Piezo-optic coefficients of MgO-doped LiNbO<sub>3</sub> crystals

Bogdan G. Mytsyk; Anatoliy S. Andrushchak; Nataliya M. Demyanyshyn; Yaroslav P. Kost'; Andriy V. Kityk; Pietro Mandracci; Wilfried Schranz

doi:10.1364/AO.48.001904

Applied Optics
Vol. 48,
Issue 10,
pp. 1904-1911
(2009)
•https://doi.org/10.1364/AO.48.001904

Piezo-optic coefficients of $Mg O$ -doped $Li Nb O_{3}$ crystals

Bogdan G. Mytsyk, Anatoliy S. Andrushchak, Nataliya M. Demyanyshyn, Yaroslav P. Kost’, Andriy V. Kityk, Pietro Mandracci, and Wilfried Schranz

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Bogdan G. Mytsyk, Anatoliy S. Andrushchak, Nataliya M. Demyanyshyn, Yaroslav P. Kost', Andriy V. Kityk, Pietro Mandracci, and Wilfried Schranz, "Piezo-optic coefficients of MgO-doped LiNbO₃ crystals," Appl. Opt. 48, 1904-1911 (2009)

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Abstract

We describe an interferometric technique suitable for determination of piezo-optic coefficients (POCs) in crystals. The method considers real nonparallelism of measured samples, thereby improving the measuring precision of POCs significantly. Corresponding equations are derived for the interferometric half-wave stress method. Using this technique we have determined a complete set of POCs of pure and $Mg O$ -doped $Li Nb O_{3}$ crystals. The reliability of the data has been confirmed by comparing the effective POCs expressed through the combinations of measured POCs and the effective POCs determined independently using highly precise optical birefringence measurements. Pure and $Mg O$ -doped $Li Nb O_{3}$ crystals reveal nearly the same magnitudes of POCs. However, $Li Nb O_{3}$ :MgO exhibits about 4 times higher resistance with respect to powerful light radiation, making it more suitable for application in acousto-optic devices that deal with superpowerful laser radiation.

