Full set of piezo-optic and elasto-optic coefficients of Ca3TaGa3Si2O14 crystals at room temperature

Bohdan Mytsyk; Yuriy Suhak; Nataliya Demyanyshyn; Oleh Buryy; Nataliya Syvorotka; Dmytro Sugak; Dmytro Sugak; Serhii Ubizskii; Holger Fritze

doi:10.1364/AO.398428

Applied Optics
Vol. 59,
Issue 28,
pp. 8951-8958
(2020)
•https://doi.org/10.1364/AO.398428

Full set of piezo-optic and elasto-optic coefficients of Ca₃TaGa₃Si₂O₁₄ crystals at room temperature

Bohdan Mytsyk, Yuriy Suhak, Nataliya Demyanyshyn, Oleh Buryy, Nataliya Syvorotka, Dmytro Sugak, Serhii Ubizskii, and Holger Fritze

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Bohdan Mytsyk, Yuriy Suhak, Nataliya Demyanyshyn, Oleh Buryy, Nataliya Syvorotka, Dmytro Sugak, Serhii Ubizskii, and Holger Fritze, "Full set of piezo-optic and elasto-optic coefficients of Ca₃TaGa₃Si₂O₁₄ crystals at room temperature," Appl. Opt. 59, 8951-8958 (2020)

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Abstract

The photoelasticity of the ${{\rm Ca}_3}{{\rm TaGa}_3}{{\rm Si}_2}{{\rm O}_{14}}$ (CTGS) crystal was studied by an interferometric method based on a single-pass Mach-Zehnder interferometer. The maximum number of sample orientations for the piezo-optic experiments was applied to prove accuracy in the determination of the piezo-optic coefficients. Based on the matrices of the piezo-optic coefficients and the elastic stiffness coefficients, all the coefficients ${p_{\textit{ik}}}$ of the elastic-optic matrix are calculated. For the highest ${p_{\textit{ik}}}$ coefficient, the acousto-optic efficiency is evaluated. The results obtained for CTGS are compared with the corresponding results for ${{\rm La}_3}{{\rm Ga}_5}{{\rm SiO}_{14}}$ (langasite) crystals. The highest acousto-optic figure of merit of CTGS ${M_2} = {1.66}\cdot{{10}^{- 15}}\;{{\rm s}^3}/{\rm kg}$ is two and three times higher, compared with langasite and strontium borate, respectively, which are often used for acousto-optic modulation of light in the ultraviolet spectral range.

