Abstract

Experimental studies and analysis of acousto-optic diffraction in α-BaB2O4 and Li2B4O7 crystals are given. Ultrasonic wave velocity, elastic compliance and stiffness coefficients, and piezo-optic and photoelastic coefficients of α-BaB2O4 and Li2B4O7 crystals are determined. The acousto-optic figure of merit has been estimated for different possible geometries of acousto-optic interaction. It is shown that the acousto-optic figures of merit for α-BaB2O4 crystals reach the value M2=(270±70)×1015s3/kg for the case of interaction with the slowest ultrasonic wave. The directions of propagation and polarization of those acoustic waves are obtained on the basis of construction of acoustic slowness surfaces. The acousto-optic diffraction is experimentally studied for α-BaB2O4 and Li2B4O7 crystals.

© 2008 Optical Society of America

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  1. R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
    [CrossRef]
  2. K. Kato, “Second-harmonic generation to 2048 Å in BaBa2O4,” IEEE J. Quantum Electron. 22, 1013-1014 (1986).
    [CrossRef]
  3. Y. Ishida and T. Yajima, “Characteristics of a new-type SHG crystal β-BaB2O4 in the femtosecond region,” Opt. Commun. 62, 197-200 (1987).
    [CrossRef]
  4. L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175-177 (1988).
    [CrossRef]
  5. C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. B 28, 235-243(1985).
  6. H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766-769 (2006).
    [CrossRef]
  7. Y. Mori, Y. K. Yap, T. Kamimura, M. Yoshimura, and T. Sasaki, “Recent development of nonlinear optical borate crystals for UV generation,” Opt. Mater. 19, 1-5 (2002).
    [CrossRef]
  8. A. S. Andrushchak, V. T. Adamiv, O. M. Krupych, I. Yu. Martynyuk-Lototska, Ya. V. Burak, and R. O. Vlokh, “Anisotropy of piezo- and elastooptical effect in β-BaB2O4 crystals,” Ferroelectrics 238, 299-305 (2000).
    [CrossRef]
  9. I. Martynyuk-Lototska, O. Mys, O. Krupych, V. Adamiv, Ya. Burak, R. Vlokh, and W. Schranz, “Elastic, piezooptic and acoustooptic properties of borate crystals (BaB2O4, Li2B4O7 and CsLiB6O10),” Integr. Ferroelectr. 63, 99-103 (2004).
    [CrossRef]
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  13. A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).
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    [CrossRef]
  17. I. Martunyuk-Lototska, O. Mys, Ya. Dyachok, T. Dudok, V. Adamiv, Ya. Burak, and R. Vlokh, “Piezooptic properties of β-BaB2O4 and Li2B4O7 crystals,” Ukr. J. Phys. Opt. 5, 19-26 (2004).
    [CrossRef]
  18. I. Martynyuk-Lototska, O. Mys, V. Adamiv, Ya. Burak, and R. Vlokh, “Elastical, piezooptical and acoustooptical properties of lithium tetra borate crystals,” Ukr. J. Phys. Opt. 3, 264-266 (2002).
    [CrossRef]
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  23. R. W. Dixon and M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205-207(1966).
    [CrossRef]
  24. R. W. Dixon, “Photoelastic properties of selected materials and their relevance for application to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149-5153 (1967).
    [CrossRef]
  25. L. Bohaty, S. Haussuhl, and J. Liebertz, “Electrooptical coefficients and temperature and pressure derivatives of the elastic constants of tetragonal Li2B4O7,” Cryst. Res. Technol. 24, 1159-1163 (1989).
    [CrossRef]
  26. V. I. Balakshii, V. N. Parygin, and L. E. Chirkov, Physical Fundamentals of Acoustooptics (Radio i Sviaz', 1985).

2006 (1)

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766-769 (2006).
[CrossRef]

2004 (3)

I. Martynyuk-Lototska, O. Mys, O. Krupych, V. Adamiv, Ya. Burak, R. Vlokh, and W. Schranz, “Elastic, piezooptic and acoustooptic properties of borate crystals (BaB2O4, Li2B4O7 and CsLiB6O10),” Integr. Ferroelectr. 63, 99-103 (2004).
[CrossRef]

I. Martynyuk-Lototska, T. Dudok, O. Krupych, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acoustooptic diffraction in borate crystals,” Ukr. J. Phys. Opt. 5, 111-114 (2004).
[CrossRef]

I. Martunyuk-Lototska, O. Mys, Ya. Dyachok, T. Dudok, V. Adamiv, Ya. Burak, and R. Vlokh, “Piezooptic properties of β-BaB2O4 and Li2B4O7 crystals,” Ukr. J. Phys. Opt. 5, 19-26 (2004).
[CrossRef]

