## Anisotropic diffraction from photorefractive gratings and Pockels tensor of Sn_{2}P_{2}S_{6}

Optics Express, Vol. 16, Issue 21, pp. 16923-16934 (2008)

http://dx.doi.org/10.1364/OE.16.016923

Acrobat PDF (390 KB)

### Abstract

The first observation of anisotropic diffraction and anisotropic self diffraction in low symmetry photorefractive crystal Sn_{2}P_{2}S_{6} is reported. From comparison of the diffraction efficiency of isotropic and anisotropic diffraction the ratios of the Pockels tensor components are deduced, including some nondiagonal components that have never been evaluated until now. The particular orientation of the optical indicatrix in Sn_{2}P_{2}S_{6} (roughly at 45° to *z*- and *x*-axes at ambient temperature) has a paradoxical consequence: The efficiency of anisotropic diffraction depends solely on diagonal components of the Pockels tensor, while the efficiency of the isotropic diffraction is considerably affected by nondiagonal components. With already known results and data presented in this article we can state that all 10 nonvanishing Pockels tensor components of the *m*-symmetry class crystal like Sn_{2}P_{2}S_{6} do manifest themselves in various types of nonlinear wave mixing.

© 2008 Optical Society of America

## 1. Introduction

_{2}P

_{2}S

_{6}, SPS) is a promising photorefractive material [1

1. A. Grabar, M. Jazbinšek, A. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter“photorefractive effects in Sn_{2}p_{2}s_{6},” in *photorefractive materials and their application 2*,
P. Günter and J.-P. Huignard, eds. (Springer-Verlag, 2007), pp. 327–362. [CrossRef]

*m*[2

2. C. D. Carpentier and R. Nitsche, “Ferroelectricity in Sn_{2}P_{2}S_{6},” Mat. Res. Bull. Pergamon Press, Inc. 9, 1097–1100 (1974); C. D. Carpentier and R. Nitsche, “Vapour growth and crystal data of the tio(seleno)-hypodiphosphates Sn_{2}P_{2}S_{6}, Sn_{2}P_{2}Se_{6}, Pb_{2}P_{2}S_{6}, Pb_{2}P_{2}Se_{6}, and their mixed crystals,” Mater. Res. Bull. **9**, 401–410 (1974). [CrossRef]

*µ*m [3

3. A. Shumelyuk, S. Odoulov, O. Oleynik, G. Brost, and A. Grabar, “Spectral sensitivity of nominally undoped photorefractive Sn_{2}P_{2}S_{6},” Appl. Phys. B **88**, 79–82 (2007). [CrossRef]

*µ*m [4

4. Roger Mosimann, M. Jazbinšek, G. Montemezzani, A. Grabar, and P. Günter, “High speed photorefraction at telecommunication wavelength 1.55 µm in Sn_{2} P_{2}S_{6},” Opt. Lett. **32**, 3230–3232 (2007). [CrossRef] [PubMed]

^{-1}but with some dopants up to 30 cm

^{-1}in the visible) [1

1. A. Grabar, M. Jazbinšek, A. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter“photorefractive effects in Sn_{2}p_{2}s_{6},” in *photorefractive materials and their application 2*,
P. Günter and J.-P. Huignard, eds. (Springer-Verlag, 2007), pp. 327–362. [CrossRef]

2. C. D. Carpentier and R. Nitsche, “Ferroelectricity in Sn_{2}P_{2}S_{6},” Mat. Res. Bull. Pergamon Press, Inc. 9, 1097–1100 (1974); C. D. Carpentier and R. Nitsche, “Vapour growth and crystal data of the tio(seleno)-hypodiphosphates Sn_{2}P_{2}S_{6}, Sn_{2}P_{2}Se_{6}, Pb_{2}P_{2}S_{6}, Pb_{2}P_{2}Se_{6}, and their mixed crystals,” Mater. Res. Bull. **9**, 401–410 (1974). [CrossRef]

6. S. G. Odoulov, A. M. 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]

7. D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn_{2}P_{2}S_{6},” Opt. Commun. **215**, 333–343 (2003). [CrossRef]

8. B. I. Sturman, S. G. Odoulov, and M. Yu. Goul’kov, “Parametric four-wave processes in photorefractive crystals,” Phys. Rep. **275**, 197–254 (1996). [CrossRef]

*r*

_{xxx}and

*r*

_{zzz}.