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Experimental Conditions	Equations
$m = 1$	$π_{12} + π_{31} \pm 2 π_{41} = - \frac{2 λ}{n_{4}^{3} σ_{\bar{4} 1 (41)}^{o}} + 2 (S_{12} + S_{13} \pm S_{14}) \frac{n_{4} - 1}{n_{4}^{3}}$	T.1
$k = 4 (\bar{4}$ )	$π_{41} = - \frac{λ}{2 n_{4}^{3}} (\frac{1}{σ_{41}^{o}} - \frac{1}{σ_{\bar{4} 1}^{o}}) - S_{14} \frac{n_{4} - 1}{n_{4}^{3}}$	T.2
$i = \bar{4}$ (4)	$π_{12} + π_{31} = - \frac{λ}{n_{4}^{3}} (\frac{1}{σ_{41}^{o}} + \frac{1}{σ_{\bar{4} 1}^{o}}) + 2 (S_{12} + S_{13}) \frac{n_{4} - 1}{n_{4}^{3}}$	T.3
$m = 4 (\bar{4}$ )	$π_{12} + π_{13} \pm π_{14} = - \frac{2 λ}{n_{1}^{3} σ_{14 (1 \bar{4})}^{o}} + (S_{11} + 2 S_{13} + S_{33} - S_{44}) \frac{n_{1} - 1}{n_{1}^{3}}$	T.4
$k = \bar{4}$ (4)	$π_{14} = - \frac{λ}{n_{1}^{3}} (\frac{1}{σ_{14}^{o}} - \frac{1}{σ_{1 \bar{4}}^{o}})$	T.5
$i = 1$	$π_{12} + π_{13} = - \frac{λ}{n_{1}^{3}} (\frac{1}{σ_{14}^{o}} + \frac{1}{σ_{1 \bar{4}}^{o}}) + (S_{11} + 2 S_{13} + S_{33} - S_{44}) \frac{n_{1} - 1}{n_{1}^{3}}$	T.6
$m = 4$ ( $\bar{4}$ )	$π_{22} + π_{23} \pm π_{24} + π_{32} + π_{33} \pm 2 π_{42} + 2 π_{44} = - \frac{4 λ}{n_{4}^{3} σ_{44 (\bar{4} \bar{4})}^{o}} + 2 (S_{11} + 2 S_{13} + S_{33} - S_{44}) \frac{n_{4} - 1}{n_{4}^{3}}$	T.7
$k = \bar{4}$ (4)	$π_{22} + π_{23} + π_{32} + π_{33} + 2 π_{44} = - \frac{2 λ}{n_{4}^{3}} (\frac{1}{σ_{44}^{o}} + \frac{1}{σ_{\bar{4} \bar{4}}^{o}}) + 2 (S_{11} + 2 S_{13} + S_{33} - S_{44}) \frac{n_{4} - 1}{n_{4}^{3}}$	T.8
$i = 4$ ( $\bar{4}$ )	$π_{24} + 2 π_{42} = - \frac{2 λ}{n_{4}^{3}} (\frac{1}{σ_{44}^{o}} - \frac{1}{σ_{\bar{4} \bar{4}}^{o}})$	T.9
$m = 4 (\bar{4}$ )	$π_{11} + π_{13} \pm π_{24} = - \frac{2 λ}{n_{1}^{3} σ_{24 (2 \bar{4})}^{o}} + 2 (S_{12} + S_{13} \pm S_{14}) \frac{n_{1} - 1}{n_{1}^{3}}$	T.10
$k = 1$ ,	$π_{24} = - \frac{λ}{n_{1}^{3}} (\frac{1}{σ_{24}^{o}} - \frac{1}{σ_{2 \bar{4}}^{o}}) + 2 S_{14} \frac{n_{1} - 1}{n_{1}^{3}}$	T.11
$i = 2$	$π_{11} + π_{13} = - \frac{λ}{n_{1}^{3}} (\frac{1}{σ_{24}^{o}} + \frac{1}{σ_{2 \bar{4}}^{o}}) + 2 (S_{12} + S_{13}) \frac{n_{1} - 1}{n_{1}^{3}}$	T.12
$m = 4 (\bar{4}$ )	$π_{31} + π_{33} = - \frac{2 λ}{n_{3}^{3} σ_{34 (3 \bar{4})}^{o}} + 2 (S_{12} + S_{13} \pm S_{14}) \frac{n_{3} - 1}{n_{3}^{3}}$	T.13
$k = 1$ $i = 3$	$π_{31} + π_{33} = - \frac{λ}{n_{3}^{3}} (\frac{1}{σ_{34}^{o}} + \frac{1}{σ_{3 \bar{4}}^{o}}) + 2 (S_{12} + S_{13}) \frac{n_{3} - 1}{n_{3}^{3}}$	T.14

