## Nonlinear optical coefficients and phase-matching conditions in Sn_{2}P_{2}S_{6}

Optics Express, Vol. 13, Issue 10, pp. 3765-3776 (2005)

http://dx.doi.org/10.1364/OPEX.13.003765

Acrobat PDF (372 KB)

### Abstract

Phase matching conditions and second and third order nonlinear optical coefficients of Sn_{2}P_{2}S_{6} crystals are reported. The coefficients for second harmonic generation (SHG) are given at λ=1542 nm and 1907 nm at room temperature. The largest coefficients at these wavelengths are *d*_{111}=17±1.5pm/V and *d*_{111}=12±1.5pm/V, respectively. The third-order subsceptibilities ^{-20}m^{2}/V^{2} and ^{-20}m^{2}/V^{2} were determined at λ=1907 nm. All measurements were performed by the Maker-Fringe technique. Based on the recently determined refractive indices, we analyze the phase-matching conditions for second harmonic generation, sum- and difference-frequency generation and parametric oscillation at room temperature. Phase-matching curves as a function of wavelength and propagation direction are given. Experimental phase-matched type I SHG at 1907 nm has been demonstrated. The results agree very well with the calculations. It is shown that phase-matched optical parametrical oscillation is possible in the whole transparency range up to 8*µ*m with an effective nonlinear coefficient *d*_{eff}≈4pm/V.

© 2005 Optical Society of America

## 1. Introduction

_{2}P

_{2}S

_{6}) is a wide bandgap semiconductor ferroelectric with very attractive photorefractive properties [1

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**, 2352–60 (1996). [CrossRef]

2. M. Jazbinsek, G. Montemezzani, P. Gunter, A. A. Grabar, I. M. Stoika, and Y. M. Vysochanskii, “Fast near infrared self-pumped phase conjugation with photorefractive Sn_{2}P_{2}S_{6},” J. Opt. Soc. Am. B. June **20**, 1241–6 (2003). [CrossRef]

3. D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Y. M. Vysochanskii, “Electro-optical properties of Sn_{2}P_{2}S_{6},” Opt. Commun. **215**, 333–43 (2003). [CrossRef]

*µ*m to λ=8

*µ*m [4] holds promise for optical parametric generation up to infrared wavelengths not accessible with standard nonlinear optical crystals. This requires the knowledge of the nonlinear optical coefficients and phase matching conditions. Up to now no coefficient had been determined; the only publication on nonlinear optics in Sn

_{2}P

_{2}S

_{6}reports a value for

*d*

_{211}[5

5. A. Anema, A. Grabar, and T. Rasing, “The nonlinear optical properties of Sn_{2}P_{2}S_{6},” Ferroelectrics **183**, 181–3 (1996). [CrossRef]

_{2}P

_{2}S

_{6}

*d*

_{211}is zero due to symmetry in the standard coordinate system). In this work we determine or estimate all 10 second-order non-linear coefficients, as well as the third-order nonlinear optical susceptibilities

_{2}P

_{2}S

_{6}are given for the wavelength range 550–2300nm at room temperature. The Sellmeier coefficients determined there allow to describe the refractive indices with an accuracy of 2·10

^{-4}in the wavelength interval indicated. These data allow us to calculate phase-matching conditions for second harmonic generation (SHG), sum- and difference-frequency generation (SFG and DFG) and optical parametric oscillation (OPO). Calculated phase-matching conditions are compared with experimental data at λ=1907 nm. A configuration for optical parametric oscillators pumped with the fundamental wavelength of a Nd:YAG laser, capable of producing radiation from 1 to 8 µm in the infrared with a high gain (

*d*

_{eff}≈4pm/V), is described.