2002 (2)

I. Martynyuk-Lototska, O. Mys, V. Adamiv, Ya. Burak, and R. Vlokh, “Elastical, piezooptical and acoustooptical properties of lithium tetra borate crystals,” Ukr. J. Phys. Opt. 3, 264-266 (2002).
[CrossRef]

Y. Mori, Y. K. Yap, T. Kamimura, M. Yoshimura, and T. Sasaki, “Recent development of nonlinear optical borate crystals for UV generation,” Opt. Mater. 19, 1-5 (2002).
[CrossRef]

2000 (1)

A. S. Andrushchak, V. T. Adamiv, O. M. Krupych, I. Yu. Martynyuk-Lototska, Ya. V. Burak, and R. O. Vlokh, “Anisotropy of piezo- and elastooptical effect in β-BaB2O4 crystals,” Ferroelectrics 238, 299-305 (2000).
[CrossRef]

1998 (1)

V. Petrov, F. Rotermund, F. Noack, R. Komatsu, T. Sugawara, and S. Uda, “Vacuum ultraviolet application of Li2B4O7 crystals: generation of 100 fs pulses down to 170 nm,” J. Appl. Phys. 84, 5887-5892 (1998).
[CrossRef]

1997 (1)

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

1989 (1)

L. Bohaty, S. Haussuhl, and J. Liebertz, “Electrooptical coefficients and temperature and pressure derivatives of the elastic constants of tetragonal Li2B4O7,” Cryst. Res. Technol. 24, 1159-1163 (1989).
[CrossRef]

1988 (1)

L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175-177 (1988).
[CrossRef]

1987 (1)

Y. Ishida and T. Yajima, “Characteristics of a new-type SHG crystal β-BaB2O4 in the femtosecond region,” Opt. Commun. 62, 197-200 (1987).
[CrossRef]

1986 (1)

K. Kato, “Second-harmonic generation to 2048 Å in BaBa2O4,” IEEE J. Quantum Electron. 22, 1013-1014 (1986).
[CrossRef]

1985 (1)

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. B 28, 235-243(1985).

1967 (2)

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for application to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149-5153 (1967).
[CrossRef]

E. P. Papadakis, “Ultrasonic phase velocity by the pulse-echo-overlap method incorporating diffraction phase corrections,” J. Acoust. Soc. Am. 42, 1045-1051 (1967).
[CrossRef]

1966 (1)

R. W. Dixon and M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205-207(1966).
[CrossRef]

Adamiv, V.

I. Martynyuk-Lototska, O. Mys, O. Krupych, V. Adamiv, Ya. Burak, R. Vlokh, and W. Schranz, “Elastic, piezooptic and acoustooptic properties of borate crystals (BaB2O4, Li2B4O7 and CsLiB6O10),” Integr. Ferroelectr. 63, 99-103 (2004).
[CrossRef]

I. Martynyuk-Lototska, T. Dudok, O. Krupych, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acoustooptic diffraction in borate crystals,” Ukr. J. Phys. Opt. 5, 111-114 (2004).
[CrossRef]

I. Martunyuk-Lototska, O. Mys, Ya. Dyachok, T. Dudok, V. Adamiv, Ya. Burak, and R. Vlokh, “Piezooptic properties of β-BaB2O4 and Li2B4O7 crystals,” Ukr. J. Phys. Opt. 5, 19-26 (2004).
[CrossRef]

I. Martynyuk-Lototska, O. Mys, V. Adamiv, Ya. Burak, and R. Vlokh, “Elastical, piezooptical and acoustooptical properties of lithium tetra borate crystals,” Ukr. J. Phys. Opt. 3, 264-266 (2002).
[CrossRef]

Adamiv, V. T.

A. S. Andrushchak, V. T. Adamiv, O. M. Krupych, I. Yu. Martynyuk-Lototska, Ya. V. Burak, and R. O. Vlokh, “Anisotropy of piezo- and elastooptical effect in β-BaB2O4 crystals,” Ferroelectrics 238, 299-305 (2000).
[CrossRef]

Andrushchak, A. S.

A. S. Andrushchak, V. T. Adamiv, O. M. Krupych, I. Yu. Martynyuk-Lototska, Ya. V. Burak, and R. O. Vlokh, “Anisotropy of piezo- and elastooptical effect in β-BaB2O4 crystals,” Ferroelectrics 238, 299-305 (2000).
[CrossRef]

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids (Krieger, 1990).

Balakshii, V. I.

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

Bohaty, L.

