Abstract

Borate nonlinear optical (NLO) crystals are widely applied in generating the important spectrum of coherent light that usual laser sources cannot cover. Besides the well-known examples of $\beta \text{-} {\rm{Ba}}{{\rm{B}}_2}{{\rm{O}}_4}$, ${\rm{Li}}{{\rm{B}}_3}{{\rm{O}}_5}$, and ${\rm{KB}}{{\rm{e}}_2}{{\rm{BO}}_3}{{\rm{F}}_2}$ in uniaxial or orthorhombic symmetry, there are some recently developed borates in monoclinic or even lower symmetries, such as ${\rm{Bi}}{{\rm{B}}_3}{{\rm{O}}_6}$ (BiBO), ${\rm{L}}{{\rm{a}}_2}{\rm{Ca}}{{\rm{B}}_{10}}{{\rm{O}}_{19}}$ (LCB), ${\rm{YC}}{{\rm{a}}_4}{\rm{O}}{({{\rm{BO}}_3})_3}$ (YCOB), and ${\rm{C}}{{\rm{a}}_5}{({{\rm{BO}}_3})_3}{\rm{F}}$ (CBOF). For those low symmetry NLO crystals, it is challenging to fully characterize their optical properties experimentally. Theoretical calculation can simultaneously give the linear optical and NLO properties with the help of a highly precise method recently developed. However, to date, there seems to be a lack of theoretical study that shows fundamental agreement with the observed values for those properties of interest. In this study, using the CRYSTAL17 code, an ab initio program based on a linear combination of atomic orbitals approach and coupled perturbed Kohn–Sham approximation for first and second order susceptibilities, properties of dielectric constant $\epsilon_{ij}$ and second order susceptibility $\chi _{\textit{ijk}}^{(2)}$ (or SHG coefficients $d_{\textit{ijk}}^{2\omega}$) matrices of the above low symmetry crystals were obtained. From the calculated dielectric $\epsilon_{ij}$ tensor, the correct principal dielectric axes were obtained through Euler rotations, and they usually agreed with experiments within several degrees. The same rotation transforms the calculated SHG coefficients into the dielectric frame, and excellent agreements are found for YCOB and LCB (a confusion of sign difference can be solved). For BiBO, it is found that special care must be taken due to the lone pair or softness of the ${\rm{B}}{{\rm{i}}^{3 +}}$ ion in the structure. Using measured refractive indices, the effective NLO coefficients ${d_{\rm{eff}}}$ and optimum phase matching conditions for harmonic generations can be predicted, especially for CBOF, which is still not fully characterized. This study shows that calculation can reproduce the measured properties with high precision and can confirm or solve disputes of different experiments for both values and signs, and hopefully the theoretical approach can play a more important role in advancing developments and applications of low symmetry NLO materials.

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