## 2. Optical frequency conversion in Sn_{2}P_{2}S_{6}

*ω*

_{1},

*ω*

_{2}, and

*ω*

_{3}, where

*ω*

_{3}=

*ω*

_{1}+

*ω*

_{2}, the vacuum wavelengths

*λ*

_{i}of the interacting waves must satisfy

*n*

_{i}are the refractive indices for the waves at frequencies

*ω*

_{i}. We use the Cartesian coordinate system as defined in Ref. 6: unit cell of Dittmar and Schäfer [7],

*y*‖

*b*is perpendicular to the mirror plane of the crystal,

*z*‖

*c*, the positive direction of the

*x*-axis and the

*z*-axis so that the piezoelectric coefficients

*d*

_{xxx}and

*d*

_{zzz}are positive and +

*y*so that

*xyz*is a right-handed system. The spherical coordinates are defined in the standard way used in physics, with

*θ*the angle between

**k**and

*z*, and

*ϕ*the counterclockwise angle from

*x*to the projection of

**k**to the

*xy*-plane.

8. F. Brehat and B. Wyncke, “Calculation of double-refraction walk-off angle along the phase-matching directions in non-linear biaxial crystals,” J. Phys. B **22**, 1891–8 (1989). [CrossRef]

**E**(

*ω*

_{1,2}) of the fundamental waves is described by

_{0}is electric constant and

*d*

_{ijk}are the nonlinear-optical coefficients. For second harmonic generation (

*ω*

_{1}=

*ω*

_{2}),

*d*

_{i jk}is symmetric in the last two indices, and the contracted notation can be used.

*ω*

_{3}along the direction of polarization of the emitted wave with frequency

*ω*

_{3}can be written as

*ω*and the axis

*i*of the Cartesian coordinate system [9

9. B. Wyncke and F. Brehat, “Calculation of the effective second-order non-linear coefficients along the phase matching directions in acentric orthorhombic biaxial crystals,” J. Phys. B **22**, 363–76 (1989). [CrossRef]

*β*

_{i}[8

8. F. Brehat and B. Wyncke, “Calculation of double-refraction walk-off angle along the phase-matching directions in non-linear biaxial crystals,” J. Phys. B **22**, 1891–8 (1989). [CrossRef]

10. J. Q. Yao and T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO_{4},” J. Appl. Phys. **55**, 65–8 (1984). [CrossRef]

*d*

_{eff}can again be derived from Eq. (4). The difference between Eqs. (5) and (3) is consistent with a continuous transition to the degenerate case, described by (5), from the sum-frequency case, described by (3), with two distinguishable fundamental fields.

11. R. C. Miller, “Optical 2nd harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. **5**, 17–9 (1964). [CrossRef]

*δ*

_{ijk}, the Miller indices, are almost independent of the frequency [12

12. W. J. Alford and A. V. Smith, “Wavelength variation of the second-order nonlinear coefficients of KNbO_{3}, KTiOPO_{4}, KTiOAsO_{4}, LiNbO_{3}, LiIO_{3}, beta -BaB_{2}O_{4}, KH_{2}PO_{4}, and LiB_{3}O_{5} crystals: a test of Miller wavelength scaling,” J. Opt. Soc. Am. B **18**, 524–33 (2001). [CrossRef]

*χ*

_{ii}=

## 3. Second harmonic generation

*ω*

_{1}=

*ω*

_{2}) and the

*d*tensor becomes symmetric in its last two indices. This allows to write it in its reduced form [13

13. D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE Journal of Quantum Electronics **28**, 2057–74 (1992). [CrossRef]

_{2}P

_{2}S

_{6}is

*d*coefficients (Kleinman symmetry), the number of independent coefficients drops from 10 to 6, being

*d*

_{15}=

*d*

_{31},

*d*

_{32}=

*d*

_{24},

*d*

_{26}=

*d*

_{12}, and

*d*

_{35}=

*d*

_{13}.

*d*

_{ip}were determined by a standard Maker-Fringe technique [14

14. J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. **41**, 1667–81 (1970). [CrossRef]

15. C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B **61**, 10,688–701 (2000). [CrossRef]

_{2}and Q-switched at 10 Hz). The samples used were an

*x*-plate and a

*z*-plate, from crystals grown at Uzhgorod University (Ukraine), oriented by Laue diffraction (precision ±6’), polished to optical quality and poled by heating above

*T*

_{C}=66°C and slowly cooling in an applied electric field of 1kV/cm.

