Third column electro-optical coefficients of monoclinic Sn2P2S6

Germano Montemezzani; Michel Aillerie; Ximeng Zheng; Hafssa Remmach; Alexander A. Grabar

doi:10.1364/OME.2.000920

Third column electro-optical coefficients of monoclinic Sn₂P₂S₆

Germano Montemezzani, Michel Aillerie, Ximeng Zheng, Hafssa Remmach, and Alexander A. Grabar

Optical Materials Express
Vol. 2,
Issue 7,
pp. 920-928
(2012)
•https://doi.org/10.1364/OME.2.000920

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Germano Montemezzani, Michel Aillerie, Ximeng Zheng, Hafssa Remmach, and Alexander A. Grabar, "Third column electro-optical coefficients of monoclinic Sn₂P₂S₆," Opt. Mater. Express 2, 920-928 (2012)

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Related Topics
Table of Contents Category
- Electro-optical Materials
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Interferometry (120.3180)
- Phase modulation (120.5060)
- Anisotropic optical materials (160.1190)
- Electro-optical materials (160.2100)

About this Article
History
- Original Manuscript: March 29, 2012
- Revised Manuscript: April 22, 2012
- Manuscript Accepted: April 23, 2012
- Published: June 14, 2012

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Abstract

All coefficients of the third-column of the unclamped electro-optic tensor of Sn₂P₂S₆ single crystals are determined by direct interferometric techniques. It is found that the largest coefficient $r_{113}^{T}$ for electric field parallel to the z-axis is ≈ 67 pm/V at the wavelength of 633 nm and room temperature.

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References

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Author
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Publication

S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, A. A. Grabar, and I. M. Stoyka, “Photorefraction in tin hypothiodiphosphate in the near infrared,” J. Opt. Soc. Am. B 13, 2352–2360 (1996).
[Crossref]
A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
[Crossref]
M. Jazbinsek, D. Haertle, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Wavelength dependence of visible and near-infrared photorefraction and phase conjugation in Sn2P2S6,” J. Opt. Soc. Am. B 22, 2459–2467 (2005).
[Crossref]
A. A. Grabar, M. Jazbinsek, A. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter, “Photorefractive effect in Sn2P2S6,” in Photorefractive Materials and Their Applications, J. P. Huignard and P. Günter, eds. (Springer, New York, 2007),Vol. 2, pp. 327–362.
[Crossref]
T. Bach, M. Jazbinsek, G. Montemezzani, P. Günter, A. A. Grabar, and Yu. M. Vysochanskii, “Tailoring of infrared photorefractive properties of Sn2P2S6 crystals by Te and Sb doping,” J. Opt. Soc. Am. B 24, 1535–1541 (2007).
[Crossref]
R. Mosimann, P. Marty, T. Bach, F. Juvalta, M. Jazbinsek, P. Günter, and A. A. Grabar, “High-speed photorefraction at telecommunication wavelength 1.55 μm in Sn2P2S6:Te,” Opt. Lett. 32, 3230–3232 (2007).
[Crossref] [PubMed]
I. V. Kedyk, P. Mathey, G. Gadret, O. Bidault, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Enhanced photorefractive properties of Bi-doped Sn2P2S6,” J. Opt. Soc. Am. B 25, 180–186 (2008).
[Crossref]
A. Shumelyuk, A. Volkov, S. Odoulov, G. Cook, and D. R. Evans, “Coupling of counterpropagating light waves in low-symmetry photorefractive crystals,” Appl. Phys. B 100, 101–108 (2010).
[Crossref]
S. Farahi, G. Montemezzani, A. A. Grabar, J.-P. Huignard, and F. Ramaz, “Photorefractive acousto-optic imaging in thick scattering media at 790 nm with a Sn2P2S6:Te crystal,” Opt. Lett. 35, 1798–1800 (2010).
[Crossref] [PubMed]
D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express13, 2047–2057 (2005). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-2047
[Crossref] [PubMed]
D. Haertle, M. Jazbinsek, G. Montemezzani, and P. Günter, “Nonlinear optical coefficients and phase-matching conditions in Sn2P2S6,” Opt. Express13, 3765–3776 (2005). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-10-3765
[Crossref] [PubMed]
D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215, 333–343 (2003).
[Crossref]
A. Volkov, A. Shumelyuk, S. Odoulov, D. R. Evans, and G. Cook, “Anisotropic diffraction from photore-fractive gratings and Pockels tensor of Sn2P2S6,” Opt. Express16, 16923–16934 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-21-16923
[Crossref] [PubMed]
P. Günter and M. Zgonik, “Clamped-unclamped electro-optic coefficient dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
[Crossref] [PubMed]
G. Montemezzani and M. Zgonik, “Space-charge driven holograms in anisotropic media,” in Photorefractive Materials and Their Applications, J. P. Huignard and P. Günter, eds. (Springer, New York, 2006),Vol. 1, pp. 83–118.
[Crossref]
Yu. M. Vysochanskii, M. I. Gurzan, M. M. Maior, E. D. Rogach, F. I. Savenko, and V. Yu. Slivka, “Piezoelectric properties of single crystals of Sn2P2S6,” Sov. Phys. Crystallogr. 35, 459–461 (1990), (Translated from Kristal-lografiya 35, 784 (1990)).
R. O’B. Carpenter, “The electro-optic effect in uniaxial crystals of the Dihydrogen Phosphate type. III. Measurement of coefficients,” J. Opt. Soc. Am 40, 225–229 (1950).
[Crossref]
M. Aillerie, N. Theofanous, and M. D. Fontana, “Measurement of the electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[Crossref]
A. A. Grabar, Yu. M. Vysochanskii, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, “Thermooptic investigations of ferroelectric Sn2P2S6,” Sov. Phys. Solid State 26, 2087–2089 (1984), (Translated from Fiz. Tverd. Tela 26, 3469–3472 (1984)).
G. Montemezzani, “Optimization of photorefractive two-wave mixing by accounting for material anisotropies: KNbO3 and BaTiO3,” Phys. Rev. A 62, 053803 (2000).
[Crossref]

