Atom-Resolved Analysis of Birefringence of Nonlinear Optical Crystals by Bader Charge Integration

Birefringence of a crystal is an important optical property. For example, birefringence is crucial to realizing phase-matching condition for nonlinear optical crystals that are applied to laser technologies. However, it is difficult to analyze the origin of birefringence and then to tune it for practical applications. Here, we developed a method to apply the Bader charge analysis to the investigation of the birefringence of crystal on an atomic scale based on the density functional theory calculation. We calculated the birefringence of nonlinear optical crystals CsPbCO₃F and KSrCO₃F as a demonstration using this method. It is shown that [CO₃]^2– and F^– make opposite contributions to the birefringence for both crystals. The birefringence contributions from cations are 22 and −29% for Pb and Cs, respectively, in the CsPbCO₃F crystal, while the contributions from Sr and K is −11 and −4% to the birefringence of KSrCO₃F, respectively. Using this Bader charge analysis method, we can obtain the individual ion’s contribution to the birefringence. The method is free of parameter and easy to be applied to many complicated structure crystals. The quantitative atomic contribution to refractive index would give important clues to the design of new nonlinear optical materials with suitable birefringence.