Bond-Charge Calculation of Nonlinear Optical Susceptibilities for Various Crystal Structures

A simple localized-bond-charge model for the calculation of nonlinear optical susceptibilities is presented. We find that there are three important contributions to the nonlinearity, namely, the bond ionicity, the difference in atomic radii of the bonded atoms, and $d$-electron contributions. By including these effects we are able with one simple theory to accurately treat a wide variety of different types of compounds including $A^{\mathrm{III}}{B}^{\mathrm{V}}$ (e.g., GaAs, GaP, InSb), $A^{\mathrm{II}}{B}^{\mathrm{VI}}$ (e.g., ZnS, ZnO, BeO), $A^{\mathrm{I}}{B}^{\mathrm{VII}}$ (e.g., CuCl, CuBr, CuI), $A^{\mathrm{IV}}{B}_2^{\mathrm{VI}}$ (e.g., Si${\mathrm{O}}_2$), multibond crystals [e.g., $A^{\mathrm{I}}{B}^{\mathrm{III}}{C}_2^{\mathrm{VI}}$ (LiGa${\mathrm{O}}_2$, AgGa${\mathrm{S}}_2$, CuIn${\mathrm{S}}_2$, CuGa${\mathrm{Se}}_2$), $A^{\mathrm{II}}{B}^{\mathrm{IV}}{C}_2^{\mathrm{V}}$ (CdGe${\mathrm{P}}_2$, CdGe${\mathrm{As}}_2$, ZnGe${\mathrm{P}}_2$), $A^{\mathrm{III}}{B}^{\mathrm{V}}{C}_4^{\mathrm{VI}}$ (AIP${\mathrm{O}}_4$), also K${\mathrm{H}}_2$P${\mathrm{O}}_4$], highly anisotropic crystals (e.g., HgS, Se, Te), as well as ferroelectrics (e.g., LiNb${\mathrm{O}}_3$, ${\mathrm{Ba}}_2$Na${\mathrm{Nb}}_5$ ${\mathrm{O}}_{15}$, LiTa${\mathrm{O}}_3$).