*x*-cut,

*y*-cut, and

*z*-cut), with the appropriate orientation and polarization of the recording waves. With the known birefringence of SPS [10

10. D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn_{2}P_{2}S_{6} at visible and infrared wavelengths,” Opt. Express **13**, 2047–2057 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-6-2047. [CrossRef] [PubMed]

## 2. Definitions

11. Yannick Petit, Benoît Boulanger, Patricia Segonds, Corinne Félix, Bertrand Ménaert, Jullien Zaccaro, and Gérald Aka, “Absorption and fluorescence anisotropies of monoclinic crystals: the case of Nd:YCOB,” Opt. Express **16**, 7997–8002 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-11-7997. [CrossRef] [PubMed]

*m*or 4

*mm*symmetry classes like LiNbO

_{3}, LiTaO

_{3}, SBN or BaTiO

_{3}. On the other hand, this complication brings new, sometimes quite unexpected effects, such as the independence of some kinds of anisotropic diffraction from the nondiagonal components of Pockels tensor.

10. D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn_{2}P_{2}S_{6} at visible and infrared wavelengths,” Opt. Express **13**, 2047–2057 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-6-2047. [CrossRef] [PubMed]

*z*-axis is defined parallel to the [001] crystallographic direction (axis

*c*), while the

*y*-axis is normal to the mirror plane and corresponds to the crystallographic

*b*-axis. The

*x*-axis is therefore perpendicular to

*y*- and

*z*-axes.

_{2}P

_{2}S

_{6}is represented as:

## 3. Anisotropic diffraction and self diffraction in birefringent photorefractivs

*k*

_{1,2}propagate and form a fringe pattern which is imprinted inside the crystal as an index grating; it has the grating vector

*n*

_{s}or external shell with a larger index

*n*

_{l}, respectively). For uniaxial crystals with negative birefringence like LiNbO

_{3}, the smaller index

*s*corresponds to extraordinary wave and larger index

*l*corresponds to ordinary wave.

_{3}[15

15. S. Odoulov and S. Odoulov, “Vectorial interactions in photovoltaic media,” Ferroelectrics91, 213–225 (1989). [CrossRef]

*n*

_{s}as well as for an eigenwave with larger index

*n*

_{l}. (For the sake of simplicity we consider all waves that propagate in the same plane defined by two recording waves, in fact the anisotropic diffraction is possible also for waves that propagate in other directions.)

*k*

^{s}

_{3}=

*k*

^{s}

_{1}or

*k*

^{s}

_{2}=

*k*

^{s}

_{5}. Thus, the diffracted waves with the orthogonal polarization appear without any auxiliary readout beams. This type of nonlinear wave mixing is called self diffraction. It is of practical interest because the selfdiffracted wave can be a phase conjugate replica of one of the recording waves providing the second wave has a plane wave front [16,17

17. N. V. Kukhtarev, E. Krätzig, H. C. Külich, R. Rupp, and J. Albers, “Anisotropic self diffraction in BaTiO_{3},” Appl. Phys. B **35**, 17–21 (1984). [CrossRef]

_{3}these coefficients are the nondiagonal components of the Pockels tensor (those with the different first two indices in the full three-index notation or

*r*

_{51}and

*r*

_{42}in contracted notation). We will show below that the expressions for the effective Pockels coefficient that couples two waves (either with identical polarizations or with orthogonal polarizations) are more complicated in low symmetry crystals like SPS.

## 4. Experiment

*µ*m, linearly polarized) is used to record the photorefractive gratings. The unexpanded beams of roughly equal intensities are used to record the grating, while a third (incoherent) beam with a smaller intensity is used to readout the grating (Fig. 2). Unless otherwise stated, the recording beams impinge upon the sample symmetrically; the readout angle and the diffraction angle are measured in air from the normal to the sample input face.

