Nonlinear optical properties of TeO${}_{2}$ crystalline phases from first principles

Nonlinear optical properties of TeO $_{2}$ crystalline phases from first principles

Nabil Berkaïne, Emmanuelle Orhan, Olivier Masson, Philippe Thomas, and Javier Junquera

Phys. Rev. B 83, 245205 – Published 22 June 2011

Abstract

We have computed second and third nonlinear optical susceptibilities of two crystalline bulk tellurium oxide polymorphs: $α$ -TeO $_{2}$ (the most stable crystalline bulk phase) and $γ$ -TeO $_{2}$ (the crystalline phase that ressembles the more to the glass phase). Third-order nonlinear susceptibilities of the crystalline phases are two orders of magnitude larger than $α$ -SiO $_{2}$ cristoballite, thus extending the experimental observations on glasses to the case of crystalline compounds. While the electronic lone pairs of Te contribute to those large values, a full explanation of the anisotropy of the third-order susceptibility tensor requires a detailed analysis of the structure, in particular, the presence of helical chains, that seems to be linked to cooperative nonlocal polarizabilty effects.

Received 28 December 2010

DOI:https://doi.org/10.1103/PhysRevB.83.245205

Authors & Affiliations

Nabil Berkaïne¹, Emmanuelle Orhan¹, Olivier Masson¹, Philippe Thomas¹, and Javier Junquera²

¹Laboratoire Science des Procédés Céramiques et de Traitements de Surface, UMR 6638 CNRS, Centre Européen de la Céramique, University of Limoges, 12 rue Atlantis, 87068 Limoges Cedex, France
²Departamento de Ciencias de la Tierra y Física de la Materia Condensada, Universidad de Cantabria, Avda. de los Castros s/n, E-39005 Santander, Spain

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Vol. 83, Iss. 24 — 15 June 2011

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Images

Figure 1
Schematic view of the $α$ -SiO $_{2}$ cristobalite unit cell in different perspectives. Si and O atoms are represented by gray and red balls, respectively. Solid lines mark the unit cell. (a) highlights the helical chains formed by the tetrahedra along $z$ , while in (b) the zigzag chains in the $x$ direction are clearly observed.Reuse & Permissions
Figure 2
Schematic view of the $α$ -TeO $_{2}$ unit cell in different perspectives. Te and O atoms are represented by gray and red balls, respectively, while the blue spheres are the lone pairs of the Te atoms. Solid lines mark the unit cell. Meaning of the panels as in Fig. 1.Reuse & Permissions
Figure 3
Schematic view of the $γ$ -TeO $_{2}$ unit cell. Te and O atoms are represented by gray and red balls, respectively, while the blue spheres are the lone pairs of the Te atoms. Solid lines mark the unit cell, repeated along the $z$ direction for the sake of clarity. The yellow dashed lines are the longest Te-O distance.Reuse & Permissions
Figure 4
Schematic view of the $γ$ -TeO $_{2}$ unit cell in different perspectives. Te and O atoms are represented by gray and red balls, respectively, while the blue spheres are the lone pairs of the Te atoms. Solid lines mark the unit cell. The two symmetry-inequivalent O atoms are labeled as $O_{I}$ and $O_{II}$ . The yellow dashed lines are the longest Te-O distance. (a) and (b) highlight the zigzag chain along the $z$ and $x$ directions, respectively. (c) Focus on the helical chain along the $y$ direction.Reuse & Permissions
Figure 5
Field-induced polarization along $y$ , $P_{y}$ , as a function of an applied electric field only with components along the $x$ and $z$ directions, $E = (E, 0, E)$ , for the $γ$ -TeO $_{2}$ phase. The $x$ axis represents the component of the field along the $x$ direction. Atomic coordinates and unit-cell lattice parameters are clamped to the optimized structure at zero external field, and only the electronic response is considered while computing the polarization. Circles are the first-principles results and the solid line is the fit to Eq. (4).Reuse & Permissions
Figure 6
(a) $χ_{yxz}^{(2)}$ component of the second-order NLO susceptibility tensor of $γ$ -TeO $_{2}$ , and (b) the $χ_{xxxx}^{(3)}$ component of the third-order NLO susceptibility tensor of $α$ -TeO $_{2}$ as a function of the size of the $N \times N \times N$ shifted Monkhorst-Pack (Ref. 32) grid. Circles and solid lines represent the results obtained with a direct fit of the polarization vs electric field curve. Squares and dashed lines have been obtained with the Richardson extrapolation formula to compute derivatives by finite differences. The lines are fits to analytical functions that would allow an extrapolation to $N \to \infty$ .Reuse & Permissions

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