L. Bohaty, S. Haussuhl, and J. Liebertz, “Electrooptical coefficients and temperature and pressure derivatives of the elastic constants of tetragonal Li2B4O7,” Cryst. Res. Technol. 24, 1159-1163 (1989).
[CrossRef]

Bosenberg, W.

L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175-177 (1988).
[CrossRef]

Burak, Ya.

I. Martynyuk-Lototska, O. Mys, O. Krupych, V. Adamiv, Ya. Burak, R. Vlokh, and W. Schranz, “Elastic, piezooptic and acoustooptic properties of borate crystals (BaB2O4, Li2B4O7 and CsLiB6O10),” Integr. Ferroelectr. 63, 99-103 (2004).
[CrossRef]

I. Martunyuk-Lototska, O. Mys, Ya. Dyachok, T. Dudok, V. Adamiv, Ya. Burak, and R. Vlokh, “Piezooptic properties of β-BaB2O4 and Li2B4O7 crystals,” Ukr. J. Phys. Opt. 5, 19-26 (2004).
[CrossRef]

I. Martynyuk-Lototska, O. Mys, V. Adamiv, Ya. Burak, and R. Vlokh, “Elastical, piezooptical and acoustooptical properties of lithium tetra borate crystals,” Ukr. J. Phys. Opt. 3, 264-266 (2002).
[CrossRef]

Burak, Ya. V.

A. S. Andrushchak, V. T. Adamiv, O. M. Krupych, I. Yu. Martynyuk-Lototska, Ya. V. Burak, and R. O. Vlokh, “Anisotropy of piezo- and elastooptical effect in β-BaB2O4 crystals,” Ferroelectrics 238, 299-305 (2000).
[CrossRef]

Chen, C. T.

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. B 28, 235-243(1985).

Cheng, L. K.

L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175-177 (1988).
[CrossRef]

Chirkov, L. E.

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

Cohen, M. G.

R. W. Dixon and M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205-207(1966).
[CrossRef]

Dixon, R. W.

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for application to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149-5153 (1967).
[CrossRef]

R. W. Dixon and M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205-207(1966).
[CrossRef]

Dudok, T.

I. Martunyuk-Lototska, O. Mys, Ya. Dyachok, T. Dudok, V. Adamiv, Ya. Burak, and R. Vlokh, “Piezooptic properties of β-BaB2O4 and Li2B4O7 crystals,” Ukr. J. Phys. Opt. 5, 19-26 (2004).
[CrossRef]

I. Martynyuk-Lototska, T. Dudok, O. Krupych, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acoustooptic diffraction in borate crystals,” Ukr. J. Phys. Opt. 5, 111-114 (2004).
[CrossRef]

Dyachok, Ya.

I. Martunyuk-Lototska, O. Mys, Ya. Dyachok, T. Dudok, V. Adamiv, Ya. Burak, and R. Vlokh, “Piezooptic properties of β-BaB2O4 and Li2B4O7 crystals,” Ukr. J. Phys. Opt. 5, 19-26 (2004).
[CrossRef]

Fujita, H.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766-769 (2006).
[CrossRef]

Fukuda, T.

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

Goutzoulis, A.

A. Goutzoulis and D. Pape, Design and Fabrication of Acousto-Optic Devices (Marcel Dekker, 1994).

Haussuhl, S.

L. Bohaty, S. Haussuhl, and J. Liebertz, “Electrooptical coefficients and temperature and pressure derivatives of the elastic constants of tetragonal Li2B4O7,” Cryst. Res. Technol. 24, 1159-1163 (1989).
[CrossRef]

Ishida, Y.

Y. Ishida and T. Yajima, “Characteristics of a new-type SHG crystal β-BaB2O4 in the femtosecond region,” Opt. Commun. 62, 197-200 (1987).
[CrossRef]

Izumida, S.

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

Jiang, A. D.

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. B 28, 235-243(1985).

Kamimura, T.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766-769 (2006).
[CrossRef]

Y. Mori, Y. K. Yap, T. Kamimura, M. Yoshimura, and T. Sasaki, “Recent development of nonlinear optical borate crystals for UV generation,” Opt. Mater. 19, 1-5 (2002).
[CrossRef]

Kato, K.

K. Kato, “Second-harmonic generation to 2048 Å in BaBa2O4,” IEEE J. Quantum Electron. 22, 1013-1014 (1986).
[CrossRef]

Komatsu, R.

V. Petrov, F. Rotermund, F. Noack, R. Komatsu, T. Sugawara, and S. Uda, “Vacuum ultraviolet application of Li2B4O7 crystals: generation of 100 fs pulses down to 170 nm,” J. Appl. Phys. 84, 5887-5892 (1998).
[CrossRef]

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

Krupych, O.

