Nonlinear optical properties of TeO$_2$ crystalline phases from first principles

We have computed second and third nonlinear optical susceptibilities of two crystalline bulk tellurium oxide polymorphs: $\alpha$-TeO$_{2}$ (the most stable crystalline bulk phase) and $\gamma$-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 $\alpha$-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 non-local polarizabilty effects. Our results demonstrate that first-principles simulations are a powerful predictive tool to estimate nonlinear optical susceptibilitites of materials.