*x*-cut sample, eigenwaves are polarized along

*y*- or

*z*-axes and for the

*z*-cut sample they are polarized along

*x*- or

*y*-axes. For

*y*-cut sample, however, the polarizations of the eigenwaves at ambient temperature are parallel neither to

*x*nor to

*z*directions but are tilted to

*χ*=47° (

*n*

_{1}) and 43° (

*n*

_{3}) with respect to x-axis Fig.2.

^{-2}or higher were measured directly as a ratio of the diffracted beam intensity to the total intensity of transmitted readout and diffracted beams.

_{1}and PD

_{2}that measure the intensities of the diffracted and the readout beams respectively are fed into the lock-in amplifier to get the diffraction efficiency.

**K**‖

*x*-axis and

**K**‖

*z*-axis; it does not occur for

**K**‖

*y*-axis. The experimental data on isotropic diffraction are not shown in Fig. 4. The dots, squares, triangles, and diamonds in Fig. 4 are the results for the readout and/or diffraction angles for the waves labelled 3,4,5,6 in Fig. 1 and Eqs. (3,4). The red and blue lines represent the dependences calculated from Eq. (3) and Eq. (4), respectively, with the birefringence data of SPS tabulated in [10

10. D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn_{2}P_{2}S_{6} at visible and infrared wavelengths,” Opt. Express **13**, 2047–2057 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-6-2047. [CrossRef] [PubMed]

*x*-cut sample. Two

*y*-polarized recording beams impinge upon the sample in the

*xy*-plane and generate a

*z*-polarized selfdiffracted wave. The open squares in Fig. 5 show the measured values, while the solid lines represent the dependences calculated from Eq. 2 with the additional condition

*k*

^{s}

_{3}=

*k*

^{s}

_{1}. The self diffraction in case of

**K**‖

*y*(symmetric incidence of two recording waves or sample tilt angle equal to zero in Fig. 5) confirms the existence of nonvanishing

*r*

_{yzy}component of the Pockels tensor in SPS.

*z*-cut sample with

*y*-polarized waves and for the

*y*-cut sample. In the latter case, two eigenwaves with the smaller index of refraction (

*n*

_{1}) record the grating; its grating vector

**K**can be aligned along

*x*-direction as well as along

*z*-direction. For all mentioned variations of self diffraction, the measured angular dependences (as shown in Fig. 5) are in good agreement with the calculated data.

8. B. I. Sturman, S. G. Odoulov, and M. Yu. Goul’kov, “Parametric four-wave processes in photorefractive crystals,” Phys. Rep. **275**, 197–254 (1996). [CrossRef]

**k**

^{e}

_{3}=

**k**

^{e}

_{1}.

## 5. Estimating the electrooptic coefficients

*η*of the index grating in photorefractive crystal is given by the following expression [9,19]

*e*⃗

_{d}and

*e*⃗

_{i}, respectively; longitudinal components of the wave vectors

*k*

_{iz}and

*k*

_{dz}; perturbation of the high frequency permittivity tensor

*δε*̂; interaction length

*d*, and light wavelength

*λ*. From the general relationship between the perturbed tensor of high frequency dielectric impermittivity and the static electric field

*E*, the amplitude of perturbation of the high frequency dielectric permittivity

*δε*̂ can be expressed as

*ε*̂ is the unperturbed tensor of the high frequency dielectric permittivity. The space charge field that affects

*δε*is

*k*

_{B}, electron charge

*e*, spatial frequency of the grating

*K*, and Debye screening length

*K*(

*k*

_{B}

*T*/

*e*) in case of insufficient effective trap density

*N*when the product of the spatial frequency and the screening length,

_{eff}*K*

^{2}ℓ

^{2}

_{s}, becomes much larger than unity.

*r*

_{ijk}from the experimentally measured values of the diffraction efficiency. As it follows from Eqs. 5–7 the efficiency depends, apart from the effective electrooptic coefficient, on other inherent properties of the material and on the experimental conditions (wavelength, sample orientation that affects low frequency permittivity

*ε*[20

20. A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, “Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques,” Appl. Phys. B **76**, 417–421 (2003). [CrossRef]

*K*, interaction length that depends on orientation and angles). The parameters like the effective interaction length are individual characteristic of a particular sample and depend on the amount of domains with the opposite orientation of spontaneous polarization.