I. Martynyuk-Lototska, O. Mys, O. Krupych, V. Adamiv, Ya. Burak, R. Vlokh, and W. Schranz, “Elastic, piezooptic and acoustooptic properties of borate crystals (BaB2O4, Li2B4O7 and CsLiB6O10),” Integr. Ferroelectr. 63, 99-103 (2004).
[CrossRef]

I. Martynyuk-Lototska, T. Dudok, O. Krupych, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acoustooptic diffraction in borate crystals,” Ukr. J. Phys. Opt. 5, 111-114 (2004).
[CrossRef]

Krupych, O. M.

A. S. Andrushchak, V. T. Adamiv, O. M. Krupych, I. Yu. Martynyuk-Lototska, Ya. V. Burak, and R. O. Vlokh, “Anisotropy of piezo- and elastooptical effect in β-BaB2O4 crystals,” Ferroelectrics 238, 299-305 (2000).
[CrossRef]

Liebertz, J.

L. Bohaty, S. Haussuhl, and J. Liebertz, “Electrooptical coefficients and temperature and pressure derivatives of the elastic constants of tetragonal Li2B4O7,” Cryst. Res. Technol. 24, 1159-1163 (1989).
[CrossRef]

Liu, Z.

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

Martunyuk-Lototska, I.

I. Martunyuk-Lototska, O. Mys, Ya. Dyachok, T. Dudok, V. Adamiv, Ya. Burak, and R. Vlokh, “Piezooptic properties of β-BaB2O4 and Li2B4O7 crystals,” Ukr. J. Phys. Opt. 5, 19-26 (2004).
[CrossRef]

Martynyuk-Lototska, I.

I. Martynyuk-Lototska, T. Dudok, O. Krupych, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acoustooptic diffraction in borate crystals,” Ukr. J. Phys. Opt. 5, 111-114 (2004).
[CrossRef]

I. Martynyuk-Lototska, O. Mys, O. Krupych, V. Adamiv, Ya. Burak, R. Vlokh, and W. Schranz, “Elastic, piezooptic and acoustooptic properties of borate crystals (BaB2O4, Li2B4O7 and CsLiB6O10),” Integr. Ferroelectr. 63, 99-103 (2004).
[CrossRef]

I. Martynyuk-Lototska, O. Mys, V. Adamiv, Ya. Burak, and R. Vlokh, “Elastical, piezooptical and acoustooptical properties of lithium tetra borate crystals,” Ukr. J. Phys. Opt. 3, 264-266 (2002).
[CrossRef]

Martynyuk-Lototska, I. Yu.

A. S. Andrushchak, V. T. Adamiv, O. M. Krupych, I. Yu. Martynyuk-Lototska, Ya. V. Burak, and R. O. Vlokh, “Anisotropy of piezo- and elastooptical effect in β-BaB2O4 crystals,” Ferroelectrics 238, 299-305 (2000).
[CrossRef]

Mori, Y.

Y. Mori, Y. K. Yap, T. Kamimura, M. Yoshimura, and T. Sasaki, “Recent development of nonlinear optical borate crystals for UV generation,” Opt. Mater. 19, 1-5 (2002).
[CrossRef]

Mys, O.

I. Martynyuk-Lototska, O. Mys, O. Krupych, V. Adamiv, Ya. Burak, R. Vlokh, and W. Schranz, “Elastic, piezooptic and acoustooptic properties of borate crystals (BaB2O4, Li2B4O7 and CsLiB6O10),” Integr. Ferroelectr. 63, 99-103 (2004).
[CrossRef]

I. Martunyuk-Lototska, O. Mys, Ya. Dyachok, T. Dudok, V. Adamiv, Ya. Burak, and R. Vlokh, “Piezooptic properties of β-BaB2O4 and Li2B4O7 crystals,” Ukr. J. Phys. Opt. 5, 19-26 (2004).
[CrossRef]

I. Martynyuk-Lototska, O. Mys, V. Adamiv, Ya. Burak, and R. Vlokh, “Elastical, piezooptical and acoustooptical properties of lithium tetra borate crystals,” Ukr. J. Phys. Opt. 3, 264-266 (2002).
[CrossRef]

Nakatsuka, M.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766-769 (2006).
[CrossRef]

Narasimhamurty, T. S.

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

Noack, F.

V. Petrov, F. Rotermund, F. Noack, R. Komatsu, T. Sugawara, and S. Uda, “Vacuum ultraviolet application of Li2B4O7 crystals: generation of 100 fs pulses down to 170 nm,” J. Appl. Phys. 84, 5887-5892 (1998).
[CrossRef]

Papadakis, E. P.