2010 (2)

A. Shumelyuk, A. Volkov, S. Odoulov, G. Cook, and D. R. Evans, “Coupling of counterpropagating light waves in low-symmetry photorefractive crystals,” Appl. Phys. B 100, 101–108 (2010).
[Crossref]

S. Farahi, G. Montemezzani, A. A. Grabar, J.-P. Huignard, and F. Ramaz, “Photorefractive acousto-optic imaging in thick scattering media at 790 nm with a Sn2P2S6:Te crystal,” Opt. Lett. 35, 1798–1800 (2010).
[Crossref] [PubMed]

2003 (1)

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215, 333–343 (2003).
[Crossref]

2001 (1)

A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
[Crossref]

2000 (2)

M. Aillerie, N. Theofanous, and M. D. Fontana, “Measurement of the electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[Crossref]

G. Montemezzani, “Optimization of photorefractive two-wave mixing by accounting for material anisotropies: KNbO3 and BaTiO3,” Phys. Rev. A 62, 053803 (2000).
[Crossref]

1996 (1)

S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, A. A. Grabar, and I. M. Stoyka, “Photorefraction in tin hypothiodiphosphate in the near infrared,” J. Opt. Soc. Am. B 13, 2352–2360 (1996).
[Crossref]

1991 (1)

P. Günter and M. Zgonik, “Clamped-unclamped electro-optic coefficient dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
[Crossref] [PubMed]

1990 (1)

Yu. M. Vysochanskii, M. I. Gurzan, M. M. Maior, E. D. Rogach, F. I. Savenko, and V. Yu. Slivka, “Piezoelectric properties of single crystals of Sn2P2S6,” Sov. Phys. Crystallogr. 35, 459–461 (1990), (Translated from Kristal-lografiya 35, 784 (1990)).

1984 (1)

A. A. Grabar, Yu. M. Vysochanskii, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, “Thermooptic investigations of ferroelectric Sn2P2S6,” Sov. Phys. Solid State 26, 2087–2089 (1984), (Translated from Fiz. Tverd. Tela 26, 3469–3472 (1984)).

