Abstract

Phase matching conditions and second and third order nonlinear optical coefficients of Sn2P2S6 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 χ1111(3)=(17±6)·10-20m2/V2 and χ2222(3)=(9±3)·10-20m2/V2 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 8µm with an effective nonlinear coefficient d eff≈4pm/V.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett. (1)

R. C. Miller, �??Optical 2nd harmonic generation in piezoelectric crystals,�?? Appl. Phys. Lett. 5, 17�??9 (1964).
[CrossRef]

Ferroelectrics (1)

A. Anema, A. Grabar, and T. Rasing, �??The nonlinear optical properties of Sn2P2S6,�?? Ferroelectrics 183, 181�??3 (1996).
[CrossRef]

IEEE Journal of Quantum Electronics (1)

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]

J. Appl. Phys. (2)

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]

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]

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

J. Phys. B (2)

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. Phys. C (1)

M. Zgonik, M. Copic, and H. Arend, �??Optical second harmonic generation in ferro- and para-electric phases of PbHPO4,�?? J. Phys. C 20, L565�??569 (1987).
[CrossRef]

Opt. Commun. (1)

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]

Opt. Express (1)

Opt. Mat. (1)

R. S. Klein, G. E. Kugel, A. Maillard, K. Polgar, and A. Peter, �??Absolute non-linear optical coefficients of LiNbO3 for near stoichiometric crystal compositions,�?? Opt. Mat. 22, 171�??4 (2003).
[CrossRef]

Phys. Rev. B (1)

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]

Soviet Physics Solid State (1)

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).

Zeitschrift fuer Naturforschung (1)

G. Dittmar and H. Schäfer, �??Die Struktur des Di-Zinn-Hexathiohypo-diphosphats Sn2P2S6,�?? Zeitschrift fuer Naturforschung 29B, 312�??7 (1974).

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Figures (10)

Fig. 1.
Fig. 1.

Maker-Fringe measurement in Sn2P2S6 at λ=1907nm and fitted theoretical curve. The sample was a z-plate, which was rotated around its y-axis. The abscissa is the external angle between the fundamental beam (p-polarized) and the z-axis of the crystal. Detected was the p-polarized part of the second harmonic signal, yielding a measurement of d 11 at the angle ζ=0° and a combination of d 11,d 13,d 15,d 31,d 33 and d 35 for other rotation angles.

Fig. 2.
Fig. 2.

Temperature dependence of d 111 at λ=1907nm measured during heating until over the phase transition (a). The solid curve is according to d 111=A(TC -T)1/2 with A=4.2K-1/2pm/V and TC =65.7°C. In (b) the coordinates are chosen so that the dependence of Fig. (a) is linear in the temperature range just below the phase transition.

Fig. 3.
Fig. 3.

Absorption constant of Sn2P2S6 at room temperature for non-polarized light propagating along the z-axis. It shows the large transparency range extending from λ=0.53 µm to λ=8 µm. This curve is calculated from measured transmission (by a PE λ 9 spectrometer for λ<1.6µm and a PE Paragon FT-IR spectrometer above that wavelength) and taking into account multiple Fresnel reflections.

Fig. 4.
Fig. 4.

Directions of phase matching in Sn2P2S6 for frequency doubling at room temperature; (a) Type I, (b) Type II. ϕ and θ are the spherical coordinates of the k vector in the crystal. Some contour curves are labeled with their corresponding fundamental wavelength in nanometers. The dashed white line corresponds to the predicted phase-matching for the laser line at 1907 nm and the white circles are experimental points.

Fig. 5.
Fig. 5.

The grey region indicates the directions that are not accessible from air in crystals cut along the Cartesian x, y, z-axes. This figure was calculated for the wavelengths in Fig. 4(a), but since the dependence on the angles ϕ and θ is much larger than that on the wavelength, it can be assumed valid for every configuration shown in this paper.

Fig. 6.
Fig. 6.

(a) Effective coefficients and (b) internal walk-off angle for type I phase-matched SHG directions and corresponding wavelengths as in Fig. 4(a).

Fig. 7.
Fig. 7.

Angle-tuning for phase-matched sum-frequency generation or optical parametric oscillation. (a) Type I, (b) Type II. Beam propagation is in the xy-plane (θ=90°). λ3 is the wavelength of the pumping beam, while λ1 and λ2 are the wavelengths of the signal and the idler. The bold lines correspond to non-critical phase matching.

Fig. 8.
Fig. 8.

Phase-matched SFG or OPO of type I for λ 3=1064nm (a) and λ 3=808nm (b). The contour lines have constant signal wavelength λ1 and λ2, where 1 λ 1 + 1 λ 2 = 1 λ 3 . The contour line labels are λ1 in micrometers. In the outer white region at λ3=1064nm no type I PM is possible. In the inner white region one of the phase-matched wavelengths diverges.

Fig. 9.
Fig. 9.

Effective nonlinear optical coefficient (continuous line) and walk-off angle (dashed line) for phase-matched SFG or OPO with beam propagating in the xy-plane (θ=90°). The dependence of d eff and the walk-off angle on the wavelengths of the interacting beams is weak. The data above is calculated for λ1=2400nm.

Fig. 10.
Fig. 10.

Effective nonlinear optical coefficient for type I phase-matched SFG or OPO with λ 3=808nm, corresponding to Fig. 8(b). Some contour lines are labeled with their value in pm/V. In the inner white region one of the phase-matched wavelengths diverges.

Tables (1)

Tables Icon

Table 1. All second order nonlinear optical tensor elements dip of Sn2P2S6 at two wavelengths of the fundamental beam. The coefficients are given according to the standard conventions [13] (e. g. d 15=d 113=d 131) and aα-quartz reference value of d Q 111=0.286pm/V at λ=1542nm and d111Q=0.277pm/V at λ=1907nm [13].

Equations (6)

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n 3 λ 3 = n 1 λ 1 + n 2 λ 2
P i ( ω 3 ) = ε 0 j k d i j k ( ω 3 , ω 1 , ω 2 ) E j ( ω 1 ) E k ( ω 2 ) ,
P ( ω 3 ) = 2 ε 0 d eff E ( ω 1 ) E ( ω 2 )
d eff = i j k d i j k ( ω 3 , ω 1 , ω 2 ) cos ( β i ( ω 3 ) ) cos ( β j ( ω 1 ) ) cos ( β k ( ω 2 ) ) ,
P ( 2 ω ) = ε 0 d eff E ( ω ) 2 ,
d i j k ( ω 3 , ω 1 , ω 2 ) = ε 0 χ ii ( ω 3 ) χ jj ( ω 1 ) χ kk ( ω 2 ) δ i j k ,

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