*d*coefficients were found by fitting the Maker-Fringe curves and comparing them to the ones of a reference crystal of

*α*-quartz. Fig. 1 shows an example of a Maker-Fringe measurement of Sn

_{2}P

_{2}S

_{6}with the corresponding fitted curve. The curve is not symmetrical with respect to the angle ζ=0°, corresponding to beams perpendicular to the crystal, since the indicatrix is not perpendicular to the Cartesian axes, and therefore the coherence length is minimal at an angle ζ≠0°. Nevertheless the theoretical curve describes the experiments nicely. The modified Kleinman symmetries

*δ*

_{15}=

*δ*

_{31}and

*δ*

_{35}=

*δ*

_{13}where used during fitting, while the other Kleinman symmetries where not used, since enough Maker-Fringe curves were available for those coefficients.

*d*

_{ip}of Sn

_{2}P

_{2}S

_{6}are shown in Table 1. Note that due to the contribution of several tensor elements in the Maker-Fringe experiments, some of their values could be determined only with a relatively low accuracy. The largest value is the diagonal coefficient

*d*

_{111}=17±1.5pm/V at λ=1542nm and

*d*

_{111}=12±1.5pm/V at 1907nm, which is higher than most of the largest coefficients of standard materials for nonlinear optics. Of special interest is also that Sn

_{2}P

_{2}S

_{6}has very large electro-optical coefficients (

3. D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Y. M. Vysochanskii, “Electro-optical properties of Sn_{2}P_{2}S_{6},” Opt. Commun. **215**, 333–43 (2003). [CrossRef]

*d*coefficient at λ=1907nm. At this wavelength the influence of temperature on the optical properties is negligible with respect to the change in nonlinear optical properties of second order. The

*d*coefficient is proportional to the electrical polarization [16

16. M. Zgonik, M. Copic, and H. 0, “Optical second harmonic generation in ferro- and para-electric phases of PbHPO_{4},” J. Phys. C **20**, L565–569 (1987). [CrossRef]

*T*

_{C}is given mainly by the acentricity parameter, i.e. the spontaneous polarization

*P*

_{S}. Therefore Fig. 2 represents the temperature dependence of the spontaneous polarization

*P*

_{S}. Close to the phase transition (

*T*

_{C}-

*T*<7°C) we see the decrease proportional to the square root of

*T*

_{C}-

*T*(Fig. 2(b). The fact that

*d*

_{111}does not vanish completely above

*T*

_{C}is explained by thermal fluctuations in the critical region just above the second-order phase transition, induced by residual defects [16

16. M. Zgonik, M. Copic, and H. 0, “Optical second harmonic generation in ferro- and para-electric phases of PbHPO_{4},” J. Phys. C **20**, L565–569 (1987). [CrossRef]

## 4. Third harmonic generation

^{-2}bar). As reference we used an α-quartz crystal and the value

^{-20}m

^{2}/V

^{2}[15

15. C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B **61**, 10,688–701 (2000). [CrossRef]

_{2}P

_{2}S

_{6}has very large

*χ*

^{(3)}coefficients:

^{-20}m

^{2}/V

^{2}

^{-20}m

^{2}/V

^{2}

_{3}[15

15. C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B **61**, 10,688–701 (2000). [CrossRef]

## 5. Phase matching

### 5.1. Second harmonic generation

_{2}P

_{2}S

_{6}phase-matched SHG is possible for a fundamental wavelength in the range between 1680nm and 8

*µ*m. The whole range is achievable by type I phase matching (incident photons have the same polarisation), while type II phase matching (incident photons are of orthogonal polarisation) is possible for λ>2324nm. The upper boundary of 8

*µ*m is given only by the end of the transparency range (see Fig. 3), which is due to phonon-phonon interactions [4].