E. P. Papadakis, “Ultrasonic phase velocity by the pulse-echo-overlap method incorporating diffraction phase corrections,” J. Acoust. Soc. Am. 42, 1045-1051 (1967).
[CrossRef]

Pape, D.

A. Goutzoulis and D. Pape, Design and Fabrication of Acousto-Optic Devices (Marcel Dekker, 1994).

Parygin, V. N.

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

Petrov, V.

V. Petrov, F. Rotermund, F. Noack, R. Komatsu, T. Sugawara, and S. Uda, “Vacuum ultraviolet application of Li2B4O7 crystals: generation of 100 fs pulses down to 170 nm,” J. Appl. Phys. 84, 5887-5892 (1998).
[CrossRef]

Rotermund, F.

V. Petrov, F. Rotermund, F. Noack, R. Komatsu, T. Sugawara, and S. Uda, “Vacuum ultraviolet application of Li2B4O7 crystals: generation of 100 fs pulses down to 170 nm,” J. Appl. Phys. 84, 5887-5892 (1998).
[CrossRef]

Sarukura, N.

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

Sasaki, T.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766-769 (2006).
[CrossRef]

Y. Mori, Y. K. Yap, T. Kamimura, M. Yoshimura, and T. Sasaki, “Recent development of nonlinear optical borate crystals for UV generation,” Opt. Mater. 19, 1-5 (2002).
[CrossRef]

Sassa, K.

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

Schranz, W.

I. Martynyuk-Lototska, O. Mys, O. Krupych, V. Adamiv, Ya. Burak, R. Vlokh, and W. Schranz, “Elastic, piezooptic and acoustooptic properties of borate crystals (BaB2O4, Li2B4O7 and CsLiB6O10),” Integr. Ferroelectr. 63, 99-103 (2004).
[CrossRef]

Segawa, Y.

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

Shaskolskaya, M. P.

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

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

Sirotin, Yu. I.

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

Smirnov, Ye.

I. Martynyuk-Lototska, T. Dudok, O. Krupych, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acoustooptic diffraction in borate crystals,” Ukr. J. Phys. Opt. 5, 111-114 (2004).
[CrossRef]

Stroud, R.

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

Sugawara, T.

V. Petrov, F. Rotermund, F. Noack, R. Komatsu, T. Sugawara, and S. Uda, “Vacuum ultraviolet application of Li2B4O7 crystals: generation of 100 fs pulses down to 170 nm,” J. Appl. Phys. 84, 5887-5892 (1998).
[CrossRef]

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

Tang, C. L.

L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175-177 (1988).
[CrossRef]

Uda, S.

V. Petrov, F. Rotermund, F. Noack, R. Komatsu, T. Sugawara, and S. Uda, “Vacuum ultraviolet application of Li2B4O7 crystals: generation of 100 fs pulses down to 170 nm,” J. Appl. Phys. 84, 5887-5892 (1998).
[CrossRef]

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

Vlokh, R.

I. Martynyuk-Lototska, O. Mys, O. Krupych, V. Adamiv, Ya. Burak, R. Vlokh, and W. Schranz, “Elastic, piezooptic and acoustooptic properties of borate crystals (BaB2O4, Li2B4O7 and CsLiB6O10),” Integr. Ferroelectr. 63, 99-103 (2004).
[CrossRef]

I. Martynyuk-Lototska, T. Dudok, O. Krupych, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acoustooptic diffraction in borate crystals,” Ukr. J. Phys. Opt. 5, 111-114 (2004).
[CrossRef]

I. Martunyuk-Lototska, O. Mys, Ya. Dyachok, T. Dudok, V. Adamiv, Ya. Burak, and R. Vlokh, “Piezooptic properties of β-BaB2O4 and Li2B4O7 crystals,” Ukr. J. Phys. Opt. 5, 19-26 (2004).
[CrossRef]

I. Martynyuk-Lototska, O. Mys, V. Adamiv, Ya. Burak, and R. Vlokh, “Elastical, piezooptical and acoustooptical properties of lithium tetra borate crystals,” Ukr. J. Phys. Opt. 3, 264-266 (2002).
[CrossRef]

Vlokh, R. O.

A. S. Andrushchak, V. T. Adamiv, O. M. Krupych, I. Yu. Martynyuk-Lototska, Ya. V. Burak, and R. O. Vlokh, “Anisotropy of piezo- and elastooptical effect in β-BaB2O4 crystals,” Ferroelectrics 238, 299-305 (2000).
[CrossRef]

Wu, B. C.

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. B 28, 235-243(1985).

Xu, J.

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

Yajima, T.

Y. Ishida and T. Yajima, “Characteristics of a new-type SHG crystal β-BaB2O4 in the femtosecond region,” Opt. Commun. 62, 197-200 (1987).
[CrossRef]

Yamanouchi, K.

