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Thermo-optical properties of uniaxial NaT(XO4)2 laser host crystals (where T = Y, La, Gd or Bi, and X = W or Mo)

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Abstract

Thermo-optic coefficients dn o/dT and dn e/dT were measured in tetragonal double tungstate and double molybdate crystals NaT(XO4)2 (where T = Y, La, Gd or Bi and X = W or Mo) by a laser beam deviation method in the spectral range 0.4–1.1 μm. Thermal expansion coefficients in the directions of a and c crystallographic axes were also measured. Analytical expressions for thermo-optic dispersion formulas were derived as series in 1/λ 2. All dn/dT values for NaT(XO4)2 crystals were found to be negative. Their absolute values satisfy the relation |dn e/dT| > |dn o/dT| for crystals without Bi and |dn o/dT| > |dn e/dT| for crystals with Bi. A clear tendency for dn/dT values to decrease with the increase of the volumetric thermal expansion coefficient α vol of the crystal was observed. This is related with dominant contribution of volumetric thermal expansion effect to the temperature dependence of the refractive index. Thermal coefficients of the optical path W = dn/dT + (n − 1)α T governing thermal lensing effect were calculated for different light propagation directions and polarizations as well as crystal athermal directions.

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Acknowledgments

This work was supported by the Spanish Ministry of Economy and Competitiveness under project MAT2011-29255-C02-01.

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Authors and Affiliations

  1. Center for Optical Materials and Technologies, Belarusian National Technical University, 65/17 Nezavisimosti Ave, 220013, Minsk, Belarus

    P. A. Loiko, K. V. Yumashev & N. V. Kuleshov

  2. Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, 28049, Madrid, Spain

    X. Han, M. D. Serrano, C. Cascales & C. Zaldo

Authors
  1. P. A. Loiko
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  2. X. Han
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  3. K. V. Yumashev
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Correspondence to K. V. Yumashev.

Appendices

Appendix 1

Measurements of thermal expansion coefficients, α, have been performed previously for several tetragonal double tungstate and double molybdate crystals (without Bi). The experiments were performed in various conditions by two experimental methods, namely, dilatometry and the variation of the unit cell lattice parameters obtained from XRD analysis. Table 4 of this Appendix summarizes the reported results along with those obtained in the present work.

Table 4 Summary of thermal expansion coefficients α (10−6 K−1) for tetragonal (uniaxial) double tungstate and double molybdate M+T3+(XO4)2 crystals reported in the literature
Full size table

Figure 4 represents typical results obtained by XRD method for undoped NaBi(WO4)2 crystal. The results show some α evolution in the first 100–200 K above room temperature and more stable value for higher temperatures. This high-temperature (T > 573 K) value agrees with the results obtained by dilatometry at lower temperatures, see for instance the good coincidence between the results presented in Table 4 for undoped NaY(WO4)2 and NaBi(WO4)2 crystals.

Fig. 4
figure 4

Thermal expansion coefficients of NaBi(WO4)2 crystal obtained from the evolution of crystal lattice parameters

Full size image

For all crystals under consideration, the anisotropy of thermal expansion coefficients (denoted as α c /α a ) commonly is close to 2. Therefore, the stress associated with non-uniform thermal expansion effect will be lower in comparison with monoclinic double tungstates. Indeed, such an anisotropy degree, α 11:α 22:α 33, equals 2.6:1:5.4 for KLu(WO4)2 or even 4.5:1:12.1 for KGd(WO4)2 [43]. With few exceptions, most of the previously reported results and those presented now agree within the uncertainties inherent to the accuracy of the methods and the variation in dopant concentration of the crystals analyzed.

Appendix 2

See Table 5.

Table 5 Anisotropy of thermo-optic coefficients dn/dT (10−6 K−1) for uniaxial double tungstate and double molybdate crystals NaT(XO4)2
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Loiko, P.A., Han, X., Yumashev, K.V. et al. Thermo-optical properties of uniaxial NaT(XO4)2 laser host crystals (where T = Y, La, Gd or Bi, and X = W or Mo). Appl. Phys. B 111, 279–287 (2013). https://doi.org/10.1007/s00340-012-5331-z

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