6. 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**, 2047–57 (2005). [CrossRef] [PubMed]

*n*=2·10

^{-4}) and fits very well to a two-oscillator Sellmeier model, which was used to extrapolate the refractive indices at longer wavelengths. Nevertheless the precision at larger wavelengths cannot be predicted and could decrease rapidly. For the calculation of

*d*

_{eff}, we numerically evaluated (4), taking into account the dispersion of the

*d*

_{i jk}, given by Eq. (6). Some analytical expressions for

*d*

_{eff}for a biaxial crystal can be found in Refs. 9 and 10.

*x*,

*y*,

*z*-axes are indicated by the grey area. For those directions oblique cuts are necessary in order to access the wished internal direction from air. In the following figures this region is

**k**with polar coordinates in the range

*ϕ*∊[0°,180°] and

*θ*∊[0°,90°] inside the crystal. In order to get the whole definition range

*ϕ*∊[0°,360°[and

*θ*∊[0°,180°] of the spherical coordinates, the following symmetries should be applied

*d*

_{eff}>3pm/V for all fundamental wavelengths λ>1980nm. Type II phase matching has large

*d*

_{eff}for other wave directions than type I, in particular

*d*

_{eff}≲2pm/V for all

*ϕ*>90°. Compared to other materials,

*d*

_{eff}of Sn

_{2}P

_{2}S

_{6}is similar to the ones of LiNbO

_{3}[17

17. R. S. Klein, G. E. Kugel, A. Maillard, K. Polgar, and A. Peter, “Absolute non-linear optical coefficients of LiNbO_{3} for near stoichiometric crystal compositions,” Opt. Mat. **22**, 171–4 (2003). [CrossRef]

18. B. Boulanger, J. P. Feve, G. Marnier, B. Menaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d^{(2)} nonlinear coefficients of KTP from second-harmonic-generation measurements,” J. Opt. Soc. Am. B **11**, 750–7 (1994). [CrossRef]

_{2}P

_{2}S

_{6}this can occur only for a beam direction parallel to the fixed main axis of the indicatrix, i. e.

**k**‖

*y*, corresponding to (

*ϕ*,

*θ*)=(90°,90°) in the figures. The fundamental wavelength for non-critical PM is

*λ*=3212.5nm for type I and 4536.5nm for type II. Again, compared to other standard nonlinear optical materials, the walk-off angles are similar to the ones of LiNbO

_{3}, and larger than in KTP, but smaller than in BBO.

_{1}=λ

_{2}for the directions for phase-matched SHG with fundamental wavelength λ

_{1}. The positions of these points were given by the curves in Fig. 4.

## 5.2. Sum-frequency generation and optical parametric oscillation

*xy*-plane are given in Fig. 7. With type I PM (left) the curves for λ

_{1}and λ

_{2}join smoothly at the wavelength which produces phase-matched second-harmonic radiation. For type II SFG (right) the phase-matching lines intersect where phase-matched SHG is possible. In Fig. 7 the non-critical PM condition (

**k**‖

*y*) is shown by a thick line: here with wavelength tuning of λ

_{3}∊[1000,1606]nm it is possible to get all the wavelengths between 1150 and 8000nm.

*ϕ*for the desired wavelengths λ

_{1}or λ

_{2}. For the Nd:YAG laser wavelength

*λ*

_{3}=1064nm this can be also seen in Fig. 8(a), looking at the bottom horizontal line, where

*θ*=90°. At this wavelength λ

_{1,2}∊[1238,7572]nm can be obtained using PM of type I. For the same configuration at the laser diode wavelength of λ

_{3}=808nm, λ

_{1}>2747nm can be accessed (Fig. 8(b)). Type II PM is also possible, with operating wavelengths similar to type I PM (see Fig. 7(b)). Generally one can access by type II PM the same signal and idler wavelengths as with type I, but the required tuning range of λ

_{3}is larger and the conversion efficiency lower.

