First-principles studies on linear and nonlinear optical effects in Ln4GaSbS9 (Ln=Ce–Nd, Sm, Gd–Tm, Lu)

Density functional theory (DFT) calculations have been performed on electronic structures of 11 middle-infrared (mid-IR) nonlinear optical quaternary sulfides: Ln4GaSbS9 (Ln=Ce–Nd, Sm, Gd–Tm, Lu). Our results show that Ln4GaSbS9 are indirect gap semiconductors with a slight band gap increase from Ce to Lu. Their linear optical properties, including refractive index, absorption coefficient and energy loss function, as well as the nonlinear optical coefficients including static d31, d32, d33 and dynamic d32, are calculated. More importantly, the strong SHG response of Ln4GaSbS9 can be attributed to the electronic transitions from S 3p states in valence bands (VB) to Sb–S and Ln–S antibonding states (CB).