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

Yap, Y. K.

Y. Mori, Y. K. Yap, T. Kamimura, M. Yoshimura, and T. Sasaki, “Recent development of nonlinear optical borate crystals for UV generation,” Opt. Mater. 19, 1-5 (2002).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

Yoshida, H.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766-769 (2006).
[CrossRef]

Yoshida, K.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766-769 (2006).
[CrossRef]

Yoshimura, M.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766-769 (2006).
[CrossRef]

Y. Mori, Y. K. Yap, T. Kamimura, M. Yoshimura, and T. Sasaki, “Recent development of nonlinear optical borate crystals for UV generation,” Opt. Mater. 19, 1-5 (2002).
[CrossRef]

You, G. M.

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. B 28, 235-243(1985).

Appl. Phys. Lett. (3)

R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, “Growth and ultraviolet application of Li2B4O7 crystals: generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers,” Appl. Phys. Lett. 70, 3492-3494 (1997).
[CrossRef]

L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175-177 (1988).
[CrossRef]

R. W. Dixon and M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205-207(1966).
[CrossRef]

Cryst. Res. Technol. (1)

L. Bohaty, S. Haussuhl, and J. Liebertz, “Electrooptical coefficients and temperature and pressure derivatives of the elastic constants of tetragonal Li2B4O7,” Cryst. Res. Technol. 24, 1159-1163 (1989).
[CrossRef]

Ferroelectrics (1)

A. S. Andrushchak, V. T. Adamiv, O. M. Krupych, I. Yu. Martynyuk-Lototska, Ya. V. Burak, and R. O. Vlokh, “Anisotropy of piezo- and elastooptical effect in β-BaB2O4 crystals,” Ferroelectrics 238, 299-305 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Kato, “Second-harmonic generation to 2048 Å in BaBa2O4,” IEEE J. Quantum Electron. 22, 1013-1014 (1986).
[CrossRef]

Integr. Ferroelectr. (1)

I. Martynyuk-Lototska, O. Mys, O. Krupych, V. Adamiv, Ya. Burak, R. Vlokh, and W. Schranz, “Elastic, piezooptic and acoustooptic properties of borate crystals (BaB2O4, Li2B4O7 and CsLiB6O10),” Integr. Ferroelectr. 63, 99-103 (2004).
[CrossRef]

J. Acoust. Soc. Am. (1)

E. P. Papadakis, “Ultrasonic phase velocity by the pulse-echo-overlap method incorporating diffraction phase corrections,” J. Acoust. Soc. Am. 42, 1045-1051 (1967).
[CrossRef]

J. Appl. Phys. (2)

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for application to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149-5153 (1967).
[CrossRef]

V. Petrov, F. Rotermund, F. Noack, R. Komatsu, T. Sugawara, and S. Uda, “Vacuum ultraviolet application of Li2B4O7 crystals: generation of 100 fs pulses down to 170 nm,” J. Appl. Phys. 84, 5887-5892 (1998).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766-769 (2006).
[CrossRef]

Opt. Commun. (1)

Y. Ishida and T. Yajima, “Characteristics of a new-type SHG crystal β-BaB2O4 in the femtosecond region,” Opt. Commun. 62, 197-200 (1987).
[CrossRef]

Opt. Mater. (1)

Y. Mori, Y. K. Yap, T. Kamimura, M. Yoshimura, and T. Sasaki, “Recent development of nonlinear optical borate crystals for UV generation,” Opt. Mater. 19, 1-5 (2002).
[CrossRef]

Sci. Sin. Ser. B (1)

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. B 28, 235-243(1985).

Ukr. J. Phys. Opt. (3)

I. Martynyuk-Lototska, T. Dudok, O. Krupych, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acoustooptic diffraction in borate crystals,” Ukr. J. Phys. Opt. 5, 111-114 (2004).
[CrossRef]

I. Martunyuk-Lototska, O. Mys, Ya. Dyachok, T. Dudok, V. Adamiv, Ya. Burak, and R. Vlokh, “Piezooptic properties of β-BaB2O4 and Li2B4O7 crystals,” Ukr. J. Phys. Opt. 5, 19-26 (2004).
[CrossRef]

I. Martynyuk-Lototska, O. Mys, V. Adamiv, Ya. Burak, and R. Vlokh, “Elastical, piezooptical and acoustooptical properties of lithium tetra borate crystals,” Ukr. J. Phys. Opt. 3, 264-266 (2002).
[CrossRef]

Other (9)

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

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

A. Goutzoulis and D. Pape, Design and Fabrication of Acousto-Optic Devices (Marcel Dekker, 1994).

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

http://www.casix.com/product/prod_cry_bbo.html.

