First-principles calculation of the second-harmonic-generation coefficients of borate crystals

We report the calculation of the second-harmonic-generation (SHG) coefficients of LiB₃O₅ (LBO), CsB₃O₅ (CBO), and BaB₂O₄ (BBO) using the linearized augmented plane-wave band method in the local-density approximation with a scissors operator that includes the renormalization of the momentum operator. The analysis that is based on the spectral and spatial decomposition of the calculated results reveals that, for the large component of SHG coefficients, the dominant source of the optical nonlinearities for these borate crystals is the nonlinear response of the high-lying $2p$ electrons of oxygen atoms, while the cations play a minor role even in the heavier Cs and Ba cases, though they dominate the conduction-band minimum. But for the small SHG component, the role of the cation became important, particularly when the isolated anionic group has little contribution due to the restriction of the symmetry. In the case of LBO and CBO, due to the linkage of anionic groups, the contributions of off-ring O atoms are almost the same as those of in-ring O atoms. Yet for BBO where there is no such linkage, the off-ring O atom plays a much more important role than the in-ring O atom does. We also find that the contribution of the virtual-hole process cannot be ignored as is usually done in the semiconductors case.