	Experimental Conditions
No	$m$	$k$	$i$	$σ_{i m}^{o}, k g f / c m$	$π_{im}$ , Br
Sample of straight cuts [(Fig. 1(a)]
1	1	2	1	$σ_{11}^{o} = 380$	$π_{11} = - 0.19 \pm 0.06$
2			3	$σ_{31}^{o} = 55$	$π_{31} = 1.40 \pm 0.19$
3	1	3	1	$σ_{11}^{o} = 345$	$π_{11} = - 0.18 \pm 0.06$
4			2	$σ_{21}^{o} = 160$	$π_{21} = 0.21 \pm 0.09$
5	2	1	2	$σ_{22}^{o} = 360$	$π_{22} = - 0.18 \pm 0.06$
6			3	$σ_{32}^{o} = 55$	$π_{32} = 1.40 \pm 0.19$
7	2	3	2	$σ_{22}^{o} = 375$	$π_{22} = - 0.21 \pm 0.06$
8			1	$σ_{12}^{o} = 155$	$π_{12} = 0.23 \pm 0.09$
9	3	1	3	$σ_{33}^{o} = - 149$	$π_{33} = - 1.20 \pm 0.09$
10			2	$σ_{23}^{o} = 110$	$π_{23} = 0.54 \pm 0.12$
11	3	2	3	$σ_{33}^{o} = - 150$	$π_{33} = - 1.20 \pm 0.09$
12			1	$σ_{13}^{o} = 112$	$π_{13} = 0.52 \pm 0.12$
${X / 45}^{\circ} = cut$ sample [(Fig. 1 (b)]
13	1	4	$\bar{4}$	$σ_{\bar{4} 1}^{o} = 94$	$π_{41} = 0.32 \pm 0.11$
14	1	$\bar{4}$	4	$σ_{41}^{o} = 61$	$π_{12} + π_{31} = 1.97 \pm 0.23$
15	4	1	2	$σ_{24}^{o} = 355$	$π_{24} = - 0.72 \pm 0.11$
16			3	$σ_{34}^{o} = 175$	$π_{31} + π_{33} = 0.25 \pm 0.11$
17	4	$\bar{4}$	1	$σ_{14}^{o} = 70$	$π_{14} = 0.61 \pm 0.20$
18			4	$σ_{44}^{o} = 350$	$π_{44} = - 0.81 \pm 0.40$
19	$\bar{4}$	1	2	$σ_{2 \bar{4}}^{o} = 115$	$π_{11} + π_{13} = 0.32 \pm 0.13$
20			3	$σ_{3 \bar{4}}^{o} = 160$	$π_{31} + π_{33} = 0.25 \pm 0.11$
21	$\bar{4}$	4	1	$σ_{1 \bar{4}}^{o} = 110$	$π_{12} + π_{13} = 1.01 \pm 0.42$
22			$\bar{4}$	$σ_{\bar{4} \bar{4}}^{o} = 130$	$π_{24} + 2 π_{42} = - 1.06 \pm 0.18$

$π_{im}$ , $10^{- 12} m^{2} / N$	$π_{11}$	$π_{12}$	$π_{13}$	$π_{31}$	$π_{33}$	$π_{14}$	$π_{41}$	$π_{44}$
CTGS (this work)	$- 0.19$	$0.22$	$0.53$	$1.40$	$- 1.20$	$0.72$	$0.32$	$- 0.81$
	$\pm 0.06$	$\pm 0.09$	$\pm 0.12$	$\pm 0.19$	$\pm 0.09$	$\pm 0.11$	$\pm 0.11$	$\pm 0.40$
LGS [6]	$- 0.17$	$0.10$	$0.30$	$0.70$	$- 1.25$	$0.32$	$0.33$	$0.35$
	$\pm 0.06$	$\pm 0.07$	$\pm 0.07$	$\pm 0.19$	$\pm 0.08$	$\pm 0.15$	$\pm 0.12$	$\pm 0.16$
Quartz [25]	1.35	2.69	1.94	3.11	0.07	−0.11	−0.34	−1.13
$p_{i m}$	$p_{11}$	$p_{12}$	$p_{13}$	$p_{31}$	$p_{33}$	$p_{14}$	$p_{41}$	$p_{44}$
CTGS (this work)	$0.008$ ^a	$0.044$	$0.096$	$0.165$	$- 0.088$	$0.029$	$0.029$	$- 0.033$
	$\pm 0.010$	$\pm 0.013$	$\pm 0.022$	$\pm 0.031$	$\pm 0.031$	$\pm 0.005$	$\pm 0.015$	$\pm 0.017$
LGS (this work)	$0.014$ ^a	$0.027$	$0.071$	$0.078$	$- 0.181$	$0.013$	$0.033$	$0.028$
	$\pm 0.016$	$\pm 0.017$	$\pm 0.021$	$\pm 0.047$	$\pm 0.049$	$\pm 0.009$	$\pm 0.027$	$\pm 0.009$
Quartz [25]	0.16	0.27	0.27	0.29	0.10	−0.030	−0.047	−0.079