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Sample Geometry	m		k	i	$σ_{im}^{0}$ and $σ_{im}^{' 0}$ , $kg / {cm}^{2}$		$π_{im}$ , $Br$	$\frac{δ Δ_{k}}{d_{k} σ_{m}}$ , $Br$	$\frac{δ Δ_{k} (π_{im})}{δ Δ_{k}}$ (%)	$\frac{δ Δ_{k} (S_{km})}{δ Δ_{k}}$ (%)
1	1	$1^{'}$	2	1	$σ_{11}^{0} = - 205$	$σ_{11}^{' 0} = - 225$	$π_{11} = - 0.50 \pm 0.03$	$+ 1.5$	$+ 200$	$- 100$
2	1	$1^{'}$	2	3	$σ_{31}^{0} = + 87$	$σ_{31}^{' 0} = + 76$	$π_{31} = + 0.50 \pm 0.08$	$- 4.0$	$+ 66$	$+ 34$
3	1	$1^{'}$	3	1	$σ_{11}^{0} = - 500$	$σ_{11}^{' 0} = - 500$	$π_{11} = - 0.40 \pm 0.02$	$+ 0.66$	$+ 360$	$- 260$
4	1	$1^{'}$	3	2	$σ_{21}^{0} = + 123$	$σ_{21}^{' 0} = + 110$	$π_{21} = + 0.18 \pm 0.05$	$- 2.8$	$+ 38$	$+ 62$
5	2	$2^{'}$	1	2	$σ_{22}^{0} = - 390$	$σ_{22}^{' 0} = - 325$	$π_{22} = - 0.40 \pm 0.02$	$+ 0.92$	$+ 260$	$- 160$
6	2	$2^{'}$	1	3	$σ_{32}^{0} = + 76$	$σ_{32}^{' 0} = + 90$	$π_{32} = + 0.49 \pm 0.07$	$- 3.95$	$+ 65$	$+ 35$
7	2	$2^{'}$	3	1	$σ_{12}^{0} = + 132$	$σ_{12}^{' 0} = + 129$	$π_{12} = + 0.13 \pm 0.04$	$- 2.5$	$+ 31$	$+ 69$
8	2	$2^{'}$	3	2	$σ_{22}^{0} = - 450$	$σ_{22}^{' 0} = - 470$	$π_{22} = - 0.41 \pm 0.02$	$+ 0.72$	$+ 340$	$- 240$
9	3	$3^{'}$	1	2	$σ_{23}^{0} = + 50$	$σ_{23}^{' 0} = + 54$	$π_{23} = + 0.76 \pm 0.10$	$- 6.25$	$+ 72$	$+ 28$
10	3	$3^{'}$	1	3	$σ_{33}^{0} = + 90$	$σ_{33}^{' 0} = + 101$	$π_{33} = + 0.34 \pm 0.06$	$- 3.4$	$+ 53$	$+ 47$
11	3	$3^{'}$	2	1	$σ_{13}^{0} = + 66$	$σ_{13}^{' 0} = + 41$	$π_{13} = + 0.79 \pm 0.10$	$- 6.4$	$+ 73$	$+ 27$
12	3	$3^{'}$	2	3	$σ_{33}^{0} = + 125$	$σ_{33}^{' 0} = + 85$	$π_{33} = + 0.30 \pm 0.06$	$- 3.2$	$+ 50$	$+ 50$
13	1	$1^{'}$	4	1	$σ_{11}^{0} = - 420$	$σ_{11}^{' 0} = - 650$	$π_{11} = - 0.47 \pm 0.03$	$+ 0.6$	$+ 470$	$- 370$
14	1	$1^{'}$	4	$\bar{4}$	$σ_{\bar{4} 1}^{0} = + 41$	$σ_{\bar{4} 1}^{' 0} = + 36$	$π_{41} = - 0.95 \pm 0.09$	$- 9.7$	$+ 79$	$+ 21$
15	1	$1^{'}$	$\bar{4}$	1	$σ_{11}^{0} = - 215$	$σ_{11}^{' 0} = - 235$	$π_{11} = - 0.41 \pm 0.03$	$+ 1.4$	$+ 174$	$- 74$
16	1	$1^{'}$	$\bar{4}$	4	$σ_{41}^{0} = - 96$	$σ_{41}^{' 0} = - 104$	$π_{41} = - 0.85 \pm 0.18$	$+ 1.45$	$+ 168$	$- 68$
17	4	$4^{'}$	$\bar{4}$	1	$σ_{14}^{0} = + 160$	$σ_{14}^{' 0} = + 125$	$π_{14} = - 0.80 \pm 0.11$	$- 3.25$	$+ 12$	$+ 88$
18	4	$4^{'}$	$\bar{4}$	4	$σ_{44}^{0} = + 27$	$σ_{44}^{' 0} = + 21$	$π_{44} = + 2.0 \pm 0.5$	$- 13.7$	$+ 79$	$+ 21$
19	$\bar{4}$	${\bar{4}}^{'}$	4	1	$σ_{1 \bar{4}}^{0} = + 48$	$σ_{1 \bar{4}}^{' 0} = + 24$	$π_{14} = - 0.80 \pm 0.11$	$- 8.0$	$+ 64$	$+ 36$
20	$\bar{4}$	${\bar{4}}^{'}$	4	$\bar{4}$	$σ_{\bar{44}}^{0} = + 53$	$σ_{\bar{44}}^{' 0} = + 48$	$π_{44} = + 2.0 \pm 0.5$	$- 6.5$	$+ 56$	$+ 44$

$π_{i m}$ , $Br$	$π_{11}$	$π_{12}$	$π_{13}$	$π_{31}$	$π_{33}$	$π_{14}$	$π_{41}$	$π_{44}$
$Li Nb O_{3} :Mg O$	$- 0.43$	$+ 0.15$	$+ 0.78$	$+ 0.50$	$+ 0.32$	$- 0.80$	$- 0.90$	$+ 2.0$
$Li Nb O_{3}$	$- 0.38$	$+ 0.09$	$+ 0.80$	$+ 0.50$	$+ 0.20$	$- 0.81$	$- 0.88$	$+ 2.25$
$Li Nb O_{3}$ ^b	$- 0.47$	$+ 0.11$	$+ 2.0$	$+ 0.47$	$+ 1.6$	$+ 0.7$	$- 1.9$	$+ 0.21$

