,
v=βρ=C11+2C123ρ,
E3=ΔB3D3=(p12e1+p12e2+p11e3)D3=(2p12+p11)eD3,
Δn3=n3(2p12+p11)e/2
pef=(2p12+p11).
M2=n6(2p12+p11)2ρv3=3n6(2p12+p11)23ρ((2C12+C11))3.
CmnopKnKopp=ρv2pm,
v2=(C11C12)/(2ρ)
v2=C11/ρ
E2=ΔB2D2=p12e1D2,
Δn2=n3p12e1/2,
M2(I)=n6p122ρ1v113.
n1*=nn3(p12sin2θB+p11cos2θB)e1/2.
pef=(p12sin2θB+p11cos2θB),
M2(II)=n6(p12sin2θB+p11cos2θB)2ρ1v113.
M2(III)=n6(p44sin2θB)2ρ1v133.
vQT12=12ρ[C11+C44(C11C44)2cos22Θ+sin22Θ(C12+C44)2],
vQT22=C44/ρ.
vQL2=12ρ[C11+C44+(C11C44)2cos22Θ+sin22Θ(C12+C44)2],
e˜1=e1cos2Θ;e˜3=e1sin2Θ;e˜5=e1sinΘcosΘ.
pef=p12cos2Θ+p13sin2Θ=p12,
pef(I)=p12cos2Θ+p13sin2Θ|p13=p12=p12sin2Θ+[p12(cos4φ+sin4φ)+sin22φ(p112p44)/2]cos2Θ,
Nmp=CmnopKnKo.
M2(I)=n6[pef(I)]2ρ1[vQL(Θ,φ)]3.
pef(II)={[p11(cos4φ+sin4φ)+sin22φ(p12+2p44)/2]cos2Θ+p12sin2Θ}×cos2(θB+Θ)[p44sin2(θB+Θ)sin2Θ]/2+sin2(θB+Θ)(p12cos2Θ+p11sin2Θ).
M2(II)=n6[pef(II)]2ρ1[vQL(Θ,φ)]3.
e˜1=e5sin2Θ;e˜3=e5sin2Θ;e˜5=e5cos2Θ.
pef(III)=cos2(θB+Θ)sin2Θ×[sin22φ(p12+2p44)/2+p11(cos4φ+sin4φ)p12]+sin2(θB+Θ)sin2Θ(p12p11)+p44sin2(θB+Θ)cos2Θ.
M2(III)=n6[pef(III)]2ρ1[vQT1(Θ,φ)]3.
e˜1=e5sin2Θ;e˜3=e5sin2Θ;e˜5=e5cos2Θ.
Δn=n3(p21e˜1+p23e˜3+p25e˜5)/2.
e˜6=e6cosΘ,e˜4=e6sinΘ.
ΔB2=p16e6cosΘ,
Δn=n3p16e6cosΘ/2,
pef(V)=p16cosΘ=sin4φcosΘ(p11p122p44)/4.
M2(V)=n6[pef(V)]2ρ1[vQT2(Θ,φ)]3.
Δn=n3p16e6cosΘcos2θB/2.
pef(VI)=[sin4φ(p11p122p44)/4]cosΘcos2θB,
M2(VI)=n6[pef(VI)]2ρ1[vQT2(Θ,φ)]3.
pef(I)=[p12sin4φ+p21cos4φ+(p112p44)sin22φ/2]cos2Θ+p12sin2Θ,
pef(II)=cos2(θB+Θ)×{[p11(cos4φ+sin4φ)+sin22φ(p12+p21+4p44)/4]cos2Θ+p21sin2Θ}+sin2(θB+Θ)(p12cos2Θ+p11sin2Θ)p44sin2(θB+Θ)sin2Θ/2,
pef(III)=cos2(θB+Θ)sin2Θ×[p11(cos4φ+sin4φ)p21+sin22φ(p12+p21+4p44)/4)]+sin2(θB+Θ)sin2Θ(p12p11)+p44sin2(θB+Θ)cos2Θ,
pef(V)=12sin2φcosΘ[(p112p44)cos2φ+p12sin2φp21cos2φ],
pef(VI)=12sin2φcosΘcos2θB[(p112p44)cos2φ+p21sin2φp12cos2φ].
pef=(p21cos4φ+p12sin4φp12+(p11p44)sin22φ/2)sin2Θ.

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