1950 (1)

R. O’B. Carpenter, “The electro-optic effect in uniaxial crystals of the Dihydrogen Phosphate type. III. Measurement of coefficients,” J. Opt. Soc. Am 40, 225–229 (1950).
[Crossref]

Aillerie, M.

Bach, T.

Bidault, O.

Caimi, G.

Carpenter, R. O’B.

R. O’B. Carpenter, “The electro-optic effect in uniaxial crystals of the Dihydrogen Phosphate type. III. Measurement of coefficients,” J. Opt. Soc. Am 40, 225–229 (1950).
[Crossref]

Cook, G.

Evans, D. R.

Farahi, S.

Fontana, M. D.

Gadret, G.

Grabar, A. A.

A. A. Grabar, M. Jazbinsek, A. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter, “Photorefractive effect in Sn2P2S6,” in Photorefractive Materials and Their Applications, J. P. Huignard and P. Günter, eds. (Springer, New York, 2007),Vol. 2, pp. 327–362.
[Crossref]

Günter, P.

P. Günter and M. Zgonik, “Clamped-unclamped electro-optic coefficient dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
[Crossref] [PubMed]

Gurzan, M. I.

Haertle, D.

Haldi, A.

Hellwig, U.

Huignard, J.-P.

Jazbinsek, M.

Juvalta, F.

Kedyk, I. V.

Maior, M. M.

Marty, P.

Mathey, P.

Molnar, A. A.

Montemezzani, G.

G. Montemezzani, “Optimization of photorefractive two-wave mixing by accounting for material anisotropies: KNbO3 and BaTiO3,” Phys. Rev. A 62, 053803 (2000).
[Crossref]

G. Montemezzani and M. Zgonik, “Space-charge driven holograms in anisotropic media,” in Photorefractive Materials and Their Applications, J. P. Huignard and P. Günter, eds. (Springer, New York, 2006),Vol. 1, pp. 83–118.
[Crossref]

Mosimann, R.

Odoulov, S.

Odoulov, S. G.

Perechinskii, S. I.

Ramaz, F.

Rogach, E. D.

Rupp, R. A.

Salo, L. A.

Savenko, F. I.

Shumelyuk, A.

Shumelyuk, A. N.

Slivka, V. Yu.

Stoika, I. M.

Stoyka, I. M.

Theofanous, N.

Volkov, A.

Vysochanskii, Y. M.

Vysochanskii, Yu. M.

Zgonik, M.

P. Günter and M. Zgonik, “Clamped-unclamped electro-optic coefficient dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
[Crossref] [PubMed]

Appl. Phys. B (2)

J. Opt. Soc. Am (1)

R. O’B. Carpenter, “The electro-optic effect in uniaxial crystals of the Dihydrogen Phosphate type. III. Measurement of coefficients,” J. Opt. Soc. Am 40, 225–229 (1950).
[Crossref]

J. Opt. Soc. Am. B (4)

Opt. Commun. (2)

Opt. Lett. (3)

P. Günter and M. Zgonik, “Clamped-unclamped electro-optic coefficient dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
[Crossref] [PubMed]

Phys. Rev. A (1)

G. Montemezzani, “Optimization of photorefractive two-wave mixing by accounting for material anisotropies: KNbO3 and BaTiO3,” Phys. Rev. A 62, 053803 (2000).
[Crossref]

Sov. Phys. Crystallogr. (1)

Sov. Phys. Solid State (1)

Other (5)

A. Volkov, A. Shumelyuk, S. Odoulov, D. R. Evans, and G. Cook, “Anisotropic diffraction from photore-fractive gratings and Pockels tensor of Sn2P2S6,” Opt. Express16, 16923–16934 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-21-16923
[Crossref] [PubMed]

D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express13, 2047–2057 (2005). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-2047
[Crossref] [PubMed]

D. Haertle, M. Jazbinsek, G. Montemezzani, and P. Günter, “Nonlinear optical coefficients and phase-matching conditions in Sn2P2S6,” Opt. Express13, 3765–3776 (2005). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-10-3765
[Crossref] [PubMed]

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Fig. 1 Mach-Zehnder type experimental arrangement used for the determination of the electro-optic coefficients.