Experimental Conditions	Equations
$m = 1$	$π_{12} + π_{31} \pm 2 π_{41} = - \frac{2 λ}{n_{4}^{3} σ_{\bar{4} 1 (41)}^{o}} + 2 (S_{12} + S_{13} \pm S_{14}) \frac{n_{4} - 1}{n_{4}^{3}}$	T.1
$k = 4 (\bar{4}$ )	$π_{41} = - \frac{λ}{2 n_{4}^{3}} (\frac{1}{σ_{41}^{o}} - \frac{1}{σ_{\bar{4} 1}^{o}}) - S_{14} \frac{n_{4} - 1}{n_{4}^{3}}$	T.2
$i = \bar{4}$ (4)	$π_{12} + π_{31} = - \frac{λ}{n_{4}^{3}} (\frac{1}{σ_{41}^{o}} + \frac{1}{σ_{\bar{4} 1}^{o}}) + 2 (S_{12} + S_{13}) \frac{n_{4} - 1}{n_{4}^{3}}$	T.3
$m = 4 (\bar{4}$ )	$π_{12} + π_{13} \pm π_{14} = - \frac{2 λ}{n_{1}^{3} σ_{14 (1 \bar{4})}^{o}} + (S_{11} + 2 S_{13} + S_{33} - S_{44}) \frac{n_{1} - 1}{n_{1}^{3}}$	T.4
$k = \bar{4}$ (4)	$π_{14} = - \frac{λ}{n_{1}^{3}} (\frac{1}{σ_{14}^{o}} - \frac{1}{σ_{1 \bar{4}}^{o}})$	T.5
$i = 1$	$π_{12} + π_{13} = - \frac{λ}{n_{1}^{3}} (\frac{1}{σ_{14}^{o}} + \frac{1}{σ_{1 \bar{4}}^{o}}) + (S_{11} + 2 S_{13} + S_{33} - S_{44}) \frac{n_{1} - 1}{n_{1}^{3}}$	T.6
$m = 4$ ( $\bar{4}$ )	$π_{22} + π_{23} \pm π_{24} + π_{32} + π_{33} \pm 2 π_{42} + 2 π_{44} = - \frac{4 λ}{n_{4}^{3} σ_{44 (\bar{4} \bar{4})}^{o}} + 2 (S_{11} + 2 S_{13} + S_{33} - S_{44}) \frac{n_{4} - 1}{n_{4}^{3}}$	T.7
$k = \bar{4}$ (4)	$π_{22} + π_{23} + π_{32} + π_{33} + 2 π_{44} = - \frac{2 λ}{n_{4}^{3}} (\frac{1}{σ_{44}^{o}} + \frac{1}{σ_{\bar{4} \bar{4}}^{o}}) + 2 (S_{11} + 2 S_{13} + S_{33} - S_{44}) \frac{n_{4} - 1}{n_{4}^{3}}$	T.8
$i = 4$ ( $\bar{4}$ )	$π_{24} + 2 π_{42} = - \frac{2 λ}{n_{4}^{3}} (\frac{1}{σ_{44}^{o}} - \frac{1}{σ_{\bar{4} \bar{4}}^{o}})$	T.9
$m = 4 (\bar{4}$ )	$π_{11} + π_{13} \pm π_{24} = - \frac{2 λ}{n_{1}^{3} σ_{24 (2 \bar{4})}^{o}} + 2 (S_{12} + S_{13} \pm S_{14}) \frac{n_{1} - 1}{n_{1}^{3}}$	T.10
$k = 1$ ,	$π_{24} = - \frac{λ}{n_{1}^{3}} (\frac{1}{σ_{24}^{o}} - \frac{1}{σ_{2 \bar{4}}^{o}}) + 2 S_{14} \frac{n_{1} - 1}{n_{1}^{3}}$	T.11
$i = 2$	$π_{11} + π_{13} = - \frac{λ}{n_{1}^{3}} (\frac{1}{σ_{24}^{o}} + \frac{1}{σ_{2 \bar{4}}^{o}}) + 2 (S_{12} + S_{13}) \frac{n_{1} - 1}{n_{1}^{3}}$	T.12
$m = 4 (\bar{4}$ )	$π_{31} + π_{33} = - \frac{2 λ}{n_{3}^{3} σ_{34 (3 \bar{4})}^{o}} + 2 (S_{12} + S_{13} \pm S_{14}) \frac{n_{3} - 1}{n_{3}^{3}}$	T.13
$k = 1$ $i = 3$	$π_{31} + π_{33} = - \frac{λ}{n_{3}^{3}} (\frac{1}{σ_{34}^{o}} + \frac{1}{σ_{3 \bar{4}}^{o}}) + 2 (S_{12} + S_{13}) \frac{n_{3} - 1}{n_{3}^{3}}$	T.14

