First-principles calculations of second order nonlinear optical coefficients in the static limit and Pockels coefficients in III-N and II-IV-N₂ compounds

The second order nonlinear optical coefficients in the static limit are evaluated using density functional perturbation theory from the electronic response to a static electric field for the group III nitrides and several II-IV-N₂ ternary nitrides. They are compared with literature results using the sum over states approach including local field effects. The effects of the scissor correction are evaluated. Good agreement is obtained for GaN, AlN and w-BN. For InN, the small or even negative gap in in the LDA at Γ causes an extreme sensitivity to the k-point summation and pseudopotentials. Similar problems occur for other very small gap II-IV-N₂ semiconductors. The nonlinear optics coefficients are showing a general trend of increasing values with smaller gaps but no clear scaling relation with the direct gaps is obtained. The Pockels coefficient, which include in addition to the electronic response, also the phonon and piezoelectric response and are also evaluated. They show that the phonon and electronic contributions to the response in these materials are comparable in magnitude.