*r*

_{xzx}and

*r*

_{zxz}.

*e*⃗

_{E}is the static electric field unit vector, the indices (1) and (2) mark any two of several possible diffraction processes, either isotropic or anisotropic.

*y*-cut sample with the grating vector

**K**parallel to the

*x*-axis. In this case, the expressions for the diffraction efficiency that enter a numerator and a denominator of Eq. 8 read

*χ*is the optical indicatrix rotation angle (see Fig. 2) the subscripts iso1 and

*iso*3 mark the isotropic diffraction of the eigenwaves with indices

*n*

_{1}and

*n*

_{3}, respectively, while

*aniso*denotes the anisotropic diffraction (either of a wave with

*n*

_{1}into a wave with

*n*

_{3}or in the opposite direction). Finally

*C*incorporates all mentioned above parameters that characterize the grating and experimental conditions and are identical for all possible types of diffraction from this grating. The difference in propagation directions for isotropic and anisotropic diffraction inside the sample is neglected here because a relevant correction factor appears to be less than 2 percent.

*χ*. With

*χ*≈45° (which is very close to real value

*χ*=43° in SPS at

*λ*=0.63

*µ*m and ambient conditions) equations Eqs. 9–11 are reduced to

*y*-cut SPS is independent of nondiagonal components

*r*

_{xzx}of the Pockels tensor while these components may affect, when being sufficiently large, the conventional isotropic diffraction. Note that this situation is quite different from that for photorefractive crystals that belong to higher symmetry classes 4

*mm*(BaTiO

_{3}) or 3

*m*(LiNbO

_{3}), where

*χ*=0 and where the anisotropic diffraction depends primarily on nondiagonal components of Pockels tensor.

_{iso1}, η

_{iso3}, and η

_{aniso}are known from the experiment and

*n*

_{1}and

*n*

_{3}are known from the literature [10

_{2}P_{2}S_{6} at visible and infrared wavelengths,” Opt. Express **13**, 2047–2057 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-6-2047. [CrossRef] [PubMed]

*r*

_{zzx}/

*r*

_{xxx}and

*r*

_{xzx}/

*r*

_{xxx}. To make unambiguous conclusions about the signs of the particular components the information concerning positive direction of crystal

*x*- and

*z*-axes is necessary. The extracted data are given in Table 1 together with already known data from [7

7. D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn_{2}P_{2}S_{6},” Opt. Commun. **215**, 333–343 (2003). [CrossRef]

*y*-cut sample the grating vector

**K**is aligned parallel to the

*z*axis the efficiencies of the three diffraction processes similar to that described by Eqs.12–14 are

*r*

_{xxz}/

*r*

_{zzz}and

*r*

_{zxz}/

*r*

_{zzz}that are tabulated in Table 2.

**K**‖

*y*-axis the isotropic diffraction is not allowed and there is no reference diffraction to compare with the anisotropic diffraction which is due to

*r*

_{yzy}and

*r*

_{yxy}. To follow the same procedure and evaluate the ratio of Pockels tensor components instead of absolute values, we study the anisotropic self diffraction in

*x*-cut and

*z*-cut samples with the grating vector

**K**tilted to 45° with respect to the

*y*-axis. In such a manner we get a desirable reference because the isotropic diffraction becomes possible with nonzero

*r*

_{yyz}and

*r*

_{zzz}for the

*x*-cut sample (or

*r*

_{xxx}and

*r*

_{yyx}for the

*z*-cut sample). Thus the anisotropic diffraction which is due to

*r*

_{yzy}(or due to

*r*

_{yxy}) can be compared to isotropic diffraction from the same grating.

*x*-cut sample, the efficiencies are given by

*z*-cut sample from the grating with the grating vector aligned along the bissector of

*yx*angle:

*r*

_{yyz}/

*r*

_{zzz},

*r*

_{yzy}/

*r*

_{yyz},

*r*

_{yyx}/

*r*

_{xxx}, and

*r*

_{yxy}/

*r*

_{yyx}. They are all given in Table 2.