	Experimental Conditions
No	$m$	$k$	$i$	$σ_{i m}^{o}, k g f / c m$	$π_{im}$ , Br
Sample of straight cuts [(Fig. 1(a)]
1	1	2	1	$σ_{11}^{o} = 380$	$π_{11} = - 0.19 \pm 0.06$
2			3	$σ_{31}^{o} = 55$	$π_{31} = 1.40 \pm 0.19$
3	1	3	1	$σ_{11}^{o} = 345$	$π_{11} = - 0.18 \pm 0.06$
4			2	$σ_{21}^{o} = 160$	$π_{21} = 0.21 \pm 0.09$
5	2	1	2	$σ_{22}^{o} = 360$	$π_{22} = - 0.18 \pm 0.06$
6			3	$σ_{32}^{o} = 55$	$π_{32} = 1.40 \pm 0.19$
7	2	3	2	$σ_{22}^{o} = 375$	$π_{22} = - 0.21 \pm 0.06$
8			1	$σ_{12}^{o} = 155$	$π_{12} = 0.23 \pm 0.09$
9	3	1	3	$σ_{33}^{o} = - 149$	$π_{33} = - 1.20 \pm 0.09$
10			2	$σ_{23}^{o} = 110$	$π_{23} = 0.54 \pm 0.12$
11	3	2	3	$σ_{33}^{o} = - 150$	$π_{33} = - 1.20 \pm 0.09$
12			1	$σ_{13}^{o} = 112$	$π_{13} = 0.52 \pm 0.12$
${X / 45}^{\circ} = cut$ sample [(Fig. 1 (b)]
13	1	4	$\bar{4}$	$σ_{\bar{4} 1}^{o} = 94$	$π_{41} = 0.32 \pm 0.11$
14	1	$\bar{4}$	4	$σ_{41}^{o} = 61$	$π_{12} + π_{31} = 1.97 \pm 0.23$
15	4	1	2	$σ_{24}^{o} = 355$	$π_{24} = - 0.72 \pm 0.11$
16			3	$σ_{34}^{o} = 175$	$π_{31} + π_{33} = 0.25 \pm 0.11$
17	4	$\bar{4}$	1	$σ_{14}^{o} = 70$	$π_{14} = 0.61 \pm 0.20$
18			4	$σ_{44}^{o} = 350$	$π_{44} = - 0.81 \pm 0.40$
19	$\bar{4}$	1	2	$σ_{2 \bar{4}}^{o} = 115$	$π_{11} + π_{13} = 0.32 \pm 0.13$
20			3	$σ_{3 \bar{4}}^{o} = 160$	$π_{31} + π_{33} = 0.25 \pm 0.11$
21	$\bar{4}$	4	1	$σ_{1 \bar{4}}^{o} = 110$	$π_{12} + π_{13} = 1.01 \pm 0.42$
22			$\bar{4}$	$σ_{\bar{4} \bar{4}}^{o} = 130$	$π_{24} + 2 π_{42} = - 1.06 \pm 0.18$

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Applied Optics