$π_{km}^{*}$ , $Br$		$π_{12}^{*}$	$π_{13}^{*}$	$π_{31}^{*}$	$π_{41}^{*}$	$π_{\bar{4} 1}^{*}$	$π_{4 \bar{4}}^{*}$	$π_{\bar{4} 4}^{*}$
$Li Nb O_{3} :Mg O$	Calculated from $π_{im}$	$10.0 \pm 0.9$	$5.9 \pm 1.3$	$6.7 \pm 0.6$	$18.8 \pm 1.2$	$1.3 \pm 1.2$	$3.1 \pm 3.2$	$20.9 \pm 3.2$
$Li Nb O_{3} :Mg O$	Determined from $δ (Δ n_{k}) / δ σ_{m}$ ^b	10.2	6.1	6.7	19.5	2.1	2.2	22.5
$Li Nb O_{3}$	Calculated from $π_{im}$	$9.9 \pm 0.9$	$7.4 \pm 1.4$	$5.6 \pm 0.5$	$17.8 \pm 1.1$	$2.0 \pm 1.1$	$1.6 \pm 2.1$	$22.6 \pm 2.1$
$Li Nb O_{3}$	Determined from $δ (Δ n_{k}) / δ σ_{m}$ ^b	9.6	7.6	5.6	16.6	1.85	2.3	19.8