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

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

B. A. Auld, Acoustic Fields and Waves in Solids (Krieger, 1990).

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

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Figures (8)

Fig. 1
Fig. 1

AO cells made on the basis of (a) α - BaB 2 O 4 and (b) Li 2 B 4 O 7 crystals and (c) experimental setup for studies of AO diffraction: 1, AO crystal; 2, piezoelectric transducer; 3, amplifier; 4, high-frequency generator; 5, oscilloscope; 6, 6 —photodetectors; 7, voltmeter.

Fig. 2
Fig. 2

Dependence of AO diffraction efficiency on the electric driving power for α - BaB 2 O 4 crystals and the case of interaction with the transverse acoustic wave.

Fig. 3
Fig. 3

Schaefer–Bergmann scattering pattern for Li 2 B 4 O 7 crystals that appears due to AO interaction of the acoustic wave excited along the x axis and the incident optical beam propagated along the y axis: (a) experimental results and (b) cross section of the surface of reciprocal acoustic wave velocity by the x z plane.

Fig. 4
Fig. 4

Dependence of AO diffraction efficiency on the electric driving power for (a) α - BaB 2 O 4 and (b) Li 2 B 4 O 7 crystals for the case of interaction with longitudinal acoustic wave (circles and squares correspond to the polarizations of incident light parallel to the z and x axes, respectively).

Fig. 5
Fig. 5

Diagram of AO interaction in α - BaB 2 O 4 crystals for the case of propagation of the acoustic wave and the incident optical wave along one of the principal axes of optical wavevector surfaces (in this particular case the value M 2 = ( 54.5 ± 7.4 ) × 10 15 s 3 / kg can be achieved).

Fig. 6
Fig. 6

Schematic representation of isotropic diffraction in α - BaB 2 O 4 and Li 2 B 4 O 7 crystals that corresponds to real experimental conditions.

Fig. 7
Fig. 7

Acoustic slowness surfaces ( 10 3 s / m ) for (a) α - BaB 2 O 4 and (b) Li 2 B 4 O 7 crystals.

Fig. 8
Fig. 8

Diagrams of AO interaction with the slowest acoustic wave in (a) α - BaB 2 O 4 and (b) Li 2 B 4 O 7 crystals.

Tables (4)

Tables Icon

Table 1 Acoustic Wave Velocities for α - BaB 2 O 4 and Li 2 B 4 O 7 Crystals

Tables Icon

Table 2 Elastic Stiffness and Elastic Compliance Coefficients for α - BaB 2 O 4 and Li 2 B 4 O 7 Crystals

Tables Icon

Table 3 PO and PE Coefficients for Li 2 B 4 O 7 and α - BaB 2 O 4 Crystals

Tables Icon

Table 4 AO Parameters of Li 2 B 4 O 7 ( ρ = 2420 kg / m 3 , n o = 1.6084 , and n e = 1.5516 [9]) and α - BaB 2 O 4 ( ρ = 3747 kg / m 3 , n o = 1.667 , and n e = 1.528 [9])

Equations (27)

