Electronic structures and optical properties of Ca5(BO3)3F: a systematical first-principles study

A first-principles study of the electronic structure, the linear optical properties and second-order NLO properties of calcium fluoroborate (Ca5(BO3)3F, or CBF) crystal has been performed within density functional theory and the independent-particle approximation. The results indicate that the calculated birefringence Δn and the second-order susceptibilities are very coincident with the experimental measured values, and the χ(2) curves show stronger anisotropy than the linear optical properties. Further analysis based on the spectral and spatial decomposition of χ(2) reveals that the main sources of the SHG response of CBF are from the planar BO3 groups (74%–77%) and Ca2+ cations (23%–26%) and can be attributed to the interband electronic transition from the nonbonding O 2p states to the B 2p and Ca 4s4p states. The packing arrangement of BO3 is the principal contributor to the significant differences among SHG tensors in CBF. Meanwhile, for a certain crystal CBF, the SHG tensors' trend can be the trend of the optical transition matrix elements, which are high when the corresponding subscript directions have more parallel BO3 triangular planes in the structure.