Vibrational contributions to the electro-optic effect of BBO, KTP and RTP crystals

Barium borate (Ba3(B3O6)2, low temperature phase, BBO), potassium titanyl phosphate (KTiOPO4, KTP) and rubidium titanyl phosphate (RbTiOPO4, RTP) are not only best performing nonlinear optical materials but also show preferable electro-optic (EO) Pockels effect that serve as practical EO modulators widely applied in laser technology. Disparity to the repeatedly measurements of their properties related to the EO effects, the mechanism leads to their large EO coefficients have never been fully studied theoretically from first-principles calculations. In this paper, using an ab initio program CRYSTAL based on a linear combination of atomic orbitals approach, the vibrational spectra of the title crystals were firstly obtained. Then the electronic and vibrational contributions to the EO effect were calculated through coupled perturbed Kohn–Sham approximation and variations of atomic displacements. The results show that the EO coefficients, as well as other properties of dielectric constants, SHG coefficients and IR and Raman spectra of the three crystals are in excellent agreement with the experimental values. It is also found that the EO coefficients of all the crystals studies are dominantly contributed from few vibrational modes at low frequencies and the vibrational contributions amount to about 60% in BBO, 90% in KTP and RTP. General rules of finding crystals with large EO effects are finally proposed based on present study and previous studies on LiNbO3 crystals.