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

M 2 = n 6 p eff 2 ρ v 3 .
v = 1 ρ C ν μ L ν L μ ,
C ν μ = C i j k l ( i , j ν = 1 , 6 ; l μ = 1 , 6 ) , L ν = { p i m j ( i j ν = 1 , 2 , 3 ) p i m j + m i p j ( i j ν = 4 , 5 , 6 ) .
C λ μ S μ ν = δ λ ν ,
π λ ν = 2 Δ λ n c 3 σ ν d λ ,
π 44 = [ Δ λ ( 1 n 1 2 + 1 n 3 2 ) 3 / 2 σ d 2 + 1 2 ( π 11 + π 13 + π 31 + π 33 ) ] , π 66 = ( 4 Δ λ σ d n 1 3 + π 11 + π 12 )
π 14 = 4 Δ λ σ d n 1 3 + π 12 + π 13 , π 41 = [ Δ λ ( 1 n 1 2 + 1 n 3 2 ) 3 / 2 σ d 2 + 1 2 ( π 21 + π 31 ) ] , π 44 = [ 2 Δ λ ( 1 n 1 2 + 1 n 3 2 ) 3 / 2 σ d 2 + 1 2 ( π 11 + π 13 + π 14 + π 31 + π 33 + 2 π 41 ) ]
p 11 = p 22 = π 11 C 11 + π 12 C 21 + π 13 C 31 , p 12 = p 21 = π 11 C 12 + π 12 C 22 + π 13 C 32 , p 13 = p 23 = π 11 C 13 + π 12 C 23 + π 13 C 33 , p 33 = π 31 C 13 + π 32 C 23 + π 33 C 33 , p 31 = p 32 = π 31 C 11 + π 32 C 21 + π 33 C 31 , p 66 = π 66 C 66 = 1 2 ( p 11 p 12 ) , p 44 = p 55 = π 44 C 44 .
p 11 = p 22 = π 11 C 11 + π 12 C 21 + π 13 C 31 + π 14 C 41 , p 12 = p 21 = π 11 C 12 + π 12 C 22 + π 13 C 32 + π 14 C 42 , p 13 = p 23 = π 11 C 13 + π 12 C 23 + π 13 C 33 , p 33 = π 31 C 13 + π 32 C 23 + π 33 C 33 , p 31 = p 32 = π 31 C 11 + π 32 C 21 + π 33 C 31 , p 44 = p 55 = 2 π 41 C 14 + π 44 C 44 , p 41 = p 42 = π 41 ( C 11 + C 12 ) + π 44 C 44 , p 14 = p 24 = C 14 ( π 11 + π 12 ) + π 14 C 44 , p 56 = p 41 , p 65 = p 14 , p 66 = 1 2 ( p 11 p 12 ) .
η = I i I 0 I i ,
3 × 10 11 m 2 / N S 11 19 × 10 11 m 2 / N ,
17 × 10 11 m 2 / N S 33 151 × 10 11 m 2 / N ,
0 m 2 / N S 12 18 × 10 11 m 2 / N ,
51 × 10 11 m 2 / N S 13 5 × 10 11 m 2 / N .
E 3 ω ± Ω = p 33 e 3 Ω D 3 ω , E 1 ω ± Ω = p 13 e 3 Ω D 1 ω
η = I I 0 = sin 2 [ π n L 2 λ 0 cos θ B Δ ε i ε i 0 ] ,
( B 1 + p 13 e 3 ) x 2 + ( B 1 + p 13 e 3 ) y 2 + ( B 3 + p 33 e 3 ) z 2 = 1.
p 13 p 33 = n o 3 n e 3 η 1 η 3 .
e j = | 0 0 0 0 0.28 e eff 0.45 e eff 0 0.45 e eff 0.72 e eff | .
( B 1 + 0.28 p 12 e eff + 0.72 p 13 e eff 0.45 p 14 e eff ) x 2 + ( B 1 + 0.28 p 11 e eff + 0.72 p 13 e eff + 0.45 p 14 e eff ) y 2 + ( B 3 + 0.28 p 31 e eff + 0.72 p 33 e eff ) z 2 2 ( 0.45 p 44 e eff + 0.28 p 41 e eff ) y z = 1 ,
E 3 ω ± Ω = B 5 D 1 ω = ( p 52 e 2 Ω + p 53 e 3 Ω + p 54 e 4 Ω ) D 1 ω .
E 3 ω ± Ω = Δ B 3 = ( p 32 e 2 Ω + p 33 e 3 Ω ) D 3 ω = ( 0.28 p 31 + 0.72 p 33 ) e eff Ω D 3 ω , E 1 ω ± Ω = Δ B 1 = ( p 12 e 2 Ω + p 13 e 3 Ω + p 14 e 4 Ω ) D 1 ω = ( 0.28 p 12 + 0.72 p 13 0.45 p 14 ) e eff Ω D 1 ω .
( 0.28 p 31 + 0.72 p 33 ) = 0.12 ± 0.08 , ( 0.28 p 12 + 0.72 p 13 0.45 p 14 ) = 0.2 ± 0.1.
e j = | 0.6 e eff 0 0.48 e eff 0 0 0 0.48 e eff 0 0.4 e eff | .
( B 1 + 0.6 p 11 e eff + 0.4 p 13 e eff ) x 2 + ( B 1 + 0.6 p 12 e eff + 0.4 p 13 e eff ) y 2 + ( B 3 + 0.6 p 31 e eff + 0.4 p 33 e eff ) z 2 0.96 p 44 e eff x z = 1.
E 3 ω ± Ω = Δ B 3 = ( p 32 e 1 Ω + p 33 e 3 Ω ) D 3 ω = ( 0.6 p 31 + 0.4 p 33 ) e eff Ω D 3 ω ,         E 1 ω ± Ω = Δ B 1 = ( p 11 e 1 Ω + p 13 e 3 Ω ) D 1 ω = ( 0.6 p 11 + 0.4 p 13 ) e eff Ω D 1 ω .
( 0.6 p 31 + 0.4 p 33 ) = 0.15 ± 0.07 , ( 0.6 p 11 + 0.4 p 13 ) = 0.22 ± 0.08.

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