Precise determination of full matrix of piezo-optic coefficients with a four-point bending technique: the example of lithium niobate crystals

Oleg Krupych; Viktoriya Savaryn; Rostyslav Vlokh

doi:10.1364/AO.53.0000B1

Applied Optics
Vol. 53,
Issue 10,
pp. B1-B7
(2014)
•https://doi.org/10.1364/AO.53.0000B1

Precise determination of full matrix of piezo-optic coefficients with a four-point bending technique: the example of lithium niobate crystals

Oleg Krupych, Viktoriya Savaryn, and Rostyslav Vlokh

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Oleg Krupych, Viktoriya Savaryn, and Rostyslav Vlokh, "Precise determination of full matrix of piezo-optic coefficients with a four-point bending technique: the example of lithium niobate crystals," Appl. Opt. 53, B1-B7 (2014)

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Abstract

A recently proposed technique representing a combination of digital imaging laser interferometry with a classical four-point bending method is applied to a canonical nonlinear optical crystal, ${LiNbO}_{3}$ , to precisely determine a full matrix of its piezo-optic coefficients (POCs). The contribution of a secondary piezo-optic effect to the POCs is investigated experimentally and analyzed theoretically. Based on the POCs thus obtained, a full matrix of strain-optic coefficients (SOCs) is calculated and the appropriate errors are estimated. A comparison of our experimental errors for the POCs and SOCs with the known reference data allows us to claim the present technique as the most precise.

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Sample Number	Long Axis		Side Axis 1		Side Axis 2
Sample Number	Direction	Size	Direction	Size	Direction	Size
1	[100]	18.1	[010]	3.16	[001]	3.03
2	[001]	18.1	[100]	3.03	[010]	2.84
3.1, 3.2, 3.3	[100]	18.1	[011]	2.63	[011]	3.13
4	[011]	18.1	[100]	3.03	[011]	2.84
5	[010]	18.1	[100]	3.03	[001]	3.14
6	[101]	18.1	[010]	3.15	[101]	3.02
7	[010]	18.1	[101]	3.03	[101]	2.84

Sample Number	POC	Stress Components	Light Propagation Direction	Compliance Component	Light Polarization Direction	Refractive Index
1	$π_{11}$	$σ_{1}$	[001]	$S_{31} = S_{13}$	[100]	$n_{o}$
	$π_{21} = π_{12}$	$σ_{1}$	[001]	$S_{31} = S_{13}$	[010]	$n_{o}$
	$π_{11}$	$σ_{1}$	[010]	$S_{21} = S_{12}$	[100]	$n_{o}$
	$π_{31}$	$σ_{1}$	[010]	$S_{21} = S_{12}$	[001]	$n_{e}$
2	$π_{33}$	$σ_{3}$	[010]	$S_{23} = S_{13}$	[001]	$n_{e}$
	$π_{13}$	$σ_{3}$	[010]	$S_{23} = S_{13}$	[100]	$n_{o}$
	$π_{33}$	$σ_{3}$	[100]	$S_{13}$	[001]	$n_{e}$
	$π_{23} = π_{13}$	$σ_{3}$	[100]	$S_{13}$	[010]	$n_{o}$
3.1, 3.2, 3.3	$π_{11}$	$σ_{1}$	$[0 \bar{1} 1]$	$(S_{12} + S_{13} - S_{14}) / 2$	[100]	$n_{o}$
	$(π_{12} + π_{31} + 2 π_{41}) / 2$	$σ_{1}$	$[0 \bar{1} 1]$	$(S_{12} + S_{13} - S_{14}) / 2$	[011]	$n_{45}$ ^a
	$π_{11}$	$σ_{1}$	[011]	$(S_{12} + S_{13} + S_{14}) / 2$	[100]	$n_{o}$
	$(π_{12} + π_{31} - 2 π_{41}) / 2$	$σ_{1}$	[011]	$(S_{12} + S_{13} + S_{14}) / 2$	[011]	$n_{45}$
4	$(π_{11} + π_{13} + π_{31} + π_{33} - π_{14} - 2 π_{41} + 2 π_{44}) / 4$	$σ_{2}$ , $σ_{3}$ , $σ_{4}$	$[0 \bar{1} 1]$	$(S_{11} + 2 S_{13} + S_{33} - S_{44}) / 4$	[011]	$n_{45}$
	$(π_{12} + π_{13} + π_{14}) / 2$	$σ_{2}$ , $σ_{3}$ , $σ_{4}$	$[0 \bar{1} 1]$	$(S_{11} + 2 S_{13} + S_{33} - S_{44}) / 4$	[100]	$n_{o}$
	$(π_{12} + π_{13} - π_{14}) / 2$	$σ_{2}$ , $σ_{3}$ , $σ_{4}$	[100]	$(S_{12} + S_{13} + S_{14}) / 2$	[010]	$n_{o}$
	$(π_{31} + π_{33}) / 2$	$σ_{2}$ , $σ_{3}$ , $σ_{4}$	[100]	$(S_{12} + S_{13} + S_{14}) / 2$	[001]	$n_{e}$
5	$π_{22} = π_{11}$	$σ_{2}$	[001]	$S_{32} = S_{13}$	[010]	$n_{o}$
	$π_{12}$	$σ_{2}$	[001]	$S_{32} = S_{13}$	[100]	$n_{o}$
	$π_{22} = π_{11}$	$σ_{2}$	[100]	$S_{12}$	[010]	$n_{o}$
	$π_{32} = π_{31}$	$σ_{2}$	[100]	$S_{12}$	[001]	$n_{e}$
6	$(π_{11} + π_{13} + π_{31} + π_{33} + 2 π_{44}) / 4$	$σ_{1}$ , $σ_{3}$ , $σ_{5}$	$[\bar{1} 01]$	$(S_{11} + 2 S_{13} + S_{33} - S_{44}) / 4$	[101]	$n_{45}$
	$(π_{12} + π_{13}) / 2$	$σ_{1}$ , $σ_{3}$ , $σ_{5}$	$[\bar{1} 01]$	$(S_{11} + 2 S_{13} + S_{33} - S_{44}) / 4$	[010]	$n_{o}$
	$(π_{11} + π_{13}) / 2$	$σ_{1}$ , $σ_{3}$ , $σ_{5}$	[010]	$(S_{12} + S_{13}) / 2$	[100]	$n_{o}$
	$(π_{31} + π_{33}) / 2$	$σ_{1}$ , $σ_{3}$ , $σ_{5}$	[010]	$(S_{12} + S_{13}) / 2$	[001]	$n_{e}$
7	$π_{22} = π_{11}$	$σ_{2}$	$[\bar{1} 01]$	$(S_{12} + S_{13}) / 2$	[010]	$n_{o}$
	$(π_{12} + π_{31}) / 2$	$σ_{2}$	$[\bar{1} 01]$	$(S_{12} + S_{13}) / 2$	[101]	$n_{45}$
	$π_{22} = π_{11}$	$σ_{2}$	[101]	$(S_{12} + S_{13}) / 2$	[010]	$n_{o}$
	$(π_{12} + π_{31}) / 2$	$σ_{2}$	[101]	$(S_{12} + S_{13}) / 2$	[101]	$n_{45}$