Sample Geometry	m		k	i	$σ_{im}^{0}$ and $σ_{im}^{' 0}$ , $kg / {cm}^{2}$		$π_{im}$ , $Br$	$\frac{δ Δ_{k}}{d_{k} σ_{m}}$ , $Br$	$\frac{δ Δ_{k} (π_{im})}{δ Δ_{k}}$ (%)	$\frac{δ Δ_{k} (S_{km})}{δ Δ_{k}}$ (%)
1	1	$1^{'}$	2	1	$σ_{11}^{0} = - 205$	$σ_{11}^{' 0} = - 225$	$π_{11} = - 0.50 \pm 0.03$	$+ 1.5$	$+ 200$	$- 100$
2	1	$1^{'}$	2	3	$σ_{31}^{0} = + 87$	$σ_{31}^{' 0} = + 76$	$π_{31} = + 0.50 \pm 0.08$	$- 4.0$	$+ 66$	$+ 34$
3	1	$1^{'}$	3	1	$σ_{11}^{0} = - 500$	$σ_{11}^{' 0} = - 500$	$π_{11} = - 0.40 \pm 0.02$	$+ 0.66$	$+ 360$	$- 260$
4	1	$1^{'}$	3	2	$σ_{21}^{0} = + 123$	$σ_{21}^{' 0} = + 110$	$π_{21} = + 0.18 \pm 0.05$	$- 2.8$	$+ 38$	$+ 62$
5	2	$2^{'}$	1	2	$σ_{22}^{0} = - 390$	$σ_{22}^{' 0} = - 325$	$π_{22} = - 0.40 \pm 0.02$	$+ 0.92$	$+ 260$	$- 160$
6	2	$2^{'}$	1	3	$σ_{32}^{0} = + 76$	$σ_{32}^{' 0} = + 90$	$π_{32} = + 0.49 \pm 0.07$	$- 3.95$	$+ 65$	$+ 35$
7	2	$2^{'}$	3	1	$σ_{12}^{0} = + 132$	$σ_{12}^{' 0} = + 129$	$π_{12} = + 0.13 \pm 0.04$	$- 2.5$	$+ 31$	$+ 69$
8	2	$2^{'}$	3	2	$σ_{22}^{0} = - 450$	$σ_{22}^{' 0} = - 470$	$π_{22} = - 0.41 \pm 0.02$	$+ 0.72$	$+ 340$	$- 240$
9	3	$3^{'}$	1	2	$σ_{23}^{0} = + 50$	$σ_{23}^{' 0} = + 54$	$π_{23} = + 0.76 \pm 0.10$	$- 6.25$	$+ 72$	$+ 28$
10	3	$3^{'}$	1	3	$σ_{33}^{0} = + 90$	$σ_{33}^{' 0} = + 101$	$π_{33} = + 0.34 \pm 0.06$	$- 3.4$	$+ 53$	$+ 47$
11	3	$3^{'}$	2	1	$σ_{13}^{0} = + 66$	$σ_{13}^{' 0} = + 41$	$π_{13} = + 0.79 \pm 0.10$	$- 6.4$	$+ 73$	$+ 27$
12	3	$3^{'}$	2	3	$σ_{33}^{0} = + 125$	$σ_{33}^{' 0} = + 85$	$π_{33} = + 0.30 \pm 0.06$	$- 3.2$	$+ 50$	$+ 50$
13	1	$1^{'}$	4	1	$σ_{11}^{0} = - 420$	$σ_{11}^{' 0} = - 650$	$π_{11} = - 0.47 \pm 0.03$	$+ 0.6$	$+ 470$	$- 370$
14	1	$1^{'}$	4	$\bar{4}$	$σ_{\bar{4} 1}^{0} = + 41$	$σ_{\bar{4} 1}^{' 0} = + 36$	$π_{41} = - 0.95 \pm 0.09$	$- 9.7$	$+ 79$	$+ 21$
15	1	$1^{'}$	$\bar{4}$	1	$σ_{11}^{0} = - 215$	$σ_{11}^{' 0} = - 235$	$π_{11} = - 0.41 \pm 0.03$	$+ 1.4$	$+ 174$	$- 74$
16	1	$1^{'}$	$\bar{4}$	4	$σ_{41}^{0} = - 96$	$σ_{41}^{' 0} = - 104$	$π_{41} = - 0.85 \pm 0.18$	$+ 1.45$	$+ 168$	$- 68$
17	4	$4^{'}$	$\bar{4}$	1	$σ_{14}^{0} = + 160$	$σ_{14}^{' 0} = + 125$	$π_{14} = - 0.80 \pm 0.11$	$- 3.25$	$+ 12$	$+ 88$
18	4	$4^{'}$	$\bar{4}$	4	$σ_{44}^{0} = + 27$	$σ_{44}^{' 0} = + 21$	$π_{44} = + 2.0 \pm 0.5$	$- 13.7$	$+ 79$	$+ 21$
19	$\bar{4}$	${\bar{4}}^{'}$	4	1	$σ_{1 \bar{4}}^{0} = + 48$	$σ_{1 \bar{4}}^{' 0} = + 24$	$π_{14} = - 0.80 \pm 0.11$	$- 8.0$	$+ 64$	$+ 36$
20	$\bar{4}$	${\bar{4}}^{'}$	4	$\bar{4}$	$σ_{\bar{44}}^{0} = + 53$	$σ_{\bar{44}}^{' 0} = + 48$	$π_{44} = + 2.0 \pm 0.5$	$- 6.5$	$+ 56$	$+ 44$

$π_{i m}$ , $Br$	$π_{11}$	$π_{12}$	$π_{13}$	$π_{31}$	$π_{33}$	$π_{14}$	$π_{41}$	$π_{44}$
$Li Nb O_{3} :Mg O$	$- 0.43$	$+ 0.15$	$+ 0.78$	$+ 0.50$	$+ 0.32$	$- 0.80$	$- 0.90$	$+ 2.0$
$Li Nb O_{3}$	$- 0.38$	$+ 0.09$	$+ 0.80$	$+ 0.50$	$+ 0.20$	$- 0.81$	$- 0.88$	$+ 2.25$
$Li Nb O_{3}$ ^b	$- 0.47$	$+ 0.11$	$+ 2.0$	$+ 0.47$	$+ 1.6$	$+ 0.7$	$- 1.9$	$+ 0.21$

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Applied Optics