*d*

_{eff}and the walk-off angle are displayed for

**k**in the

*xy*-plane (

*θ*=90°). These two parameters depend very little on the interacting wavelengths, and

*d*

_{eff}> 3pm/V for type I PM in the range

*ϕ*=30°…150°, while for type II

*d*

_{eff}is around 2pm/V in the whole range of

*ϕ*. The largest contributions to

*d*

_{eff}around the non-critical PM direction (

*θ*=

*ϕ*=90°) are given by

*d*

_{111}and

*d*

_{133}, with these two contributions having the same sign for type I and different one for type II PM. With

*ϕ*moving away from 90°, the term with

*d*

_{133}becomes dominant for type I, while for type II many terms roughly balance each other. The efficiency for general beam directions is shown in Fig. 10 for λ

_{3}=808nm. It is highest for

*θ*near 90°, and remains large as long as the internal angle between

**k**and the

*xy*-plane does not exceed 20–30°. The same figure at

*λ*

_{3}=1064nm is very similar. By pumping at that wavelength, with a crystal cut perpendicularly to (

*θ*=90°,

*ϕ*=45°), one can for example access all wavelengths λ

_{1,2}>1200 nm by type I phase-matched angle-tuning and with

*d*

_{eff}≈4pm/V.

## 6. Conclusions

_{2}P

_{2}S

_{6}were measured for λ=1542 nm and 1907 nm at room temperature. The largest coefficients at these wavelengths are

*d*

_{111}=17±1.5pm/V and

*d*

_{111}=12±1.5pm/V, respectively. Third order subsceptibilities

^{-20}m

^{2}/V

^{2}and

^{-20}m

^{2}/V

^{2}were measured at λ=1907 nm. The temperature dependence of d111 confirmed the temperature dependence of the spontaneous polarization within a temperature range of about 7°C below the Curie temperature

*T*

_{C}≈66°C.

_{2}P

_{2}S

_{6}, we have analyzed various nonlinear optical second-order interactions. Phase-matching configurations for various wavelengths and beam propagation directions have been studied. The principal polarization directions, walk-off angles, acceptance angles, and effective nonlinear-optical coefficients have been calculated numerically for arbitrary beam propagation directions in this biaxial crystal. Phase matching has been found to be possible in a large variety of configurations. For example type I phase-matched optical parametric generation from 1.2 to 8

*µ*m with

*d*

_{eff}≈4pm/V is possible using a Nd:Yag pumping laser and similarly from 2.3 to 8

*µ*m using a laser at 808nm.

*µ*m, the possibility for phase matching in the whole transparent range, the good nonlinear efficiency at phase matching, the very large electro-optical coefficients and the absence of hygroscopicity. The walk-off angle ranges between 0 and 2°, similarly to LiNbO

_{3}but larger than in KTP. Damage threshold studies will be required to fully assess the potentiality of this crystal for high-power near infrared frequency conversion.

## Acknowledgments

## References and links

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 |

2. | M. Jazbinsek, G. Montemezzani, P. Gunter, A. A. Grabar, I. M. Stoika, and Y. M. Vysochanskii, “Fast near infrared self-pumped phase conjugation with photorefractive Sn |

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

4. | M. I. Gurzan, A. P. Buturlakin, V. S. Gerasimenko, N. F. Korde, and V. Y. Slivka, “Optical properties of Sn |

5. | A. Anema, A. Grabar, and T. Rasing, “The nonlinear optical properties of Sn |

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

7. | G. Dittmar and H. Schäfer, “Die Struktur des Di-Zinn-Hexathiohypo-diphosphats Sn |

8. | F. Brehat and B. Wyncke, “Calculation of double-refraction walk-off angle along the phase-matching directions in non-linear biaxial crystals,” J. Phys. B |

9. | B. Wyncke and F. Brehat, “Calculation of the effective second-order non-linear coefficients along the phase matching directions in acentric orthorhombic biaxial crystals,” J. Phys. B |

10. | J. Q. Yao and T. S. Fahlen, “Calculations of optimum phase match parameters for the biaxial crystal KTiOPO |

11. | R. C. Miller, “Optical 2nd harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. |