POC	$π_{11}$	$π_{12}$	$π_{13}$	$π_{31}$	$π_{33}$	$π_{14}$	$π_{41}$	$π_{44}$
The present data, B	$- 0.376 \pm 0.069$	$0.197 \pm 0.039$	$0.662 \pm 0.065$	$0.529 \pm 0.025$	$0.253 \pm 0.024$	$0.875 \pm 0.071$	$- 0.228 \pm 0.051$	$2.060 \pm 0.071$
Data of Ref. [19], B	$- 0.40 \pm 0.07$	$0.224 \pm 0.009$	$0.66 \pm 0.02$	$0.51 \pm 0.02$	$0.251 \pm 0.008$	–	–	–
Data of Ref. [24], B	$- 0.38$	0.09	0.80	0.50	0.20	$- 0.81$	$- 0.88$	2.25
Data of Ref. [17], B						$0.887 \pm 0.028$

SOC	$p_{11}$	$p_{12}$	$p_{13}$	$p_{31}$	$p_{33}$	$p_{14}$	$p_{41}$	$p_{44}$
Our data	$- 0.023 \pm 0.017$	$0.076 \pm 0.014$	$0.147 \pm 0.019$	$0.157 \pm 0.007$	$0.141 \pm 0.013$	$0.057 \pm 0.004$	$- 0.051 \pm 0.011$	$0.126 \pm 0.004$
Data of Ref. [26]	$- 0.021 \pm 0.018$	$0.060 \pm 0.019$	$0.172 \pm 0.029$	$0.141 \pm 0.017$	$0.118 \pm 0.020$	$- 0.052 \pm 0.007$	$- 0.109 \pm 0.017$	$0.121 \pm 0.019$
Data of Ref. [27]	$- 0.026$	0.090	0.133	0.179	0.071	$- 0.075$	$- 0.151$	0.146

Sample Number	Long Axis		Side Axis 1		Side Axis 2
Sample Number	Direction	Size	Direction	Size	Direction	Size
1	[100]	18.1	[010]	3.16	[001]	3.03
2	[001]	18.1	[100]	3.03	[010]	2.84
3.1, 3.2, 3.3	[100]	18.1	[011]	2.63	[011]	3.13
4	[011]	18.1	[100]	3.03	[011]	2.84
5	[010]	18.1	[100]	3.03	[001]	3.14
6	[101]	18.1	[010]	3.15	[101]	3.02
7	[010]	18.1	[101]	3.03	[101]	2.84

Abstract

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Applied Optics