Designing next-generation non-linear optical crystals: polar chalcopyrite Li₂PbGeS₄ with a large NLO response,...

We have explored the electronic structure and linear and non-linear optical (NLO) susceptibilities for the two tensor components of the noncentrosymmetric Li₂PbGeS₄ polar chalcopyrite using the all-electron full potential linear augmented plane wave method. The electronic properties and orbital hybridization of Li₂PbGeS₄ are determined on the basis of the calculated band structure and density of states. The calculated electronic charge density plot shows the ionic and partial covalent bonding behavior between the Ge and S atoms. The generalized gradient approximation shows that the calculated band-gap (E _g) is about 2.26 eV, while the modified Becke-Johnson potential brings the calculated E _g value (2.39 eV) very close to the experimental one (2.41 eV). The linear optical properties exhibit considerable anisotropy, which favors the enhanced phase-matching conditions necessary for the observation of the second harmonic generation and optical parametric oscillation. We aimed to explore the NLO susceptibilities and the microscopic first hyperpolarizability β _ijk , which are the vector components along the dipole moment direction of Li₂PbGeS₄. The obtained NLO susceptibilities show that |χ ⁽²⁾ ₁₂₃(ω)| is the dominant component, which exhibits the highest value at a zero limit |χ ⁽²⁾ ₁₂₃(0)| of about 24.0 pm V^-1, in comparison to that of |χ ⁽²⁾ ₃₂₁(0)| (12.0 pm V^-1). In contrast, it is 60 pm V^-1 for |χ ⁽²⁾ ₁₂₃(ω)| and 25 pm V^-1 for |χ ⁽²⁾ ₃₁₂(ω)| at λ = 1064 nm, which is around twice (d ₁₄ = 30) that of the experimental value of the well-known KTiOPO₄ (KTP) single crystal. In addition, we have calculated the β _ijk for |χ ⁽²⁾ ₁₂₃(ω)| and |χ ⁽²⁾ ₃₂₁(ω)| of the Li₂PbGeS₄ compound at the static limit and at λ = 1064 nm. These values are 8.593 × 10^-30 esu for β ₁₂₃ and 4.296 × 10^-30 esu for β ₃₂₁ at the static limit, while it is 21.483 × 10^-30 esu for β ₁₂₃ and 8.952 × 10^-30 esu for β ₃₂₁ at λ = 1064 nm. These calculations show that Li₂PbGeS₄ exhibits larger second harmonic generation (SHG) and microscopic first hyperpolarizability compared with the well-known KTP.