*x*-axis) and from experimental errors of the diffraction efficiency measurements define the error bars shown in Table 1 and Table 2. The statistical spread of the measured data (two samples with different areas in each, reproducibility of data) was never beyond the indicated error bars.

*y*-cut sample.

*r*

_{xxx}(

*r*

_{yyx}can be reduced to

*r*

_{xxx}because their ratio is known) while the others can be normalized to

*r*

_{zzz}(in similar way

*r*

_{yyz}can be reduced to

*r*

_{zzz}). To get the hierarchy of all 10 Pockels coefficients we need to normalize all components to a common coefficient, e.g., to the largest coefficient

*r*

_{xxx}. To do this it is necessary to interrelate at least two coefficients that have a different last index, one with

*x*and the other with

*z*. By comparing the absolute values of the diffraction efficiency for two different crystal cuts, for example, for

*x*-cut and

*z*-cut while keeping the polarization of the recording waves along y direction, the ratio

*r*

_{yyx}/

*r*

_{yyz}can be found. According to the data reported in [20

20. A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, “Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques,” Appl. Phys. B **76**, 417–421 (2003). [CrossRef]

*r*

_{yyx}/

*r*

_{yyz}≈7.0±1.0. The reliability of the last procedure is however not very high because of all of the factors discussed above (difference in domain structure seen by the recording fringes, difference in screening effects because of the anisotropy of the dielectric permittivity, etc.) Larger statistics of different SPS samples are necessary to get reliable data on the absolute values of the Pockels tensor components.

## 6. Conclusions

*r*

_{xxx},

*r*

_{yyx},

*r*

_{zzx},

*r*

_{xxz},

*r*

_{yyz}, and

*r*

_{zzz}manifest themselves in polarization isotropic diffraction from the space charge gratings. The ratios of these components have been found via recording and reading out of photorefractive gratings in

*x*-cut and

*z*-cut samples.

*y*-cut samples depends solely on the linear combination of the diagonal components as, for example,

*r*-

_{xxx}*r*. This allows for an independent check of the measured ratios of the Pockels components.

_{zzx}*r*and

_{xzx}*r*are involved in isotropic diffraction in y-cut samples together with at least two diagonal components. To decouple a nondiagonal component it is necessary to perform three measurements of the diffraction efficiency, for isotropic diffraction of waves with two orthogonal eigenpolarizations and for anisotropic diffraction. Another possibility consists in using of data on diagonal components already available from other experiments.

_{zxz}*r*and

_{yzy}*r*are extracted from measurements of anisotropic diffraction in

_{yxy}*x*-cut and

*z*-cut samples.

## Acknowledgments

## References and links

1. | A. Grabar, M. Jazbinšek, A. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter“photorefractive effects in Sn |

2. | C. D. Carpentier and R. Nitsche, “Ferroelectricity in Sn |

3. | A. Shumelyuk, S. Odoulov, O. Oleynik, G. Brost, and A. Grabar, “Spectral sensitivity of nominally undoped photorefractive Sn |

4. | Roger Mosimann, M. Jazbinšek, G. Montemezzani, A. Grabar, and P. Günter, “High speed photorefraction at telecommunication wavelength 1.55 µm in Sn |

5. | A. A. Grabar, R. I. Muzhikash, A. D. Kostyuk, and Yu. M. Vysochanskiy, “Investigation of the switching process in the domain structure of ferroelectric Sn |

6. | S. G. Odoulov, A. M. 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 |

7. | D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn |

8. | B. I. Sturman, S. G. Odoulov, and M. Yu. Goul’kov, “Parametric four-wave processes in photorefractive crystals,” Phys. Rep. |

9. | M. P. Petrov, S. J. Stepanov, and A. V. Khomenko, |

10. | D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn |

11. | Yannick Petit, Benoît Boulanger, Patricia Segonds, Corinne Félix, Bertrand Ménaert, Jullien Zaccaro, and Gérald Aka, “Absorption and fluorescence anisotropies of monoclinic crystals: the case of Nd:YCOB,” Opt. Express |