12. | W. J. Alford and A. V. Smith, “Wavelength variation of the second-order nonlinear coefficients of KNbO |

13. | D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE Journal of Quantum Electronics |

14. | J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. |

15. | C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B |

16. | M. Zgonik, M. Copic, and H. 0, “Optical second harmonic generation in ferro- and para-electric phases of PbHPO |

17. | R. S. Klein, G. E. Kugel, A. Maillard, K. Polgar, and A. Peter, “Absolute non-linear optical coefficients of LiNbO |

18. | B. Boulanger, J. P. Feve, G. Marnier, B. Menaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d |

**OCIS Codes**

(160.4330) Materials : Nonlinear optical materials

(190.2620) Nonlinear optics : Harmonic generation and mixing

**ToC Category:**

Research Papers

**History**

Original Manuscript: April 15, 2005

Revised Manuscript: May 3, 2005

Published: May 16, 2005

**Citation**

D. Haertle, M. Jazbinšek, G. Montemezzani, and P. Günter, "Nonlinear optical coefficients and phase-matching conditions in Sn_{2}P_{2}S_{6}," Opt. Express **13**, 3765-3776 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-10-3765

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### References

- 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�??60 (1996). [CrossRef]
- M. Jazbinsek, G. Montemezzani, P. Gunter, A. A. Grabar, I. M. Stoika, and Y. M. Vysochanskii, �??Fast near-infrared self-pumped phase conjugation with photorefractive Sn2P2S6,�?? J. Opt. Soc. Am. B. June 20, 1241�??6 (2003). [CrossRef]
- D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Y. M. Vysochanskii, �??Electro-optical properties of Sn2P2S6,�?? Opt. Commun. 215, 333�??43 (2003). [CrossRef]
- M. I. Gurzan, A. P. Buturlakin, V. S. Gerasimenko, N. F. Korde, and V. Y. Slivka, �??Optical properties of Sn2P2S6 crystals,�?? Soviet Physics Solid State 19, 1794�??5 (1977).
- A. Anema, A. Grabar, and T. Rasing, �??The nonlinear optical properties of Sn2P2S6,�?? Ferroelectrics 183, 181�??3 (1996). [CrossRef]
- D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, �??Refractive indices of Sn2P2S6 at visible and infrared wavelengths,�?? Opt. Express 13, 2047�??57 (2005). [CrossRef] [PubMed]
- G. Dittmar and H. Schäfer, �??Die Struktur des Di-Zinn-Hexathiohypo-diphosphats Sn2P2S6,�?? Zeitschrift fuer Naturforschung 29B, 312�??7 (1974).
- F. Brehat and B. Wyncke, �??Calculation of double-refraction walk-off angle along the phase-matching directions in non-linear biaxial crystals,�?? J. Phys. B 22, 1891�??8 (1989). [CrossRef]
- B. Wyncke and F. Brehat, �??Calculation of the effective second-order non-linear coefficients along the phase matching directions in acentric orthorhombic biaxial crystals,�?? J. Phys. B 22, 363�??76 (1989). [CrossRef]
- J. Q. Yao and T. S. Fahlen, �??Calculations of optimum phase match parameters for the biaxial crystal KTiOPO4,�?? J. Appl. Phys. 55, 65�??8 (1984). [CrossRef]
- R. C. Miller, �??Optical 2nd harmonic generation in piezoelectric crystals,�?? Appl. Phys. Lett. 5, 17�??9 (1964). [CrossRef]
- W. J. Alford and A. V. Smith, �??Wavelength variation of the second-order nonlinear coefficients of KNbO3, KTiOPO4, KTiOAsO4, LiNbO3, LiIO3, beta -BaB2O4, KH2PO4, and LiB3O5 crystals: a test of Miller wavelength scaling,�?? J. Opt. Soc. Am. B 18, 524�??33 (2001). [CrossRef]
- D. A. Roberts, �??Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,�?? IEEE Journal of Quantum Electronics 28, 2057�??74 (1992). [CrossRef]
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