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Fig. 2 Crystal configurations for the interferometric measurement of the third-column electro-optic coefficients of Sn₂P₂S₆. A) Measurement of r₂₂₃; B) r₃₃₃; C) r_slow; D) r_fast. The thick double arrow give the polarization direction of the corresponding eigenwave. For Sn₂P₂S₆ the angle α in C) and D) is α ≈ 43.3 deg for λ = 633 nm and room temperature. The positive direction of the applied electric field E₃ is always towards the bottom (+ẑ).

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Tables (2)

Table 1 Unclamped Electro-Optical Coefficients of Sn₂P₂S₆ at λ = 633 nm

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Table 2 Ratio of Electro-Optic Coefficients from Direct Electro-Optic Measurements and Estimated from Photorefractive Diffraction Experiments

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Equations (11)

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Δ ϕ_{E} = \frac{2 π}{λ} L Δ n + \frac{2 π}{λ} (n - 1) Δ L = \frac{2 π L}{λ} [- \frac{n^{3}}{2} r_{eff} + (n - 1) d_{eff}] E

r_{eff} = \frac{2 λ d}{π L n^{3}} \frac{Δ I_{E}}{Δ I_{\max} Δ V},

r_{i j k} = (\begin{matrix} r_{111} & 0 & r_{113} \\ r_{221} & 0 & r_{223} \\ r_{331} & 0 & r_{333} \\ 0 & r_{322} & 0 \\ r_{131} & 0 & r_{133} \\ 0 & r_{122} & 0 \end{matrix})

{(\frac{1}{n^{2}})}_{i j} (E) = (\begin{matrix} {(1 / n^{2})}_{11} & 0 & {(1 / n^{2})}_{13} \\ 0 & {(1 / n^{2})}_{22} & 0 \\ {(1 / n^{2})}_{13} & 0 & {(1 / n^{2})}_{33} \end{matrix}) + (\begin{matrix} r_{113} E & 0 & r_{133} E \\ 0 & r_{223} E & 0 \\ r_{133} E & 0 & r_{333} E \end{matrix}),

Δ (\frac{1}{n^{2}}) = Δ {(\frac{1}{n^{2}})}_{i j} {\hat{d}}_{i} {\hat{d}}_{j} .

r_{slow} = r_{113} {cos}^{2} α + r_{333} {sin}^{2} α - 2 r_{133} sin α cos α \approx \frac{1}{2} (r_{113} + r_{333}) - r_{133},

r_{fast} = r_{113} {sin}^{2} α + r_{333} {cos}^{2} α + 2 r_{133} sin α cos α \approx \frac{1}{2} (r_{113} + r_{333}) + r_{133} .

r_{113} = r_{fast} + r_{slow} - r_{333}

r_{133} = \frac{r_{fast} {cos}^{2} α - r_{slow} {sin}^{2} α - r_{333} cos 2 α}{sin 2 α} \approx \frac{1}{2} (r_{fast} - r_{slow}) .

Δ n \equiv - \frac{{\tilde{n}}^{3}}{2} r_{c} E_{3} = - (\frac{n_{1}^{3}}{2} r_{fast} - \frac{n_{3}^{3}}{2} r_{slow}) E_{3},

r_{c} = r_{113} \frac{n_{1}^{3} {sin}^{2} α - n_{3}^{3} {cos}^{2} α}{n_{z}^{3}} + r_{333} \frac{n_{1}^{3} {cos}^{2} α - n_{3}^{3} {sin}^{2} α}{n_{z}^{3}} + r_{133} \frac{n_{1}^{3} + n_{3}^{3}}{n_{z}^{3}} sin 2 α .