12. | Daniel Haertle, “Photorefractive and nonlinear properties of Sn |

13. | ANSI/IEEE, Std 176 - IEEE Standard on Piezoelectricity, p.242 (IEEE, Inc; 345 East 47th Street, New York, NY 10017, USA, 1987). |

14. | G. Dittmar and H. Schäfer, “Die Stuktur des Di-Zinn-Hexathiohypodiphoshatus Sn |

15. | S. Odoulov and S. Odoulov, “Vectorial interactions in photovoltaic media,” Ferroelectrics91, 213–225 (1989). [CrossRef] |

16. | N. Kukhtarev and S. Odoulov, “Wavefront inversion in anisotropic self-diffraction of laser beams,” Sov. Techn. Phys. Lett. |

17. | N. V. Kukhtarev, E. Krätzig, H. C. Külich, R. Rupp, and J. Albers, “Anisotropic self diffraction in BaTiO |

18. | A. Shumelyuk, A. Volkov, A. Selinger, M. Imlau, and S. Odoulov, “Frequency-degenerate nonlinear light scattering in low-symmetry crystals,” Opt. Lett. |

19. | L. Solymar, D. Webb, and A. Grunnet-Jepsen, |

20. | A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, “Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques,” Appl. Phys. B |

**OCIS Codes**

(050.7330) Diffraction and gratings : Volume gratings

(160.2100) Materials : Electro-optical materials

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(190.5330) Nonlinear optics : Photorefractive optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: August 21, 2008

Revised Manuscript: September 15, 2008

Manuscript Accepted: September 15, 2008

Published: October 8, 2008

**Citation**

Serguey Odoulov, Alexandr Volkov, Alexandr Shumelyuk, Dean R. Evans, and Gary Cook, "Anisotropic diffraction from photorefractive gratings and Pockels tensor of Sn_{2}P_{2}S_{6}," Opt. Express **16**, 16923-16934 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16923

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### References

- A. Grabar, M. Jazbinšek, A. Shumelyuk, Yu.M. Vysochanskii, G. Montemezzani, and P. Günter, "Photorefractive effects in Sn2P2S6," in Photorefractive materials and their applications 2, P. G¨unter, and J.-P. Huignard, eds. (Springer-Verlag, 2007), pp. 327-362. [CrossRef]
- C. D. Carpentier and R. Nitsche, "Ferroelectricity in Sn2P2S6," Mat. Res. Bull. Pergamon Press, Inc. 9,1097-1100 (1974); [CrossRef]
- C. D. Carpentier and R. Nitsche, "Vapour growth and crystal data of the tio(seleno)-hypodiphosphates Sn2P2S6, Sn2P2Se6, Pb2P2S6, Pb2P2Se6, and their mixed crystals," Mater. Res. Bull. 9, 401-410 (1974). [CrossRef]
- A. Shumelyuk, S. Odoulov, O. Oleynik, G. Brost, and A. Grabar, "Spectral sensitivity of nominally undoped photorefractive Sn2P2S6," Appl. Phys. B 88, 79-82 (2007). [CrossRef] [PubMed]
- R. Mosimann, M. Jazbinšek, G. Montemezzani, A. Grabar, and P. Günter, "High speed photorefraction at telecommunication wavelength 1.55 μm in Sn2 P2S6," Opt. Lett. 32, 3230-3232 (2007).
- A. A. Grabar, R. I. Muzhikash, A. D. Kostyuk, and Yu.M. Vysochanskiy, "Investigation of the switching process in the domain structure of ferroelectric Sn2P2S6 by the dynamic holographic method," Sov. Phys. Solid State 33, 1314-1316 (1991). [CrossRef]
- S. G. Odoulov, A. M. 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]
- 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]
- B. I. Sturman, S. G. Odoulov, and M. Yu. Goul�??kov, "Parametric four-wave processes in photorefractive crystals," Phys. Rep. 275, 197-254 (1996).
- M. P. Petrov, S. J. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991). [CrossRef] [PubMed]
- D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, "Refractive indices of Sn2P2S6 at visible and infrared wavelengths," Opt. Express 13, 2047-2057 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-6-2047. [CrossRef] [PubMed]
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