Motivated by the discovery of more and more phosphates with relatively strong nonlinear optic effect, we studied the mechanism of the second-harmonic generation (SHG) effect in several phosphates by band model and first-principles calculations. When the energy of an incident photon is much smaller than the band gap of material, the SHG is almost frequency independent and determined by the combination of Berry connection and a symmetric tensor. The SHG effect in phosphates can be enhanced by the enhancement of orbital hybridization or the reduction of charge-transfer energy, which results in widened bandwidth of occupied state and reduced band gap in the electronic structure, respectively. By the first-principles calculation on the electronic structures of several phosphates-BPO4, LiCs2PO4, beta-Li3VO4, and beta-Li3PO4-we interpreted the relatively strong SHG effect in LiCs2PO4 and beta-Li3VO4 as the consequence of the reduced charge-transfer energy compared to their parent beta-Li3PO4, while the enhanced SHG in BPO4 is resulting from enhanced orbital hybridization.

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