Coefficient	Value [pm/V]	Reference
r₂₂₃	+21.7 ± 3.8	This work
r₃₃₃	+24.7 ± 3.7	This work
r_fast	+58.9 ± 5.1	This work
r_slow	+32.6 ± 2.3	This work
r_c (meas.)	+26.5 ± 1.5	This work
r₁₁₃	+67 ± 7	This work
r₁₃₃	+14.4 ± 3.0	This work
r_c (calc.)	+23.1 ± 5.6	This work
r₁₁₁	+174 ± 10	[12]
r₂₂₁	+92 ± 8	[12]
r₃₃₁	+140 ± 18	[12]
r₁₃₁	+25 ± 15	[12]

Coefficient ratio	Direct electro-optic measurement (This work and [12])	Photorefractive measurement ([13])
r₁₁₃/r₃₃₃	2.7 ± 0.7	1.7 ± 0.6
r₂₂₃/r₃₃₃	0.87 ± 0.28	0.69 ± 0.03
r₁₃₃/r₃₃₃	0.58 ± 0.20	1.8 ± 0.4
r₂₂₃/r₂₂₁	0.24 ± 0.06	0.14 ± 0.02
r₃₃₁/r₁₁₁	0.80 ± 0.15	0.87 ± 0.02
r₂₂₁/r₁₁₁	0.53 ± 0.08	0.53 ± 0.02
r₁₃₁/r₁₁₁	0.14 ± 0.09	0.12 ± 0.07

Coefficient	Value [pm/V]	Reference
r₂₂₃	+21.7 ± 3.8	This work
r₃₃₃	+24.7 ± 3.7	This work
r_fast	+58.9 ± 5.1	This work
r_slow	+32.6 ± 2.3	This work
r_c (meas.)	+26.5 ± 1.5	This work
r₁₁₃	+67 ± 7	This work
r₁₃₃	+14.4 ± 3.0	This work
r_c (calc.)	+23.1 ± 5.6	This work
r₁₁₁	+174 ± 10	[12]
r₂₂₁	+92 ± 8	[12]
r₃₃₁	+140 ± 18	[12]
r₁₃₁	+25 ± 15	[12]

Coefficient ratio	Direct electro-optic measurement (This work and [12])	Photorefractive measurement ([13])
r₁₁₃/r₃₃₃	2.7 ± 0.7	1.7 ± 0.6
r₂₂₃/r₃₃₃	0.87 ± 0.28	0.69 ± 0.03
r₁₃₃/r₃₃₃	0.58 ± 0.20	1.8 ± 0.4
r₂₂₃/r₂₂₁	0.24 ± 0.06	0.14 ± 0.02
r₃₃₁/r₁₁₁	0.80 ± 0.15	0.87 ± 0.02
r₂₂₁/r₁₁₁	0.53 ± 0.08	0.53 ± 0.02
r₁₃₁/r₁₁₁	0.14 ± 0.09	0.12 ± 0.07

Abstract

References

2010 (2)

2008 (1)

2007 (2)

2005 (1)

2003 (1)

2001 (1)

2000 (2)

1996 (1)

1991 (1)

1990 (1)

1984 (1)

1950 (1)

Aillerie, M.

Bach, T.

Bidault, O.

Caimi, G.

Carpenter, R. O’B.

Cook, G.

Evans, D. R.

Farahi, S.

Fontana, M. D.

Gadret, G.

Grabar, A. A.

Günter, P.

Gurzan, M. I.

Haertle, D.

Haldi, A.

Hellwig, U.

Huignard, J.-P.

Jazbinsek, M.

Juvalta, F.

Kedyk, I. V.

Maior, M. M.

Marty, P.

Mathey, P.

Molnar, A. A.

Montemezzani, G.

Mosimann, R.

Odoulov, S.

Odoulov, S. G.

Perechinskii, S. I.

Ramaz, F.

Rogach, E. D.

Rupp, R. A.

Salo, L. A.

Savenko, F. I.

Shumelyuk, A.

Shumelyuk, A. N.

Slivka, V. Yu.

Stoika, I. M.

Stoyka, I. M.

Theofanous, N.

Volkov, A.

Vysochanskii, Y. M.

Vysochanskii, Yu. M.

Zgonik, M.

Appl. Phys. B (2)

J. Opt. Soc. Am (1)

J. Opt. Soc. Am. B (4)

Opt. Commun. (2)

Opt. Lett. (3)

Phys. Rev. A (1)

Sov. Phys. Crystallogr. (1)

Sov. Phys. Solid State (1)

Other (5)

Cited By

Figures (2)

Tables (2)

Equations (11)

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